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Search, Evaluate, and Read Evidence","\u002Fen\u002Facademic-writing\u002F02-reading-and-literature-matrix","en\u002Facademic-writing\u002F02-reading-and-literature-matrix",{"title":27,"path":28,"stem":29},"3. From Sources to Synthesis and Argument","\u002Fen\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs","en\u002Facademic-writing\u002F03-arguments-outlines-and-paragraphs",{"title":31,"path":32,"stem":33},"4. Literature Review and a Defensible Gap","\u002Fen\u002Facademic-writing\u002F04-writing-the-literature-review","en\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":35,"path":36,"stem":37},"5. Research Design, Evidence, and Core Sections","\u002Fen\u002Facademic-writing\u002F05-core-sections-and-evidence","en\u002Facademic-writing\u002F05-core-sections-and-evidence",{"title":39,"path":40,"stem":41},"6. Citation, Paraphrasing, Integrity, and AI","\u002Fen\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity","en\u002Facademic-writing\u002F06-citation-paraphrasing-and-integrity",{"title":43,"path":44,"stem":45},"7. Revision, Review, and Submission","\u002Fen\u002Facademic-writing\u002F07-revision-style-and-submission","en\u002Facademic-writing\u002F07-revision-style-and-submission",{"title":47,"path":48,"stem":49},"8. Research Workbook","\u002Fen\u002Facademic-writing\u002F08-literature-review-checklist-and-template","en\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":51,"path":52,"stem":53},"9. Research Workflow and Tools","\u002Fen\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management","en\u002Facademic-writing\u002F09-tools-for-academic-writing-and-literature-management",{"title":55,"path":56,"stem":57},"10. Worked Project — From Question to Defensible Conclusion","\u002Fen\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain","en\u002Facademic-writing\u002F10-worked-example-from-block-structure-to-question-chain",{"title":59,"path":60,"stem":61,"children":62,"page":249},"Accounting","\u002Fen\u002Faccounting","en\u002Faccounting",[63,69,87,93,193],{"title":64,"path":65,"stem":66,"children":67},"Accounting — From Evidence to Decisions","\u002Fen\u002Faccounting\u002F00-index","en\u002Faccounting\u002F00-index",[68],{"title":64,"path":65,"stem":66},{"title":70,"path":71,"stem":72,"children":73},"Accounting Appendix","\u002Fen\u002Faccounting\u002Fappendix","en\u002Faccounting\u002Fappendix\u002Findex",[74,75,79,83],{"title":70,"path":71,"stem":72},{"title":76,"path":77,"stem":78},"Worked Examples and Error Diagnosis","\u002Fen\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls","en\u002Faccounting\u002Fappendix\u002F24-examples-pitfalls",{"title":80,"path":81,"stem":82},"Accounting Glossary","\u002Fen\u002Faccounting\u002Fappendix\u002F26-glossary","en\u002Faccounting\u002Fappendix\u002F26-glossary",{"title":84,"path":85,"stem":86},"Reading and Evidence Map","\u002Fen\u002Faccounting\u002Fappendix\u002F27-reading-map","en\u002Faccounting\u002Fappendix\u002F27-reading-map",{"title":88,"path":89,"stem":90,"children":91},"Northstar Record-to-Decision Capstone","\u002Fen\u002Faccounting\u002Fcapstone","en\u002Faccounting\u002Fcapstone\u002Findex",[92],{"title":88,"path":89,"stem":90},{"title":94,"path":95,"stem":96,"children":97},"Financial Accounting","\u002Fen\u002Faccounting\u002Ffinancial-accounting","en\u002Faccounting\u002Ffinancial-accounting\u002Findex",[98,99,117,131,165,179],{"title":94,"path":95,"stem":96},{"title":100,"path":101,"stem":102,"children":103},"1. Foundations","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002Findex",[104,105,109,113],{"title":100,"path":101,"stem":102},{"title":106,"path":107,"stem":108},"Objectives and Qualitative Characteristics","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F01-objectives-qualitative-characteristics",{"title":110,"path":111,"stem":112},"Equation and Elements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F02-equation-elements",{"title":114,"path":115,"stem":116},"Accrual Basis, Estimates and Periods","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles","en\u002Faccounting\u002Ffinancial-accounting\u002F01-foundations\u002F03-accounting-bases-principles",{"title":118,"path":119,"stem":120,"children":121},"2. Recording Transactions","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002Findex",[122,123,127],{"title":118,"path":119,"stem":120},{"title":124,"path":125,"stem":126},"Double-Entry and Debit\u002FCredit","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F04-double-entry-dr-cr",{"title":128,"path":129,"stem":130},"Accounting Cycle","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle","en\u002Faccounting\u002Ffinancial-accounting\u002F02-recording-transactions\u002F05-accounting-cycle",{"title":132,"path":133,"stem":134,"children":135},"3. Measurement and Adjustments","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002Findex",[136,137,141,145,149,153,157,161],{"title":132,"path":133,"stem":134},{"title":138,"path":139,"stem":140},"Revenue Recognition","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F07-revenue-recognition",{"title":142,"path":143,"stem":144},"Inventory","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F08-inventory",{"title":146,"path":147,"stem":148},"Receivables and Expected Credit Losses","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F09-receivables",{"title":150,"path":151,"stem":152},"Property, Plant and Equipment","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F10-ppe",{"title":154,"path":155,"stem":156},"Intangible Assets","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F11-intangibles",{"title":158,"path":159,"stem":160},"Leases","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F12-leases",{"title":162,"path":163,"stem":164},"Current and Deferred Income Tax","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax","en\u002Faccounting\u002Ffinancial-accounting\u002F03-measurement-adjustments\u002F13-income-tax",{"title":166,"path":167,"stem":168,"children":169},"4. Reporting and Cash","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002Findex",[170,171,175],{"title":166,"path":167,"stem":168},{"title":172,"path":173,"stem":174},"Linked Financial Statements","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F06-financial-statements",{"title":176,"path":177,"stem":178},"Cash, Reconciliation and Internal Control","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control","en\u002Faccounting\u002Ffinancial-accounting\u002F04-reporting-cash\u002F14-cash-control",{"title":180,"path":181,"stem":182,"children":183},"5. Analysis and Comparison","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002Findex",[184,185,189],{"title":180,"path":181,"stem":182},{"title":186,"path":187,"stem":188},"Ratio Analysis","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F15-ratio-analysis",{"title":190,"path":191,"stem":192},"IFRS versus US GAAP","\u002Fen\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap","en\u002Faccounting\u002Ffinancial-accounting\u002F05-analysis-comparison\u002F25-ifrs-gaap",{"title":194,"path":195,"stem":196,"children":197},"Management Accounting","\u002Fen\u002Faccounting\u002Fmanagement-accounting","en\u002Faccounting\u002Fmanagement-accounting\u002Findex",[198,199,217,235],{"title":194,"path":195,"stem":196},{"title":200,"path":201,"stem":202,"children":203},"1. Cost Foundations","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002Findex",[204,205,209,213],{"title":200,"path":201,"stem":202},{"title":206,"path":207,"stem":208},"Cost Concepts and Behaviour","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F16-cost-concepts",{"title":210,"path":211,"stem":212},"Costing Systems","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F17-costing-systems",{"title":214,"path":215,"stem":216},"Variable and Absorption Costing","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption","en\u002Faccounting\u002Fmanagement-accounting\u002F01-cost-foundations\u002F19-variable-vs-absorption",{"title":218,"path":219,"stem":220,"children":221},"2. Planning and Control","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002Findex",[222,223,227,231],{"title":218,"path":219,"stem":220},{"title":224,"path":225,"stem":226},"Cost–Volume–Profit Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F18-cvp-analysis",{"title":228,"path":229,"stem":230},"Budgeting and Variance Analysis","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F20-budgeting-variances",{"title":232,"path":233,"stem":234},"Performance Measurement","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement","en\u002Faccounting\u002Fmanagement-accounting\u002F02-planning-control\u002F21-performance-measurement",{"title":236,"path":237,"stem":238,"children":239},"3. Decisions and Investment","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002Findex",[240,241,245],{"title":236,"path":237,"stem":238},{"title":242,"path":243,"stem":244},"Short-Term Decisions","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F22-short-term-decisions",{"title":246,"path":247,"stem":248},"Capital Budgeting","\u002Fen\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting","en\u002Faccounting\u002Fmanagement-accounting\u002F03-decisions-investment\u002F23-capital-budgeting",false,{"title":251,"path":252,"stem":253,"children":254,"page":249},"Business Analytics","\u002Fen\u002Fbusiness-analytics","en\u002Fbusiness-analytics",[255,261,279,305,335,365,383,400],{"title":256,"path":257,"stem":258,"children":259},"Business Analytics — From Data to Defensible Action","\u002Fen\u002Fbusiness-analytics\u002F00-index","en\u002Fbusiness-analytics\u002F00-index",[260],{"title":256,"path":257,"stem":258},{"title":262,"path":263,"stem":264,"children":265},"0. Decision and Data Foundations","\u002Fen\u002Fbusiness-analytics\u002F00-intro","en\u002Fbusiness-analytics\u002F00-intro\u002Findex",[266,267,271,275],{"title":262,"path":263,"stem":264},{"title":268,"path":269,"stem":270},"Decision Framing","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing","en\u002Fbusiness-analytics\u002F00-intro\u002F01-decision-framing",{"title":272,"path":273,"stem":274},"Data Contracts","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts","en\u002Fbusiness-analytics\u002F00-intro\u002F02-data-contracts",{"title":276,"path":277,"stem":278},"Reproducible Analytics Workflow","\u002Fen\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow","en\u002Fbusiness-analytics\u002F00-intro\u002F03-reproducible-workflow",{"title":280,"path":281,"stem":282,"children":283},"1. Descriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive","en\u002Fbusiness-analytics\u002F01-descriptive\u002Findex",[284,285,289,293,297,301],{"title":280,"path":281,"stem":282},{"title":286,"path":287,"stem":288},"Distributions and Exploratory Data Analysis","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda","en\u002Fbusiness-analytics\u002F01-descriptive\u002F04-distributions-eda",{"title":290,"path":291,"stem":292},"KPIs and Denominators","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators","en\u002Fbusiness-analytics\u002F01-descriptive\u002F05-kpis-denominators",{"title":294,"path":295,"stem":296},"Segments, Cohorts and Funnels","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels","en\u002Fbusiness-analytics\u002F01-descriptive\u002F06-segmentation-cohorts-funnels",{"title":298,"path":299,"stem":300},"Visual Evidence and Data Stories","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story","en\u002Fbusiness-analytics\u002F01-descriptive\u002F07-visualisation-story",{"title":302,"path":303,"stem":304},"Experiments and Causal Boundaries","\u002Fen\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary","en\u002Fbusiness-analytics\u002F01-descriptive\u002F08-experiments-causal-boundary",{"title":306,"path":307,"stem":308,"children":309},"2. Predictive Analytics","\u002Fen\u002Fbusiness-analytics\u002F02-predictive","en\u002Fbusiness-analytics\u002F02-predictive\u002Findex",[310,311,315,319,323,327,331],{"title":306,"path":307,"stem":308},{"title":312,"path":313,"stem":314},"Validation, Baselines and Leakage","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage","en\u002Fbusiness-analytics\u002F02-predictive\u002F09-validation-leakage",{"title":316,"path":317,"stem":318},"Regression and Forecasting","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting","en\u002Fbusiness-analytics\u002F02-predictive\u002F10-regression-forecasting",{"title":320,"path":321,"stem":322},"Classification and Calibration","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration","en\u002Fbusiness-analytics\u002F02-predictive\u002F11-classification-calibration",{"title":324,"path":325,"stem":326},"Trees and Ensembles","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles","en\u002Fbusiness-analytics\u002F02-predictive\u002F12-trees-ensembles",{"title":328,"path":329,"stem":330},"Decision Metrics and Thresholds","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds","en\u002Fbusiness-analytics\u002F02-predictive\u002F13-decision-metrics-thresholds",{"title":332,"path":333,"stem":334},"Explainability, Monitoring and Drift","\u002Fen\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift","en\u002Fbusiness-analytics\u002F02-predictive\u002F14-explainability-drift",{"title":336,"path":337,"stem":338,"children":339},"3. Prescriptive Analytics","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive","en\u002Fbusiness-analytics\u002F03-prescriptive\u002Findex",[340,341,345,349,353,357,361],{"title":336,"path":337,"stem":338},{"title":342,"path":343,"stem":344},"Decision-Making under Uncertainty","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F15-decision-uncertainty",{"title":346,"path":347,"stem":348},"Linear Optimisation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F16-linear-optimization",{"title":350,"path":351,"stem":352},"Inventory and Allocation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F17-inventory-allocation",{"title":354,"path":355,"stem":356},"Queueing and Simulation","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F18-queueing-simulation",{"title":358,"path":359,"stem":360},"Pricing and Revenue Management","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F19-pricing-experimentation",{"title":362,"path":363,"stem":364},"Causal Targeting and Policy Learning","\u002Fen\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting","en\u002Fbusiness-analytics\u002F03-prescriptive\u002F20-causal-targeting",{"title":366,"path":367,"stem":368,"children":369},"4. Deployment and Governance","\u002Fen\u002Fbusiness-analytics\u002F04-deployment","en\u002Fbusiness-analytics\u002F04-deployment\u002Findex",[370,371,375,379],{"title":366,"path":367,"stem":368},{"title":372,"path":373,"stem":374},"Data Products and Monitoring","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring","en\u002Fbusiness-analytics\u002F04-deployment\u002F21-data-products-monitoring",{"title":376,"path":377,"stem":378},"Governance, Fairness and Privacy","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy","en\u002Fbusiness-analytics\u002F04-deployment\u002F22-governance-fairness-privacy",{"title":380,"path":381,"stem":382},"Adoption and Business Value","\u002Fen\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value","en\u002Fbusiness-analytics\u002F04-deployment\u002F23-adoption-value",{"title":384,"path":385,"stem":386,"children":387},"Appendix and Revision Tools","\u002Fen\u002Fbusiness-analytics\u002Fappendix","en\u002Fbusiness-analytics\u002Fappendix\u002Findex",[388,389,393,397],{"title":384,"path":385,"stem":386},{"title":390,"path":391,"stem":392},"Formula and Decision Map","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map","en\u002Fbusiness-analytics\u002Fappendix\u002F24-formula-map",{"title":394,"path":395,"stem":396},"Worked Examples and Pitfalls","\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls","en\u002Fbusiness-analytics\u002Fappendix\u002F25-worked-examples-pitfalls",{"title":84,"path":398,"stem":399},"\u002Fen\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map","en\u002Fbusiness-analytics\u002Fappendix\u002F26-reading-map",{"title":401,"path":402,"stem":403,"children":404},"Capstone — The Evening Delivery Promise","\u002Fen\u002Fbusiness-analytics\u002Fcapstone","en\u002Fbusiness-analytics\u002Fcapstone\u002Findex",[405],{"title":401,"path":402,"stem":403},{"title":407,"path":408,"stem":409,"children":410,"page":249},"Financial Economic Time Series","\u002Fen\u002Ffinancial-economic-time-series","en\u002Ffinancial-economic-time-series",[411,417,423,429,435,441,447,453,459,465,471],{"title":412,"path":413,"stem":414,"children":415},"Financial and Economic Time Series — Course Guide","\u002Fen\u002Ffinancial-economic-time-series\u002F00-intro","en\u002Ffinancial-economic-time-series\u002F00-intro\u002Findex",[416],{"title":412,"path":413,"stem":414},{"title":418,"path":419,"stem":420,"children":421},"Three Versions of Time Series","\u002Fen\u002Ffinancial-economic-time-series\u002F01-bridge","en\u002Ffinancial-economic-time-series\u002F01-bridge\u002Findex",[422],{"title":418,"path":419,"stem":420},{"title":424,"path":425,"stem":426,"children":427},"Data, Clocks, and Transformations","\u002Fen\u002Ffinancial-economic-time-series\u002F02-data-transformations","en\u002Ffinancial-economic-time-series\u002F02-data-transformations\u002Findex",[428],{"title":424,"path":425,"stem":426},{"title":430,"path":431,"stem":432,"children":433},"Predictive Regressions and Persistent Predictors","\u002Fen\u002Ffinancial-economic-time-series\u002F03-predictive-regressions","en\u002Ffinancial-economic-time-series\u002F03-predictive-regressions\u002Findex",[434],{"title":430,"path":431,"stem":432},{"title":436,"path":437,"stem":438,"children":439},"Volatility, Tails, and Financial Risk","\u002Fen\u002Ffinancial-economic-time-series\u002F04-volatility-risk","en\u002Ffinancial-economic-time-series\u002F04-volatility-risk\u002Findex",[440],{"title":436,"path":437,"stem":438},{"title":442,"path":443,"stem":444,"children":445},"Unit Roots, Cointegration, and Error Correction","\u002Fen\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration","en\u002Ffinancial-economic-time-series\u002F05-unit-roots-cointegration\u002Findex",[446],{"title":442,"path":443,"stem":444},{"title":448,"path":449,"stem":450,"children":451},"VAR, Structural Identification, and Local Projections","\u002Fen\u002Ffinancial-economic-time-series\u002F06-var-identification","en\u002Ffinancial-economic-time-series\u002F06-var-identification\u002Findex",[452],{"title":448,"path":449,"stem":450},{"title":454,"path":455,"stem":456,"children":457},"State Space, Mixed Frequency, and Nowcasting","\u002Fen\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting","en\u002Ffinancial-economic-time-series\u002F07-state-space-nowcasting\u002Findex",[458],{"title":454,"path":455,"stem":456},{"title":460,"path":461,"stem":462,"children":463},"Forecast Evaluation for Decisions","\u002Fen\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation","en\u002Ffinancial-economic-time-series\u002F08-forecast-evaluation\u002Findex",[464],{"title":460,"path":461,"stem":462},{"title":466,"path":467,"stem":468,"children":469},"Integrated R Laboratory","\u002Fen\u002Ffinancial-economic-time-series\u002F09-r-laboratory","en\u002Ffinancial-economic-time-series\u002F09-r-laboratory\u002Findex",[470],{"title":466,"path":467,"stem":468},{"title":472,"path":473,"stem":474,"children":475},"Capstones, Data, and Reading Ladder","\u002Fen\u002Ffinancial-economic-time-series\u002F10-capstone-readings","en\u002Ffinancial-economic-time-series\u002F10-capstone-readings\u002Findex",[476],{"title":472,"path":473,"stem":474},{"title":478,"path":479,"stem":480,"children":481,"page":249},"Intro To Economics","\u002Fen\u002Fintro-to-economics","en\u002Fintro-to-economics",[482,486,490,494,498,502,506,510,514,518,522,526,530],{"title":483,"path":484,"stem":485},"Introduction to Economics — Decisions, Markets, and the Macroeconomy","\u002Fen\u002Fintro-to-economics\u002F00-intro","en\u002Fintro-to-economics\u002F00-intro",{"title":487,"path":488,"stem":489},"Chapter 1 — Choice, Opportunity Cost, and Trade","\u002Fen\u002Fintro-to-economics\u002F01-foundations","en\u002Fintro-to-economics\u002F01-foundations",{"title":491,"path":492,"stem":493},"Chapter 2 — Demand, Supply, Equilibrium, and Welfare","\u002Fen\u002Fintro-to-economics\u002F02-demand-and-supply","en\u002Fintro-to-economics\u002F02-demand-and-supply",{"title":495,"path":496,"stem":497},"Chapter 3 — Elasticity, Revenue, and Tax Incidence","\u002Fen\u002Fintro-to-economics\u002F03-elasticity","en\u002Fintro-to-economics\u002F03-elasticity",{"title":499,"path":500,"stem":501},"Chapter 4 — Firms, Market Power, and Market Failure","\u002Fen\u002Fintro-to-economics\u002F04-market-structures","en\u002Fintro-to-economics\u002F04-market-structures",{"title":503,"path":504,"stem":505},"Chapter 5 — GDP, Income, Wealth, and Welfare","\u002Fen\u002Fintro-to-economics\u002F05-gdp-and-wealth","en\u002Fintro-to-economics\u002F05-gdp-and-wealth",{"title":507,"path":508,"stem":509},"Chapter 6 — Inflation, Purchasing Power, and Labour Markets","\u002Fen\u002Fintro-to-economics\u002F06-inflation-and-unemployment","en\u002Fintro-to-economics\u002F06-inflation-and-unemployment",{"title":511,"path":512,"stem":513},"Chapter 7 — Productivity, Technology, and Economic Growth","\u002Fen\u002Fintro-to-economics\u002F07-economic-growth","en\u002Fintro-to-economics\u002F07-economic-growth",{"title":515,"path":516,"stem":517},"Chapter 8 — Money, Credit, and Banking","\u002Fen\u002Fintro-to-economics\u002F08-money-and-banking","en\u002Fintro-to-economics\u002F08-money-and-banking",{"title":519,"path":520,"stem":521},"Chapter 9 — Business Cycles, AD–AS, and Monetary Policy","\u002Fen\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as","en\u002Fintro-to-economics\u002F09-monetary-policy-and-ad-as",{"title":523,"path":524,"stem":525},"Chapter 10 — Fiscal Policy, Distribution, and Public Debt","\u002Fen\u002Fintro-to-economics\u002F10-fiscal-policy","en\u002Fintro-to-economics\u002F10-fiscal-policy",{"title":527,"path":528,"stem":529},"Chapter 11 — Trade, Capital Flows, and Exchange Rates","\u002Fen\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates","en\u002Fintro-to-economics\u002F11-open-economy-and-exchange-rates",{"title":531,"path":532,"stem":533},"Chapter 12 — Integrated Economic Analysis Studio","\u002Fen\u002Fintro-to-economics\u002F12-review-and-case-studies","en\u002Fintro-to-economics\u002F12-review-and-case-studies",{"title":535,"path":536,"stem":537,"children":538,"page":249},"Microeconometrics","\u002Fen\u002Fmicroeconometrics","en\u002Fmicroeconometrics",[539,557,563,581,603,629,651,673,691,709],{"title":540,"path":541,"stem":542,"children":543},"0. Causal Questions and Designs","\u002Fen\u002Fmicroeconometrics\u002F00-foundations","en\u002Fmicroeconometrics\u002F00-foundations\u002Findex",[544,545,549,553],{"title":540,"path":541,"stem":542},{"title":546,"path":547,"stem":548},"Causal Questions and Estimands","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands","en\u002Fmicroeconometrics\u002F00-foundations\u002F01-causal-question-estimands",{"title":550,"path":551,"stem":552},"Potential Outcomes and Experiments","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments","en\u002Fmicroeconometrics\u002F00-foundations\u002F02-potential-outcomes-experiments",{"title":554,"path":555,"stem":556},"Causal Diagrams and Controls","\u002Fen\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls","en\u002Fmicroeconometrics\u002F00-foundations\u002F03-dags-controls",{"title":558,"path":559,"stem":560,"children":561},"Microeconometrics — Designing Credible Counterfactuals","\u002Fen\u002Fmicroeconometrics\u002F00-index","en\u002Fmicroeconometrics\u002F00-index",[562],{"title":558,"path":559,"stem":560},{"title":564,"path":565,"stem":566,"children":567},"1. Regression and Inference","\u002Fen\u002Fmicroeconometrics\u002F01-regression","en\u002Fmicroeconometrics\u002F01-regression\u002Findex",[568,569,573,577],{"title":564,"path":565,"stem":566},{"title":570,"path":571,"stem":572},"OLS as a Projection","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection","en\u002Fmicroeconometrics\u002F01-regression\u002F04-ols-projection",{"title":574,"path":575,"stem":576},"FWL, Selection and Controls","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls","en\u002Fmicroeconometrics\u002F01-regression\u002F05-fwl-selection-controls",{"title":578,"path":579,"stem":580},"Inference and Clustering","\u002Fen\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering","en\u002Fmicroeconometrics\u002F01-regression\u002F06-inference-clustering",{"title":582,"path":583,"stem":584,"children":585},"2. Instruments and Panel Data","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002Findex",[586,587,591,595,599],{"title":582,"path":583,"stem":584},{"title":588,"path":589,"stem":590},"Instrumental Variables","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F07-iv-identification",{"title":592,"path":593,"stem":594},"Weak Instruments and LATE","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F08-weak-iv-late",{"title":596,"path":597,"stem":598},"Panel Fixed Effects","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F09-panel-fixed-effects",{"title":600,"path":601,"stem":602},"Dynamic Panels and Limits","\u002Fen\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel","en\u002Fmicroeconometrics\u002F02-iv-panel\u002F10-dynamic-panel",{"title":604,"path":605,"stem":606,"children":607},"3. Policy Evaluation Designs","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs","en\u002Fmicroeconometrics\u002F03-policy-designs\u002Findex",[608,609,613,617,621,625],{"title":604,"path":605,"stem":606},{"title":610,"path":611,"stem":612},"Difference-in-Differences","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F11-did-core",{"title":614,"path":615,"stem":616},"Staggered DID and Event Studies","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F12-staggered-event-studies",{"title":618,"path":619,"stem":620},"Regression Discontinuity","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F13-rdd",{"title":622,"path":623,"stem":624},"Matching, Weighting and Overlap","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F14-matching-weighting",{"title":626,"path":627,"stem":628},"Synthetic Control","\u002Fen\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control","en\u002Fmicroeconometrics\u002F03-policy-designs\u002F15-synthetic-control",{"title":630,"path":631,"stem":632,"children":633},"Module 4 — Choice and Limited Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002Findex",[634,635,639,643,647],{"title":630,"path":631,"stem":632},{"title":636,"path":637,"stem":638},"Binary Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F16-binary-choice",{"title":640,"path":641,"stem":642},"Multinomial and Ordered Choice","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F17-multinomial-choice",{"title":644,"path":645,"stem":646},"Count Outcomes","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F18-count-outcomes",{"title":648,"path":649,"stem":650},"Censoring, Truncation and Selection","\u002Fen\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection","en\u002Fmicroeconometrics\u002F04-outcomes-choice\u002F19-censoring-selection",{"title":652,"path":653,"stem":654,"children":655},"Module 5 — Modern Causal Analysis","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal","en\u002Fmicroeconometrics\u002F05-modern-causal\u002Findex",[656,657,661,665,669],{"title":652,"path":653,"stem":654},{"title":658,"path":659,"stem":660},"Double Machine Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F20-dml",{"title":662,"path":663,"stem":664},"Heterogeneity and Policy Learning","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F21-heterogeneity-policy",{"title":666,"path":667,"stem":668},"Sensitivity and Partial Identification","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F22-sensitivity-partial-id",{"title":670,"path":671,"stem":672},"External Validity and Transport","\u002Fen\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity","en\u002Fmicroeconometrics\u002F05-modern-causal\u002F23-external-validity",{"title":674,"path":675,"stem":676,"children":677},"Module 6 — From Data to Auditable Evidence","\u002Fen\u002Fmicroeconometrics\u002F06-workflow","en\u002Fmicroeconometrics\u002F06-workflow\u002Findex",[678,679,683,687],{"title":674,"path":675,"stem":676},{"title":680,"path":681,"stem":682},"Data Provenance","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance","en\u002Fmicroeconometrics\u002F06-workflow\u002F24-data-provenance",{"title":684,"path":685,"stem":686},"Reproducibility and Reporting","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting","en\u002Fmicroeconometrics\u002F06-workflow\u002F25-reproducibility-reporting",{"title":688,"path":689,"stem":690},"Paper and Evidence Audit","\u002Fen\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit","en\u002Fmicroeconometrics\u002F06-workflow\u002F26-paper-audit",{"title":692,"path":693,"stem":694,"children":695},"Appendix — Revision and Evidence Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix","en\u002Fmicroeconometrics\u002Fappendix\u002Findex",[696,697,701,705],{"title":692,"path":693,"stem":694},{"title":698,"path":699,"stem":700},"Formula and Design Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map","en\u002Fmicroeconometrics\u002Fappendix\u002F27-formula-design-map",{"title":702,"path":703,"stem":704},"Ten Worked Microeconometric Pitfalls","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls","en\u002Fmicroeconometrics\u002Fappendix\u002F28-worked-pitfalls",{"title":706,"path":707,"stem":708},"Reading and Software Map","\u002Fen\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map","en\u002Fmicroeconometrics\u002Fappendix\u002F29-reading-software-map",{"title":710,"path":711,"stem":712,"children":713},"Capstone — Should Northbridge Expand Pathways?","\u002Fen\u002Fmicroeconometrics\u002Fcapstone","en\u002Fmicroeconometrics\u002Fcapstone\u002Findex",[714],{"title":710,"path":711,"stem":712},{"title":716,"path":717,"stem":718,"children":719,"page":249},"Microeconomics","\u002Fen\u002Fmicroeconomics","en\u002Fmicroeconomics",[720,726,732,738,744,750,756,762,768,774,780,786,792],{"title":721,"path":722,"stem":723,"children":724},"Advanced Microeconomics — Course Guide","\u002Fen\u002Fmicroeconomics\u002F00-intro","en\u002Fmicroeconomics\u002F00-intro\u002Findex",[725],{"title":721,"path":722,"stem":723},{"title":727,"path":728,"stem":729,"children":730},"Module 1 — Choice, Duality, and Revealed Preference","\u002Fen\u002Fmicroeconomics\u002F01-fundations","en\u002Fmicroeconomics\u002F01-fundations\u002Findex",[731],{"title":727,"path":728,"stem":729},{"title":733,"path":734,"stem":735,"children":736},"Module 2 — Comparative Statics and Welfare Measurement","\u002Fen\u002Fmicroeconomics\u002F02-comparative-statics","en\u002Fmicroeconomics\u002F02-comparative-statics\u002Findex",[737],{"title":733,"path":734,"stem":735},{"title":739,"path":740,"stem":741,"children":742},"Module 3 — Choice under Risk and Insurance","\u002Fen\u002Fmicroeconomics\u002F03-uncertainty","en\u002Fmicroeconomics\u002F03-uncertainty\u002Findex",[743],{"title":739,"path":740,"stem":741},{"title":745,"path":746,"stem":747,"children":748},"Module 4 — General Equilibrium and Welfare","\u002Fen\u002Fmicroeconomics\u002F04-general-equilibrium","en\u002Fmicroeconomics\u002F04-general-equilibrium\u002Findex",[749],{"title":745,"path":746,"stem":747},{"title":751,"path":752,"stem":753,"children":754},"Module 5 — Static, Dynamic, and Repeated Games","\u002Fen\u002Fmicroeconomics\u002F05-game-theory","en\u002Fmicroeconomics\u002F05-game-theory\u002Findex",[755],{"title":751,"path":752,"stem":753},{"title":757,"path":758,"stem":759,"children":760},"Module 6 — Oligopoly, Entry, and Algorithmic Pricing","\u002Fen\u002Fmicroeconomics\u002F06-oligopoly","en\u002Fmicroeconomics\u002F06-oligopoly\u002Findex",[761],{"title":757,"path":758,"stem":759},{"title":763,"path":764,"stem":765,"children":766},"Module 7 — Information Economics and Contracts","\u002Fen\u002Fmicroeconomics\u002F07-information-economics","en\u002Fmicroeconomics\u002F07-information-economics\u002Findex",[767],{"title":763,"path":764,"stem":765},{"title":769,"path":770,"stem":771,"children":772},"Module 8 — Mechanism Design and Auctions","\u002Fen\u002Fmicroeconomics\u002F08-mechanism-design","en\u002Fmicroeconomics\u002F08-mechanism-design\u002Findex",[773],{"title":769,"path":770,"stem":771},{"title":775,"path":776,"stem":777,"children":778},"Module 9 — Behavioural and Experimental Microeconomics","\u002Fen\u002Fmicroeconomics\u002F09-behavioural-economics","en\u002Fmicroeconomics\u002F09-behavioural-economics\u002Findex",[779],{"title":775,"path":776,"stem":777},{"title":781,"path":782,"stem":783,"children":784},"Module 10 — Externalities, Public Goods, and Collective Action","\u002Fen\u002Fmicroeconomics\u002F10-externalities-public-goods","en\u002Fmicroeconomics\u002F10-externalities-public-goods\u002Findex",[785],{"title":781,"path":782,"stem":783},{"title":787,"path":788,"stem":789,"children":790},"Module 11 — Matching and Market Design","\u002Fen\u002Fmicroeconomics\u002F11-market-design","en\u002Fmicroeconomics\u002F11-market-design\u002Findex",[791],{"title":787,"path":788,"stem":789},{"title":793,"path":794,"stem":795,"children":796},"Module 12 — Integrated Microeconomic Design Studio","\u002Fen\u002Fmicroeconomics\u002F12-review","en\u002Fmicroeconomics\u002F12-review\u002Findex",[797],{"title":793,"path":794,"stem":795},{"title":799,"path":800,"stem":801,"children":802},"Playground","\u002Fen\u002Fplayground","en\u002Fplayground\u002Findex",[803,804,808,812,816,820],{"title":799,"path":800,"stem":801},{"title":805,"path":806,"stem":807},"Typst Plugin Playground","\u002Fen\u002Fplayground\u002F01-typstex","en\u002Fplayground\u002F01-typstex",{"title":809,"path":810,"stem":811},"Citation Plugin Test","\u002Fen\u002Fplayground\u002F02-citation","en\u002Fplayground\u002F02-citation",{"title":813,"path":814,"stem":815},"Pyodide Playground","\u002Fen\u002Fplayground\u002F03-pyodide","en\u002Fplayground\u002F03-pyodide",{"title":817,"path":818,"stem":819},"WebR Playground","\u002Fen\u002Fplayground\u002F04-webr","en\u002Fplayground\u002F04-webr",{"title":821,"path":822,"stem":823},"Chart.js 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文献综述的构建与写作","\u002Fzh\u002Facademic-writing\u002F04-writing-the-literature-review","zh\u002Facademic-writing\u002F04-writing-the-literature-review",{"title":1056,"path":1057,"stem":1058},"8. 文献综述清单与模板","\u002Fzh\u002Facademic-writing\u002F08-literature-review-checklist-and-template","zh\u002Facademic-writing\u002F08-literature-review-checklist-and-template",{"title":1060,"path":1061,"stem":1062},"10. 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中的均值–方差分析（第三章）、CAPM（第四章）和因子模型（第五章），可以把本章视为这些理论在“量化策略回测”场景下的工程化版本：同样的随机收益和风险度量，但更强调信息集、自洽性以及可实现性。",[1792,1804,1805],{},"在整个章节中，我们默认读者已经接受资产收益是一个随机过程这一基本假设：",[1807,1808,1811],"span",{"className":1809},[1810],"katex-display",[1807,1812,1815,1887],{"className":1813},[1814],"katex",[1807,1816,1819],{"className":1817},[1818],"katex-mathml",[1820,1821,1824],"math",{"xmlns":1822,"display":1823},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1825,1826,1827,1882],"semantics",{},[1828,1829,1830,1835,1853,1873,1876,1880],"mrow",{},[1831,1832,1834],"mo",{"stretchy":1833},"false","{",[1836,1837,1838,1842],"msub",{},[1839,1840,1841],"mi",{},"r",[1828,1843,1844,1846,1850],{},[1839,1845,1792],{},[1831,1847,1849],{"separator":1848},"true",",",[1839,1851,1852],{},"t",[1854,1855,1856,1859,1870],"msubsup",{},[1831,1857,1858],{"stretchy":1833},"}",[1828,1860,1861,1863,1866],{},[1839,1862,1852],{},[1831,1864,1865],{},"=",[1867,1868,1869],"mn",{},"1",[1839,1871,1872],{},"T",[1831,1874,1875],{},"∼",[1877,1878,1879],"mtext",{},"某个未知的数据生成过程 (DGP)",[1831,1881,1849],{"separator":1848},[1883,1884,1886],"annotation",{"encoding":1885},"application\u002Fx-tex","\\{r_{p,t}\\}_{t=1}^T \\sim \\text{某个未知的数据生成过程 (DGP)},",[1807,1888,1891,2051],{"className":1889,"ariaHidden":1848},[1890],"katex-html",[1807,1892,1895,1900,1904,1973,2040,2045,2048],{"className":1893},[1894],"base",[1807,1896],{"className":1897,"style":1899},[1898],"strut","height:1.1774em;vertical-align:-0.2861em;",[1807,1901,1834],{"className":1902},[1903],"mopen",[1807,1905,1908,1913],{"className":1906},[1907],"mord",[1807,1909,1841],{"className":1910,"style":1912},[1907,1911],"mathnormal","margin-right:0.0278em;",[1807,1914,1917],{"className":1915},[1916],"msupsub",[1807,1918,1922,1964],{"className":1919},[1920,1921],"vlist-t","vlist-t2",[1807,1923,1926,1959],{"className":1924},[1925],"vlist-r",[1807,1927,1931],{"className":1928,"style":1930},[1929],"vlist","height:0.2806em;",[1807,1932,1934,1939],{"style":1933},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1807,1935],{"className":1936,"style":1938},[1937],"pstrut","height:2.7em;",[1807,1940,1946],{"className":1941},[1942,1943,1944,1945],"sizing","reset-size6","size3","mtight",[1807,1947,1949,1952,1956],{"className":1948},[1907,1945],[1807,1950,1792],{"className":1951},[1907,1911,1945],[1807,1953,1849],{"className":1954},[1955,1945],"mpunct",[1807,1957,1852],{"className":1958},[1907,1911,1945],[1807,1960,1963],{"className":1961},[1962],"vlist-s","​",[1807,1965,1967],{"className":1966},[1925],[1807,1968,1971],{"className":1969,"style":1970},[1929],"height:0.2861em;",[1807,1972],{},[1807,1974,1977,1980],{"className":1975},[1976],"mclose",[1807,1978,1858],{"className":1979},[1976],[1807,1981,1983],{"className":1982},[1916],[1807,1984,1986,2031],{"className":1985},[1920,1921],[1807,1987,1989,2028],{"className":1988},[1925],[1807,1990,1993,2015],{"className":1991,"style":1992},[1929],"height:0.8913em;",[1807,1994,1996,1999],{"style":1995},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1807,1997],{"className":1998,"style":1938},[1937],[1807,2000,2002],{"className":2001},[1942,1943,1944,1945],[1807,2003,2005,2008,2012],{"className":2004},[1907,1945],[1807,2006,1852],{"className":2007},[1907,1911,1945],[1807,2009,1865],{"className":2010},[2011,1945],"mrel",[1807,2013,1869],{"className":2014},[1907,1945],[1807,2016,2018,2021],{"style":2017},"top:-3.113em;margin-right:0.05em;",[1807,2019],{"className":2020,"style":1938},[1937],[1807,2022,2024],{"className":2023},[1942,1943,1944,1945],[1807,2025,1872],{"className":2026,"style":2027},[1907,1911,1945],"margin-right:0.1389em;",[1807,2029,1963],{"className":2030},[1962],[1807,2032,2034],{"className":2033},[1925],[1807,2035,2038],{"className":2036,"style":2037},[1929],"height:0.247em;",[1807,2039],{},[1807,2041],{"className":2042,"style":2044},[2043],"mspace","margin-right:0.2778em;",[1807,2046,1875],{"className":2047},[2011],[1807,2049],{"className":2050,"style":2044},[2043],[1807,2052,2054,2058,2071],{"className":2053},[1894],[1807,2055],{"className":2056,"style":2057},[1898],"height:1em;vertical-align:-0.25em;",[1807,2059,2062,2067],{"className":2060},[1907,2061],"text",[1807,2063,2066],{"className":2064},[1907,2065],"cjk_fallback","某个未知的数据生成过程",[1807,2068,2070],{"className":2069},[1907]," (DGP)",[1807,2072,1849],{"className":2073},[1955],[1792,2075,2076],{},"回测所做的工作，是利用有限样本对这一 DGP 的某些特征（如均值、方差、尾部行为等）进行估计，并据此判断策略在未来是否值得投入真实资本。所有的绩效指标和检验，都隐含着关于这一 DGP 的统计假设，这一点在后续的计量方法章节会进一步展开。",[2078,2079,2081],"h2",{"id":2080},"论文精读模块从预测收益到可交易组合","论文精读模块：从“预测收益”到“可交易组合”",[1792,2083,2084,2085,2114,2115,2192,2193,2249],{},"这一章的 fundamental 是回测纪律：任何策略都必须在时点 ",[1807,2086,2088,2101],{"className":2087},[1814],[1807,2089,2091],{"className":2090},[1818],[1820,2092,2093],{"xmlns":1822},[1825,2094,2095,2099],{},[1828,2096,2097],{},[1839,2098,1852],{},[1883,2100,1852],{"encoding":1885},[1807,2102,2104],{"className":2103,"ariaHidden":1848},[1890],[1807,2105,2107,2111],{"className":2106},[1894],[1807,2108],{"className":2109,"style":2110},[1898],"height:0.6151em;",[1807,2112,1852],{"className":2113},[1907,1911]," 的信息集 ",[1807,2116,2118,2138],{"className":2117},[1814],[1807,2119,2121],{"className":2120},[1818],[1820,2122,2123],{"xmlns":1822},[1825,2124,2125,2135],{},[1828,2126,2127],{},[1836,2128,2129,2133],{},[1839,2130,2132],{"mathvariant":2131},"script","I",[1839,2134,1852],{},[1883,2136,2137],{"encoding":1885},"\\mathcal{I}_t",[1807,2139,2141],{"className":2140,"ariaHidden":1848},[1890],[1807,2142,2144,2148],{"className":2143},[1894],[1807,2145],{"className":2146,"style":2147},[1898],"height:0.8333em;vertical-align:-0.15em;",[1807,2149,2151,2156],{"className":2150},[1907],[1807,2152,2132],{"className":2153,"style":2155},[1907,2154],"mathcal","margin-right:0.0738em;",[1807,2157,2159],{"className":2158},[1916],[1807,2160,2162,2183],{"className":2161},[1920,1921],[1807,2163,2165,2180],{"className":2164},[1925],[1807,2166,2168],{"className":2167,"style":1930},[1929],[1807,2169,2171,2174],{"style":2170},"top:-2.55em;margin-left:-0.0738em;margin-right:0.05em;",[1807,2172],{"className":2173,"style":1938},[1937],[1807,2175,2177],{"className":2176},[1942,1943,1944,1945],[1807,2178,1852],{"className":2179},[1907,1911,1945],[1807,2181,1963],{"className":2182},[1962],[1807,2184,2186],{"className":2185},[1925],[1807,2187,2190],{"className":2188,"style":2189},[1929],"height:0.15em;",[1807,2191],{}," 下生成仓位，然后到 ",[1807,2194,2196,2215],{"className":2195},[1814],[1807,2197,2199],{"className":2198},[1818],[1820,2200,2201],{"xmlns":1822},[1825,2202,2203,2212],{},[1828,2204,2205,2207,2210],{},[1839,2206,1852],{},[1831,2208,2209],{},"+",[1867,2211,1869],{},[1883,2213,2214],{"encoding":1885},"t+1",[1807,2216,2218,2239],{"className":2217,"ariaHidden":1848},[1890],[1807,2219,2221,2225,2228,2232,2236],{"className":2220},[1894],[1807,2222],{"className":2223,"style":2224},[1898],"height:0.6984em;vertical-align:-0.0833em;",[1807,2226,1852],{"className":2227},[1907,1911],[1807,2229],{"className":2230,"style":2231},[2043],"margin-right:0.2222em;",[1807,2233,2209],{"className":2234},[2235],"mbin",[1807,2237],{"className":2238,"style":2231},[2043],[1807,2240,2242,2246],{"className":2241},[1894],[1807,2243],{"className":2244,"style":2245},[1898],"height:0.6444em;",[1807,2247,1869],{"className":2248},[1907]," 才观察收益。前沿机器学习论文没有改变这条规则，反而让它更重要。模型越复杂，越容易在信息集、训练窗口、文本数据和调参过程中发生前视偏差。",[1792,2251,2252],{},"一个现代量化策略可以拆成四个函数：",[1807,2254,2256],{"className":2255},[1810],[1807,2257,2259,2427],{"className":2258},[1814],[1807,2260,2262],{"className":2261},[1818],[1820,2263,2264],{"xmlns":1822,"display":1823},[1825,2265,2266,2424],{},[1828,2267,2268,2275,2277,2280,2283,2289,2292,2294,2297,2310,2312,2315,2317,2323,2325,2327,2329,2336,2338,2341,2343,2353,2355,2367,2369,2376,2378,2380,2382,2398,2400,2409,2421],{},[1836,2269,2270,2273],{},[1839,2271,2272],{},"s",[1839,2274,1852],{},[1831,2276,1865],{},[1839,2278,2279],{},"f",[1831,2281,2282],{"stretchy":1833},"(",[1836,2284,2285,2287],{},[1839,2286,2132],{"mathvariant":2131},[1839,2288,1852],{},[1831,2290,2291],{"stretchy":1833},")",[1831,2293,1849],{"separator":1848},[2043,2295],{"width":2296},"2em",[1836,2298,2299,2308],{},[2300,2301,2302,2305],"mover",{"accent":1848},[1839,2303,2304],{},"μ",[1831,2306,2307],{},"^",[1839,2309,1852],{},[1831,2311,1865],{},[1839,2313,2314],{},"h",[1831,2316,2282],{"stretchy":1833},[1836,2318,2319,2321],{},[1839,2320,2272],{},[1839,2322,1852],{},[1831,2324,2291],{"stretchy":1833},[1831,2326,1849],{"separator":1848},[2043,2328],{"width":2296},[1836,2330,2331,2334],{},[1839,2332,2333],{},"w",[1839,2335,1852],{},[1831,2337,1865],{},[1839,2339,2340],{},"G",[1831,2342,2282],{"stretchy":1833},[1836,2344,2345,2351],{},[2300,2346,2347,2349],{"accent":1848},[1839,2348,2304],{},[1831,2350,2307],{},[1839,2352,1852],{},[1831,2354,1849],{"separator":1848},[1836,2356,2357,2365],{},[2300,2358,2359,2363],{"accent":1848},[1839,2360,2362],{"mathvariant":2361},"normal","Σ",[1831,2364,2307],{},[1839,2366,1852],{},[1831,2368,1849],{"separator":1848},[1836,2370,2371,2374],{},[1839,2372,2373],{},"c",[1839,2375,1852],{},[1831,2377,2291],{"stretchy":1833},[1831,2379,1849],{"separator":1848},[2043,2381],{"width":2296},[1836,2383,2384,2386],{},[1839,2385,1841],{},[1828,2387,2388,2390,2392,2394,2396],{},[1839,2389,1792],{},[1831,2391,1849],{"separator":1848},[1839,2393,1852],{},[1831,2395,2209],{},[1867,2397,1869],{},[1831,2399,1865],{},[1854,2401,2402,2404,2406],{},[1839,2403,2333],{},[1839,2405,1852],{},[1839,2407,2408],{"mathvariant":2361},"⊤",[1836,2410,2411,2413],{},[1839,2412,1841],{},[1828,2414,2415,2417,2419],{},[1839,2416,1852],{},[1831,2418,2209],{},[1867,2420,1869],{},[1839,2422,2423],{"mathvariant":2361},".",[1883,2425,2426],{"encoding":1885},"s_t=f(\\mathcal{I}_t),\\qquad\n\\hat\\mu_t=h(s_t),\\qquad\nw_t=G(\\hat\\mu_t,\\hat\\Sigma_t,c_t),\\qquad\nr_{p,t+1}=w_t^\\top r_{t+1}.",[1807,2428,2430,2487,2649,2764,3056],{"className":2429,"ariaHidden":1848},[1890],[1807,2431,2433,2437,2478,2481,2484],{"className":2432},[1894],[1807,2434],{"className":2435,"style":2436},[1898],"height:0.5806em;vertical-align:-0.15em;",[1807,2438,2440,2443],{"className":2439},[1907],[1807,2441,2272],{"className":2442},[1907,1911],[1807,2444,2446],{"className":2445},[1916],[1807,2447,2449,2470],{"className":2448},[1920,1921],[1807,2450,2452,2467],{"className":2451},[1925],[1807,2453,2455],{"className":2454,"style":1930},[1929],[1807,2456,2458,2461],{"style":2457},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1807,2459],{"className":2460,"style":1938},[1937],[1807,2462,2464],{"className":2463},[1942,1943,1944,1945],[1807,2465,1852],{"className":2466},[1907,1911,1945],[1807,2468,1963],{"className":2469},[1962],[1807,2471,2473],{"className":2472},[1925],[1807,2474,2476],{"className":2475,"style":2189},[1929],[1807,2477],{},[1807,2479],{"className":2480,"style":2044},[2043],[1807,2482,1865],{"className":2483},[2011],[1807,2485],{"className":2486,"style":2044},[2043],[1807,2488,2490,2493,2497,2500,2540,2543,2546,2550,2554,2640,2643,2646],{"className":2489},[1894],[1807,2491],{"className":2492,"style":2057},[1898],[1807,2494,2279],{"className":2495,"style":2496},[1907,1911],"margin-right:0.1076em;",[1807,2498,2282],{"className":2499},[1903],[1807,2501,2503,2506],{"className":2502},[1907],[1807,2504,2132],{"className":2505,"style":2155},[1907,2154],[1807,2507,2509],{"className":2508},[1916],[1807,2510,2512,2532],{"className":2511},[1920,1921],[1807,2513,2515,2529],{"className":2514},[1925],[1807,2516,2518],{"className":2517,"style":1930},[1929],[1807,2519,2520,2523],{"style":2170},[1807,2521],{"className":2522,"style":1938},[1937],[1807,2524,2526],{"className":2525},[1942,1943,1944,1945],[1807,2527,1852],{"className":2528},[1907,1911,1945],[1807,2530,1963],{"className":2531},[1962],[1807,2533,2535],{"className":2534},[1925],[1807,2536,2538],{"className":2537,"style":2189},[1929],[1807,2539],{},[1807,2541,2291],{"className":2542},[1976],[1807,2544,1849],{"className":2545},[1955],[1807,2547],{"className":2548,"style":2549},[2043],"margin-right:2em;",[1807,2551],{"className":2552,"style":2553},[2043],"margin-right:0.1667em;",[1807,2555,2557,2606],{"className":2556},[1907],[1807,2558,2561],{"className":2559},[1907,2560],"accent",[1807,2562,2564,2597],{"className":2563},[1920,1921],[1807,2565,2567,2594],{"className":2566},[1925],[1807,2568,2571,2581],{"className":2569,"style":2570},[1929],"height:0.6944em;",[1807,2572,2574,2578],{"style":2573},"top:-3em;",[1807,2575],{"className":2576,"style":2577},[1937],"height:3em;",[1807,2579,2304],{"className":2580},[1907,1911],[1807,2582,2583,2586],{"style":2573},[1807,2584],{"className":2585,"style":2577},[1937],[1807,2587,2591],{"className":2588,"style":2590},[2589],"accent-body","left:-0.2222em;",[1807,2592,2307],{"className":2593},[1907],[1807,2595,1963],{"className":2596},[1962],[1807,2598,2600],{"className":2599},[1925],[1807,2601,2604],{"className":2602,"style":2603},[1929],"height:0.1944em;",[1807,2605],{},[1807,2607,2609],{"className":2608},[1916],[1807,2610,2612,2632],{"className":2611},[1920,1921],[1807,2613,2615,2629],{"className":2614},[1925],[1807,2616,2618],{"className":2617,"style":1930},[1929],[1807,2619,2620,2623],{"style":2457},[1807,2621],{"className":2622,"style":1938},[1937],[1807,2624,2626],{"className":2625},[1942,1943,1944,1945],[1807,2627,1852],{"className":2628},[1907,1911,1945],[1807,2630,1963],{"className":2631},[1962],[1807,2633,2635],{"className":2634},[1925],[1807,2636,2638],{"className":2637,"style":2189},[1929],[1807,2639],{},[1807,2641],{"className":2642,"style":2044},[2043],[1807,2644,1865],{"className":2645},[2011],[1807,2647],{"className":2648,"style":2044},[2043],[1807,2650,2652,2655,2658,2661,2701,2704,2707,2710,2713,2755,2758,2761],{"className":2651},[1894],[1807,2653],{"className":2654,"style":2057},[1898],[1807,2656,2314],{"className":2657},[1907,1911],[1807,2659,2282],{"className":2660},[1903],[1807,2662,2664,2667],{"className":2663},[1907],[1807,2665,2272],{"className":2666},[1907,1911],[1807,2668,2670],{"className":2669},[1916],[1807,2671,2673,2693],{"className":2672},[1920,1921],[1807,2674,2676,2690],{"className":2675},[1925],[1807,2677,2679],{"className":2678,"style":1930},[1929],[1807,2680,2681,2684],{"style":2457},[1807,2682],{"className":2683,"style":1938},[1937],[1807,2685,2687],{"className":2686},[1942,1943,1944,1945],[1807,2688,1852],{"className":2689},[1907,1911,1945],[1807,2691,1963],{"className":2692},[1962],[1807,2694,2696],{"className":2695},[1925],[1807,2697,2699],{"className":2698,"style":2189},[1929],[1807,2700],{},[1807,2702,2291],{"className":2703},[1976],[1807,2705,1849],{"className":2706},[1955],[1807,2708],{"className":2709,"style":2549},[2043],[1807,2711],{"className":2712,"style":2553},[2043],[1807,2714,2716,2720],{"className":2715},[1907],[1807,2717,2333],{"className":2718,"style":2719},[1907,19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,[1937],[1807,3016,3018],{"className":3017},[1942,1943,1944,1945],[1807,3019,3021,3024,3027,3030,3033],{"className":3020},[1907,1945],[1807,3022,1792],{"className":3023},[1907,1911,1945],[1807,3025,1849],{"className":3026},[1955,1945],[1807,3028,1852],{"className":3029},[1907,1911,1945],[1807,3031,2209],{"className":3032},[2235,1945],[1807,3034,1869],{"className":3035},[1907,1945],[1807,3037,1963],{"className":3038},[1962],[1807,3040,3042],{"className":3041},[1925],[1807,3043,3045],{"className":3044,"style":1970},[1929],[1807,3046],{},[1807,3048],{"className":3049,"style":2044},[2043],[1807,3051,1865],{"className":3052},[2011],[1807,3054],{"className":3055,"style":2044},[2043],[1807,3057,3059,3063,3116,3166],{"className":3058},[1894],[1807,3060],{"className":3061,"style":3062},[1898],"height:1.1461em;vertical-align:-0.247em;",[1807,3064,3066,3069],{"className":3065},[1907],[1807,3067,2333],{"className":3068,"style":2719},[1907,1911],[1807,3070,3072],{"className":3071},[1916],[1807,3073,3075,3108],{"className":3074},[1920,1921],[1807,3076,3078,3105],{"className":3077},[1925],[1807,3079,3082,3094],{"className":3080,"style":3081},[1929],"height:0.8991em;",[1807,3083,3085,3088],{"style":3084},"top:-2.453em;margin-left:-0.0269em;margin-right:0.05em;",[1807,3086],{"className":3087,"style":1938},[1937],[1807,3089,3091],{"className":3090},[1942,1943,1944,1945],[1807,3092,1852],{"className":3093},[1907,1911,1945],[1807,3095,3096,3099],{"style":2017},[1807,3097],{"className":3098,"style":1938},[1937],[1807,3100,3102],{"className":3101},[1942,1943,1944,1945],[1807,3103,2408],{"className":3104},[1907,1945],[1807,3106,1963],{"className":3107},[1962],[1807,3109,3111],{"className":3110},[1925],[1807,3112,3114],{"className":3113,"style":2037},[1929],[1807,3115],{},[1807,3117,3119,3122],{"className":3118},[1907],[1807,3120,1841],{"className":3121,"style":1912},[1907,1911],[1807,3123,3125],{"className":3124},[1916],[1807,3126,3128,3157],{"className":3127},[1920,1921],[1807,3129,3131,3154],{"className":3130},[1925],[1807,3132,3134],{"className":3133,"style":3009},[1929],[1807,3135,3136,3139],{"style":1933},[1807,3137],{"className":3138,"style":1938},[1937],[1807,3140,3142],{"className":3141},[1942,1943,1944,1945],[1807,3143,3145,3148,3151],{"className":3144},[1907,1945],[1807,3146,1852],{"className":3147},[1907,1911,1945],[1807,3149,2209],{"className":3150},[2235,1945],[1807,3152,1869],{"className":3153},[1907,1945],[1807,3155,1963],{"className":3156},[1962],[1807,3158,3160],{"className":3159},[1925],[1807,3161,3164],{"className":3162,"style":3163},[1929],"height:0.2083em;",[1807,3165],{},[1807,3167,2423],{"className":3168},[1907],[1792,3170,3171,3172,3242,3243,3357,3358,3461,3462,3532,3533,3561,3562,3591],{},"这里 ",[1807,3173,3175,3193],{"className":3174},[1814],[1807,3176,3178],{"className":3177},[1818],[1820,3179,3180],{"xmlns":1822},[1825,3181,3182,3190],{},[1828,3183,3184],{},[1836,3185,3186,3188],{},[1839,3187,2272],{},[1839,3189,1852],{},[1883,3191,3192],{"encoding":1885},"s_t",[1807,3194,3196],{"className":3195,"ariaHidden":1848},[1890],[1807,3197,3199,3202],{"className":3198},[1894],[1807,3200],{"className":3201,"style":2436},[1898],[1807,3203,3205,3208],{"className":3204},[1907],[1807,3206,2272],{"className":3207},[1907,1911],[1807,3209,3211],{"className":3210},[1916],[1807,3212,3214,3234],{"className":3213},[1920,1921],[1807,3215,3217,3231],{"className":3216},[1925],[1807,3218,3220],{"className":3219,"style":1930},[1929],[1807,3221,3222,3225],{"style":2457},[1807,3223],{"className":3224,"style":1938},[1937],[1807,3226,3228],{"className":3227},[1942,1943,1944,1945],[1807,3229,1852],{"className":3230},[1907,1911,1945],[1807,3232,1963],{"className":3233},[1962],[1807,3235,3237],{"className":3236},[1925],[1807,3238,3240],{"className":3239,"style":2189},[1929],[1807,3241],{}," 是信号，",[1807,3244,3246,3268],{"className":3245},[1814],[1807,3247,3249],{"className":3248},[1818],[1820,3250,3251],{"xmlns":1822},[1825,3252,3253,3265],{},[1828,3254,3255],{},[1836,3256,3257,3263],{},[2300,3258,3259,3261],{"accent":1848},[1839,3260,2304],{},[1831,3262,2307],{},[1839,3264,1852],{},[1883,3266,3267],{"encoding":1885},"\\hat\\mu_t",[1807,3269,3271],{"className":3270,"ariaHidden":1848},[1890],[1807,3272,3274,3278],{"className":3273},[1894],[1807,3275],{"className":3276,"style":3277},[1898],"height:0.8889em;vertical-align:-0.1944em;",[1807,3279,3281,3323],{"className":3280},[1907],[1807,3282,3284],{"className":3283},[1907,2560],[1807,3285,3287,3315],{"className":3286},[1920,1921],[1807,3288,3290,3312],{"className":3289},[1925],[1807,3291,3293,3301],{"className":3292,"style":2570},[1929],[1807,3294,3295,3298],{"style":2573},[1807,3296],{"className":3297,"style":2577},[1937],[1807,3299,2304],{"className":3300},[1907,1911],[1807,3302,3303,3306],{"style":2573},[1807,3304],{"className":3305,"style":2577},[1937],[1807,3307,3309],{"className":3308,"style":2590},[2589],[1807,3310,2307],{"className":3311},[1907],[1807,3313,1963],{"className":3314},[1962],[1807,3316,3318],{"className":3317},[1925],[1807,3319,3321],{"className":3320,"style":2603},[1929],[1807,3322],{},[1807,3324,3326],{"className":3325},[1916],[1807,3327,3329,3349],{"className":3328},[1920,1921],[1807,3330,3332,3346],{"className":3331},[1925],[1807,3333,3335],{"className":3334,"style":1930},[1929],[1807,3336,3337,3340],{"style":2457},[1807,3338],{"className":3339,"style":1938},[1937],[1807,3341,3343],{"className":3342},[1942,1943,1944,1945],[1807,3344,1852],{"className":3345},[1907,1911,1945],[1807,3347,1963],{"className":3348},[1962],[1807,3350,3352],{"className":3351},[1925],[1807,3353,3355],{"className":3354,"style":2189},[1929],[1807,3356],{}," 是预期收益或评分，",[1807,3359,3361,3383],{"className":3360},[1814],[1807,3362,3364],{"className":3363},[1818],[1820,3365,3366],{"xmlns":1822},[1825,3367,3368,3380],{},[1828,3369,3370],{},[1836,3371,3372,3378],{},[2300,3373,3374,3376],{"accent":1848},[1839,3375,2362],{"mathvariant":2361},[1831,3377,2307],{},[1839,3379,1852],{},[1883,3381,3382],{"encoding":1885},"\\hat\\Sigma_t",[1807,3384,3386],{"className":3385,"ariaHidden":1848},[1890],[1807,3387,3389,3393],{"className":3388},[1894],[1807,3390],{"className":3391,"style":3392},[1898],"height:1.0968em;vertical-align:-0.15em;",[1807,3394,3396,3427],{"className":3395},[1907],[1807,3397,3399],{"className":3398},[1907,2560],[1807,3400,3402],{"className":3401},[1920],[1807,3403,3405],{"className":3404},[1925],[1807,3406,3408,3416],{"className":3407,"style":2877},[1929],[1807,3409,3410,3413],{"style":2573},[1807,3411],{"className":3412,"style":2577},[1937],[1807,3414,2362],{"className":3415},[1907],[1807,3417,3418,3421],{"style":2888},[1807,3419],{"className":3420,"style":2577},[1937],[1807,3422,3424],{"className":3423,"style":2895},[2589],[1807,3425,2307],{"className":3426},[1907],[1807,3428,3430],{"className":3429},[1916],[1807,3431,3433,3453],{"className":3432},[1920,1921],[1807,3434,3436,3450],{"className":3435},[1925],[1807,3437,3439],{"className":3438,"style":1930},[1929],[1807,3440,3441,3444],{"style":2457},[1807,3442],{"className":3443,"style":1938},[1937],[1807,3445,3447],{"className":3446},[1942,1943,1944,1945],[1807,3448,1852],{"className":3449},[1907,1911,1945],[1807,3451,1963],{"className":3452},[1962],[1807,3454,3456],{"className":3455},[1925],[1807,3457,3459],{"className":3458,"style":2189},[1929],[1807,3460],{}," 是风险估计，",[1807,3463,3465,3483],{"className":3464},[1814],[1807,3466,3468],{"className":3467},[1818],[1820,3469,3470],{"xmlns":1822},[1825,3471,3472,3480],{},[1828,3473,3474],{},[1836,3475,3476,3478],{},[1839,3477,2373],{},[1839,3479,1852],{},[1883,3481,3482],{"encoding":1885},"c_t",[1807,3484,3486],{"className":3485,"ariaHidden":1848},[1890],[1807,3487,3489,3492],{"className":3488},[1894],[1807,3490],{"className":3491,"style":2436},[1898],[1807,3493,3495,3498],{"className":3494},[1907],[1807,3496,2373],{"className":3497},[1907,1911],[1807,3499,3501],{"className":3500},[1916],[1807,3502,3504,3524],{"className":3503},[1920,1921],[1807,3505,3507,3521],{"className":3506},[1925],[1807,3508,3510],{"className":3509,"style":1930},[1929],[1807,3511,3512,3515],{"style":2457},[1807,3513],{"className":3514,"style":1938},[1937],[1807,3516,3518],{"className":3517},[1942,1943,1944,1945],[1807,3519,1852],{"className":3520},[1907,1911,1945],[1807,3522,1963],{"className":3523},[1962],[1807,3525,3527],{"className":3526},[1925],[1807,3528,3530],{"className":3529,"style":2189},[1929],[1807,3531],{}," 是交易成本和约束。很多初学者只盯着 ",[1807,3534,3536,3549],{"className":3535},[1814],[1807,3537,3539],{"className":3538},[1818],[1820,3540,3541],{"xmlns":1822},[1825,3542,3543,3547],{},[1828,3544,3545],{},[1839,3546,2279],{},[1883,3548,2279],{"encoding":1885},[1807,3550,3552],{"className":3551,"ariaHidden":1848},[1890],[1807,3553,3555,3558],{"className":3554},[1894],[1807,3556],{"className":3557,"style":3277},[1898],[1807,3559,2279],{"className":3560,"style":2496},[1907,1911],"，也就是“模型预测准不准”。但真正的回测成败往往发生在 ",[1807,3563,3565,3578],{"className":3564},[1814],[1807,3566,3568],{"className":3567},[1818],[1820,3569,3570],{"xmlns":1822},[1825,3571,3572,3576],{},[1828,3573,3574],{},[1839,3575,2340],{},[1883,3577,2340],{"encoding":1885},[1807,3579,3581],{"className":3580,"ariaHidden":1848},[1890],[1807,3582,3584,3588],{"className":3583},[1894],[1807,3585],{"className":3586,"style":3587},[1898],"height:0.6833em;",[1807,3589,2340],{"className":3590},[1907,1911],"：预测如何变成权重，权重如何受到成本、换手、容量和风险暴露限制。",[1792,3593,3594,3601,3602,3606],{},[3595,3596,3600],"a",{"href":3597,"rel":3598},"https:\u002F\u002Fdoi.org\u002F10.3386\u002Fw34861",[3599],"nofollow","Wang et al. (2026)"," 的 NBER 工作论文 ",[3603,3604,3605],"em",{},"Machine Learning Meets Markowitz"," 可以作为本章的前沿主读。它不是简单说机器学习预测更好，而是把预测模型接到 Markowitz 组合选择上。学生读这类论文时，要把它和均值—方差公式连起来：",[1807,3608,3610],{"className":3609},[1810],[1807,3611,3613,3674],{"className":3612},[1814],[1807,3614,3616],{"className":3615},[1818],[1820,3617,3618],{"xmlns":1822,"display":1823},[1825,3619,3620,3671],{},[1828,3621,3622,3635,3638,3645,3647,3650,3659,3665,3667,3669],{},[3623,3624,3625,3633],"munder",{},[1828,3626,3627,3630],{},[1839,3628,3629],{},"max",[1831,3631,3632],{},"⁡",[1839,3634,2333],{},[1877,3636,3637],{},"  ",[3639,3640,3641,3643],"msup",{},[1839,3642,2333],{},[1839,3644,2408],{"mathvariant":2361},[1839,3646,2304],{},[1831,3648,3649],{},"−",[3651,3652,3653,3656],"mfrac",{},[1839,3654,3655],{},"γ",[1867,3657,3658],{},"2",[3639,3660,3661,3663],{},[1839,3662,2333],{},[1839,3664,2408],{"mathvariant":2361},[1839,3666,2362],{"mathvariant":2361},[1839,3668,2333],{},[1839,3670,2423],{"mathvariant":2361},[1883,3672,3673],{"encoding":1885},"\\max_w\\; w^\\top \\mu-\\frac{\\gamma}{2}w^\\top\\Sigma w.",[1807,3675,3677,3780],{"className":3676,"ariaHidden":1848},[1890],[1807,3678,3680,3684,3733,3736,3739,3768,3771,3774,3777],{"className":3679},[1894],[1807,3681],{"className":3682,"style":3683},[1898],"height:1.5991em;vertical-align:-0.7em;",[1807,3685,3689],{"className":3686},[3687,3688],"mop","op-limits",[1807,3690,3692,3724],{"className":3691},[1920,1921],[1807,3693,3695,3721],{"className":3694},[1925],[1807,3696,3699,3711],{"className":3697,"style":3698},[1929],"height:0.4306em;",[1807,3700,3702,3705],{"style":3701},"top:-2.4em;margin-left:0em;",[1807,3703],{"className":3704,"style":2577},[1937],[1807,3706,3708],{"className":3707},[1942,1943,1944,1945],[1807,3709,2333],{"className":3710,"style":2719},[1907,1911,1945],[1807,3712,3713,3716],{"style":2573},[1807,3714],{"className":3715,"style":2577},[1937],[1807,3717,3718],{},[1807,3719,3629],{"className":3720},[3687],[1807,3722,1963],{"className":3723},[1962],[1807,3725,3727],{"className":3726},[1925],[1807,3728,3731],{"className":3729,"style":3730},[1929],"height:0.7em;",[1807,3732],{},[1807,3734],{"className":3735,"style":2044},[2043],[1807,3737],{"className":3738,"style":2553},[2043],[1807,3740,3742,3745],{"className":3741},[1907],[1807,3743,2333],{"className":3744,"style":2719},[1907,1911],[1807,3746,3748],{"className":3747},[1916],[1807,3749,3751],{"className":3750},[1920],[1807,3752,3754],{"className":3753},[1925],[1807,3755,3757],{"className":3756,"style":3081},[1929],[1807,3758,3759,3762],{"style":2017},[1807,3760],{"className":3761,"style":1938},[1937],[1807,3763,3765],{"className":3764},[1942,1943,1944,1945],[1807,3766,2408],{"className":3767},[1907,1945],[1807,3769,2304],{"className":3770},[1907,1911],[1807,3772],{"className":3773,"style":2231},[2043],[1807,3775,3649],{"className":3776},[2235],[1807,3778],{"className":3779,"style":2231},[2043],[1807,3781,3783,3787,3858,3887,3890,3893],{"className":3782},[1894],[1807,3784],{"className":3785,"style":3786},[1898],"height:1.7936em;vertical-align:-0.686em;",[1807,3788,3790,3794,3855],{"className":3789},[1907],[1807,3791],{"className":3792},[1903,3793],"nulldelimiter",[1807,3795,3797],{"className":3796},[3651],[1807,3798,3800,3846],{"className":3799},[1920,1921],[1807,3801,3803,3843],{"className":3802},[1925],[1807,3804,3807,3819,3830],{"className":3805,"style":3806},[1929],"height:1.1076em;",[1807,3808,3810,3813],{"style":3809},"top:-2.314em;",[1807,3811],{"className":3812,"style":2577},[1937],[1807,3814,3816],{"className":3815},[1907],[1807,3817,3658],{"className":3818},[1907],[1807,3820,3822,3825],{"style":3821},"top:-3.23em;",[1807,3823],{"className":3824,"style":2577},[1937],[1807,3826],{"className":3827,"style":3829},[3828],"frac-line","border-bottom-width:0.04em;",[1807,3831,3833,3836],{"style":3832},"top:-3.677em;",[1807,3834],{"className":3835,"style":2577},[1937],[1807,3837,3839],{"className":3838},[1907],[1807,3840,3655],{"className":3841,"style":3842},[1907,1911],"margin-right:0.0556em;",[1807,3844,1963],{"className":3845},[1962],[1807,3847,3849],{"className":3848},[1925],[1807,3850,3853],{"className":3851,"style":3852},[1929],"height:0.686em;",[1807,3854],{},[1807,3856],{"className":3857},[1976,3793],[1807,3859,3861,3864],{"className":3860},[1907],[1807,3862,2333],{"className":3863,"style":2719},[1907,1911],[1807,3865,3867],{"className":3866},[1916],[1807,3868,3870],{"className":3869},[1920],[1807,3871,3873],{"className":3872},[1925],[1807,3874,3876],{"className":3875,"style":3081},[1929],[1807,3877,3878,3881],{"style":2017},[1807,3879],{"className":3880,"style":1938},[1937],[1807,3882,3884],{"className":3883},[1942,1943,1944,1945],[1807,3885,2408],{"className":3886},[1907,1945],[1807,3888,2362],{"className":3889},[1907],[1807,3891,2333],{"className":3892,"style":2719},[1907,1911],[1807,3894,2423],{"className":3895},[1907],[1792,3897,3898,3899,3929,3930,3959,3960,3988,3989,4061],{},"传统 Markowitz 的难点是 ",[1807,3900,3902,3916],{"className":3901},[1814],[1807,3903,3905],{"className":3904},[1818],[1820,3906,3907],{"xmlns":1822},[1825,3908,3909,3913],{},[1828,3910,3911],{},[1839,3912,2304],{},[1883,3914,3915],{"encoding":1885},"\\mu",[1807,3917,3919],{"className":3918,"ariaHidden":1848},[1890],[1807,3920,3922,3926],{"className":3921},[1894],[1807,3923],{"className":3924,"style":3925},[1898],"height:0.625em;vertical-align:-0.1944em;",[1807,3927,2304],{"className":3928},[1907,1911]," 和 ",[1807,3931,3933,3947],{"className":3932},[1814],[1807,3934,3936],{"className":3935},[1818],[1820,3937,3938],{"xmlns":1822},[1825,3939,3940,3944],{},[1828,3941,3942],{},[1839,3943,2362],{"mathvariant":2361},[1883,3945,3946],{"encoding":1885},"\\Sigma",[1807,3948,3950],{"className":3949,"ariaHidden":1848},[1890],[1807,3951,3953,3956],{"className":3952},[1894],[1807,3954],{"className":3955,"style":3587},[1898],[1807,3957,2362],{"className":3958},[1907]," 都要估计，而且 ",[1807,3961,3963,3976],{"className":3962},[1814],[1807,3964,3966],{"className":3965},[1818],[1820,3967,3968],{"xmlns":1822},[1825,3969,3970,3974],{},[1828,3971,3972],{},[1839,3973,2304],{},[1883,3975,3915],{"encoding":1885},[1807,3977,3979],{"className":3978,"ariaHidden":1848},[1890],[1807,3980,3982,3985],{"className":3981},[1894],[1807,3983],{"className":3984,"style":3925},[1898],[1807,3986,2304],{"className":3987},[1907,1911]," 的估计误差会被优化器放大。机器学习能提供更灵活的 ",[1807,3990,3992,4010],{"className":3991},[1814],[1807,3993,3995],{"className":3994},[1818],[1820,3996,3997],{"xmlns":1822},[1825,3998,3999,4007],{},[1828,4000,4001],{},[2300,4002,4003,4005],{"accent":1848},[1839,4004,2304],{},[1831,4006,2307],{},[1883,4008,4009],{"encoding":1885},"\\hat\\mu",[1807,4011,4013],{"className":4012,"ariaHidden":1848},[1890],[1807,4014,4016,4019],{"className":4015},[1894],[1807,4017],{"className":4018,"style":3277},[1898],[1807,4020,4022],{"className":4021},[1907,2560],[1807,4023,4025,4053],{"className":4024},[1920,1921],[1807,4026,4028,4050],{"className":4027},[1925],[1807,4029,4031,4039],{"className":4030,"style":2570},[1929],[1807,4032,4033,4036],{"style":2573},[1807,4034],{"className":4035,"style":2577},[1937],[1807,4037,2304],{"className":4038},[1907,1911],[1807,4040,4041,4044],{"style":2573},[1807,4042],{"className":4043,"style":2577},[1937],[1807,4045,4047],{"className":4046,"style":2590},[2589],[1807,4048,2307],{"className":4049},[1907],[1807,4051,1963],{"className":4052},[1962],[1807,4054,4056],{"className":4055},[1925],[1807,4057,4059],{"className":4058,"style":2603},[1929],[1807,4060],{},"，但如果没有收缩、约束和成本控制，组合可能变得极端。这就是为什么“预测误差下降”不等于“策略更好”。论文中的表格如果只报告 forecast loss，你要继续找组合绩效、换手率、交易成本和风险暴露。",[1792,4063,4064,4065,4070],{},"近年的金融深度学习综述，如 ",[3595,4066,4069],{"href":4067,"rel":4068},"https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.iref.2025.104719",[3599],"Giantsidi and Tarantola (2025)","，适合放在背景层：它说明深度模型能捕捉非线性、时变关系和复杂交互。但在回测讲义中，综述的作用不是证明“深度学习先进”，而是提醒你每一种模型都要经过同一组策略检验：",[4072,4073,4074,4090],"table",{},[4075,4076,4077],"thead",{},[4078,4079,4080,4084,4087],"tr",{},[4081,4082,4083],"th",{},"检验层",[4081,4085,4086],{},"要回答的问题",[4081,4088,4089],{},"常见失败方式",[4091,4092,4093,4134,4145,4156,4167],"tbody",{},[4078,4094,4095,4099,4131],{},[4096,4097,4098],"td",{},"信息集检验",[4096,4100,4101,4102,4130],{},"数据在 ",[1807,4103,4105,4118],{"className":4104},[1814],[1807,4106,4108],{"className":4107},[1818],[1820,4109,4110],{"xmlns":1822},[1825,4111,4112,4116],{},[1828,4113,4114],{},[1839,4115,1852],{},[1883,4117,1852],{"encoding":1885},[1807,4119,4121],{"className":4120,"ariaHidden":1848},[1890],[1807,4122,4124,4127],{"className":4123},[1894],[1807,4125],{"className":4126,"style":2110},[1898],[1807,4128,1852],{"className":4129},[1907,1911]," 时点是否已经发布、可交易、可获取",[4096,4132,4133],{},"使用修订后财报、未来指数成分、未来文本训练语料。",[4078,4135,4136,4139,4142],{},[4096,4137,4138],{},"训练窗口检验",[4096,4140,4141],{},"模型是否只用过去数据训练和调参",[4096,4143,4144],{},"用全样本标准化、全样本选特征、全样本调参。",[4078,4146,4147,4150,4153],{},[4096,4148,4149],{},"组合映射检验",[4096,4151,4152],{},"信号如何变成仓位",[4096,4154,4155],{},"预测分数好，但权重集中、换手过高、容量不足。",[4078,4157,4158,4161,4164],{},[4096,4159,4160],{},"成本压力检验",[4096,4162,4163],{},"交易成本、滑点和冲击成本后是否仍有效",[4096,4165,4166],{},"小市值、低流动性组合在纸面上赚钱，实盘难执行。",[4078,4168,4169,4172,4175],{},[4096,4170,4171],{},"因子暴露检验",[4096,4173,4174],{},"收益是否只是市场、价值、动量或行业暴露",[4096,4176,4177],{},"策略 alpha 在因子回归后消失。",[1792,4179,4180,3601,4185,4188,4189,4258],{},[3595,4181,4184],{"href":4182,"rel":4183},"https:\u002F\u002Fdoi.org\u002F10.3386\u002Fw35247",[3599],"Kelly et al. (2026)",[3603,4186,4187],{},"Scaling Point-in-Time Language Models"," 可以作为“信息集检验”的最新案例。普通大语言模型可能在训练语料中见过未来文本，如果直接拿来做历史回测，就会把未来信息带回过去。point-in-time 模型按月份只使用当时以前的文本训练，目的就是让文本 embedding 满足 ",[1807,4190,4192,4209],{"className":4191},[1814],[1807,4193,4195],{"className":4194},[1818],[1820,4196,4197],{"xmlns":1822},[1825,4198,4199,4207],{},[1828,4200,4201],{},[1836,4202,4203,4205],{},[1839,4204,2132],{"mathvariant":2131},[1839,4206,1852],{},[1883,4208,2137],{"encoding":1885},[1807,4210,4212],{"className":4211,"ariaHidden":1848},[1890],[1807,4213,4215,4218],{"className":4214},[1894],[1807,4216],{"className":4217,"style":2147},[1898],[1807,4219,4221,4224],{"className":4220},[1907],[1807,4222,2132],{"className":4223,"style":2155},[1907,2154],[1807,4225,4227],{"className":4226},[1916],[1807,4228,4230,4250],{"className":4229},[1920,1921],[1807,4231,4233,4247],{"className":4232},[1925],[1807,4234,4236],{"className":4235,"style":1930},[1929],[1807,4237,4238,4241],{"style":2170},[1807,4239],{"className":4240,"style":1938},[1937],[1807,4242,4244],{"className":4243},[1942,1943,1944,1945],[1807,4245,1852],{"className":4246},[1907,1911,1945],[1807,4248,1963],{"className":4249},[1962],[1807,4251,4253],{"className":4252},[1925],[1807,4254,4256],{"className":4255,"style":2189},[1929],[1807,4257],{}," 约束。这个例子比泛泛说“避免 look-ahead bias”更具体：不是只有价格数据会穿越，文本模型、新闻语料和公司披露 embedding 也会穿越。",[1792,4260,4261,4262,4347],{},"因此，本章后面所有绩效指标都要放在这个系统里理解。夏普比率、最大回撤、Calmar、alpha 和 t 统计量不是孤立数字，而是对同一个策略函数 ",[1807,4263,4265,4289],{"className":4264},[1814],[1807,4266,4268],{"className":4267},[1818],[1820,4269,4270],{"xmlns":1822},[1825,4271,4272,4286],{},[1828,4273,4274,4276,4278,4284],{},[1839,4275,2340],{},[1831,4277,2282],{"stretchy":1833},[1836,4279,4280,4282],{},[1839,4281,2132],{"mathvariant":2131},[1839,4283,1852],{},[1831,4285,2291],{"stretchy":1833},[1883,4287,4288],{"encoding":1885},"G(\\mathcal{I}_t)",[1807,4290,4292],{"className":4291,"ariaHidden":1848},[1890],[1807,4293,4295,4298,4301,4304,4344],{"className":4294},[1894],[1807,4296],{"className":4297,"style":2057},[1898],[1807,4299,2340],{"className":4300},[1907,1911],[1807,4302,2282],{"className":4303},[1903],[1807,4305,4307,4310],{"className":4306},[1907],[1807,4308,2132],{"className":4309,"style":2155},[1907,2154],[1807,4311,4313],{"className":4312},[1916],[1807,4314,4316,4336],{"className":4315},[1920,1921],[1807,4317,4319,4333],{"className":4318},[1925],[1807,4320,4322],{"className":4321,"style":1930},[1929],[1807,4323,4324,4327],{"style":2170},[1807,4325],{"className":4326,"style":1938},[1937],[1807,4328,4330],{"className":4329},[1942,1943,1944,1945],[1807,4331,1852],{"className":4332},[1907,1911,1945],[1807,4334,1963],{"className":4335},[1962],[1807,4337,4339],{"className":4338},[1925],[1807,4340,4342],{"className":4341,"style":2189},[1929],[1807,4343],{},[1807,4345,2291],{"className":4346},[1976]," 的不同诊断。一个合格的回测报告至少应说明：",[4349,4350,4351,4355,4358,4361,4364],"ol",{},[4352,4353,4354],"li",{},"数据在什么时间点可用；",[4352,4356,4357],{},"模型如何滚动训练和调参；",[4352,4359,4360],{},"预测如何转成权重；",[4352,4362,4363],{},"成本和约束怎样进入；",[4352,4365,4366],{},"因子暴露和样本外稳定性是否被检查。",[1792,4368,4369],{},"做到这一步，前沿模型才真正进入量化研究，而不是停留在“换一个更复杂的预测器”。",[2078,4371,4373],{"id":4372},"_1-策略收益的形式化表示","1. 策略收益的形式化表示",[1792,4375,4376,4377,4475,4476,4505,4506,4534,4535,4563,4564,4614],{},"设 ",[1807,4378,4380,4409],{"className":4379},[1814],[1807,4381,4383],{"className":4382},[1818],[1820,4384,4385],{"xmlns":1822},[1825,4386,4387,4406],{},[1828,4388,4389,4391,4404],{},[1831,4390,1834],{"stretchy":1833},[1836,4392,4393,4395],{},[1839,4394,1841],{},[1828,4396,4397,4400,4402],{},[1839,4398,4399],{},"i",[1831,4401,1849],{"separator":1848},[1839,4403,1852],{},[1831,4405,1858],{"stretchy":1833},[1883,4407,4408],{"encoding":1885},"\\{r_{i,t}\\}",[1807,4410,4412],{"className":4411,"ariaHidden":1848},[1890],[1807,4413,4415,4419,4422,4472],{"className":4414},[1894],[1807,4416],{"className":4417,"style":4418},[1898],"height:1.0361em;vertical-align:-0.2861em;",[1807,4420,1834],{"className":4421},[1903],[1807,4423,4425,4428],{"className":4424},[1907],[1807,4426,1841],{"className":4427,"style":1912},[1907,1911],[1807,4429,4431],{"className":4430},[1916],[1807,4432,4434,4464],{"className":4433},[1920,1921],[1807,4435,4437,4461],{"className":4436},[1925],[1807,4438,4441],{"className":4439,"style":4440},[1929],"height:0.3117em;",[1807,4442,4443,4446],{"style":1933},[1807,4444],{"className":4445,"style":1938},[1937],[1807,4447,4449],{"className":4448},[1942,1943,1944,1945],[1807,4450,4452,4455,4458],{"className":4451},[1907,1945],[1807,4453,4399],{"className":4454},[1907,1911,1945],[1807,4456,1849],{"className":4457},[1955,1945],[1807,4459,1852],{"className":4460},[1907,1911,1945],[1807,4462,1963],{"className":4463},[1962],[1807,4465,4467],{"className":4466},[1925],[1807,4468,4470],{"className":4469,"style":1970},[1929],[1807,4471],{},[1807,4473,1858],{"className":4474},[1976]," 为资产 ",[1807,4477,4479,4492],{"className":4478},[1814],[1807,4480,4482],{"className":4481},[1818],[1820,4483,4484],{"xmlns":1822},[1825,4485,4486,4490],{},[1828,4487,4488],{},[1839,4489,4399],{},[1883,4491,4399],{"encoding":1885},[1807,4493,4495],{"className":4494,"ariaHidden":1848},[1890],[1807,4496,4498,4502],{"className":4497},[1894],[1807,4499],{"className":4500,"style":4501},[1898],"height:0.6595em;",[1807,4503,4399],{"className":4504},[1907,1911]," 在时间 ",[1807,4507,4509,4522],{"className":4508},[1814],[1807,4510,4512],{"className":4511},[1818],[1820,4513,4514],{"xmlns":1822},[1825,4515,4516,4520],{},[1828,4517,4518],{},[1839,4519,1852],{},[1883,4521,1852],{"encoding":1885},[1807,4523,4525],{"className":4524,"ariaHidden":1848},[1890],[1807,4526,4528,4531],{"className":4527},[1894],[1807,4529],{"className":4530,"style":2110},[1898],[1807,4532,1852],{"className":4533},[1907,1911]," 的简单收益率（可理解为“从 ",[1807,4536,4538,4551],{"className":4537},[1814],[1807,4539,4541],{"className":4540},[1818],[1820,4542,4543],{"xmlns":1822},[1825,4544,4545,4549],{},[1828,4546,4547],{},[1839,4548,1852],{},[1883,4550,1852],{"encoding":1885},[1807,4552,4554],{"className":4553,"ariaHidden":1848},[1890],[1807,4555,4557,4560],{"className":4556},[1894],[1807,4558],{"className":4559,"style":2110},[1898],[1807,4561,1852],{"className":4562},[1907,1911]," 到 ",[1807,4565,4567,4584],{"className":4566},[1814],[1807,4568,4570],{"className":4569},[1818],[1820,4571,4572],{"xmlns":1822},[1825,4573,4574,4582],{},[1828,4575,4576,4578,4580],{},[1839,4577,1852],{},[1831,4579,2209],{},[1867,4581,1869],{},[1883,4583,2214],{"encoding":1885},[1807,4585,4587,4605],{"className":4586,"ariaHidden":1848},[1890],[1807,4588,4590,4593,4596,4599,4602],{"className":4589},[1894],[1807,4591],{"className":4592,"style":2224},[1898],[1807,4594,1852],{"className":4595},[1907,1911],[1807,4597],{"className":4598,"style":2231},[2043],[1807,4600,2209],{"className":4601},[2235],[1807,4603],{"className":4604,"style":2231},[2043],[1807,4606,4608,4611],{"className":4607},[1894],[1807,4609],{"className":4610,"style":2245},[1898],[1807,4612,1869],{"className":4613},[1907]," 的收益率”）：",[1807,4616,4618],{"className":4617},[1810],[1807,4619,4621,4719],{"className":4620},[1814],[1807,4622,4624],{"className":4623},[1818],[1820,4625,4626],{"xmlns":1822,"display":1823},[1825,4627,4628,4716],{},[1828,4629,4630,4646,4648,4714],{},[1836,4631,4632,4634],{},[1839,4633,1841],{},[1828,4635,4636,4638,4640,4642,4644],{},[1839,4637,4399],{},[1831,4639,1849],{"separator":1848},[1839,4641,1852],{},[1831,4643,2209],{},[1867,4645,1869],{},[1831,4647,1865],{},[3651,4649,4650,4702],{},[1828,4651,4652,4669,4671,4683,4685],{},[1836,4653,4654,4657],{},[1839,4655,4656],{},"P",[1828,4658,4659,4661,4663,4665,4667],{},[1839,4660,4399],{},[1831,4662,1849],{"separator":1848},[1839,4664,1852],{},[1831,4666,2209],{},[1867,4668,1869],{},[1831,4670,3649],{},[1836,4672,4673,4675],{},[1839,4674,4656],{},[1828,4676,4677,4679,4681],{},[1839,4678,4399],{},[1831,4680,1849],{"separator":1848},[1839,4682,1852],{},[1831,4684,2209],{},[1836,4686,4687,4690],{},[1839,4688,4689],{},"D",[1828,4691,4692,4694,4696,4698,4700],{},[1839,4693,4399],{},[1831,4695,1849],{"separator":1848},[1839,4697,1852],{},[1831,4699,2209],{},[1867,4701,1869],{},[1836,4703,4704,4706],{},[1839,4705,4656],{},[1828,4707,4708,4710,4712],{},[1839,4709,4399],{},[1831,4711,1849],{"separator":1848},[1839,4713,1852],{},[1831,4715,1849],{"separator":1848},[1883,4717,4718],{"encoding":1885}," r_{i,t+1} = \\frac{P_{i,t+1} - P_{i,t} + D_{i,t+1}}{P_{i,t}} ,",[1807,4720,4722,4793],{"className":4721,"ariaHidden":1848},[1890],[1807,4723,4725,4729,4784,4787,4790],{"className":4724},[1894],[1807,4726],{"className":4727,"style":4728},[1898],"height:0.7167em;vertical-align:-0.2861em;",[1807,4730,4732,4735],{"className":4731},[1907],[1807,4733,1841],{"className":4734,"style":1912},[1907,1911],[1807,4736,4738],{"className":4737},[1916],[1807,4739,4741,4776],{"className":4740},[1920,1921],[1807,4742,4744,4773],{"className":4743},[1925],[1807,4745,4747],{"className":4746,"style":4440},[1929],[1807,4748,4749,4752],{"style":1933},[1807,4750],{"className":4751,"style":1938},[1937],[1807,4753,4755],{"className":4754},[1942,1943,1944,1945],[1807,4756,4758,4761,4764,4767,4770],{"className":4757},[1907,1945],[1807,4759,4399],{"className":4760},[1907,1911,1945],[1807,4762,1849],{"className":4763},[1955,1945],[1807,4765,1852],{"className":4766},[1907,1911,1945],[1807,4768,2209],{"className":4769},[2235,1945],[1807,4771,1869],{"className":4772},[1907,1945],[1807,4774,1963],{"className":4775},[1962],[1807,4777,4779],{"className":4778},[1925],[1807,4780,4782],{"className":4781,"style":1970},[1929],[1807,4783],{},[1807,4785],{"className":4786,"style":2044},[2043],[1807,4788,1865],{"className":4789},[2011],[1807,4791],{"className":4792,"style":2044},[2043],[1807,4794,4796,4800,5085],{"className":4795},[1894],[1807,4797],{"className":4798,"style":4799},[1898],"height:2.3324em;vertical-align:-0.9721em;",[1807,4801,4803,4806,5082],{"className":4802},[1907],[1807,4804],{"className":4805},[1903,3793],[1807,4807,4809],{"className":4808},[3651],[1807,4810,4812,5073],{"className":4811},[1920,1921],[1807,4813,4815,5070],{"className":4814},[1925],[1807,4816,4819,4877,4885],{"className":4817,"style":4818},[1929],"height:1.3603em;",[1807,4820,4821,4824],{"style":3809},[1807,4822],{"className":4823,"style":2577},[1937],[1807,4825,4827],{"className":4826},[1907],[1807,4828,4830,4833],{"className":4829},[1907],[1807,4831,4656],{"className":4832,"style":2027},[1907,1911],[1807,4834,4836],{"className":4835},[1916],[1807,4837,4839,4869],{"className":4838},[1920,1921],[1807,4840,4842,4866],{"className":4841},[1925],[1807,4843,4845],{"className":4844,"style":4440},[1929],[1807,4846,4848,4851],{"style":4847},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1807,4849],{"className":4850,"style":1938},[1937],[1807,4852,4854],{"className":4853},[1942,1943,1944,1945],[1807,4855,4857,4860,4863],{"className":4856},[1907,1945],[1807,4858,4399],{"className":4859},[1907,1911,1945],[1807,4861,1849],{"className":4862},[1955,1945],[1807,4864,1852],{"className":4865},[1907,1911,1945],[1807,4867,1963],{"className":4868},[1962],[1807,4870,4872],{"className":4871},[1925],[1807,4873,4875],{"className":4874,"style":1970},[1929],[1807,4876],{},[1807,4878,4879,4882],{"style":3821},[1807,4880],{"className":4881,"style":2577},[1937],[1807,4883],{"className":4884,"style":3829},[3828],[1807,4886,4887,4890],{"style":3832},[1807,4888],{"className":4889,"style":2577},[1937],[1807,4891,4893,4948,4951,4954,4957,5006,5009,5012,5015],{"className":4892},[1907],[1807,4894,4896,4899],{"className":4895},[1907],[1807,4897,4656],{"className":4898,"style":2027},[1907,1911],[1807,4900,4902],{"className":4901},[1916],[1807,4903,4905,4940],{"className":4904},[1920,1921],[1807,4906,4908,4937],{"className":4907},[1925],[1807,4909,4911],{"className":4910,"style":4440},[1929],[1807,4912,4913,4916],{"style":4847},[1807,4914],{"className":4915,"style":1938},[1937],[1807,4917,4919],{"className":4918},[1942,1943,1944,1945],[1807,4920,4922,4925,4928,4931,4934],{"className":4921},[1907,1945],[1807,4923,4399],{"className":4924},[1907,1911,1945],[1807,4926,1849],{"className":4927},[1955,1945],[1807,4929,1852],{"className":4930},[1907,1911,1945],[1807,4932,2209],{"className":4933},[2235,1945],[1807,4935,1869],{"className":4936},[1907,1945],[1807,4938,1963],{"className":4939},[1962],[1807,4941,4943],{"className":4942},[1925],[1807,4944,4946],{"className":4945,"style":1970},[1929],[1807,4947],{},[1807,4949],{"className":4950,"style":2231},[2043],[1807,4952,3649],{"className":4953},[2235],[1807,4955],{"className":4956,"style":2231},[2043],[1807,4958,4960,4963],{"className":4959},[1907],[1807,4961,4656],{"className":4962,"style":2027},[1907,1911],[1807,4964,4966],{"className":4965},[1916],[1807,4967,4969,4998],{"className":4968},[1920,1921],[1807,4970,4972,4995],{"className":4971},[1925],[1807,4973,4975],{"className":4974,"style":4440},[1929],[1807,4976,4977,4980],{"style":4847},[1807,4978],{"className":4979,"style":1938},[1937],[1807,4981,4983],{"className":4982},[1942,1943,1944,1945],[1807,4984,4986,4989,4992],{"className":4985},[1907,1945],[1807,4987,4399],{"className":4988},[1907,1911,1945],[1807,4990,1849],{"className":4991},[1955,1945],[1807,4993,1852],{"className":4994},[1907,1911,1945],[1807,4996,1963],{"className":4997},[1962],[1807,4999,5001],{"className":5000},[1925],[1807,5002,5004],{"className":5003,"style":1970},[1929],[1807,5005],{},[1807,5007],{"className":5008,"style":2231},[2043],[1807,5010,2209],{"className":5011},[2235],[1807,5013],{"className":5014,"style":2231},[2043],[1807,5016,5018,5021],{"className":5017},[1907],[1807,5019,4689],{"className":5020,"style":1912},[1907,1911],[1807,5022,5024],{"className":5023},[1916],[1807,5025,5027,5062],{"className":5026},[1920,1921],[1807,5028,5030,5059],{"className":5029},[1925],[1807,5031,5033],{"className":5032,"style":4440},[1929],[1807,5034,5035,5038],{"style":1933},[1807,5036],{"className":5037,"style":1938},[1937],[1807,5039,5041],{"className":5040},[1942,1943,1944,1945],[1807,5042,5044,5047,5050,5053,5056],{"className":5043},[1907,1945],[1807,5045,4399],{"className":5046},[1907,1911,1945],[1807,5048,1849],{"className":5049},[1955,1945],[1807,5051,1852],{"className":5052},[1907,1911,1945],[1807,5054,2209],{"className":5055},[2235,1945],[1807,5057,1869],{"className":5058},[1907,1945],[1807,5060,1963],{"className":5061},[1962],[1807,5063,5065],{"className":5064},[1925],[1807,5066,5068],{"className":5067,"style":1970},[1929],[1807,5069],{},[1807,5071,1963],{"className":5072},[1962],[1807,5074,5076],{"className":5075},[1925],[1807,5077,5080],{"className":5078,"style":5079},[1929],"height:0.9721em;",[1807,5081],{},[1807,5083],{"className":5084},[1976,3793],[1807,5086,1849],{"className":5087},[1955],[1792,5089,5090,5091,5177,5178,5273],{},"其中 ",[1807,5092,5094,5118],{"className":5093},[1814],[1807,5095,5097],{"className":5096},[1818],[1820,5098,5099],{"xmlns":1822},[1825,5100,5101,5115],{},[1828,5102,5103],{},[1836,5104,5105,5107],{},[1839,5106,4656],{},[1828,5108,5109,5111,5113],{},[1839,5110,4399],{},[1831,5112,1849],{"separator":1848},[1839,5114,1852],{},[1883,5116,5117],{"encoding":1885},"P_{i,t}",[1807,5119,5121],{"className":5120,"ariaHidden":1848},[1890],[1807,5122,5124,5128],{"className":5123},[1894],[1807,5125],{"className":5126,"style":5127},[1898],"height:0.9694em;vertical-align:-0.2861em;",[1807,5129,5131,5134],{"className":5130},[1907],[1807,5132,4656],{"className":5133,"style":2027},[1907,1911],[1807,5135,5137],{"className":5136},[1916],[1807,5138,5140,5169],{"className":5139},[1920,1921],[1807,5141,5143,5166],{"className":5142},[1925],[1807,5144,5146],{"className":5145,"style":4440},[1929],[1807,5147,5148,5151],{"style":4847},[1807,5149],{"className":5150,"style":1938},[1937],[1807,5152,5154],{"className":5153},[1942,1943,1944,1945],[1807,5155,5157,5160,5163],{"className":5156},[1907,1945],[1807,5158,4399],{"className":5159},[1907,1911,1945],[1807,5161,1849],{"className":5162},[1955,1945],[1807,5164,1852],{"className":5165},[1907,1911,1945],[1807,5167,1963],{"className":5168},[1962],[1807,5170,5172],{"className":5171},[1925],[1807,5173,5175],{"className":5174,"style":1970},[1929],[1807,5176],{}," 为价格，",[1807,5179,5181,5209],{"className":5180},[1814],[1807,5182,5184],{"className":5183},[1818],[1820,5185,5186],{"xmlns":1822},[1825,5187,5188,5206],{},[1828,5189,5190],{},[1836,5191,5192,5194],{},[1839,5193,4689],{},[1828,5195,5196,5198,5200,5202,5204],{},[1839,5197,4399],{},[1831,5199,1849],{"separator":1848},[1839,5201,1852],{},[1831,5203,2209],{},[1867,5205,1869],{},[1883,5207,5208],{"encoding":1885},"D_{i,t+1}",[1807,5210,5212],{"className":5211,"ariaHidden":1848},[1890],[1807,5213,5215,5218],{"className":5214},[1894],[1807,5216],{"className":5217,"style":5127},[1898],[1807,5219,5221,5224],{"className":5220},[1907],[1807,5222,4689],{"className":5223,"style":1912},[1907,1911],[1807,5225,5227],{"className":5226},[1916],[1807,5228,5230,5265],{"className":5229},[1920,1921],[1807,5231,5233,5262],{"className":5232},[1925],[1807,5234,5236],{"className":5235,"style":4440},[1929],[1807,5237,5238,5241],{"style":1933},[1807,5239],{"className":5240,"style":1938},[1937],[1807,5242,5244],{"className":5243},[1942,1943,1944,1945],[1807,5245,5247,5250,5253,5256,5259],{"className":5246},[1907,1945],[1807,5248,4399],{"className":5249},[1907,1911,1945],[1807,5251,1849],{"className":5252},[1955,1945],[1807,5254,1852],{"className":5255},[1907,1911,1945],[1807,5257,2209],{"className":5258},[2235,1945],[1807,5260,1869],{"className":5261},[1907,1945],[1807,5263,1963],{"className":5264},[1962],[1807,5266,5268],{"className":5267},[1925],[1807,5269,5271],{"className":5270,"style":1970},[1929],[1807,5272],{}," 为期间分红或利息。",[1792,5275,5276,5277,5305,5306,5587],{},"若我们在时点 ",[1807,5278,5280,5293],{"className":5279},[1814],[1807,5281,5283],{"className":5282},[1818],[1820,5284,5285],{"xmlns":1822},[1825,5286,5287,5291],{},[1828,5288,5289],{},[1839,5290,1852],{},[1883,5292,1852],{"encoding":1885},[1807,5294,5296],{"className":5295,"ariaHidden":1848},[1890],[1807,5297,5299,5302],{"className":5298},[1894],[1807,5300],{"className":5301,"style":2110},[1898],[1807,5303,1852],{"className":5304},[1907,1911]," 持有权重向量 ",[1807,5307,5309,5369],{"className":5308},[1814],[1807,5310,5312],{"className":5311},[1818],[1820,5313,5314],{"xmlns":1822},[1825,5315,5316,5366],{},[1828,5317,5318,5324,5326,5328,5340,5342,5345,5347,5360],{},[1836,5319,5320,5322],{},[1839,5321,2333],{},[1839,5323,1852],{},[1831,5325,1865],{},[1831,5327,2282],{"stretchy":1833},[1836,5329,5330,5332],{},[1839,5331,2333],{},[1828,5333,5334,5336,5338],{},[1867,5335,1869],{},[1831,5337,1849],{"separator":1848},[1839,5339,1852],{},[1831,5341,1849],{"separator":1848},[1831,5343,5344],{},"…",[1831,5346,1849],{"separator":1848},[1836,5348,5349,5351],{},[1839,5350,2333],{},[1828,5352,5353,5356,5358],{},[1839,5354,5355],{},"N",[1831,5357,1849],{"separator":1848},[1839,5359,1852],{},[3639,5361,5362,5364],{},[1831,5363,2291],{"stretchy":1833},[1839,5365,2408],{"mathvariant":2361},[1883,5367,5368],{"encoding":1885},"w_t = (w_{1,t}, \\dots, w_{N,t})^\\top",[1807,5370,5372,5427],{"className":5371,"ariaHidden":1848},[1890],[1807,5373,5375,5378,5418,5421,5424],{"className":5374},[1894],[1807,5376],{"className":5377,"style":2436},[1898],[1807,5379,5381,5384],{"className":5380},[1907],[1807,5382,2333],{"className":5383,"style":2719},[1907,1911],[1807,5385,5387],{"className":5386},[1916],[1807,5388,5390,5410],{"className":5389},[1920,1921],[1807,5391,5393,5407],{"className":5392},[1925],[1807,5394,5396],{"className":5395,"style":1930},[1929],[1807,5397,5398,5401],{"style":2734},[1807,5399],{"className":5400,"style":1938},[1937],[1807,5402,5404],{"className":5403},[1942,1943,1944,1945],[1807,5405,1852],{"className":5406},[1907,1911,1945],[1807,5408,1963],{"className":5409},[1962],[1807,5411,5413],{"className":5412},[1925],[1807,5414,5416],{"className":5415,"style":2189},[1929],[1807,5417],{},[1807,5419],{"className":5420,"style":2044},[2043],[1807,5422,1865],{"className":5423},[2011],[1807,5425],{"className":5426,"style":2044},[2043],[1807,5428,5430,5434,5437,5486,5489,5492,5496,5499,5502,5505,5556],{"className":5429},[1894],[1807,5431],{"className":5432,"style":5433},[1898],"height:1.1352em;vertical-align:-0.2861em;",[1807,5435,2282],{"className":5436},[1903],[1807,5438,5440,5443],{"className":5439},[1907],[1807,5441,2333],{"className":5442,"style":2719},[1907,1911],[1807,5444,5446],{"className":5445},[1916],[1807,5447,5449,5478],{"className":5448},[1920,1921],[1807,5450,5452,5475],{"className":5451},[1925],[1807,5453,5455],{"className":5454,"style":3009},[1929],[1807,5456,5457,5460],{"style":2734},[1807,5458],{"className":5459,"style":1938},[1937],[1807,5461,5463],{"className":5462},[1942,1943,1944,1945],[1807,5464,5466,5469,5472],{"className":5465},[1907,1945],[1807,5467,1869],{"className":5468},[1907,1945],[1807,5470,1849],{"className":5471},[1955,1945],[1807,5473,1852],{"className":5474},[1907,1911,1945],[1807,5476,1963],{"className":5477},[1962],[1807,5479,5481],{"className":5480},[1925],[1807,5482,5484],{"className":5483,"style":1970},[1929],[1807,5485],{},[1807,5487,1849],{"className":5488},[1955],[1807,5490],{"className":5491,"style":2553},[2043],[1807,5493,5344],{"className":5494},[5495],"minner",[1807,5497],{"className":5498,"style":2553},[2043],[1807,5500,1849],{"className":5501},[1955],[1807,5503],{"className":5504,"style":2553},[2043],[1807,5506,5508,5511],{"className":5507},[1907],[1807,5509,2333],{"className":5510,"style":2719},[1907,1911],[1807,5512,5514],{"className":5513},[1916],[1807,5515,5517,5548],{"className":5516},[1920,1921],[1807,5518,5520,5545],{"className":5519},[1925],[1807,5521,5524],{"className":5522,"style":5523},[1929],"height:0.3283em;",[1807,5525,5526,5529],{"style":2734},[1807,5527],{"className":5528,"style":1938},[1937],[1807,5530,5532],{"className":5531},[1942,1943,1944,1945],[1807,5533,5535,5539,5542],{"className":5534},[1907,1945],[1807,5536,5355],{"className":5537,"style":5538},[1907,1911,1945],"margin-right:0.109em;",[1807,5540,1849],{"className":5541},[1955,1945],[1807,5543,1852],{"className":5544},[1907,1911,1945],[1807,5546,1963],{"className":5547},[1962],[1807,5549,5551],{"className":5550},[1925],[1807,5552,5554],{"className":5553,"style":1970},[1929],[1807,5555],{},[1807,5557,5559,5562],{"className":5558},[1976],[1807,5560,2291],{"className":5561},[1976],[1807,5563,5565],{"className":5564},[1916],[1807,5566,5568],{"className":5567},[1920],[1807,5569,5571],{"className":5570},[1925],[1807,5572,5575],{"className":5573,"style":5574},[1929],"height:0.8491em;",[1807,5576,5578,5581],{"style":5577},"top:-3.063em;margin-right:0.05em;",[1807,5579],{"className":5580,"style":1938},[1937],[1807,5582,5584],{"className":5583},[1942,1943,1944,1945],[1807,5585,2408],{"className":5586},[1907,1945],"，满足",[5589,5590,5591,5787],"ul",{},[4352,5592,5593,5786],{},[1807,5594,5596,5639],{"className":5595},[1814],[1807,5597,5599],{"className":5598},[1818],[1820,5600,5601],{"xmlns":1822},[1825,5602,5603,5636],{},[1828,5604,5605,5620,5632,5634],{},[1854,5606,5607,5610,5618],{},[1831,5608,5609],{},"∑",[1828,5611,5612,5614,5616],{},[1839,5613,4399],{},[1831,5615,1865],{},[1867,5617,1869],{},[1839,5619,5355],{},[1836,5621,5622,5624],{},[1839,5623,2333],{},[1828,5625,5626,5628,5630],{},[1839,5627,4399],{},[1831,5629,1849],{"separator":1848},[1839,5631,1852],{},[1831,5633,1865],{},[1867,5635,1869],{},[1883,5637,5638],{"encoding":1885},"\\sum_{i=1}^N w_{i,t} = 1",[1807,5640,5642,5777],{"className":5641,"ariaHidden":1848},[1890],[1807,5643,5645,5649,5716,5719,5768,5771,5774],{"className":5644},[1894],[1807,5646],{"className":5647,"style":5648},[1898],"height:1.2809em;vertical-align:-0.2997em;",[1807,5650,5652,5658],{"className":5651},[3687],[1807,5653,5609],{"className":5654,"style":5657},[3687,5655,5656],"op-symbol","small-op","position:relative;top:0em;",[1807,5659,5661],{"className":5660},[1916],[1807,5662,5664,5707],{"className":5663},[1920,1921],[1807,5665,5667,5704],{"className":5666},[1925],[1807,5668,5671,5692],{"className":5669,"style":5670},[1929],"height:0.9812em;",[1807,5672,5674,5677],{"style":5673},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1807,5675],{"className":5676,"style":1938},[1937],[1807,5678,5680],{"className":5679},[1942,1943,1944,1945],[1807,5681,5683,5686,5689],{"className":5682},[1907,1945],[1807,5684,4399],{"className":5685},[1907,1911,1945],[1807,5687,1865],{"className":5688},[2011,1945],[1807,5690,1869],{"className":5691},[1907,1945],[1807,5693,5695,5698],{"style":5694},"top:-3.2029em;margin-right:0.05em;",[1807,5696],{"className":5697,"style":1938},[1937],[1807,5699,5701],{"className":5700},[1942,1943,1944,1945],[1807,5702,5355],{"className":5703,"style":5538},[1907,1911,1945],[1807,5705,1963],{"className":5706},[1962],[1807,5708,5710],{"className":5709},[1925],[1807,5711,5714],{"className":5712,"style":5713},[1929],"height:0.2997em;",[1807,5715],{},[1807,5717],{"className":5718,"style":2553},[2043],[1807,5720,5722,5725],{"className":5721},[1907],[1807,5723,2333],{"className":5724,"style":2719},[1907,1911],[1807,5726,5728],{"className":5727},[1916],[1807,5729,5731,5760],{"className":5730},[1920,1921],[1807,5732,5734,5757],{"className":5733},[1925],[1807,5735,5737],{"className":5736,"style":4440},[1929],[1807,5738,5739,5742],{"style":2734},[1807,5740],{"className":5741,"style":1938},[1937],[1807,5743,5745],{"className":5744},[1942,1943,1944,1945],[1807,5746,5748,5751,5754],{"className":5747},[1907,1945],[1807,5749,4399],{"className":5750},[1907,1911,1945],[1807,5752,1849],{"className":5753},[1955,1945],[1807,5755,1852],{"className":5756},[1907,1911,1945],[1807,5758,1963],{"className":5759},[1962],[1807,5761,5763],{"className":5762},[1925],[1807,5764,5766],{"className":5765,"style":1970},[1929],[1807,5767],{},[1807,5769],{"className":5770,"style":2044},[2043],[1807,5772,1865],{"className":5773},[2011],[1807,5775],{"className":5776,"style":2044},[2043],[1807,5778,5780,5783],{"className":5779},[1894],[1807,5781],{"className":5782,"style":2245},[1898],[1807,5784,1869],{"className":5785},[1907],"（单元资金约束），",[4352,5788,5789,5790,5875,5876,5986],{},"如允许多空，则 ",[1807,5791,5793,5817],{"className":5792},[1814],[1807,5794,5796],{"className":5795},[1818],[1820,5797,5798],{"xmlns":1822},[1825,5799,5800,5814],{},[1828,5801,5802],{},[1836,5803,5804,5806],{},[1839,5805,2333],{},[1828,5807,5808,5810,5812],{},[1839,5809,4399],{},[1831,5811,1849],{"separator":1848},[1839,5813,1852],{},[1883,5815,5816],{"encoding":1885},"w_{i,t}",[1807,5818,5820],{"className":5819,"ariaHidden":1848},[1890],[1807,5821,5823,5826],{"className":5822},[1894],[1807,5824],{"className":5825,"style":4728},[1898],[1807,5827,5829,5832],{"className":5828},[1907],[1807,5830,2333],{"className":5831,"style":2719},[1907,1911],[1807,5833,5835],{"className":5834},[1916],[1807,5836,5838,5867],{"className":5837},[1920,1921],[1807,5839,5841,5864],{"className":5840},[1925],[1807,5842,5844],{"className":5843,"style":4440},[1929],[1807,5845,5846,5849],{"style":2734},[1807,5847],{"className":5848,"style":1938},[1937],[1807,5850,5852],{"className":5851},[1942,1943,1944,1945],[1807,5853,5855,5858,5861],{"className":5854},[1907,1945],[1807,5856,4399],{"className":5857},[1907,1911,1945],[1807,5859,1849],{"className":5860},[1955,1945],[1807,5862,1852],{"className":5863},[1907,1911,1945],[1807,5865,1963],{"className":5866},[1962],[1807,5868,5870],{"className":5869},[1925],[1807,5871,5873],{"className":5872,"style":1970},[1929],[1807,5874],{}," 可为负；如要求多头，则 ",[1807,5877,5879,5909],{"className":5878},[1814],[1807,5880,5882],{"className":5881},[1818],[1820,5883,5884],{"xmlns":1822},[1825,5885,5886,5906],{},[1828,5887,5888,5900,5903],{},[1836,5889,5890,5892],{},[1839,5891,2333],{},[1828,5893,5894,5896,5898],{},[1839,5895,4399],{},[1831,5897,1849],{"separator":1848},[1839,5899,1852],{},[1831,5901,5902],{},"≥",[1867,5904,5905],{},"0",[1883,5907,5908],{"encoding":1885},"w_{i,t} \\ge 0",[1807,5910,5912,5977],{"className":5911,"ariaHidden":1848},[1890],[1807,5913,5915,5919,5968,5971,5974],{"className":5914},[1894],[1807,5916],{"className":5917,"style":5918},[1898],"height:0.9221em;vertical-align:-0.2861em;",[1807,5920,5922,5925],{"className":5921},[1907],[1807,5923,2333],{"className":5924,"style":2719},[1907,1911],[1807,5926,5928],{"className":5927},[1916],[1807,5929,5931,5960],{"className":5930},[1920,1921],[1807,5932,5934,5957],{"className":5933},[1925],[1807,5935,5937],{"className":5936,"style":4440},[1929],[1807,5938,5939,5942],{"style":2734},[1807,5940],{"className":5941,"style":1938},[1937],[1807,5943,5945],{"className":5944},[1942,1943,1944,1945],[1807,5946,5948,5951,5954],{"className":5947},[1907,1945],[1807,5949,4399],{"className":5950},[1907,1911,1945],[1807,5952,1849],{"className":5953},[1955,1945],[1807,5955,1852],{"className":5956},[1907,1911,1945],[1807,5958,1963],{"className":5959},[1962],[1807,5961,5963],{"className":5962},[1925],[1807,5964,5966],{"className":5965,"style":1970},[1929],[1807,5967],{},[1807,5969],{"className":5970,"style":2044},[2043],[1807,5972,5902],{"className":5973},[2011],[1807,5975],{"className":5976,"style":2044},[2043],[1807,5978,5980,5983],{"className":5979},[1894],[1807,5981],{"className":5982,"style":2245},[1898],[1807,5984,5905],{"className":5985},[1907],"。",[1792,5988,5989,5990,4563,6018,6068,6069,6073],{},"则从 ",[1807,5991,5993,6006],{"className":5992},[1814],[1807,5994,5996],{"className":5995},[1818],[1820,5997,5998],{"xmlns":1822},[1825,5999,6000,6004],{},[1828,6001,6002],{},[1839,6003,1852],{},[1883,6005,1852],{"encoding":1885},[1807,6007,6009],{"className":6008,"ariaHidden":1848},[1890],[1807,6010,6012,6015],{"className":6011},[1894],[1807,6013],{"className":6014,"style":2110},[1898],[1807,6016,1852],{"className":6017},[1907,1911],[1807,6019,6021,6038],{"className":6020},[1814],[1807,6022,6024],{"className":6023},[1818],[1820,6025,6026],{"xmlns":1822},[1825,6027,6028,6036],{},[1828,6029,6030,6032,6034],{},[1839,6031,1852],{},[1831,6033,2209],{},[1867,6035,1869],{},[1883,6037,2214],{"encoding":1885},[1807,6039,6041,6059],{"className":6040,"ariaHidden":1848},[1890],[1807,6042,6044,6047,6050,6053,6056],{"className":6043},[1894],[1807,6045],{"className":6046,"style":2224},[1898],[1807,6048,1852],{"className":6049},[1907,1911],[1807,6051],{"className":6052,"style":2231},[2043],[1807,6054,2209],{"className":6055},[2235],[1807,6057],{"className":6058,"style":2231},[2043],[1807,6060,6062,6065],{"className":6061},[1894],[1807,6063],{"className":6064,"style":2245},[1898],[1807,6066,1869],{"className":6067},[1907]," 的",[6070,6071,6072],"strong",{},"策略组合收益率","可写作：",[1807,6075,6077],{"className":6076},[1810],[1807,6078,6080,6132],{"className":6079},[1814],[1807,6081,6083],{"className":6082},[1818],[1820,6084,6085],{"xmlns":1822,"display":1823},[1825,6086,6087,6129],{},[1828,6088,6089,6105,6107,6115,6127],{},[1836,6090,6091,6093],{},[1839,6092,1841],{},[1828,6094,6095,6097,6099,6101,6103],{},[1839,6096,1792],{},[1831,6098,1849],{"separator":1848},[1839,6100,1852],{},[1831,6102,2209],{},[1867,6104,1869],{},[1831,6106,1865],{},[1854,6108,6109,6111,6113],{},[1839,6110,2333],{},[1839,6112,1852],{},[1839,6114,2408],{"mathvariant":2361},[1836,6116,6117,6119],{},[1839,6118,1841],{},[1828,6120,6121,6123,6125],{},[1839,6122,1852],{},[1831,6124,2209],{},[1867,6126,1869],{},[1831,6128,1849],{"separator":1848},[1883,6130,6131],{"encoding":1885}," r_{p,t+1} = w_t^\\top r_{t+1},",[1807,6133,6135,6205],{"className":6134,"ariaHidden":1848},[1890],[1807,6136,6138,6141,6196,6199,6202],{"className":6137},[1894],[1807,6139],{"className":6140,"style":4728},[1898],[1807,6142,6144,6147],{"className":6143},[1907],[1807,6145,1841],{"className":6146,"style":1912},[1907,1911],[1807,6148,6150],{"className":6149},[1916],[1807,6151,6153,6188],{"className":6152},[1920,1921],[1807,6154,6156,6185],{"className":6155},[1925],[1807,6157,6159],{"className":6158,"style":3009},[1929],[1807,6160,6161,6164],{"style":1933},[1807,6162],{"className":6163,"style":1938},[1937],[1807,6165,6167],{"className":6166},[1942,1943,1944,1945],[1807,6168,6170,6173,6176,6179,6182],{"className":6169},[1907,1945],[1807,6171,1792],{"className":6172},[1907,1911,1945],[1807,6174,1849],{"className":6175},[1955,1945],[1807,6177,1852],{"className":6178},[1907,1911,1945],[1807,6180,2209],{"className":6181},[2235,1945],[1807,6183,1869],{"className":6184},[1907,1945],[1807,6186,1963],{"className":6187},[1962],[1807,6189,6191],{"className":6190},[1925],[1807,6192,6194],{"className":6193,"style":1970},[1929],[1807,6195],{},[1807,6197],{"className":6198,"style":2044},[2043],[1807,6200,1865],{"className":6201},[2011],[1807,6203],{"className":6204,"style":2044},[2043],[1807,6206,6208,6211,6262,6311],{"className":6207},[1894],[1807,6209],{"className":6210,"style":3062},[1898],[1807,6212,6214,6217],{"className":6213},[1907],[1807,6215,2333],{"className":6216,"style":2719},[1907,1911],[1807,6218,6220],{"className":6219},[1916],[1807,6221,6223,6254],{"className":6222},[1920,1921],[1807,6224,6226,6251],{"className":6225},[1925],[1807,6227,6229,6240],{"className":6228,"style":3081},[1929],[1807,6230,6231,6234],{"style":3084},[1807,6232],{"className":6233,"style":1938},[1937],[1807,6235,6237],{"className":6236},[1942,1943,1944,1945],[1807,6238,1852],{"className":6239},[1907,1911,1945],[1807,6241,6242,6245],{"style":2017},[1807,6243],{"className":6244,"style":1938},[1937],[1807,6246,6248],{"className":6247},[1942,1943,1944,1945],[1807,6249,2408],{"className":6250},[1907,1945],[1807,6252,1963],{"className":6253},[1962],[1807,6255,6257],{"className":6256},[1925],[1807,6258,6260],{"className":6259,"style":2037},[1929],[1807,6261],{},[1807,6263,6265,6268],{"className":6264},[1907],[1807,6266,1841],{"className":6267,"style":1912},[1907,1911],[1807,6269,6271],{"className":6270},[1916],[1807,6272,6274,6303],{"className":6273},[1920,1921],[1807,6275,6277,6300],{"className":6276},[1925],[1807,6278,6280],{"className":6279,"style":3009},[1929],[1807,6281,6282,6285],{"style":1933},[1807,6283],{"className":6284,"style":1938},[1937],[1807,6286,6288],{"className":6287},[1942,1943,1944,1945],[1807,6289,6291,6294,6297],{"className":6290},[1907,1945],[1807,6292,1852],{"className":6293},[1907,1911,1945],[1807,6295,2209],{"className":6296},[2235,1945],[1807,6298,1869],{"className":6299},[1907,1945],[1807,6301,1963],{"className":6302},[1962],[1807,6304,6306],{"className":6305},[1925],[1807,6307,6309],{"className":6308,"style":3163},[1929],[1807,6310],{},[1807,6312,1849],{"className":6313},[1955],[1792,6315,5090,6316,5986],{},[1807,6317,6319,6391],{"className":6318},[1814],[1807,6320,6322],{"className":6321},[1818],[1820,6323,6324],{"xmlns":1822},[1825,6325,6326,6388],{},[1828,6327,6328,6340,6342,6344,6360,6362,6364,6366,6382],{},[1836,6329,6330,6332],{},[1839,6331,1841],{},[1828,6333,6334,6336,6338],{},[1839,6335,1852],{},[1831,6337,2209],{},[1867,6339,1869],{},[1831,6341,1865],{},[1831,6343,2282],{"stretchy":1833},[1836,6345,6346,6348],{},[1839,6347,1841],{},[1828,6349,6350,6352,6354,6356,6358],{},[1867,6351,1869],{},[1831,6353,1849],{"separator":1848},[1839,6355,1852],{},[1831,6357,2209],{},[1867,6359,1869],{},[1831,6361,1849],{"separator":1848},[1831,6363,5344],{},[1831,6365,1849],{"separator":1848},[1836,6367,6368,6370],{},[1839,6369,1841],{},[1828,6371,6372,6374,6376,6378,6380],{},[1839,6373,5355],{},[1831,6375,1849],{"separator":1848},[1839,6377,1852],{},[1831,6379,2209],{},[1867,6381,1869],{},[3639,6383,6384,6386],{},[1831,6385,2291],{"stretchy":1833},[1839,6387,2408],{"mathvariant":2361},[1883,6389,6390],{"encoding":1885},"r_{t+1} = (r_{1,t+1}, \\dots, r_{N,t+1})^\\top",[1807,6392,6394,6459],{"className":6393,"ariaHidden":1848},[1890],[1807,6395,6397,6401,6450,6453,6456],{"className":6396},[1894],[1807,6398],{"className":6399,"style":6400},[1898],"height:0.6389em;vertical-align:-0.2083em;",[1807,6402,6404,6407],{"className":6403},[1907],[1807,6405,1841],{"className":6406,"style":1912},[1907,1911],[1807,6408,6410],{"className":6409},[1916],[1807,6411,6413,6442],{"className":6412},[1920,1921],[1807,6414,6416,6439],{"className":6415},[1925],[1807,6417,6419],{"className":6418,"style":3009},[1929],[1807,6420,6421,6424],{"style":1933},[1807,6422],{"className":6423,"style":1938},[1937],[1807,6425,6427],{"className":6426},[1942,1943,1944,1945],[1807,6428,6430,6433,6436],{"className":6429},[1907,1945],[1807,6431,1852],{"className":6432},[1907,1911,1945],[1807,6434,2209],{"className":6435},[2235,1945],[1807,6437,1869],{"className":6438},[1907,1945],[1807,6440,1963],{"className":6441},[1962],[1807,6443,6445],{"className":6444},[1925],[1807,6446,6448],{"className":6447,"style":3163},[1929],[1807,6449],{},[1807,6451],{"className":6452,"style":2044},[2043],[1807,6454,1865],{"className":6455},[2011],[1807,6457],{"className":6458,"style":2044},[2043],[1807,6460,6462,6465,6468,6523,6526,6529,6532,6535,6538,6541,6596],{"className":6461},[1894],[1807,6463],{"className":6464,"style":5433},[1898],[1807,6466,2282],{"className":6467},[1903],[1807,6469,6471,6474],{"className":6470},[1907],[1807,6472,1841],{"className":6473,"style":1912},[1907,1911],[1807,6475,6477],{"className":6476},[1916],[1807,6478,6480,6515],{"className":6479},[1920,1921],[1807,6481,6483,6512],{"className":6482},[1925],[1807,6484,6486],{"className":6485,"style":3009},[1929],[1807,6487,6488,6491],{"style":1933},[1807,6489],{"className":6490,"style":1938},[1937],[1807,6492,6494],{"className":6493},[1942,1943,1944,1945],[1807,6495,6497,6500,6503,6506,6509],{"className":6496},[1907,1945],[1807,6498,1869],{"className":6499},[1907,1945],[1807,6501,1849],{"className":6502},[1955,1945],[1807,6504,1852],{"className":6505},[1907,1911,1945],[1807,6507,2209],{"className":6508},[2235,1945],[1807,6510,1869],{"className":6511},[1907,1945],[1807,6513,1963],{"className":6514},[1962],[1807,6516,6518],{"className":6517},[1925],[1807,6519,6521],{"className":6520,"style":1970},[1929],[1807,6522],{},[1807,6524,1849],{"className":6525},[1955],[1807,6527],{"className":6528,"style":2553},[2043],[1807,6530,5344],{"className":6531},[5495],[1807,6533],{"className":6534,"style":2553},[2043],[1807,6536,1849],{"className":6537},[1955],[1807,6539],{"className":6540,"style":2553},[2043],[1807,6542,6544,6547],{"className":6543},[1907],[1807,6545,1841],{"className":6546,"style":1912},[1907,1911],[1807,6548,6550],{"className":6549},[1916],[1807,6551,6553,6588],{"className":6552},[1920,1921],[1807,6554,6556,6585],{"className":6555},[1925],[1807,6557,6559],{"className":6558,"style":5523},[1929],[1807,6560,6561,6564],{"style":1933},[1807,6562],{"className":6563,"style":1938},[1937],[1807,6565,6567],{"className":6566},[1942,1943,1944,1945],[1807,6568,6570,6573,6576,6579,6582],{"className":6569},[1907,1945],[1807,6571,5355],{"className":6572,"style":5538},[1907,1911,1945],[1807,6574,1849],{"className":6575},[1955,1945],[1807,6577,1852],{"className":6578},[1907,1911,1945],[1807,6580,2209],{"className":6581},[2235,1945],[1807,6583,1869],{"className":6584},[1907,1945],[1807,6586,1963],{"className":6587},[1962],[1807,6589,6591],{"className":6590},[1925],[1807,6592,6594],{"className":6593,"style":1970},[1929],[1807,6595],{},[1807,6597,6599,6602],{"className":6598},[1976],[1807,6600,2291],{"className":6601},[1976],[1807,6603,6605],{"className":6604},[1916],[1807,6606,6608],{"className":6607},[1920],[1807,6609,6611],{"className":6610},[1925],[1807,6612,6614],{"className":6613,"style":5574},[1929],[1807,6615,6616,6619],{"style":5577},[1807,6617],{"className":6618,"style":1938},[1937],[1807,6620,6622],{"className":6621},[1942,1943,1944,1945],[1807,6623,2408],{"className":6624},[1907,1945],[1792,6626,6627,6628,6698,6699,6850,6851,6921,6922,6950],{},"在静态策略（权重固定）情况下，长期收益率序列就是上述式子的时间序列；在动态策略中，",[1807,6629,6631,6649],{"className":6630},[1814],[1807,6632,6634],{"className":6633},[1818],[1820,6635,6636],{"xmlns":1822},[1825,6637,6638,6646],{},[1828,6639,6640],{},[1836,6641,6642,6644],{},[1839,6643,2333],{},[1839,6645,1852],{},[1883,6647,6648],{"encoding":1885},"w_t",[1807,6650,6652],{"className":6651,"ariaHidden":1848},[1890],[1807,6653,6655,6658],{"className":6654},[1894],[1807,6656],{"className":6657,"style":2436},[1898],[1807,6659,6661,6664],{"className":6660},[1907],[1807,6662,2333],{"className":6663,"style":2719},[1907,1911],[1807,6665,6667],{"className":6666},[1916],[1807,6668,6670,6690],{"className":6669},[1920,1921],[1807,6671,6673,6687],{"className":6672},[1925],[1807,6674,6676],{"className":6675,"style":1930},[1929],[1807,6677,6678,6681],{"style":2734},[1807,6679],{"className":6680,"style":1938},[1937],[1807,6682,6684],{"className":6683},[1942,1943,1944,1945],[1807,6685,1852],{"className":6686},[1907,1911,1945],[1807,6688,1963],{"className":6689},[1962],[1807,6691,6693],{"className":6692},[1925],[1807,6694,6696],{"className":6695,"style":2189},[1929],[1807,6697],{}," 会随时间根据信号调整，需要显式写成 ",[1807,6700,6702,6736],{"className":6701},[1814],[1807,6703,6705],{"className":6704},[1818],[1820,6706,6707],{"xmlns":1822},[1825,6708,6709,6733],{},[1828,6710,6711,6717,6719,6722,6724,6731],{},[1836,6712,6713,6715],{},[1839,6714,2333],{},[1839,6716,1852],{},[1831,6718,1865],{},[1839,6720,6721],{},"g",[1831,6723,2282],{"stretchy":1833},[1836,6725,6726,6729],{},[1839,6727,6728],{},"x",[1839,6730,1852],{},[1831,6732,2291],{"stretchy":1833},[1883,6734,6735],{"encoding":1885},"w_t = g(x_t)",[1807,6737,6739,6794],{"className":6738,"ariaHidden":1848},[1890],[1807,6740,6742,6745,6785,6788,6791],{"className":6741},[1894],[1807,6743],{"className":6744,"style":2436},[1898],[1807,6746,6748,6751],{"className":6747},[1907],[1807,6749,2333],{"className":6750,"style":2719},[1907,1911],[1807,6752,6754],{"className":6753},[1916],[1807,6755,6757,6777],{"className":6756},[1920,1921],[1807,6758,6760,6774],{"className":6759},[1925],[1807,6761,6763],{"className":6762,"style":1930},[1929],[1807,6764,6765,6768],{"style":2734},[1807,6766],{"className":6767,"style":1938},[1937],[1807,6769,6771],{"className":6770},[1942,1943,1944,1945],[1807,6772,1852],{"className":6773},[1907,1911,1945],[1807,6775,1963],{"className":6776},[1962],[1807,6778,6780],{"className":6779},[1925],[1807,6781,6783],{"className":6782,"style":2189},[1929],[1807,6784],{},[1807,6786],{"className":6787,"style":2044},[2043],[1807,6789,1865],{"className":6790},[2011],[1807,6792],{"className":6793,"style":2044},[2043],[1807,6795,6797,6800,6804,6807,6847],{"className":6796},[1894],[1807,6798],{"className":6799,"style":2057},[1898],[1807,6801,6721],{"className":6802,"style":6803},[1907,1911],"margin-right:0.0359em;",[1807,6805,2282],{"className":6806},[1903],[1807,6808,6810,6813],{"className":6809},[1907],[1807,6811,6728],{"className":6812},[1907,1911],[1807,6814,6816],{"className":6815},[1916],[1807,6817,6819,6839],{"className":6818},[1920,1921],[1807,6820,6822,6836],{"className":6821},[1925],[1807,6823,6825],{"className":6824,"style":1930},[1929],[1807,6826,6827,6830],{"style":2457},[1807,6828],{"className":6829,"style":1938},[1937],[1807,6831,6833],{"className":6832},[1942,1943,1944,1945],[1807,6834,1852],{"className":6835},[1907,1911,1945],[1807,6837,1963],{"className":6838},[1962],[1807,6840,6842],{"className":6841},[1925],[1807,6843,6845],{"className":6844,"style":2189},[1929],[1807,6846],{},[1807,6848,2291],{"className":6849},[1976],"，其中 ",[1807,6852,6854,6872],{"className":6853},[1814],[1807,6855,6857],{"className":6856},[1818],[1820,6858,6859],{"xmlns":1822},[1825,6860,6861,6869],{},[1828,6862,6863],{},[1836,6864,6865,6867],{},[1839,6866,6728],{},[1839,6868,1852],{},[1883,6870,6871],{"encoding":1885},"x_t",[1807,6873,6875],{"className":6874,"ariaHidden":1848},[1890],[1807,6876,6878,6881],{"className":6877},[1894],[1807,6879],{"className":6880,"style":2436},[1898],[1807,6882,6884,6887],{"className":6883},[1907],[1807,6885,6728],{"className":6886},[1907,1911],[1807,6888,6890],{"className":6889},[1916],[1807,6891,6893,6913],{"className":6892},[1920,1921],[1807,6894,6896,6910],{"className":6895},[1925],[1807,6897,6899],{"className":6898,"style":1930},[1929],[1807,6900,6901,6904],{"style":2457},[1807,6902],{"className":6903,"style":1938},[1937],[1807,6905,6907],{"className":6906},[1942,1943,1944,1945],[1807,6908,1852],{"className":6909},[1907,1911,1945],[1807,6911,1963],{"className":6912},[1962],[1807,6914,6916],{"className":6915},[1925],[1807,6917,6919],{"className":6918,"style":2189},[1929],[1807,6920],{}," 是我们在时点 ",[1807,6923,6925,6938],{"className":6924},[1814],[1807,6926,6928],{"className":6927},[1818],[1820,6929,6930],{"xmlns":1822},[1825,6931,6932,6936],{},[1828,6933,6934],{},[1839,6935,1852],{},[1883,6937,1852],{"encoding":1885},[1807,6939,6941],{"className":6940,"ariaHidden":1848},[1890],[1807,6942,6944,6947],{"className":6943},[1894],[1807,6945],{"className":6946,"style":2110},[1898],[1807,6948,1852],{"className":6949},[1907,1911]," 可观测的信息集（包括因子、价格、成交量等）。",[1792,6952,6953],{},"在资产定价文献中，常假设",[1807,6955,6957],{"className":6956},[1810],[1807,6958,6960,7041],{"className":6959},[1814],[1807,6961,6963],{"className":6962},[1818],[1820,6964,6965],{"xmlns":1822,"display":1823},[1825,6966,6967,7038],{},[1828,6968,6969,6985,6987,6994,6996,7005,7017,7019,7036],{},[1836,6970,6971,6973],{},[1839,6972,1841],{},[1828,6974,6975,6977,6979,6981,6983],{},[1839,6976,4399],{},[1831,6978,1849],{"separator":1848},[1839,6980,1852],{},[1831,6982,2209],{},[1867,6984,1869],{},[1831,6986,1865],{},[1836,6988,6989,6992],{},[1839,6990,6991],{},"α",[1839,6993,4399],{},[1831,6995,2209],{},[1854,6997,6998,7001,7003],{},[1839,6999,7000],{},"β",[1839,7002,4399],{},[1839,7004,2408],{"mathvariant":2361},[1836,7006,7007,7009],{},[1839,7008,2279],{},[1828,7010,7011,7013,7015],{},[1839,7012,1852],{},[1831,7014,2209],{},[1867,7016,1869],{},[1831,7018,2209],{},[1836,7020,7021,7024],{},[1839,7022,7023],{},"ϵ",[1828,7025,7026,7028,7030,7032,7034],{},[1839,7027,4399],{},[1831,7029,1849],{"separator":1848},[1839,7031,1852],{},[1831,7033,2209],{},[1867,7035,1869],{},[1831,7037,1849],{"separator":1848},[1883,7039,7040],{"encoding":1885}," r_{i,t+1} = \\alpha_i + \\beta_i^\\top f_{t+1} + \\epsilon_{i,t+1},",[1807,7042,7044,7114,7172,7290],{"className":7043,"ariaHidden":1848},[1890],[1807,7045,7047,7050,7105,7108,7111],{"className":7046},[1894],[1807,7048],{"className":7049,"style":4728},[1898],[1807,7051,7053,7056],{"className":7052},[1907],[1807,7054,1841],{"className":7055,"style":1912},[1907,1911],[1807,7057,7059],{"className":7058},[1916],[1807,7060,7062,7097],{"className":7061},[1920,1921],[1807,7063,7065,7094],{"className":7064},[1925],[1807,7066,7068],{"className":7067,"style":4440},[1929],[1807,7069,7070,7073],{"style":1933},[1807,7071],{"className":7072,"style":1938},[1937],[1807,7074,7076],{"className":7075},[1942,1943,1944,1945],[1807,7077,7079,7082,7085,7088,7091],{"className":7078},[1907,1945],[1807,7080,4399],{"className":7081},[1907,1911,1945],[1807,7083,1849],{"className":7084},[1955,1945],[1807,7086,1852],{"className":7087},[1907,1911,1945],[1807,7089,2209],{"className":7090},[2235,1945],[1807,7092,1869],{"className":7093},[1907,1945],[1807,7095,1963],{"className":7096},[1962],[1807,7098,7100],{"className":7099},[1925],[1807,7101,7103],{"className":7102,"style":1970},[1929],[1807,7104],{},[1807,7106],{"className":7107,"style":2044},[2043],[1807,7109,1865],{"className":7110},[2011],[1807,7112],{"className":7113,"style":2044},[2043],[1807,7115,7117,7121,7163,7166,7169],{"className":7116},[1894],[1807,7118],{"className":7119,"style":7120},[1898],"height:0.7333em;vertical-align:-0.15em;",[1807,7122,7124,7128],{"className":7123},[1907],[1807,7125,6991],{"className":7126,"style":7127},[1907,1911],"margin-right:0.0037em;",[1807,7129,7131],{"className":7130},[1916],[1807,7132,7134,7155],{"className":7133},[1920,1921],[1807,7135,7137,7152],{"className":7136},[1925],[1807,7138,7140],{"className":7139,"style":4440},[1929],[1807,7141,7143,7146],{"style":7142},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1807,7144],{"className":7145,"style":1938},[1937],[1807,7147,7149],{"className":7148},[1942,1943,1944,1945],[1807,7150,4399],{"className":7151},[1907,1911,1945],[1807,7153,1963],{"className":7154},[1962],[1807,7156,7158],{"className":7157},[1925],[1807,7159,7161],{"className":7160,"style":2189},[1929],[1807,7162],{},[1807,7164],{"className":7165,"style":2231},[2043],[1807,7167,2209],{"className":7168},[2235],[1807,7170],{"className":7171,"style":2231},[2043],[1807,7173,7175,7178,7231,7281,7284,7287],{"className":7174},[1894],[1807,7176],{"className":7177,"style":3062},[1898],[1807,7179,7181,7185],{"className":7180},[1907],[1807,7182,7000],{"className":7183,"style":7184},[1907,1911],"margin-right:0.0528em;",[1807,7186,7188],{"className":7187},[1916],[1807,7189,7191,7223],{"className":7190},[1920,1921],[1807,7192,7194,7220],{"className":7193},[1925],[1807,7195,7197,7209],{"className":7196,"style":3081},[1929],[1807,7198,7200,7203],{"style":7199},"top:-2.453em;margin-left:-0.0528em;margin-right:0.05em;",[1807,7201],{"className":7202,"style":1938},[1937],[1807,7204,7206],{"className":7205},[1942,1943,1944,1945],[1807,7207,4399],{"className":7208},[1907,1911,1945],[1807,7210,7211,7214],{"style":2017},[1807,7212],{"className":7213,"style":1938},[1937],[1807,7215,7217],{"className":7216},[1942,1943,1944,1945],[1807,7218,2408],{"className":7219},[1907,1945],[1807,7221,1963],{"className":7222},[1962],[1807,7224,7226],{"className":7225},[1925],[1807,7227,7229],{"className":7228,"style":2037},[1929],[1807,7230],{},[1807,7232,7234,7237],{"className":7233},[1907],[1807,7235,2279],{"className":7236,"style":2496},[1907,1911],[1807,7238,7240],{"className":7239},[1916],[1807,7241,7243,7273],{"className":7242},[1920,1921],[1807,7244,7246,7270],{"className":7245},[1925],[1807,7247,7249],{"className":7248,"style":3009},[1929],[1807,7250,7252,7255],{"style":7251},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1807,7253],{"className":7254,"style":1938},[1937],[1807,7256,7258],{"className":7257},[1942,1943,1944,1945],[1807,7259,7261,7264,7267],{"className":7260},[1907,1945],[1807,7262,1852],{"className":7263},[1907,1911,1945],[1807,7265,2209],{"className":7266},[2235,1945],[1807,7268,1869],{"className":7269},[1907,1945],[1807,7271,1963],{"className":7272},[1962],[1807,7274,7276],{"className":7275},[1925],[1807,7277,7279],{"className":7278,"style":3163},[1929],[1807,7280],{},[1807,7282],{"className":7283,"style":2231},[2043],[1807,7285,2209],{"className":7286},[2235],[1807,7288],{"className":7289,"style":2231},[2043],[1807,7291,7293,7296,7351],{"className":7292},[1894],[1807,7294],{"className":7295,"style":4728},[1898],[1807,7297,7299,7302],{"className":7298},[1907],[1807,7300,7023],{"className":7301},[1907,1911],[1807,7303,7305],{"className":7304},[1916],[1807,7306,7308,7343],{"className":7307},[1920,1921],[1807,7309,7311,7340],{"className":7310},[1925],[1807,7312,7314],{"className":7313,"style":4440},[1929],[1807,7315,7316,7319],{"style":2457},[1807,7317],{"className":7318,"style":1938},[1937],[1807,7320,7322],{"className":7321},[1942,1943,1944,1945],[1807,7323,7325,7328,7331,7334,7337],{"className":7324},[1907,1945],[1807,7326,4399],{"className":7327},[1907,1911,1945],[1807,7329,1849],{"className":7330},[1955,1945],[1807,7332,1852],{"className":7333},[1907,1911,1945],[1807,7335,2209],{"className":7336},[2235,1945],[1807,7338,1869],{"className":7339},[1907,1945],[1807,7341,1963],{"className":7342},[1962],[1807,7344,7346],{"className":7345},[1925],[1807,7347,7349],{"className":7348,"style":1970},[1929],[1807,7350],{},[1807,7352,1849],{"className":7353},[1955],[1792,7355,5090,7356,7442,7443,7514,7515,7585,7586,7615,7616,7644],{},[1807,7357,7359,7383],{"className":7358},[1814],[1807,7360,7362],{"className":7361},[1818],[1820,7363,7364],{"xmlns":1822},[1825,7365,7366,7380],{},[1828,7367,7368],{},[1836,7369,7370,7372],{},[1839,7371,2279],{},[1828,7373,7374,7376,7378],{},[1839,7375,1852],{},[1831,7377,2209],{},[1867,7379,1869],{},[1883,7381,7382],{"encoding":1885},"f_{t+1}",[1807,7384,7386],{"className":7385,"ariaHidden":1848},[1890],[1807,7387,7389,7393],{"className":7388},[1894],[1807,7390],{"className":7391,"style":7392},[1898],"height:0.9028em;vertical-align:-0.2083em;",[1807,7394,7396,7399],{"className":7395},[1907],[1807,7397,2279],{"className":7398,"style":2496},[1907,1911],[1807,7400,7402],{"className":7401},[1916],[1807,7403,7405,7434],{"className":7404},[1920,1921],[1807,7406,7408,7431],{"className":7407},[1925],[1807,7409,7411],{"className":7410,"style":3009},[1929],[1807,7412,7413,7416],{"style":7251},[1807,7414],{"className":7415,"style":1938},[1937],[1807,7417,7419],{"className":7418},[1942,1943,1944,1945],[1807,7420,7422,7425,7428],{"className":7421},[1907,1945],[1807,7423,1852],{"className":7424},[1907,1911,1945],[1807,7426,2209],{"className":7427},[2235,1945],[1807,7429,1869],{"className":7430},[1907,1945],[1807,7432,1963],{"className":7433},[1962],[1807,7435,7437],{"className":7436},[1925],[1807,7438,7440],{"className":7439,"style":3163},[1929],[1807,7441],{}," 为系统性因子（如 Fama–French 因子），",[1807,7444,7446,7464],{"className":7445},[1814],[1807,7447,7449],{"className":7448},[1818],[1820,7450,7451],{"xmlns":1822},[1825,7452,7453,7461],{},[1828,7454,7455],{},[1836,7456,7457,7459],{},[1839,7458,7000],{},[1839,7460,4399],{},[1883,7462,7463],{"encoding":1885},"\\beta_i",[1807,7465,7467],{"className":7466,"ariaHidden":1848},[1890],[1807,7468,7470,7473],{"className":7469},[1894],[1807,7471],{"className":7472,"style":3277},[1898],[1807,7474,7476,7479],{"className":7475},[1907],[1807,7477,7000],{"className":7478,"style":7184},[1907,1911],[1807,7480,7482],{"className":7481},[1916],[1807,7483,7485,7506],{"className":7484},[1920,1921],[1807,7486,7488,7503],{"className":7487},[1925],[1807,7489,7491],{"className":7490,"style":4440},[1929],[1807,7492,7494,7497],{"style":7493},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1807,7495],{"className":7496,"style":1938},[1937],[1807,7498,7500],{"className":7499},[1942,1943,1944,1945],[1807,7501,4399],{"className":7502},[1907,1911,1945],[1807,7504,1963],{"className":7505},[1962],[1807,7507,7509],{"className":7508},[1925],[1807,7510,7512],{"className":7511,"style":2189},[1929],[1807,7513],{}," 为暴露，",[1807,7516,7518,7536],{"className":7517},[1814],[1807,7519,7521],{"className":7520},[1818],[1820,7522,7523],{"xmlns":1822},[1825,7524,7525,7533],{},[1828,7526,7527],{},[1836,7528,7529,7531],{},[1839,7530,6991],{},[1839,7532,4399],{},[1883,7534,7535],{"encoding":1885},"\\alpha_i",[1807,7537,7539],{"className":7538,"ariaHidden":1848},[1890],[1807,7540,7542,7545],{"className":7541},[1894],[1807,7543],{"className":7544,"style":2436},[1898],[1807,7546,7548,7551],{"className":7547},[1907],[1807,7549,6991],{"className":7550,"style":7127},[1907,1911],[1807,7552,7554],{"className":7553},[1916],[1807,7555,7557,7577],{"className":7556},[1920,1921],[1807,7558,7560,7574],{"className":7559},[1925],[1807,7561,7563],{"className":7562,"style":4440},[1929],[1807,7564,7565,7568],{"style":7142},[1807,7566],{"className":7567,"style":1938},[1937],[1807,7569,7571],{"className":7570},[1942,1943,1944,1945],[1807,7572,4399],{"className":7573},[1907,1911,1945],[1807,7575,1963],{"className":7576},[1962],[1807,7578,7580],{"className":7579},[1925],[1807,7581,7583],{"className":7582,"style":2189},[1929],[1807,7584],{}," 为资产特有超额收益。如果我们的量化策略主要通过 ",[1807,7587,7589,7603],{"className":7588},[1814],[1807,7590,7592],{"className":7591},[1818],[1820,7593,7594],{"xmlns":1822},[1825,7595,7596,7600],{},[1828,7597,7598],{},[1839,7599,6991],{},[1883,7601,7602],{"encoding":1885},"\\alpha",[1807,7604,7606],{"className":7605,"ariaHidden":1848},[1890],[1807,7607,7609,7612],{"className":7608},[1894],[1807,7610],{"className":7611,"style":3698},[1898],[1807,7613,6991],{"className":7614,"style":7127},[1907,1911]," 部分获利，那么回测的目标就是估计并验证这一 ",[1807,7617,7619,7632],{"className":7618},[1814],[1807,7620,7622],{"className":7621},[1818],[1820,7623,7624],{"xmlns":1822},[1825,7625,7626,7630],{},[1828,7627,7628],{},[1839,7629,6991],{},[1883,7631,7602],{"encoding":1885},[1807,7633,7635],{"className":7634,"ariaHidden":1848},[1890],[1807,7636,7638,7641],{"className":7637},[1894],[1807,7639],{"className":7640,"style":3698},[1898],[1807,7642,6991],{"className":7643,"style":7127},[1907,1911]," 序列在样本内外是否显著为正。",[1792,7646,7647],{},"在策略层面，也可以定义“策略因子模型”：",[1807,7649,7651],{"className":7650},[1810],[1807,7652,7654,7750],{"className":7653},[1814],[1807,7655,7657],{"className":7656},[1818],[1820,7658,7659],{"xmlns":1822,"display":1823},[1825,7660,7661,7747],{},[1828,7662,7663,7679,7681,7697,7699,7705,7707,7715,7727,7729,7745],{},[1836,7664,7665,7667],{},[1839,7666,1841],{},[1828,7668,7669,7671,7673,7675,7677],{},[1839,7670,1792],{},[1831,7672,1849],{"separator":1848},[1839,7674,1852],{},[1831,7676,2209],{},[1867,7678,1869],{},[1831,7680,3649],{},[1836,7682,7683,7685],{},[1839,7684,1841],{},[1828,7686,7687,7689,7691,7693,7695],{},[1839,7688,2279],{},[1831,7690,1849],{"separator":1848},[1839,7692,1852],{},[1831,7694,2209],{},[1867,7696,1869],{},[1831,7698,1865],{},[1836,7700,7701,7703],{},[1839,7702,6991],{},[1839,7704,1792],{},[1831,7706,2209],{},[1854,7708,7709,7711,7713],{},[1839,7710,7000],{},[1839,7712,1792],{},[1839,7714,2408],{"mathvariant":2361},[1836,7716,7717,7719],{},[1839,7718,2279],{},[1828,7720,7721,7723,7725],{},[1839,7722,1852],{},[1831,7724,2209],{},[1867,7726,1869],{},[1831,7728,2209],{},[1836,7730,7731,7733],{},[1839,7732,7023],{},[1828,7734,7735,7737,7739,7741,7743],{},[1839,7736,1792],{},[1831,7738,1849],{"separator":1848},[1839,7740,1852],{},[1831,7742,2209],{},[1867,7744,1869],{},[1831,7746,1849],{"separator":1848},[1883,7748,7749],{"encoding":1885},"r_{p,t+1} - r_{f,t+1} = \\alpha_p + \\beta_p^\\top f_{t+1} + \\epsilon_{p,t+1},",[1807,7751,7753,7824,7895,7951,8068],{"className":7752,"ariaHidden":1848},[1890],[1807,7754,7756,7760,7815,7818,7821],{"className":7755},[1894],[1807,7757],{"className":7758,"style":7759},[1898],"height:0.8694em;vertical-align:-0.2861em;",[1807,7761,7763,7766],{"className":7762},[1907],[1807,7764,1841],{"className":7765,"style":1912},[1907,1911],[1807,7767,7769],{"className":7768},[1916],[1807,7770,7772,7807],{"className":7771},[1920,1921],[1807,7773,7775,7804],{"className":7774},[1925],[1807,7776,7778],{"className":7777,"style":3009},[1929],[1807,7779,7780,7783],{"style":1933},[1807,7781],{"className":7782,"style":1938},[1937],[1807,7784,7786],{"className":7785},[1942,1943,1944,1945],[1807,7787,7789,7792,7795,7798,7801],{"className":7788},[1907,1945],[1807,7790,1792],{"className":7791},[1907,1911,1945],[1807,7793,1849],{"className":7794},[1955,1945],[1807,7796,1852],{"className":7797},[1907,1911,1945],[1807,7799,2209],{"className":7800},[2235,1945],[1807,7802,1869],{"className":7803},[1907,1945],[1807,7805,1963],{"className":7806},[1962],[1807,7808,7810],{"className":7809},[1925],[1807,7811,7813],{"className":7812,"style":1970},[1929],[1807,7814],{},[1807,7816],{"className":7817,"style":2231},[2043],[1807,7819,3649],{"className":7820},[2235],[1807,7822],{"className":7823,"style":2231},[2043],[1807,7825,7827,7830,7886,7889,7892],{"className":7826},[1894],[1807,7828],{"className":7829,"style":4728},[1898],[1807,7831,7833,7836],{"className":7832},[1907],[1807,7834,1841],{"className":7835,"style":1912},[1907,1911],[1807,7837,7839],{"className":7838},[1916],[1807,7840,7842,7878],{"className":7841},[1920,1921],[1807,7843,7845,7875],{"className":7844},[1925],[1807,7846,7849],{"className":7847,"style":7848},[1929],"height:0.3361em;",[1807,7850,7851,7854],{"style":1933},[1807,7852],{"className":7853,"style":1938},[1937],[1807,7855,7857],{"className":7856},[1942,1943,1944,1945],[1807,7858,7860,7863,7866,7869,7872],{"className":7859},[1907,1945],[1807,7861,2279],{"className":7862,"style":2496},[1907,1911,1945],[1807,7864,1849],{"className":7865},[1955,1945],[1807,7867,1852],{"className":7868},[1907,1911,1945],[1807,7870,2209],{"className":7871},[2235,1945],[1807,7873,1869],{"className":7874},[1907,1945],[1807,7876,1963],{"className":7877},[1962],[1807,7879,7881],{"className":7880},[1925],[1807,7882,7884],{"className":7883,"style":1970},[1929],[1807,7885],{},[1807,7887],{"className":7888,"style":2044},[2043],[1807,7890,1865],{"className":7891},[2011],[1807,7893],{"className":7894,"style":2044},[2043],[1807,7896,7898,7901,7942,7945,7948],{"className":7897},[1894],[1807,7899],{"className":7900,"style":7759},[1898],[1807,7902,7904,7907],{"className":7903},[1907],[1807,7905,6991],{"className":7906,"style":7127},[1907,1911],[1807,7908,7910],{"className":7909},[1916],[1807,7911,7913,7934],{"className":7912},[1920,1921],[1807,7914,7916,7931],{"className":7915},[1925],[1807,7917,7920],{"className":7918,"style":7919},[1929],"height:0.1514em;",[1807,7921,7922,7925],{"style":7142},[1807,7923],{"className":7924,"style":1938},[1937],[1807,7926,7928],{"className":7927},[1942,1943,1944,1945],[1807,7929,1792],{"className":7930},[1907,1911,1945],[1807,7932,1963],{"className":7933},[1962],[1807,7935,7937],{"className":7936},[1925],[1807,7938,7940],{"className":7939,"style":1970},[1929],[1807,7941],{},[1807,7943],{"className":7944,"style":2231},[2043],[1807,7946,2209],{"className":7947},[2235],[1807,7949],{"className":7950,"style":2231},[2043],[1807,7952,7954,7958,8010,8059,8062,8065],{"className":7953},[1894],[1807,7955],{"className":7956,"style":7957},[1898],"height:1.2822em;vertical-align:-0.3831em;",[1807,7959,7961,7964],{"className":7960},[1907],[1807,7962,7000],{"className":7963,"style":7184},[1907,1911],[1807,7965,7967],{"className":7966},[1916],[1807,7968,7970,8001],{"className":7969},[1920,1921],[1807,7971,7973,7998],{"className":7972},[1925],[1807,7974,7976,7987],{"className":7975,"style":3081},[1929],[1807,7977,7978,7981],{"style":7199},[1807,7979],{"className":7980,"style":1938},[1937],[1807,7982,7984],{"className":7983},[1942,1943,1944,1945],[1807,7985,1792],{"className":7986},[1907,1911,1945],[1807,7988,7989,7992],{"style":2017},[1807,7990],{"className":7991,"style":1938},[1937],[1807,7993,7995],{"className":7994},[1942,1943,1944,1945],[1807,7996,2408],{"className":7997},[1907,1945],[1807,7999,1963],{"className":8000},[1962],[1807,8002,8004],{"className":8003},[1925],[1807,8005,8008],{"className":8006,"style":8007},[1929],"height:0.3831em;",[1807,8009],{},[1807,8011,8013,8016],{"className":8012},[1907],[1807,8014,2279],{"className":8015,"style":2496},[1907,1911],[1807,8017,8019],{"className":8018},[1916],[1807,8020,8022,8051],{"className":8021},[1920,1921],[1807,8023,8025,8048],{"className":8024},[1925],[1807,8026,8028],{"className":8027,"style":3009},[1929],[1807,8029,8030,8033],{"style":7251},[1807,8031],{"className":8032,"style":1938},[1937],[1807,8034,8036],{"className":8035},[1942,1943,1944,1945],[1807,8037,8039,8042,8045],{"className":8038},[1907,1945],[1807,8040,1852],{"className":8041},[1907,1911,1945],[1807,8043,2209],{"className":8044},[2235,1945],[1807,8046,1869],{"className":8047},[1907,1945],[1807,8049,1963],{"className":8050},[1962],[1807,8052,8054],{"className":8053},[1925],[1807,8055,8057],{"className":8056,"style":3163},[1929],[1807,8058],{},[1807,8060],{"className":8061,"style":2231},[2043],[1807,8063,2209],{"className":8064},[2235],[1807,8066],{"className":8067,"style":2231},[2043],[1807,8069,8071,8074,8129],{"className":8070},[1894],[1807,8072],{"className":8073,"style":4728},[1898],[1807,8075,8077,8080],{"className":8076},[1907],[1807,8078,7023],{"className":8079},[1907,1911],[1807,8081,8083],{"className":8082},[1916],[1807,8084,8086,8121],{"className":8085},[1920,1921],[1807,8087,8089,8118],{"className":8088},[1925],[1807,8090,8092],{"className":8091,"style":3009},[1929],[1807,8093,8094,8097],{"style":2457},[1807,8095],{"className":8096,"style":1938},[1937],[1807,8098,8100],{"className":8099},[1942,1943,1944,1945],[1807,8101,8103,8106,8109,8112,8115],{"className":8102},[1907,1945],[1807,8104,1792],{"className":8105},[1907,1911,1945],[1807,8107,1849],{"className":8108},[1955,1945],[1807,8110,1852],{"className":8111},[1907,1911,1945],[1807,8113,2209],{"className":8114},[2235,1945],[1807,8116,1869],{"className":8117},[1907,1945],[1807,8119,1963],{"className":8120},[1962],[1807,8122,8124],{"className":8123},[1925],[1807,8125,8127],{"className":8126,"style":1970},[1929],[1807,8128],{},[1807,8130,1849],{"className":8131},[1955],[1792,8133,5090,8134,8229,8230,8325,8326,8396,8397,8466],{},[1807,8135,8137,8165],{"className":8136},[1814],[1807,8138,8140],{"className":8139},[1818],[1820,8141,8142],{"xmlns":1822},[1825,8143,8144,8162],{},[1828,8145,8146],{},[1836,8147,8148,8150],{},[1839,8149,1841],{},[1828,8151,8152,8154,8156,8158,8160],{},[1839,8153,1792],{},[1831,8155,1849],{"separator":1848},[1839,8157,1852],{},[1831,8159,2209],{},[1867,8161,1869],{},[1883,8163,8164],{"encoding":1885},"r_{p,t+1}",[1807,8166,8168],{"className":8167,"ariaHidden":1848},[1890],[1807,8169,8171,8174],{"className":8170},[1894],[1807,8172],{"className":8173,"style":4728},[1898],[1807,8175,8177,8180],{"className":8176},[1907],[1807,8178,1841],{"className":8179,"style":1912},[1907,1911],[1807,8181,8183],{"className":8182},[1916],[1807,8184,8186,8221],{"className":8185},[1920,1921],[1807,8187,8189,8218],{"className":8188},[1925],[1807,8190,8192],{"className":8191,"style":3009},[1929],[1807,8193,8194,8197],{"style":1933},[1807,8195],{"className":8196,"style":1938},[1937],[1807,8198,8200],{"className":8199},[1942,1943,1944,1945],[1807,8201,8203,8206,8209,8212,8215],{"className":8202},[1907,1945],[1807,8204,1792],{"className":8205},[1907,1911,1945],[1807,8207,1849],{"className":8208},[1955,1945],[1807,8210,1852],{"className":8211},[1907,1911,1945],[1807,8213,2209],{"className":8214},[2235,1945],[1807,8216,1869],{"className":8217},[1907,1945],[1807,8219,1963],{"className":8220},[1962],[1807,8222,8224],{"className":8223},[1925],[1807,8225,8227],{"className":8226,"style":1970},[1929],[1807,8228],{}," 是策略收益，",[1807,8231,8233,8261],{"className":8232},[1814],[1807,8234,8236],{"className":8235},[1818],[1820,8237,8238],{"xmlns":1822},[1825,8239,8240,8258],{},[1828,8241,8242],{},[1836,8243,8244,8246],{},[1839,8245,1841],{},[1828,8247,8248,8250,8252,8254,8256],{},[1839,8249,2279],{},[1831,8251,1849],{"separator":1848},[1839,8253,1852],{},[1831,8255,2209],{},[1867,8257,1869],{},[1883,8259,8260],{"encoding":1885},"r_{f,t+1}",[1807,8262,8264],{"className":8263,"ariaHidden":1848},[1890],[1807,8265,8267,8270],{"className":8266},[1894],[1807,8268],{"className":8269,"style":4728},[1898],[1807,8271,8273,8276],{"className":8272},[1907],[1807,8274,1841],{"className":8275,"style":1912},[1907,1911],[1807,8277,8279],{"className":8278},[1916],[1807,8280,8282,8317],{"className":8281},[1920,1921],[1807,8283,8285,8314],{"className":8284},[1925],[1807,8286,8288],{"className":8287,"style":7848},[1929],[1807,8289,8290,8293],{"style":1933},[1807,8291],{"className":8292,"style":1938},[1937],[1807,8294,8296],{"className":8295},[1942,1943,1944,1945],[1807,8297,8299,8302,8305,8308,8311],{"className":8298},[1907,1945],[1807,8300,2279],{"className":8301,"style":2496},[1907,1911,1945],[1807,8303,1849],{"className":8304},[1955,1945],[1807,8306,1852],{"className":8307},[1907,1911,1945],[1807,8309,2209],{"className":8310},[2235,1945],[1807,8312,1869],{"className":8313},[1907,1945],[1807,8315,1963],{"className":8316},[1962],[1807,8318,8320],{"className":8319},[1925],[1807,8321,8323],{"className":8322,"style":1970},[1929],[1807,8324],{}," 为无风险收益，",[1807,8327,8329,8347],{"className":8328},[1814],[1807,8330,8332],{"className":8331},[1818],[1820,8333,8334],{"xmlns":1822},[1825,8335,8336,8344],{},[1828,8337,8338],{},[1836,8339,8340,8342],{},[1839,8341,6991],{},[1839,8343,1792],{},[1883,8345,8346],{"encoding":1885},"\\alpha_p",[1807,8348,8350],{"className":8349,"ariaHidden":1848},[1890],[1807,8351,8353,8356],{"className":8352},[1894],[1807,8354],{"className":8355,"style":4728},[1898],[1807,8357,8359,8362],{"className":8358},[1907],[1807,8360,6991],{"className":8361,"style":7127},[1907,1911],[1807,8363,8365],{"className":8364},[1916],[1807,8366,8368,8388],{"className":8367},[1920,1921],[1807,8369,8371,8385],{"className":8370},[1925],[1807,8372,8374],{"className":8373,"style":7919},[1929],[1807,8375,8376,8379],{"style":7142},[1807,8377],{"className":8378,"style":1938},[1937],[1807,8380,8382],{"className":8381},[1942,1943,1944,1945],[1807,8383,1792],{"className":8384},[1907,1911,1945],[1807,8386,1963],{"className":8387},[1962],[1807,8389,8391],{"className":8390},[1925],[1807,8392,8394],{"className":8393,"style":1970},[1929],[1807,8395],{}," 即策略在控制市场和风格因子后的超额收益。经典的“因子回归”就是通过对 ",[1807,8398,8400,8417],{"className":8399},[1814],[1807,8401,8403],{"className":8402},[1818],[1820,8404,8405],{"xmlns":1822},[1825,8406,8407,8415],{},[1828,8408,8409],{},[1836,8410,8411,8413],{},[1839,8412,6991],{},[1839,8414,1792],{},[1883,8416,8346],{"encoding":1885},[1807,8418,8420],{"className":8419,"ariaHidden":1848},[1890],[1807,8421,8423,8426],{"className":8422},[1894],[1807,8424],{"className":8425,"style":4728},[1898],[1807,8427,8429,8432],{"className":8428},[1907],[1807,8430,6991],{"className":8431,"style":7127},[1907,1911],[1807,8433,8435],{"className":8434},[1916],[1807,8436,8438,8458],{"className":8437},[1920,1921],[1807,8439,8441,8455],{"className":8440},[1925],[1807,8442,8444],{"className":8443,"style":7919},[1929],[1807,8445,8446,8449],{"style":7142},[1807,8447],{"className":8448,"style":1938},[1937],[1807,8450,8452],{"className":8451},[1942,1943,1944,1945],[1807,8453,1792],{"className":8454},[1907,1911,1945],[1807,8456,1963],{"className":8457},[1962],[1807,8459,8461],{"className":8460},[1925],[1807,8462,8464],{"className":8463,"style":1970},[1929],[1807,8465],{}," 做 t 检验来判断策略是否存在统计显著的 alpha。",[2078,8468,8470],{"id":8469},"_2-线性因子模型与横截面回归","2. 线性因子模型与横截面回归",[1792,8472,8473],{},"多因子模型的经典形式（参见 Fama & MacBeth, 1973）是在横截面上回归资产收益率与因子暴露：",[1807,8475,8477],{"className":8476},[1810],[1807,8478,8480,8590],{"className":8479},[1814],[1807,8481,8483],{"className":8482},[1818],[1820,8484,8485],{"xmlns":1822,"display":1823},[1825,8486,8487,8587],{},[1828,8488,8489,8505,8507,8520,8522,8539,8551,8567,8569,8585],{},[1836,8490,8491,8493],{},[1839,8492,1841],{},[1828,8494,8495,8497,8499,8501,8503],{},[1839,8496,4399],{},[1831,8498,1849],{"separator":1848},[1839,8500,1852],{},[1831,8502,2209],{},[1867,8504,1869],{},[1831,8506,1865],{},[1836,8508,8509,8512],{},[1839,8510,8511],{},"λ",[1828,8513,8514,8516,8518],{},[1867,8515,5905],{},[1831,8517,1849],{"separator":1848},[1839,8519,1852],{},[1831,8521,2209],{},[8523,8524,8525,8527,8536],"munderover",{},[1831,8526,5609],{},[1828,8528,8529,8532,8534],{},[1839,8530,8531],{},"k",[1831,8533,1865],{},[1867,8535,1869],{},[1839,8537,8538],{},"K",[1836,8540,8541,8543],{},[1839,8542,8511],{},[1828,8544,8545,8547,8549],{},[1839,8546,8531],{},[1831,8548,1849],{"separator":1848},[1839,8550,1852],{},[1836,8552,8553,8555],{},[1839,8554,2279],{},[1828,8556,8557,8559,8561,8563,8565],{},[1839,8558,8531],{},[1831,8560,1849],{"separator":1848},[1839,8562,4399],{},[1831,8564,1849],{"separator":1848},[1839,8566,1852],{},[1831,8568,2209],{},[1836,8570,8571,8573],{},[1839,8572,7023],{},[1828,8574,8575,8577,8579,8581,8583],{},[1839,8576,4399],{},[1831,8578,1849],{"separator":1848},[1839,8580,1852],{},[1831,8582,2209],{},[1867,8584,1869],{},[1831,8586,1849],{"separator":1848},[1883,8588,8589],{"encoding":1885}," r_{i,t+1} = \\lambda_{0,t} + \\sum_{k=1}^K \\lambda_{k,t} f_{k,i,t} + \\epsilon_{i,t+1},",[1807,8591,8593,8663,8728,8924],{"className":8592,"ariaHidden":1848},[1890],[1807,8594,8596,8599,8654,8657,8660],{"className":8595},[1894],[1807,8597],{"className":8598,"style":4728},[1898],[1807,8600,8602,8605],{"className":8601},[1907],[1807,8603,1841],{"className":8604,"style":1912},[1907,1911],[1807,8606,8608],{"className":8607},[1916],[1807,8609,8611,8646],{"className":8610},[1920,1921],[1807,8612,8614,8643],{"className":8613},[1925],[1807,8615,8617],{"className":8616,"style":4440},[1929],[1807,8618,8619,8622],{"style":1933},[1807,8620],{"className":8621,"style":1938},[1937],[1807,8623,8625],{"className":8624},[1942,1943,1944,1945],[1807,8626,8628,8631,8634,8637,8640],{"className":8627},[1907,1945],[1807,8629,4399],{"className":8630},[1907,1911,1945],[1807,8632,1849],{"className":8633},[1955,1945],[1807,8635,1852],{"className":8636},[1907,1911,1945],[1807,8638,2209],{"className":8639},[2235,1945],[1807,8641,1869],{"className":8642},[1907,1945],[1807,8644,1963],{"className":8645},[1962],[1807,8647,8649],{"className":8648},[1925],[1807,8650,8652],{"className":8651,"style":1970},[1929],[1807,8653],{},[1807,8655],{"className":8656,"style":2044},[2043],[1807,8658,1865],{"className":8659},[2011],[1807,8661],{"className":8662,"style":2044},[2043],[1807,8664,8666,8670,8719,8722,8725],{"className":8665},[1894],[1807,8667],{"className":8668,"style":8669},[1898],"height:0.9805em;vertical-align:-0.2861em;",[1807,8671,8673,8676],{"className":8672},[1907],[1807,8674,8511],{"className":8675},[1907,1911],[1807,8677,8679],{"className":8678},[1916],[1807,8680,8682,8711],{"className":8681},[1920,1921],[1807,8683,8685,8708],{"className":8684},[1925],[1807,8686,8688],{"className":8687,"style":3009},[1929],[1807,8689,8690,8693],{"style":2457},[1807,8691],{"className":8692,"style":1938},[1937],[1807,8694,8696],{"className":8695},[1942,1943,1944,1945],[1807,8697,8699,8702,8705],{"className":8698},[1907,1945],[1807,8700,5905],{"className":8701},[1907,1945],[1807,8703,1849],{"className":8704},[1955,1945],[1807,8706,1852],{"className":8707},[1907,1911,1945],[1807,8709,1963],{"className":8710},[1962],[1807,8712,8714],{"className":8713},[1925],[1807,8715,8717],{"className":8716,"style":1970},[1929],[1807,8718],{},[1807,8720],{"className":8721,"style":2231},[2043],[1807,8723,2209],{"className":8724},[2235],[1807,8726],{"className":8727,"style":2231},[2043],[1807,8729,8731,8735,8808,8811,8860,8915,8918,8921],{"className":8730},[1894],[1807,8732],{"className":8733,"style":8734},[1898],"height:3.1304em;vertical-align:-1.3021em;",[1807,8736,8738],{"className":8737},[3687,3688],[1807,8739,8741,8799],{"className":8740},[1920,1921],[1807,8742,8744,8796],{"className":8743},[1925],[1807,8745,8748,8771,8783],{"className":8746,"style":8747},[1929],"height:1.8283em;",[1807,8749,8751,8755],{"style":8750},"top:-1.8479em;margin-left:0em;",[1807,8752],{"className":8753,"style":8754},[1937],"height:3.05em;",[1807,8756,8758],{"className":8757},[1942,1943,1944,1945],[1807,8759,8761,8765,8768],{"className":8760},[1907,1945],[1807,8762,8531],{"className":8763,"style":8764},[1907,1911,1945],"margin-right:0.0315em;",[1807,8766,1865],{"className":8767},[2011,1945],[1807,8769,1869],{"className":8770},[1907,1945],[1807,8772,8774,8777],{"style":8773},"top:-3.05em;",[1807,8775],{"className":8776,"style":8754},[1937],[1807,8778,8779],{},[1807,8780,5609],{"className":8781},[3687,5655,8782],"large-op",[1807,8784,8786,8789],{"style":8785},"top:-4.3em;margin-left:0em;",[1807,8787],{"className":8788,"style":8754},[1937],[1807,8790,8792],{"className":8791},[1942,1943,1944,1945],[1807,8793,8538],{"className":8794,"style":8795},[1907,1911,1945],"margin-right:0.0715em;",[1807,8797,1963],{"className":8798},[1962],[1807,8800,8802],{"className":8801},[1925],[1807,8803,8806],{"className":8804,"style":8805},[1929],"height:1.3021em;",[1807,8807],{},[1807,8809],{"className":8810,"style":2553},[2043],[1807,8812,8814,8817],{"className":8813},[1907],[1807,8815,8511],{"className":8816},[1907,1911],[1807,8818,8820],{"className":8819},[1916],[1807,8821,8823,8852],{"className":8822},[1920,1921],[1807,8824,8826,8849],{"className":8825},[1925],[1807,8827,8829],{"className":8828,"style":7848},[1929],[1807,8830,8831,8834],{"style":2457},[1807,8832],{"className":8833,"style":1938},[1937],[1807,8835,8837],{"className":8836},[1942,1943,1944,1945],[1807,8838,8840,8843,8846],{"className":8839},[1907,1945],[1807,8841,8531],{"className":8842,"style":8764},[1907,1911,1945],[1807,8844,1849],{"className":8845},[1955,1945],[1807,8847,1852],{"className":8848},[1907,1911,1945],[1807,8850,1963],{"className":8851},[1962],[1807,8853,8855],{"className":8854},[1925],[1807,8856,8858],{"className":8857,"style":1970},[1929],[1807,8859],{},[1807,8861,8863,8866],{"className":8862},[1907],[1807,8864,2279],{"className":8865,"style":2496},[1907,1911],[1807,8867,8869],{"className":8868},[1916],[1807,8870,8872,8907],{"className":8871},[1920,1921],[1807,8873,8875,8904],{"className":8874},[1925],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",[1807,9089,9091,9104],{"className":9090},[1814],[1807,9092,9094],{"className":9093},[1818],[1820,9095,9096],{"xmlns":1822},[1825,9097,9098,9102],{},[1828,9099,9100],{},[1839,9101,4399],{},[1883,9103,4399],{"encoding":1885},[1807,9105,9107],{"className":9106,"ariaHidden":1848},[1890],[1807,9108,9110,9113],{"className":9109},[1894],[1807,9111],{"className":9112,"style":4501},[1898],[1807,9114,4399],{"className":9115},[1907,1911]," 在时点 ",[1807,9118,9120,9133],{"className":9119},[1814],[1807,9121,9123],{"className":9122},[1818],[1820,9124,9125],{"xmlns":1822},[1825,9126,9127,9131],{},[1828,9128,9129],{},[1839,9130,1852],{},[1883,9132,1852],{"encoding":1885},[1807,9134,9136],{"className":9135,"ariaHidden":1848},[1890],[1807,9137,9139,9142],{"className":9138},[1894],[1807,9140],{"className":9141,"style":2110},[1898],[1807,9143,1852],{"className":9144},[1907,1911]," 上的第 ",[1807,9147,9149,9162],{"className":9148},[1814],[1807,9150,9152],{"className":9151},[1818],[1820,9153,9154],{"xmlns":1822},[1825,9155,9156,9160],{},[1828,9157,9158],{},[1839,9159,8531],{},[1883,9161,8531],{"encoding":1885},[1807,9163,9165],{"className":9164,"ariaHidden":1848},[1890],[1807,9166,9168,9171],{"className":9167},[1894],[1807,9169],{"className":9170,"style":2570},[1898],[1807,9172,8531],{"className":9173,"style":8764},[1907,1911]," 个因子暴露；",[4352,9176,9177,9262,9263,9291],{},[1807,9178,9180,9204],{"className":9179},[1814],[1807,9181,9183],{"className":9182},[1818],[1820,9184,9185],{"xmlns":1822},[1825,9186,9187,9201],{},[1828,9188,9189],{},[1836,9190,9191,9193],{},[1839,9192,8511],{},[1828,9194,9195,9197,9199],{},[1839,9196,8531],{},[1831,9198,1849],{"separator":1848},[1839,9200,1852],{},[1883,9202,9203],{"encoding":1885},"\\lambda_{k,t}",[1807,9205,9207],{"className":9206,"ariaHidden":1848},[1890],[1807,9208,9210,9213],{"className":9209},[1894],[1807,9211],{"className":9212,"style":8669},[1898],[1807,9214,9216,9219],{"className":9215},[1907],[1807,9217,8511],{"className":9218},[1907,1911],[1807,9220,9222],{"className":9221},[1916],[1807,9223,9225,9254],{"className":9224},[1920,1921],[1807,9226,9228,9251],{"className":9227},[1925],[1807,9229,9231],{"className":9230,"style":7848},[1929],[1807,9232,9233,9236],{"style":2457},[1807,9234],{"className":9235,"style":1938},[1937],[1807,9237,9239],{"className":9238},[1942,1943,1944,1945],[1807,9240,9242,9245,9248],{"className":9241},[1907,1945],[1807,9243,8531],{"className":9244,"style":8764},[1907,1911,1945],[1807,9246,1849],{"className":9247},[1955,1945],[1807,9249,1852],{"className":9250},[1907,1911,1945],[1807,9252,1963],{"className":9253},[1962],[1807,9255,9257],{"className":9256},[1925],[1807,9258,9260],{"className":9259,"style":1970},[1929],[1807,9261],{},"：截面上第 ",[1807,9264,9266,9279],{"className":9265},[1814],[1807,9267,9269],{"className":9268},[1818],[1820,9270,9271],{"xmlns":1822},[1825,9272,9273,9277],{},[1828,9274,9275],{},[1839,9276,8531],{},[1883,9278,8531],{"encoding":1885},[1807,9280,9282],{"className":9281,"ariaHidden":1848},[1890],[1807,9283,9285,9288],{"className":9284},[1894],[1807,9286],{"className":9287,"style":2570},[1898],[1807,9289,8531],{"className":9290,"style":8764},[1907,1911]," 个因子的价格（risk premium）。",[1792,9293,9294,9295,9323,9324,9419],{},"对每个时间截面 ",[1807,9296,9298,9311],{"className":9297},[1814],[1807,9299,9301],{"className":9300},[1818],[1820,9302,9303],{"xmlns":1822},[1825,9304,9305,9309],{},[1828,9306,9307],{},[1839,9308,1852],{},[1883,9310,1852],{"encoding":1885},[1807,9312,9314],{"className":9313,"ariaHidden":1848},[1890],[1807,9315,9317,9320],{"className":9316},[1894],[1807,9318],{"className":9319,"style":2110},[1898],[1807,9321,1852],{"className":9322},[1907,1911]," 分别做一次回归，就得到一条时间序列 ",[1807,9325,9327,9355],{"className":9326},[1814],[1807,9328,9330],{"className":9329},[1818],[1820,9331,9332],{"xmlns":1822},[1825,9333,9334,9352],{},[1828,9335,9336,9338,9350],{},[1831,9337,1834],{"stretchy":1833},[1836,9339,9340,9342],{},[1839,9341,8511],{},[1828,9343,9344,9346,9348],{},[1839,9345,8531],{},[1831,9347,1849],{"separator":1848},[1839,9349,1852],{},[1831,9351,1858],{"stretchy":1833},[1883,9353,9354],{"encoding":1885},"\\{\\lambda_{k,t}\\}",[1807,9356,9358],{"className":9357,"ariaHidden":1848},[1890],[1807,9359,9361,9364,9367,9416],{"className":9360},[1894],[1807,9362],{"className":9363,"style":4418},[1898],[1807,9365,1834],{"className":9366},[1903],[1807,9368,9370,9373],{"className":9369},[1907],[1807,9371,8511],{"className":9372},[1907,1911],[1807,9374,9376],{"className":9375},[1916],[1807,9377,9379,9408],{"className":9378},[1920,1921],[1807,9380,9382,9405],{"className":9381},[1925],[1807,9383,9385],{"className":9384,"style":7848},[1929],[1807,9386,9387,9390],{"style":2457},[1807,9388],{"className":9389,"style":1938},[1937],[1807,9391,9393],{"className":9392},[1942,1943,1944,1945],[1807,9394,9396,9399,9402],{"className":9395},[1907,1945],[1807,9397,8531],{"className":9398,"style":8764},[1907,1911,1945],[1807,9400,1849],{"className":9401},[1955,1945],[1807,9403,1852],{"className":9404},[1907,1911,1945],[1807,9406,1963],{"className":9407},[1962],[1807,9409,9411],{"className":9410},[1925],[1807,9412,9414],{"className":9413,"style":1970},[1929],[1807,9415],{},[1807,9417,1858],{"className":9418},[1976],"，其均值",[1807,9421,9423],{"className":9422},[1810],[1807,9424,9426,9483],{"className":9425},[1814],[1807,9427,9429],{"className":9428},[1818],[1820,9430,9431],{"xmlns":1822,"display":1823},[1825,9432,9433,9480],{},[1828,9434,9435,9446,9448,9454,9468],{},[1836,9436,9437,9444],{},[2300,9438,9439,9441],{"accent":1848},[1839,9440,8511],{},[1831,9442,9443],{},"ˉ",[1839,9445,8531],{},[1831,9447,1865],{},[3651,9449,9450,9452],{},[1867,9451,1869],{},[1839,9453,1872],{},[8523,9455,9456,9458,9466],{},[1831,9457,5609],{},[1828,9459,9460,9462,9464],{},[1839,9461,1852],{},[1831,9463,1865],{},[1867,9465,1869],{},[1839,9467,1872],{},[1836,9469,9470,9472],{},[1839,9471,8511],{},[1828,9473,9474,9476,9478],{},[1839,9475,8531],{},[1831,9477,1849],{"separator":1848},[1839,9479,1852],{},[1883,9481,9482],{"encoding":1885}," \\bar{\\lambda}_k = \\frac{1}{T} \\sum_{t=1}^T \\lambda_{k,t}",[1807,9484,9486,9572],{"className":9485,"ariaHidden":1848},[1890],[1807,9487,9489,9493,9563,9566,9569],{"className":9488},[1894],[1807,9490],{"className":9491,"style":9492},[1898],"height:0.9812em;vertical-align:-0.15em;",[1807,9494,9496,9529],{"className":9495},[1907],[1807,9497,9499],{"className":9498},[1907,2560],[1807,9500,9502],{"className":9501},[1920],[1807,9503,9505],{"className":9504},[1925],[1807,9506,9509,9517],{"className":9507,"style":9508},[1929],"height:0.8312em;",[1807,9510,9511,9514],{"style":2573},[1807,9512],{"className":9513,"style":2577},[1937],[1807,9515,8511],{"className":9516},[1907,1911],[1807,9518,9520,9523],{"style":9519},"top:-3.2634em;",[1807,9521],{"className":9522,"style":2577},[1937],[1807,9524,9526],{"className":9525,"style":2895},[2589],[1807,9527,9443],{"className":9528},[1907],[1807,9530,9532],{"className":9531},[1916],[1807,9533,9535,9555],{"className":9534},[1920,1921],[1807,9536,9538,9552],{"className":9537},[1925],[1807,9539,9541],{"className":9540,"style":7848},[1929],[1807,9542,9543,9546],{"style":2457},[1807,9544],{"className":9545,"style":1938},[1937],[1807,9547,9549],{"className":9548},[1942,1943,1944,1945],[1807,9550,8531],{"className":9551,"style":8764},[1907,1911,1945],[1807,9553,1963],{"className":9554},[1962],[1807,9556,9558],{"className":9557},[1925],[1807,9559,9561],{"className":9560,"style":2189},[1929],[1807,9562],{},[1807,9564],{"className":9565,"style":2044},[2043],[1807,9567,1865],{"className":9568},[2011],[1807,9570],{"className":9571,"style":2044},[2043],[1807,9573,9575,9579,9642,9645,9711,9714],{"className":9574},[1894],[1807,9576],{"className":9577,"style":9578},[1898],"height:3.0954em;vertical-align:-1.2671em;",[1807,9580,9582,9585,9639],{"className":9581},[1907],[1807,9583],{"className":9584},[1903,3793],[1807,9586,9588],{"className":9587},[3651],[1807,9589,9591,9631],{"className":9590},[1920,1921],[1807,9592,9594,9628],{"className":9593},[1925],[1807,9595,9598,9609,9617],{"className":9596,"style":9597},[1929],"height:1.3214em;",[1807,9599,9600,9603],{"style":3809},[1807,9601],{"className":9602,"style":2577},[1937],[1807,9604,9606],{"className":9605},[1907],[1807,9607,1872],{"className":9608,"style":2027},[1907,1911],[1807,9610,9611,9614],{"style":3821},[1807,9612],{"className":9613,"style":2577},[1937],[1807,9615],{"className":9616,"style":3829},[3828],[1807,9618,9619,9622],{"style":3832},[1807,9620],{"className":9621,"style":2577},[1937],[1807,9623,9625],{"className":9624},[1907],[1807,9626,1869],{"className":9627},[1907],[1807,9629,1963],{"className":9630},[1962],[1807,9632,9634],{"className":9633},[1925],[1807,9635,9637],{"className":9636,"style":3852},[1929],[1807,9638],{},[1807,9640],{"className":9641},[1976,3793],[1807,9643],{"className":9644,"style":2553},[2043],[1807,9646,9648],{"className":9647},[3687,3688],[1807,9649,9651,9702],{"className":9650},[1920,1921],[1807,9652,9654,9699],{"className":9653},[1925],[1807,9655,9657,9678,9688],{"className":9656,"style":8747},[1929],[1807,9658,9660,9663],{"style":9659},"top:-1.8829em;margin-left:0em;",[1807,9661],{"className":9662,"style":8754},[1937],[1807,9664,9666],{"className":9665},[1942,1943,1944,1945],[1807,9667,9669,9672,9675],{"className":9668},[1907,1945],[1807,9670,1852],{"className":9671},[1907,1911,1945],[1807,9673,1865],{"className":9674},[2011,1945],[1807,9676,1869],{"className":9677},[1907,1945],[1807,9679,9680,9683],{"style":8773},[1807,9681],{"className":9682,"style":8754},[1937],[1807,9684,9685],{},[1807,9686,5609],{"className":9687},[3687,5655,8782],[1807,9689,9690,9693],{"style":8785},[1807,9691],{"className":9692,"style":8754},[1937],[1807,9694,9696],{"className":9695},[1942,1943,1944,1945],[1807,9697,1872],{"className":9698,"style":2027},[1907,1911,1945],[1807,9700,1963],{"className":9701},[1962],[1807,9703,9705],{"className":9704},[1925],[1807,9706,9709],{"className":9707,"style":9708},[1929],"height:1.2671em;",[1807,9710],{},[1807,9712],{"className":9713,"style":2553},[2043],[1807,9715,9717,9720],{"className":9716},[1907],[1807,9718,8511],{"className":9719},[1907,1911],[1807,9721,9723],{"className":9722},[1916],[1807,9724,9726,9755],{"className":9725},[1920,1921],[1807,9727,9729,9752],{"className":9728},[1925],[1807,9730,9732],{"className":9731,"style":7848},[1929],[1807,9733,9734,9737],{"style":2457},[1807,9735],{"className":9736,"style":1938},[1937],[1807,9738,9740],{"className":9739},[1942,1943,1944,1945],[1807,9741,9743,9746,9749],{"className":9742},[1907,1945],[1807,9744,8531],{"className":9745,"style":8764},[1907,1911,1945],[1807,9747,1849],{"className":9748},[1955,1945],[1807,9750,1852],{"className":9751},[1907,1911,1945],[1807,9753,1963],{"className":9754},[1962],[1807,9756,9758],{"className":9757},[1925],[1807,9759,9761],{"className":9760,"style":1970},[1929],[1807,9762],{},[1792,9764,9765,9766,9794,9795,9897],{},"可以理解为第 ",[1807,9767,9769,9782],{"className":9768},[1814],[1807,9770,9772],{"className":9771},[1818],[1820,9773,9774],{"xmlns":1822},[1825,9775,9776,9780],{},[1828,9777,9778],{},[1839,9779,8531],{},[1883,9781,8531],{"encoding":1885},[1807,9783,9785],{"className":9784,"ariaHidden":1848},[1890],[1807,9786,9788,9791],{"className":9787},[1894],[1807,9789],{"className":9790,"style":2570},[1898],[1807,9792,8531],{"className":9793,"style":8764},[1907,1911]," 个因子的平均风险溢价。若 ",[1807,9796,9798,9820],{"className":9797},[1814],[1807,9799,9801],{"className":9800},[1818],[1820,9802,9803],{"xmlns":1822},[1825,9804,9805,9817],{},[1828,9806,9807],{},[1836,9808,9809,9815],{},[2300,9810,9811,9813],{"accent":1848},[1839,9812,8511],{},[1831,9814,9443],{},[1839,9816,8531],{},[1883,9818,9819],{"encoding":1885},"\\bar{\\lambda}_k",[1807,9821,9823],{"className":9822,"ariaHidden":1848},[1890],[1807,9824,9826,9829],{"className":9825},[1894],[1807,9827],{"className":9828,"style":9492},[1898],[1807,9830,9832,9863],{"className":9831},[1907],[1807,9833,9835],{"className":9834},[1907,2560],[1807,9836,9838],{"className":9837},[1920],[1807,9839,9841],{"className":9840},[1925],[1807,9842,9844,9852],{"className":9843,"style":9508},[1929],[1807,9845,9846,9849],{"style":2573},[1807,9847],{"className":9848,"style":2577},[1937],[1807,9850,8511],{"className":9851},[1907,1911],[1807,9853,9854,9857],{"style":9519},[1807,9855],{"className":9856,"style":2577},[1937],[1807,9858,9860],{"className":9859,"style":2895},[2589],[1807,9861,9443],{"className":9862},[1907],[1807,9864,9866],{"className":9865},[1916],[1807,9867,9869,9889],{"className":9868},[1920,1921],[1807,9870,9872,9886],{"className":9871},[1925],[1807,9873,9875],{"className":9874,"style":7848},[1929],[1807,9876,9877,9880],{"style":2457},[1807,9878],{"className":9879,"style":1938},[1937],[1807,9881,9883],{"className":9882},[1942,1943,1944,1945],[1807,9884,8531],{"className":9885,"style":8764},[1907,1911,1945],[1807,9887,1963],{"className":9888},[1962],[1807,9890,9892],{"className":9891},[1925],[1807,9893,9895],{"className":9894,"style":2189},[1929],[1807,9896],{}," 在统计上显著为正（例如 t 统计显著大于 0），则可以认为该因子在样本期内“有价格”，可以用来构建策略。",[1792,9899,9900],{},"在更偏“策略构建”的视角下，我们也可以反过来：",[5589,9902,9903,9906,9909],{},[4352,9904,9905],{},"先从数据中抽象出一组因子；",[4352,9907,9908],{},"通过上述横截面回归检验其溢价是否存在；",[4352,9910,9911],{},"然后基于因子暴露构建组合权重（在后续章节详细讨论）。",[1792,9913,9914],{},"形式上，Fama–MacBeth 两步法可以概括为：",[4349,9916,9917,10457],{},[4352,9918,9919,9922,9923,9926,9927,9955,9956,10349,10351,10352,10456],{},[6070,9920,9921],{},"第一步（时间序列回归）","：",[9924,9925],"br",{},"对每个资产 ",[1807,9928,9930,9943],{"className":9929},[1814],[1807,9931,9933],{"className":9932},[1818],[1820,9934,9935],{"xmlns":1822},[1825,9936,9937,9941],{},[1828,9938,9939],{},[1839,9940,4399],{},[1883,9942,4399],{"encoding":1885},[1807,9944,9946],{"className":9945,"ariaHidden":1848},[1890],[1807,9947,9949,9952],{"className":9948},[1894],[1807,9950],{"className":9951,"style":4501},[1898],[1807,9953,4399],{"className":9954},[1907,1911],"，在时间序列维度上回归收益对因子：",[1807,9957,9959],{"className":9958},[1810],[1807,9960,9962,10042],{"className":9961},[1814],[1807,9963,9965],{"className":9964},[1818],[1820,9966,9967],{"xmlns":1822,"display":1823},[1825,9968,9969,10039],{},[1828,9970,9971,9987,9989,9995,9997,10006,10018,10020,10037],{},[1836,9972,9973,9975],{},[1839,9974,1841],{},[1828,9976,9977,9979,9981,9983,9985],{},[1839,9978,4399],{},[1831,9980,1849],{"separator":1848},[1839,9982,1852],{},[1831,9984,2209],{},[1867,9986,1869],{},[1831,9988,1865],{},[1836,9990,9991,9993],{},[1839,9992,3595],{},[1839,9994,4399],{},[1831,9996,2209],{},[1854,9998,9999,10002,10004],{},[1839,10000,10001],{},"b",[1839,10003,4399],{},[1839,10005,2408],{"mathvariant":2361},[1836,10007,10008,10010],{},[1839,10009,2279],{},[1828,10011,10012,10014,10016],{},[1839,10013,1852],{},[1831,10015,2209],{},[1867,10017,1869],{},[1831,10019,2209],{},[1836,10021,10022,10025],{},[1839,10023,10024],{},"u",[1828,10026,10027,10029,10031,10033,10035],{},[1839,10028,4399],{},[1831,10030,1849],{"separator":1848},[1839,10032,1852],{},[1831,10034,2209],{},[1867,10036,1869],{},[1831,10038,1849],{"separator":1848},[1883,10040,10041],{"encoding":1885},"r_{i,t+1} = a_i + b_i^\\top f_{t+1} + u_{i,t+1},",[1807,10043,10045,10115,10170,10285],{"className":10044,"ariaHidden":1848},[1890],[1807,10046,10048,10051,10106,10109,10112],{"className":10047},[1894],[1807,10049],{"className":10050,"style":4728},[1898],[1807,10052,10054,10057],{"className":10053},[1907],[1807,10055,1841],{"className":10056,"style":1912},[1907,1911],[1807,10058,10060],{"className":10059},[1916],[1807,10061,10063,10098],{"className":10062},[1920,1921],[1807,10064,10066,10095],{"className":10065},[1925],[1807,10067,10069],{"className":10068,"style":4440},[1929],[1807,10070,10071,10074],{"style":1933},[1807,10072],{"className":10073,"style":1938},[1937],[1807,10075,10077],{"className":10076},[1942,1943,1944,1945],[1807,10078,10080,10083,10086,10089,10092],{"className":10079},[1907,1945],[1807,10081,4399],{"className":10082},[1907,1911,1945],[1807,10084,1849],{"className":10085},[1955,1945],[1807,10087,1852],{"className":10088},[1907,1911,1945],[1807,10090,2209],{"className":10091},[2235,1945],[1807,10093,1869],{"className":10094},[1907,1945],[1807,10096,1963],{"className":10097},[1962],[1807,10099,10101],{"className":10100},[1925],[1807,10102,10104],{"className":10103,"style":1970},[1929],[1807,10105],{},[1807,10107],{"className":10108,"style":2044},[2043],[1807,10110,1865],{"className":10111},[2011],[1807,10113],{"className":10114,"style":2044},[2043],[1807,10116,10118,10121,10161,10164,10167],{"className":10117},[1894],[1807,10119],{"className":10120,"style":7120},[1898],[1807,10122,10124,10127],{"className":10123},[1907],[1807,10125,3595],{"className":10126},[1907,1911],[1807,10128,10130],{"className":10129},[1916],[1807,10131,10133,10153],{"className":10132},[1920,1921],[1807,10134,10136,10150],{"className":10135},[1925],[1807,10137,10139],{"className":10138,"style":4440},[1929],[1807,10140,10141,10144],{"style":2457},[1807,10142],{"className":10143,"style":1938},[1937],[1807,10145,10147],{"className":10146},[1942,1943,1944,1945],[1807,10148,4399],{"className":10149},[1907,1911,1945],[1807,10151,1963],{"className":10152},[1962],[1807,10154,10156],{"className":10155},[1925],[1807,10157,10159],{"className":10158,"style":2189},[1929],[1807,10160],{},[1807,10162],{"className":10163,"style":2231},[2043],[1807,10165,2209],{"className":10166},[2235],[1807,10168],{"className":10169,"style":2231},[2043],[1807,10171,10173,10176,10227,10276,10279,10282],{"className":10172},[1894],[1807,10174],{"className":10175,"style":3062},[1898],[1807,10177,10179,10182],{"className":10178},[1907],[1807,10180,10001],{"className":10181},[1907,1911],[1807,10183,10185],{"className":10184},[1916],[1807,10186,10188,10219],{"className":10187},[1920,1921],[1807,10189,10191,10216],{"className":10190},[1925],[1807,10192,10194,10205],{"className":10193,"style":3081},[1929],[1807,10195,10196,10199],{"style":1995},[1807,10197],{"className":10198,"style":1938},[1937],[1807,10200,10202],{"className":10201},[1942,1943,1944,1945],[1807,10203,4399],{"className":10204},[1907,1911,1945],[1807,10206,10207,10210],{"style":2017},[1807,10208],{"className":10209,"style":1938},[1937],[1807,10211,10213],{"className":10212},[1942,1943,1944,1945],[1807,10214,2408],{"className":10215},[1907,1945],[1807,10217,1963],{"className":10218},[1962],[1807,10220,10222],{"className":10221},[1925],[1807,10223,10225],{"className":10224,"style":2037},[1929],[1807,10226],{},[1807,10228,10230,10233],{"className":10229},[1907],[1807,10231,2279],{"className":10232,"style":2496},[1907,1911],[1807,10234,10236],{"className":10235},[1916],[1807,10237,10239,10268],{"className":10238},[1920,1921],[1807,10240,10242,10265],{"className":10241},[1925],[1807,10243,10245],{"className":10244,"style":3009},[1929],[1807,10246,10247,10250],{"style":7251},[1807,10248],{"className":10249,"style":1938},[1937],[1807,10251,10253],{"className":10252},[1942,1943,1944,1945],[1807,10254,10256,10259,10262],{"className":10255},[1907,1945],[1807,10257,1852],{"className":10258},[1907,1911,1945],[1807,10260,2209],{"className":10261},[2235,1945],[1807,10263,1869],{"className":10264},[1907,1945],[1807,10266,1963],{"className":10267},[1962],[1807,10269,10271],{"className":10270},[1925],[1807,10272,10274],{"className":10273,"style":3163},[1929],[1807,10275],{},[1807,10277],{"className":10278,"style":2231},[2043],[1807,10280,2209],{"className":10281},[2235],[1807,10283],{"className":10284,"style":2231},[2043],[1807,10286,10288,10291,10346],{"className":10287},[1894],[1807,10289],{"className":10290,"style":4728},[1898],[1807,10292,10294,10297],{"className":10293},[1907],[1807,10295,10024],{"className":10296},[1907,1911],[1807,10298,10300],{"className":10299},[1916],[1807,10301,10303,10338],{"className":10302},[1920,1921],[1807,10304,10306,10335],{"className":10305},[1925],[1807,10307,10309],{"className":10308,"style":4440},[1929],[1807,10310,10311,10314],{"style":2457},[1807,10312],{"className":10313,"style":1938},[1937],[1807,10315,10317],{"className":10316},[1942,1943,1944,1945],[1807,10318,10320,10323,10326,10329,10332],{"className":10319},[1907,1945],[1807,10321,4399],{"className":10322},[1907,1911,1945],[1807,10324,1849],{"className":10325},[1955,1945],[1807,10327,1852],{"className":10328},[1907,1911,1945],[1807,10330,2209],{"className":10331},[2235,1945],[1807,10333,1869],{"className":10334},[1907,1945],[1807,10336,1963],{"className":10337},[1962],[1807,10339,10341],{"className":10340},[1925],[1807,10342,10344],{"className":10343,"style":1970},[1929],[1807,10345],{},[1807,10347,1849],{"className":10348},[1955],[9924,10350],{},"得到每个资产的暴露估计 ",[1807,10353,10355,10377],{"className":10354},[1814],[1807,10356,10358],{"className":10357},[1818],[1820,10359,10360],{"xmlns":1822},[1825,10361,10362,10374],{},[1828,10363,10364],{},[1836,10365,10366,10372],{},[2300,10367,10368,10370],{"accent":1848},[1839,10369,10001],{},[1831,10371,2307],{},[1839,10373,4399],{},[1883,10375,10376],{"encoding":1885},"\\hat{b}_i",[1807,10378,10380],{"className":10379,"ariaHidden":1848},[1890],[1807,10381,10383,10387],{"className":10382},[1894],[1807,10384],{"className":10385,"style":10386},[1898],"height:1.1079em;vertical-align:-0.15em;",[1807,10388,10390,10422],{"className":10389},[1907],[1807,10391,10393],{"className":10392},[1907,2560],[1807,10394,10396],{"className":10395},[1920],[1807,10397,10399],{"className":10398},[1925],[1807,10400,10403,10411],{"className":10401,"style":10402},[1929],"height:0.9579em;",[1807,10404,10405,10408],{"style":2573},[1807,10406],{"className":10407,"style":2577},[1937],[1807,10409,10001],{"className":10410},[1907,1911],[1807,10412,10413,10416],{"style":9519},[1807,10414],{"className":10415,"style":2577},[1937],[1807,10417,10419],{"className":10418,"style":2895},[2589],[1807,10420,2307],{"className":10421},[1907],[1807,10423,10425],{"className":10424},[1916],[1807,10426,10428,10448],{"className":10427},[1920,1921],[1807,10429,10431,10445],{"className":10430},[1925],[1807,10432,10434],{"className":10433,"style":4440},[1929],[1807,10435,10436,10439],{"style":2457},[1807,10437],{"className":10438,"style":1938},[1937],[1807,10440,10442],{"className":10441},[1942,1943,1944,1945],[1807,10443,4399],{"className":10444},[1907,1911,1945],[1807,10446,1963],{"className":10447},[1962],[1807,10449,10451],{"className":10450},[1925],[1807,10452,10454],{"className":10453,"style":2189},[1929],[1807,10455],{},"；",[4352,10458,10459,9922,10462,10464,10465,10889,10891,10892,10972,10973,11034],{},[6070,10460,10461],{},"第二步（横截面回归）",[9924,10463],{},"在每个截面上，用第一步得到的暴露解释截面收益：",[1807,10466,10468],{"className":10467},[1810],[1807,10469,10471,10553],{"className":10470},[1814],[1807,10472,10474],{"className":10473},[1818],[1820,10475,10476],{"xmlns":1822,"display":1823},[1825,10477,10478,10550],{},[1828,10479,10480,10496,10498,10510,10512,10520,10530,10532,10548],{},[1836,10481,10482,10484],{},[1839,10483,1841],{},[1828,10485,10486,10488,10490,10492,10494],{},[1839,10487,4399],{},[1831,10489,1849],{"separator":1848},[1839,10491,1852],{},[1831,10493,2209],{},[1867,10495,1869],{},[1831,10497,1865],{},[1836,10499,10500,10502],{},[1839,10501,8511],{},[1828,10503,10504,10506,10508],{},[1867,10505,5905],{},[1831,10507,1849],{"separator":1848},[1839,10509,1852],{},[1831,10511,2209],{},[1854,10513,10514,10516,10518],{},[1839,10515,8511],{},[1839,10517,1852],{},[1839,10519,2408],{"mathvariant":2361},[1836,10521,10522,10528],{},[2300,10523,10524,10526],{"accent":1848},[1839,10525,10001],{},[1831,10527,2307],{},[1839,10529,4399],{},[1831,10531,2209],{},[1836,10533,10534,10536],{},[1839,10535,7023],{},[1828,10537,10538,10540,10542,10544,10546],{},[1839,10539,4399],{},[1831,10541,1849],{"separator":1848},[1839,10543,1852],{},[1831,10545,2209],{},[1867,10547,1869],{},[1831,10549,1849],{"separator":1848},[1883,10551,10552],{"encoding":1885},"r_{i,t+1} = \\lambda_{0,t} + \\lambda_t^\\top \\hat{b}_i + \\epsilon_{i,t+1},",[1807,10554,10556,10626,10690,10825],{"className":10555,"ariaHidden":1848},[1890],[1807,10557,10559,10562,10617,10620,10623],{"className":10558},[1894],[1807,10560],{"className":10561,"style":4728},[1898],[1807,10563,10565,10568],{"className":10564},[1907],[1807,10566,1841],{"className":10567,"style":1912},[1907,1911],[1807,10569,10571],{"className":10570},[1916],[1807,10572,10574,10609],{"className":10573},[1920,1921],[1807,10575,10577,10606],{"className":10576},[1925],[1807,10578,10580],{"className":10579,"style":4440},[1929],[1807,10581,10582,10585],{"style":1933},[1807,10583],{"className":10584,"style":1938},[1937],[1807,10586,10588],{"className":10587},[1942,1943,1944,1945],[1807,10589,10591,10594,10597,10600,10603],{"className":10590},[1907,1945],[1807,10592,4399],{"className":10593},[1907,1911,1945],[1807,10595,1849],{"className":10596},[1955,1945],[1807,10598,1852],{"className":10599},[1907,1911,1945],[1807,10601,2209],{"className":10602},[2235,1945],[1807,10604,1869],{"className":10605},[1907,1945],[1807,10607,1963],{"className":10608},[1962],[1807,10610,10612],{"className":10611},[1925],[1807,10613,10615],{"className":10614,"style":1970},[1929],[1807,10616],{},[1807,10618],{"className":10619,"style":2044},[2043],[1807,10621,1865],{"className":10622},[2011],[1807,10624],{"className":10625,"style":2044},[2043],[1807,10627,10629,10632,10681,10684,10687],{"className":10628},[1894],[1807,10630],{"className":10631,"style":8669},[1898],[1807,10633,10635,10638],{"className":10634},[1907],[1807,10636,8511],{"className":10637},[1907,1911],[1807,10639,10641],{"className":10640},[1916],[1807,10642,10644,10673],{"className":10643},[1920,1921],[1807,10645,10647,10670],{"className":10646},[1925],[1807,10648,10650],{"className":10649,"style":3009},[1929],[1807,10651,10652,10655],{"style":2457},[1807,10653],{"className":10654,"style":1938},[1937],[1807,10656,10658],{"className":10657},[1942,1943,1944,1945],[1807,10659,10661,10664,10667],{"className":10660},[1907,1945],[1807,10662,5905],{"className":10663},[1907,1945],[1807,10665,1849],{"className":10666},[1955,1945],[1807,10668,1852],{"className":10669},[1907,1911,1945],[1807,10671,1963],{"className":10672},[1962],[1807,10674,10676],{"className":10675},[1925],[1807,10677,10679],{"className":10678,"style":1970},[1929],[1807,10680],{},[1807,10682],{"className":10683,"style":2231},[2043],[1807,10685,2209],{"className":10686},[2235],[1807,10688],{"className":10689,"style":2231},[2043],[1807,10691,10693,10697,10748,10816,10819,10822],{"className":10692},[1894],[1807,10694],{"className":10695,"style":10696},[1898],"height:1.2049em;vertical-align:-0.247em;",[1807,10698,10700,10703],{"className":10699},[1907],[1807,10701,8511],{"className":10702},[1907,1911],[1807,10704,10706],{"className":10705},[1916],[1807,10707,10709,10740],{"className":10708},[1920,1921],[1807,10710,10712,10737],{"className":10711},[1925],[1807,10713,10715,10726],{"className":10714,"style":3081},[1929],[1807,10716,10717,10720],{"style":1995},[1807,10718],{"className":10719,"style":1938},[1937],[1807,10721,10723],{"className":10722},[1942,1943,1944,1945],[1807,10724,1852],{"className":10725},[1907,1911,1945],[1807,10727,10728,10731],{"style":2017},[1807,10729],{"className":10730,"style":1938},[1937],[1807,10732,10734],{"className":10733},[1942,1943,1944,1945],[1807,10735,2408],{"className":10736},[1907,1945],[1807,10738,1963],{"className":10739},[1962],[1807,10741,10743],{"className":10742},[1925],[1807,10744,10746],{"className":10745,"style":2037},[1929],[1807,10747],{},[1807,10749,10751,10782],{"className":10750},[1907],[1807,10752,10754],{"className":10753},[1907,2560],[1807,10755,10757],{"className":10756},[1920],[1807,10758,10760],{"className":10759},[1925],[1807,10761,10763,10771],{"className":10762,"style":10402},[1929],[1807,10764,10765,10768],{"style":2573},[1807,10766],{"className":10767,"style":2577},[1937],[1807,10769,10001],{"className":10770},[1907,1911],[1807,10772,10773,10776],{"style":9519},[1807,10774],{"className":10775,"style":2577},[1937],[1807,10777,10779],{"className":10778,"style":2895},[2589],[1807,10780,2307],{"className":10781},[1907],[1807,10783,10785],{"className":10784},[1916],[1807,10786,10788,10808],{"className":10787},[1920,1921],[1807,10789,10791,10805],{"className":10790},[1925],[1807,10792,10794],{"className":10793,"style":4440},[1929],[1807,10795,10796,10799],{"style":2457},[1807,10797],{"className":10798,"style":1938},[1937],[1807,10800,10802],{"className":10801},[1942,1943,1944,1945],[1807,10803,4399],{"className":10804},[1907,1911,1945],[1807,10806,1963],{"className":10807},[1962],[1807,10809,10811],{"className":10810},[1925],[1807,10812,10814],{"className":10813,"style":2189},[1929],[1807,10815],{},[1807,10817],{"className":10818,"style":2231},[2043],[1807,10820,2209],{"className":10821},[2235],[1807,10823],{"className":10824,"style":2231},[2043],[1807,10826,10828,10831,10886],{"className":10827},[1894],[1807,10829],{"className":10830,"style":4728},[1898],[1807,10832,10834,10837],{"className":10833},[1907],[1807,10835,7023],{"className":10836},[1907,1911],[1807,10838,10840],{"className":10839},[1916],[1807,10841,10843,10878],{"className":10842},[1920,1921],[1807,10844,10846,10875],{"className":10845},[1925],[1807,10847,10849],{"className":10848,"style":4440},[1929],[1807,10850,10851,10854],{"style":2457},[1807,10852],{"className":10853,"style":1938},[1937],[1807,10855,10857],{"className":10856},[1942,1943,1944,1945],[1807,10858,10860,10863,10866,10869,10872],{"className":10859},[1907,1945],[1807,10861,4399],{"className":10862},[1907,1911,1945],[1807,10864,1849],{"className":10865},[1955,1945],[1807,10867,1852],{"className":10868},[1907,1911,1945],[1807,10870,2209],{"className":10871},[2235,1945],[1807,10873,1869],{"className":10874},[1907,1945],[1807,10876,1963],{"className":10877},[1962],[1807,10879,10881],{"className":10880},[1925],[1807,10882,10884],{"className":10883,"style":1970},[1929],[1807,10885],{},[1807,10887,1849],{"className":10888},[1955],[9924,10890],{},"进而对 ",[1807,10893,10895,10917],{"className":10894},[1814],[1807,10896,10898],{"className":10897},[1818],[1820,10899,10900],{"xmlns":1822},[1825,10901,10902,10914],{},[1828,10903,10904,10906,10912],{},[1831,10905,1834],{"stretchy":1833},[1836,10907,10908,10910],{},[1839,10909,8511],{},[1839,10911,1852],{},[1831,10913,1858],{"stretchy":1833},[1883,10915,10916],{"encoding":1885},"\\{\\lambda_t\\}",[1807,10918,10920],{"className":10919,"ariaHidden":1848},[1890],[1807,10921,10923,10926,10929,10969],{"className":10922},[1894],[1807,10924],{"className":10925,"style":2057},[1898],[1807,10927,1834],{"className":10928},[1903],[1807,10930,10932,10935],{"className":10931},[1907],[1807,10933,8511],{"className":10934},[1907,1911],[1807,10936,10938],{"className":10937},[1916],[1807,10939,10941,10961],{"className":10940},[1920,1921],[1807,10942,10944,10958],{"className":10943},[1925],[1807,10945,10947],{"className":10946,"style":1930},[1929],[1807,10948,10949,10952],{"style":2457},[1807,10950],{"className":10951,"style":1938},[1937],[1807,10953,10955],{"className":10954},[1942,1943,1944,1945],[1807,10956,1852],{"className":10957},[1907,1911,1945],[1807,10959,1963],{"className":10960},[1962],[1807,10962,10964],{"className":10963},[1925],[1807,10965,10967],{"className":10966,"style":2189},[1929],[1807,10968],{},[1807,10970,1858],{"className":10971},[1976]," 求平均，得到因子的平均价格 ",[1807,10974,10976,10994],{"className":10975},[1814],[1807,10977,10979],{"className":10978},[1818],[1820,10980,10981],{"xmlns":1822},[1825,10982,10983,10991],{},[1828,10984,10985],{},[2300,10986,10987,10989],{"accent":1848},[1839,10988,8511],{},[1831,10990,9443],{},[1883,10992,10993],{"encoding":1885},"\\bar{\\lambda}",[1807,10995,10997],{"className":10996,"ariaHidden":1848},[1890],[1807,10998,11000,11003],{"className":10999},[1894],[1807,11001],{"className":11002,"style":9508},[1898],[1807,11004,11006],{"className":11005},[1907,2560],[1807,11007,11009],{"className":11008},[1920],[1807,11010,11012],{"className":11011},[1925],[1807,11013,11015,11023],{"className":11014,"style":9508},[1929],[1807,11016,11017,11020],{"style":2573},[1807,11018],{"className":11019,"style":2577},[1937],[1807,11021,8511],{"className":11022},[1907,1911],[1807,11024,11025,11028],{"style":9519},[1807,11026],{"className":11027,"style":2577},[1937],[1807,11029,11031],{"className":11030,"style":2895},[2589],[1807,11032,9443],{"className":11033},[1907],"。这一框架可以推广到更一般的规格，包括引入工具变量、控制特定特征等，在资产定价实证与量化因子研究中非常常见。",[2078,11036,11038],{"id":11037},"_3-策略回测的基本结构","3. 策略回测的基本结构",[1792,11040,11041],{},"形式上，一个离散时间回测可以写作如下伪代码：",[4349,11043,11044,11119],{},[4352,11045,11046,11047,10456],{},"初始化资本 ",[1807,11048,11050,11069],{"className":11049},[1814],[1807,11051,11053],{"className":11052},[1818],[1820,11054,11055],{"xmlns":1822},[1825,11056,11057,11066],{},[1828,11058,11059],{},[1836,11060,11061,11064],{},[1839,11062,11063],{},"V",[1867,11065,5905],{},[1883,11067,11068],{"encoding":1885},"V_0",[1807,11070,11072],{"className":11071,"ariaHidden":1848},[1890],[1807,11073,11075,11078],{"className":11074},[1894],[1807,11076],{"className":11077,"style":2147},[1898],[1807,11079,11081,11084],{"className":11080},[1907],[1807,11082,11063],{"className":11083,"style":2231},[1907,1911],[1807,11085,11087],{"className":11086},[1916],[1807,11088,11090,11111],{"className":11089},[1920,1921],[1807,11091,11093,11108],{"className":11092},[1925],[1807,11094,11096],{"className":11095,"style":3009},[1929],[1807,11097,11099,11102],{"style":11098},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1807,11100],{"className":11101,"style":1938},[1937],[1807,11103,11105],{"className":11104},[1942,1943,1944,1945],[1807,11106,5905],{"className":11107},[1907,1945],[1807,11109,1963],{"className":11110},[1962],[1807,11112,11114],{"className":11113},[1925],[1807,11115,11117],{"className":11116,"style":2189},[1929],[1807,11118],{},[4352,11120,11121,11122,11238,11239],{},"对每个交易日（或任意时间步） ",[1807,11123,11125,11159],{"className":11124},[1814],[1807,11126,11128],{"className":11127},[1818],[1820,11129,11130],{"xmlns":1822},[1825,11131,11132,11156],{},[1828,11133,11134,11136,11138,11140,11142,11144,11146,11148,11150,11152,11154],{},[1839,11135,1852],{},[1831,11137,1865],{},[1867,11139,5905],{},[1831,11141,1849],{"separator":1848},[1867,11143,1869],{},[1831,11145,1849],{"separator":1848},[1831,11147,5344],{},[1831,11149,1849],{"separator":1848},[1839,11151,1872],{},[1831,11153,3649],{},[1867,11155,1869],{},[1883,11157,11158],{"encoding":1885},"t = 0, 1, \\dots, T-1",[1807,11160,11162,11180,11229],{"className":11161,"ariaHidden":1848},[1890],[1807,11163,11165,11168,11171,11174,11177],{"className":11164},[1894],[1807,11166],{"className":11167,"style":2110},[1898],[1807,11169,1852],{"className":11170},[1907,1911],[1807,11172],{"className":11173,"style":2044},[2043],[1807,11175,1865],{"className":11176},[2011],[1807,11178],{"className":11179,"style":2044},[2043],[1807,11181,11183,11187,11190,11193,11196,11199,11202,11205,11208,11211,11214,11217,11220,11223,11226],{"className":11182},[1894],[1807,11184],{"className":11185,"style":11186},[1898],"height:0.8778em;vertical-align:-0.1944em;",[1807,11188,5905],{"className":11189},[1907],[1807,11191,1849],{"className":11192},[1955],[1807,11194],{"className":11195,"style":2553},[2043],[1807,11197,1869],{"className":11198},[1907],[1807,11200,1849],{"className":11201},[1955],[1807,11203],{"className":11204,"style":2553},[2043],[1807,11206,5344],{"className":11207},[5495],[1807,11209],{"className":11210,"style":2553},[2043],[1807,11212,1849],{"className":11213},[1955],[1807,11215],{"className":11216,"style":2553},[2043],[1807,11218,1872],{"className":11219,"style":2027},[1907,1911],[1807,11221],{"className":11222,"style":2231},[2043],[1807,11224,3649],{"className":11225},[2235],[1807,11227],{"className":11228,"style":2231},[2043],[1807,11230,11232,11235],{"className":11231},[1894],[1807,11233],{"className":11234,"style":2245},[1898],[1807,11236,1869],{"className":11237},[1907],"：\n",[4349,11240,11241,11433,11618,11785],{},[4352,11242,11243,11244,11313,11314,10456],{},"根据信息集 ",[1807,11245,11247,11264],{"className":11246},[1814],[1807,11248,11250],{"className":11249},[1818],[1820,11251,11252],{"xmlns":1822},[1825,11253,11254,11262],{},[1828,11255,11256],{},[1836,11257,11258,11260],{},[1839,11259,2132],{"mathvariant":2131},[1839,11261,1852],{},[1883,11263,2137],{"encoding":1885},[1807,11265,11267],{"className":11266,"ariaHidden":1848},[1890],[1807,11268,11270,11273],{"className":11269},[1894],[1807,11271],{"className":11272,"style":2147},[1898],[1807,11274,11276,11279],{"className":11275},[1907],[1807,11277,2132],{"className":11278,"style":2155},[1907,2154],[1807,11280,11282],{"className":11281},[1916],[1807,11283,11285,11305],{"className":11284},[1920,1921],[1807,11286,11288,11302],{"className":11287},[1925],[1807,11289,11291],{"className":11290,"style":1930},[1929],[1807,11292,11293,11296],{"style":2170},[1807,11294],{"className":11295,"style":1938},[1937],[1807,11297,11299],{"className":11298},[1942,1943,1944,1945],[1807,11300,1852],{"className":11301},[1907,1911,1945],[1807,11303,1963],{"className":11304},[1962],[1807,11306,11308],{"className":11307},[1925],[1807,11309,11311],{"className":11310,"style":2189},[1929],[1807,11312],{}," 计算信号或目标权重 ",[1807,11315,11317,11350],{"className":11316},[1814],[1807,11318,11320],{"className":11319},[1818],[1820,11321,11322],{"xmlns":1822},[1825,11323,11324,11347],{},[1828,11325,11326],{},[1854,11327,11328,11330,11332],{},[1839,11329,2333],{},[1839,11331,1852],{},[1828,11333,11334,11336,11338,11340,11342,11345],{},[1839,11335,1852],{},[1839,11337,3595],{},[1839,11339,1841],{},[1839,11341,6721],{},[1839,11343,11344],{},"e",[1839,11346,1852],{},[1883,11348,11349],{"encoding":1885},"w_t^{target}",[1807,11351,11353],{"className":11352,"ariaHidden":1848},[1890],[1807,11354,11356,11360],{"className":11355},[1894],[1807,11357],{"className":11358,"style":11359},[1898],"height:1.1572em;vertical-align:-0.2458em;",[1807,11361,11363,11366],{"className":11362},[1907],[1807,11364,2333],{"className":11365,"style":2719},[1907,1911],[1807,11367,11369],{"className":11368},[1916],[1807,11370,11372,11424],{"className":11371},[1920,1921],[1807,11373,11375,11421],{"className":11374},[1925],[1807,11376,11379,11391],{"className":11377,"style":11378},[1929],"height:0.9115em;",[1807,11380,11382,11385],{"style":11381},"top:-2.4542em;margin-left:-0.0269em;margin-right:0.05em;",[1807,11383],{"className":11384,"style":1938},[1937],[1807,11386,11388],{"className":11387},[1942,1943,1944,1945],[1807,11389,1852],{"className":11390},[1907,1911,1945],[1807,11392,11394,11397],{"style":11393},"top:-3.1809em;margin-right:0.05em;",[1807,11395],{"className":11396,"style":1938},[1937],[1807,11398,11400],{"className":11399},[1942,1943,1944,1945],[1807,11401,11403,11406,11409,11412,11415,11418],{"className":11402},[1907,1945],[1807,11404,1852],{"className":11405},[1907,1911,1945],[1807,11407,3595],{"className":11408},[1907,1911,1945],[1807,11410,1841],{"className":11411,"style":1912},[1907,1911,1945],[1807,11413,6721],{"className":11414,"style":6803},[1907,1911,1945],[1807,11416,11344],{"className":11417},[1907,1911,1945],[1807,11419,1852],{"className":11420},[1907,1911,1945],[1807,11422,1963],{"className":11423},[1962],[1807,11425,11427],{"className":11426},[1925],[1807,11428,11431],{"className":11429,"style":11430},[1929],"height:0.2458em;",[1807,11432],{},[4352,11434,11435,11436,11505,11506,10456],{},"根据交易约束、成本模型，将实际权重 ",[1807,11437,11439,11456],{"className":11438},[1814],[1807,11440,11442],{"className":11441},[1818],[1820,11443,11444],{"xmlns":1822},[1825,11445,11446,11454],{},[1828,11447,11448],{},[1836,11449,11450,11452],{},[1839,11451,2333],{},[1839,11453,1852],{},[1883,11455,6648],{"encoding":1885},[1807,11457,11459],{"className":11458,"ariaHidden":1848},[1890],[1807,11460,11462,11465],{"className":11461},[1894],[1807,11463],{"className":11464,"style":2436},[1898],[1807,11466,11468,11471],{"className":11467},[1907],[1807,11469,2333],{"className":11470,"style":2719},[1907,1911],[1807,11472,11474],{"className":11473},[1916],[1807,11475,11477,11497],{"className":11476},[1920,1921],[1807,11478,11480,11494],{"className":11479},[1925],[1807,11481,11483],{"className":11482,"style":1930},[1929],[1807,11484,11485,11488],{"style":2734},[1807,11486],{"className":11487,"style":1938},[1937],[1807,11489,11491],{"className":11490},[1942,1943,1944,1945],[1807,11492,1852],{"className":11493},[1907,1911,1945],[1807,11495,1963],{"className":11496},[1962],[1807,11498,11500],{"className":11499},[1925],[1807,11501,11503],{"className":11502,"style":2189},[1929],[1807,11504],{}," 调整为靠近 ",[1807,11507,11509,11540],{"className":11508},[1814],[1807,11510,11512],{"className":11511},[1818],[1820,11513,11514],{"xmlns":1822},[1825,11515,11516,11538],{},[1828,11517,11518],{},[1854,11519,11520,11522,11524],{},[1839,11521,2333],{},[1839,11523,1852],{},[1828,11525,11526,11528,11530,11532,11534,11536],{},[1839,11527,1852],{},[1839,11529,3595],{},[1839,11531,1841],{},[1839,11533,6721],{},[1839,11535,11344],{},[1839,11537,1852],{},[1883,11539,11349],{"encoding":1885},[1807,11541,11543],{"className":11542,"ariaHidden":1848},[1890],[1807,11544,11546,11549],{"className":11545},[1894],[1807,11547],{"className":11548,"style":11359},[1898],[1807,11550,11552,11555],{"className":11551},[1907],[1807,11553,2333],{"className":11554,"style":2719},[1907,1911],[1807,11556,11558],{"className":11557},[1916],[1807,11559,11561,11610],{"className":11560},[1920,1921],[1807,11562,11564,11607],{"className":11563},[1925],[1807,11565,11567,11578],{"className":11566,"style":11378},[1929],[1807,11568,11569,11572],{"style":11381},[1807,11570],{"className":11571,"style":1938},[1937],[1807,11573,11575],{"className":11574},[1942,1943,1944,1945],[1807,11576,1852],{"className":11577},[1907,1911,1945],[1807,11579,11580,11583],{"style":11393},[1807,11581],{"className":11582,"style":1938},[1937],[1807,11584,11586],{"className":11585},[1942,1943,1944,1945],[1807,11587,11589,11592,11595,11598,11601,11604],{"className":11588},[1907,1945],[1807,11590,1852],{"className":11591},[1907,1911,1945],[1807,11593,3595],{"className":11594},[1907,1911,1945],[1807,11596,1841],{"className":11597,"style":1912},[1907,1911,1945],[1807,11599,6721],{"className":11600,"style":6803},[1907,1911,1945],[1807,11602,11344],{"className":11603},[1907,1911,1945],[1807,11605,1852],{"className":11606},[1907,1911,1945],[1807,11608,1963],{"className":11609},[1962],[1807,11611,11613],{"className":11612},[1925],[1807,11614,11616],{"className":11615,"style":11430},[1929],[1807,11617],{},[4352,11619,11620,11621,4563,11649,11699,11700,10456],{},"观察从 ",[1807,11622,11624,11637],{"className":11623},[1814],[1807,11625,11627],{"className":11626},[1818],[1820,11628,11629],{"xmlns":1822},[1825,11630,11631,11635],{},[1828,11632,11633],{},[1839,11634,1852],{},[1883,11636,1852],{"encoding":1885},[1807,11638,11640],{"className":11639,"ariaHidden":1848},[1890],[1807,11641,11643,11646],{"className":11642},[1894],[1807,11644],{"className":11645,"style":2110},[1898],[1807,11647,1852],{"className":11648},[1907,1911],[1807,11650,11652,11669],{"className":11651},[1814],[1807,11653,11655],{"className":11654},[1818],[1820,11656,11657],{"xmlns":1822},[1825,11658,11659,11667],{},[1828,11660,11661,11663,11665],{},[1839,11662,1852],{},[1831,11664,2209],{},[1867,11666,1869],{},[1883,11668,2214],{"encoding":1885},[1807,11670,11672,11690],{"className":11671,"ariaHidden":1848},[1890],[1807,11673,11675,11678,11681,11684,11687],{"className":11674},[1894],[1807,11676],{"className":11677,"style":2224},[1898],[1807,11679,1852],{"className":11680},[1907,1911],[1807,11682],{"className":11683,"style":2231},[2043],[1807,11685,2209],{"className":11686},[2235],[1807,11688],{"className":11689,"style":2231},[2043],[1807,11691,11693,11696],{"className":11692},[1894],[1807,11694],{"className":11695,"style":2245},[1898],[1807,11697,1869],{"className":11698},[1907]," 的资产收益 ",[1807,11701,11703,11727],{"className":11702},[1814],[1807,11704,11706],{"className":11705},[1818],[1820,11707,11708],{"xmlns":1822},[1825,11709,11710,11724],{},[1828,11711,11712],{},[1836,11713,11714,11716],{},[1839,11715,1841],{},[1828,11717,11718,11720,11722],{},[1839,11719,1852],{},[1831,11721,2209],{},[1867,11723,1869],{},[1883,11725,11726],{"encoding":1885},"r_{t+1}",[1807,11728,11730],{"className":11729,"ariaHidden":1848},[1890],[1807,11731,11733,11736],{"className":11732},[1894],[1807,11734],{"className":11735,"style":6400},[1898],[1807,11737,11739,11742],{"className":11738},[1907],[1807,11740,1841],{"className":11741,"style":1912},[1907,1911],[1807,11743,11745],{"className":11744},[1916],[1807,11746,11748,11777],{"className":11747},[1920,1921],[1807,11749,11751,11774],{"className":11750},[1925],[1807,11752,11754],{"className":11753,"style":3009},[1929],[1807,11755,11756,11759],{"style":1933},[1807,11757],{"className":11758,"style":1938},[1937],[1807,11760,11762],{"className":11761},[1942,1943,1944,1945],[1807,11763,11765,11768,11771],{"className":11764},[1907,1945],[1807,11766,1852],{"className":11767},[1907,1911,1945],[1807,11769,2209],{"className":11770},[2235,1945],[1807,11772,1869],{"className":11773},[1907,1945],[1807,11775,1963],{"className":11776},[1962],[1807,11778,11780],{"className":11779},[1925],[1807,11781,11783],{"className":11782,"style":3163},[1929],[1807,11784],{},[4352,11786,11787,11788,5986],{},"更新组合价值：",[1807,11789,11791,11847],{"className":11790},[1814],[1807,11792,11794],{"className":11793},[1818],[1820,11795,11796],{"xmlns":1822},[1825,11797,11798,11844],{},[1828,11799,11800,11812,11814,11820,11822,11824,11826,11842],{},[1836,11801,11802,11804],{},[1839,11803,11063],{},[1828,11805,11806,11808,11810],{},[1839,11807,1852],{},[1831,11809,2209],{},[1867,11811,1869],{},[1831,11813,1865],{},[1836,11815,11816,11818],{},[1839,11817,11063],{},[1839,11819,1852],{},[1831,11821,2282],{"stretchy":1833},[1867,11823,1869],{},[1831,11825,2209],{},[1836,11827,11828,11830],{},[1839,11829,1841],{},[1828,11831,11832,11834,11836,11838,11840],{},[1839,11833,1792],{},[1831,11835,1849],{"separator":1848},[1839,11837,1852],{},[1831,11839,2209],{},[1867,11841,1869],{},[1831,11843,2291],{"stretchy":1833},[1883,11845,11846],{"encoding":1885},"V_{t+1} = V_t (1 + r_{p,t+1})",[1807,11848,11850,11915,11976],{"className":11849,"ariaHidden":1848},[1890],[1807,11851,11853,11857,11906,11909,11912],{"className":11852},[1894],[1807,11854],{"className":11855,"style":11856},[1898],"height:0.8917em;vertical-align:-0.2083em;",[1807,11858,11860,11863],{"className":11859},[1907],[1807,11861,11063],{"className":11862,"style":2231},[1907,1911],[1807,11864,11866],{"className":11865},[1916],[1807,11867,11869,11898],{"className":11868},[1920,1921],[1807,11870,11872,11895],{"className":11871},[1925],[1807,11873,11875],{"className":11874,"style":3009},[1929],[1807,11876,11877,11880],{"style":11098},[1807,11878],{"className":11879,"style":1938},[1937],[1807,11881,11883],{"className":11882},[1942,1943,1944,1945],[1807,11884,11886,11889,11892],{"className":11885},[1907,1945],[1807,11887,1852],{"className":11888},[1907,1911,1945],[1807,11890,2209],{"className":11891},[2235,1945],[1807,11893,1869],{"className":11894},[1907,1945],[1807,11896,1963],{"className":11897},[1962],[1807,11899,11901],{"className":11900},[1925],[1807,11902,11904],{"className":11903,"style":3163},[1929],[1807,11905],{},[1807,11907],{"className":11908,"style":2044},[2043],[1807,11910,1865],{"className":11911},[2011],[1807,11913],{"className":11914,"style":2044},[2043],[1807,11916,11918,11921,11961,11964,11967,11970,11973],{"className":11917},[1894],[1807,11919],{"className":11920,"style":2057},[1898],[1807,11922,11924,11927],{"className":11923},[1907],[1807,11925,11063],{"className":11926,"style":2231},[1907,1911],[1807,11928,11930],{"className":11929},[1916],[1807,11931,11933,11953],{"className":11932},[1920,1921],[1807,11934,11936,11950],{"className":11935},[1925],[1807,11937,11939],{"className":11938,"style":1930},[1929],[1807,11940,11941,11944],{"style":11098},[1807,11942],{"className":11943,"style":1938},[1937],[1807,11945,11947],{"className":11946},[1942,1943,1944,1945],[1807,11948,1852],{"className":11949},[1907,1911,1945],[1807,11951,1963],{"className":11952},[1962],[1807,11954,11956],{"className":11955},[1925],[1807,11957,11959],{"className":11958,"style":2189},[1929],[1807,11960],{},[1807,11962,2282],{"className":11963},[1903],[1807,11965,1869],{"className":11966},[1907],[1807,11968],{"className":11969,"style":2231},[2043],[1807,11971,2209],{"className":11972},[2235],[1807,11974],{"className":11975,"style":2231},[2043],[1807,11977,11979,11982,12037],{"className":11978},[1894],[1807,11980],{"className":11981,"style":4418},[1898],[1807,11983,11985,11988],{"className":11984},[1907],[1807,11986,1841],{"className":11987,"style":1912},[1907,1911],[1807,11989,11991],{"className":11990},[1916],[1807,11992,11994,12029],{"className":11993},[1920,1921],[1807,11995,11997,12026],{"className":11996},[1925],[1807,11998,12000],{"className":11999,"style":3009},[1929],[1807,12001,12002,12005],{"style":1933},[1807,12003],{"className":12004,"style":1938},[1937],[1807,12006,12008],{"className":12007},[1942,1943,1944,1945],[1807,12009,12011,12014,12017,12020,12023],{"className":12010},[1907,1945],[1807,12012,1792],{"className":12013},[1907,1911,1945],[1807,12015,1849],{"className":12016},[1955,1945],[1807,12018,1852],{"className":12019},[1907,1911,1945],[1807,12021,2209],{"className":12022},[2235,1945],[1807,12024,1869],{"className":12025},[1907,1945],[1807,12027,1963],{"className":12028},[1962],[1807,12030,12032],{"className":12031},[1925],[1807,12033,12035],{"className":12034,"style":1970},[1929],[1807,12036],{},[1807,12038,2291],{"className":12039},[1976],[1792,12041,12042],{},"关键点在于：",[5589,12044,12045,12150],{},[4352,12046,12047,12149],{},[6070,12048,12049,12050,12119,12120,12148],{},"信息集 ",[1807,12051,12053,12070],{"className":12052},[1814],[1807,12054,12056],{"className":12055},[1818],[1820,12057,12058],{"xmlns":1822},[1825,12059,12060,12068],{},[1828,12061,12062],{},[1836,12063,12064,12066],{},[1839,12065,2132],{"mathvariant":2131},[1839,12067,1852],{},[1883,12069,2137],{"encoding":1885},[1807,12071,12073],{"className":12072,"ariaHidden":1848},[1890],[1807,12074,12076,12079],{"className":12075},[1894],[1807,12077],{"className":12078,"style":2147},[1898],[1807,12080,12082,12085],{"className":12081},[1907],[1807,12083,2132],{"className":12084,"style":2155},[1907,2154],[1807,12086,12088],{"className":12087},[1916],[1807,12089,12091,12111],{"className":12090},[1920,1921],[1807,12092,12094,12108],{"className":12093},[1925],[1807,12095,12097],{"className":12096,"style":1930},[1929],[1807,12098,12099,12102],{"style":2170},[1807,12100],{"className":12101,"style":1938},[1937],[1807,12103,12105],{"className":12104},[1942,1943,1944,1945],[1807,12106,1852],{"className":12107},[1907,1911,1945],[1807,12109,1963],{"className":12110},[1962],[1807,12112,12114],{"className":12113},[1925],[1807,12115,12117],{"className":12116,"style":2189},[1929],[1807,12118],{}," 必须只包含在 ",[1807,12121,12123,12136],{"className":12122},[1814],[1807,12124,12126],{"className":12125},[1818],[1820,12127,12128],{"xmlns":1822},[1825,12129,12130,12134],{},[1828,12131,12132],{},[1839,12133,1852],{},[1883,12135,1852],{"encoding":1885},[1807,12137,12139],{"className":12138,"ariaHidden":1848},[1890],[1807,12140,12142,12145],{"className":12141},[1894],[1807,12143],{"className":12144,"style":2110},[1898],[1807,12146,1852],{"className":12147},[1907,1911]," 时刻真正可见的数据","，以避免前视偏差；",[4352,12151,12152],{},"交易成本、滑点、成交约束等需要在步骤 2 中明确建模，而不是简单假设“按收盘价全额成交”。",[1792,12154,12155,12156,12187,12188,9922],{},"从概率论的角度，可以将回测视为在一族可行策略集合 ",[1807,12157,12159,12173],{"className":12158},[1814],[1807,12160,12162],{"className":12161},[1818],[1820,12163,12164],{"xmlns":1822},[1825,12165,12166,12170],{},[1828,12167,12168],{},[1839,12169,2340],{"mathvariant":2131},[1883,12171,12172],{"encoding":1885},"\\mathcal{G}",[1807,12174,12176],{"className":12175,"ariaHidden":1848},[1890],[1807,12177,12179,12183],{"className":12178},[1894],[1807,12180],{"className":12181,"style":12182},[1898],"height:0.7805em;vertical-align:-0.0972em;",[1807,12184,2340],{"className":12185,"style":12186},[1907,2154],"margin-right:0.0593em;"," 上选取一个映射 ",[1807,12189,12191,12210],{"className":12190},[1814],[1807,12192,12194],{"className":12193},[1818],[1820,12195,12196],{"xmlns":1822},[1825,12197,12198,12207],{},[1828,12199,12200,12202,12205],{},[1839,12201,2340],{},[1831,12203,12204],{},"∈",[1839,12206,2340],{"mathvariant":2131},[1883,12208,12209],{"encoding":1885},"G\\in\\mathcal{G}",[1807,12211,12213,12232],{"className":12212,"ariaHidden":1848},[1890],[1807,12214,12216,12220,12223,12226,12229],{"className":12215},[1894],[1807,12217],{"className":12218,"style":12219},[1898],"height:0.7224em;vertical-align:-0.0391em;",[1807,12221,2340],{"className":12222},[1907,1911],[1807,12224],{"className":12225,"style":2044},[2043],[1807,12227,12204],{"className":12228},[2011],[1807,12230],{"className":12231,"style":2044},[2043],[1807,12233,12235,12238],{"className":12234},[1894],[1807,12236],{"className":12237,"style":12182},[1898],[1807,12239,2340],{"className":12240,"style":12186},[1907,2154],[1807,12242,12244],{"className":12243},[1810],[1807,12245,12247,12281],{"className":12246},[1814],[1807,12248,12250],{"className":12249},[1818],[1820,12251,12252],{"xmlns":1822,"display":1823},[1825,12253,12254,12278],{},[1828,12255,12256,12262,12264,12266,12268,12274,12276],{},[1836,12257,12258,12260],{},[1839,12259,2333],{},[1839,12261,1852],{},[1831,12263,1865],{},[1839,12265,2340],{},[1831,12267,2282],{"stretchy":1833},[1836,12269,12270,12272],{},[1839,12271,2132],{"mathvariant":2131},[1839,12273,1852],{},[1831,12275,2291],{"stretchy":1833},[1831,12277,1849],{"separator":1848},[1883,12279,12280],{"encoding":1885},"w_t = G(\\mathcal{I}_t),",[1807,12282,12284,12339],{"className":12283,"ariaHidden":1848},[1890],[1807,12285,12287,12290,12330,12333,12336],{"className":12286},[1894],[1807,12288],{"className":12289,"style":2436},[1898],[1807,12291,12293,12296],{"className":12292},[1907],[1807,12294,2333],{"className":12295,"style":2719},[1907,1911],[1807,12297,12299],{"className":12298},[1916],[1807,12300,12302,12322],{"className":12301},[1920,1921],[1807,12303,12305,12319],{"className":12304},[1925],[1807,12306,12308],{"className":12307,"style":1930},[1929],[1807,12309,12310,12313],{"style":2734},[1807,12311],{"className":12312,"style":1938},[1937],[1807,12314,12316],{"className":12315},[1942,1943,1944,1945],[1807,12317,1852],{"className":12318},[1907,1911,1945],[1807,12320,1963],{"className":12321},[1962],[1807,12323,12325],{"className":12324},[1925],[1807,12326,12328],{"className":12327,"style":2189},[1929],[1807,12329],{},[1807,12331],{"className":12332,"style":2044},[2043],[1807,12334,1865],{"className":12335},[2011],[1807,12337],{"className":12338,"style":2044},[2043],[1807,12340,12342,12345,12348,12351,12391,12394],{"className":12341},[1894],[1807,12343],{"className":12344,"style":2057},[1898],[1807,12346,2340],{"className":12347},[1907,1911],[1807,12349,2282],{"className":12350},[1903],[1807,12352,12354,12357],{"className":12353},[1907],[1807,12355,2132],{"className":12356,"style":2155},[1907,2154],[1807,12358,12360],{"className":12359},[1916],[1807,12361,12363,12383],{"className":12362},[1920,1921],[1807,12364,12366,12380],{"className":12365},[1925],[1807,12367,12369],{"className":12368,"style":1930},[1929],[1807,12370,12371,12374],{"style":2170},[1807,12372],{"className":12373,"style":1938},[1937],[1807,12375,12377],{"className":12376},[1942,1943,1944,1945],[1807,12378,1852],{"className":12379},[1907,1911,1945],[1807,12381,1963],{"className":12382},[1962],[1807,12384,12386],{"className":12385},[1925],[1807,12387,12389],{"className":12388,"style":2189},[1929],[1807,12390],{},[1807,12392,2291],{"className":12393},[1976],[1807,12395,1849],{"className":12396},[1955],[1792,12398,12399,12400,12505,12506,12534,12535,12563],{},"并在给定 DGP 的情况下，评估相应的收益过程 ",[1807,12401,12403,12435],{"className":12402},[1814],[1807,12404,12406],{"className":12405},[1818],[1820,12407,12408],{"xmlns":1822},[1825,12409,12410,12432],{},[1828,12411,12412,12414,12430],{},[1831,12413,1834],{"stretchy":1833},[1836,12415,12416,12418],{},[1839,12417,1841],{},[1828,12419,12420,12422,12424,12426,12428],{},[1839,12421,1792],{},[1831,12423,1849],{"separator":1848},[1839,12425,1852],{},[1831,12427,2209],{},[1867,12429,1869],{},[1831,12431,1858],{"stretchy":1833},[1883,12433,12434],{"encoding":1885},"\\{r_{p,t+1}\\}",[1807,12436,12438],{"className":12437,"ariaHidden":1848},[1890],[1807,12439,12441,12444,12447,12502],{"className":12440},[1894],[1807,12442],{"className":12443,"style":4418},[1898],[1807,12445,1834],{"className":12446},[1903],[1807,12448,12450,12453],{"className":12449},[1907],[1807,12451,1841],{"className":12452,"style":1912},[1907,1911],[1807,12454,12456],{"className":12455},[1916],[1807,12457,12459,12494],{"className":12458},[1920,1921],[1807,12460,12462,12491],{"className":12461},[1925],[1807,12463,12465],{"className":12464,"style":3009},[1929],[1807,12466,12467,12470],{"style":1933},[1807,12468],{"className":12469,"style":1938},[1937],[1807,12471,12473],{"className":12472},[1942,1943,1944,1945],[1807,12474,12476,12479,12482,12485,12488],{"className":12475},[1907,1945],[1807,12477,1792],{"className":12478},[1907,1911,1945],[1807,12480,1849],{"className":12481},[1955,1945],[1807,12483,1852],{"className":12484},[1907,1911,1945],[1807,12486,2209],{"className":12487},[2235,1945],[1807,12489,1869],{"className":12490},[1907,1945],[1807,12492,1963],{"className":12493},[1962],[1807,12495,12497],{"className":12496},[1925],[1807,12498,12500],{"className":12499,"style":1970},[1929],[1807,12501],{},[1807,12503,1858],{"className":12504},[1976]," 的性质。不同的策略类（线性策略、阈值策略、机器学习策略等）对应不同的函数空间 ",[1807,12507,12509,12522],{"className":12508},[1814],[1807,12510,12512],{"className":12511},[1818],[1820,12513,12514],{"xmlns":1822},[1825,12515,12516,12520],{},[1828,12517,12518],{},[1839,12519,2340],{"mathvariant":2131},[1883,12521,12172],{"encoding":1885},[1807,12523,12525],{"className":12524,"ariaHidden":1848},[1890],[1807,12526,12528,12531],{"className":12527},[1894],[1807,12529],{"className":12530,"style":12182},[1898],[1807,12532,2340],{"className":12533,"style":12186},[1907,2154],"，回测的本质是对“在过去样本中表现较好”的那些 ",[1807,12536,12538,12551],{"className":12537},[1814],[1807,12539,12541],{"className":12540},[1818],[1820,12542,12543],{"xmlns":1822},[1825,12544,12545,12549],{},[1828,12546,12547],{},[1839,12548,2340],{},[1883,12550,2340],{"encoding":1885},[1807,12552,12554],{"className":12553,"ariaHidden":1848},[1890],[1807,12555,12557,12560],{"className":12556},[1894],[1807,12558],{"className":12559,"style":3587},[1898],[1807,12561,2340],{"className":12562},[1907,1911]," 进行筛选和诊断。",[2078,12565,12567],{"id":12566},"_4-绩效指标的数学定义","4. 绩效指标的数学定义",[1792,12569,12570,12571,12739],{},"回测产出的主要对象是策略收益率时间序列 ",[1807,12572,12574,12614],{"className":12573},[1814],[1807,12575,12577],{"className":12576},[1818],[1820,12578,12579],{"xmlns":1822},[1825,12580,12581,12611],{},[1828,12582,12583,12585,12597],{},[1831,12584,1834],{"stretchy":1833},[1836,12586,12587,12589],{},[1839,12588,1841],{},[1828,12590,12591,12593,12595],{},[1839,12592,1792],{},[1831,12594,1849],{"separator":1848},[1839,12596,1852],{},[1854,12598,12599,12601,12609],{},[1831,12600,1858],{"stretchy":1833},[1828,12602,12603,12605,12607],{},[1839,12604,1852],{},[1831,12606,1865],{},[1867,12608,1869],{},[1839,12610,1872],{},[1883,12612,12613],{"encoding":1885},"\\{r_{p,t}\\}_{t=1}^T",[1807,12615,12617],{"className":12616,"ariaHidden":1848},[1890],[1807,12618,12620,12624,12627,12676],{"className":12619},[1894],[1807,12621],{"className":12622,"style":12623},[1898],"height:1.1274em;vertical-align:-0.2861em;",[1807,12625,1834],{"className":12626},[1903],[1807,12628,12630,12633],{"className":12629},[1907],[1807,12631,1841],{"className":12632,"style":1912},[1907,1911],[1807,12634,12636],{"className":12635},[1916],[1807,12637,12639,12668],{"className":12638},[1920,1921],[1807,12640,12642,12665],{"className":12641},[1925],[1807,12643,12645],{"className":12644,"style":1930},[1929],[1807,12646,12647,12650],{"style":1933},[1807,12648],{"className":12649,"style":1938},[1937],[1807,12651,12653],{"className":12652},[1942,1943,1944,1945],[1807,12654,12656,12659,12662],{"className":12655},[1907,1945],[1807,12657,1792],{"className":12658},[1907,1911,1945],[1807,12660,1849],{"className":12661},[1955,1945],[1807,12663,1852],{"className":12664},[1907,1911,1945],[1807,12666,1963],{"className":12667},[1962],[1807,12669,12671],{"className":12670},[1925],[1807,12672,12674],{"className":12673,"style":1970},[1929],[1807,12675],{},[1807,12677,12679,12682],{"className":12678},[1976],[1807,12680,1858],{"className":12681},[1976],[1807,12683,12685],{"className":12684},[1916],[1807,12686,12688,12730],{"className":12687},[1920,1921],[1807,12689,12691,12727],{"className":12690},[1925],[1807,12692,12695,12716],{"className":12693,"style":12694},[1929],"height:0.8413em;",[1807,12696,12698,12701],{"style":12697},"top:-2.4519em;margin-left:0em;margin-right:0.05em;",[1807,12699],{"className":12700,"style":1938},[1937],[1807,12702,12704],{"className":12703},[1942,1943,1944,1945],[1807,12705,12707,12710,12713],{"className":12706},[1907,1945],[1807,12708,1852],{"className":12709},[1907,1911,1945],[1807,12711,1865],{"className":12712},[2011,1945],[1807,12714,1869],{"className":12715},[1907,1945],[1807,12717,12718,12721],{"style":5577},[1807,12719],{"className":12720,"style":1938},[1937],[1807,12722,12724],{"className":12723},[1942,1943,1944,1945],[1807,12725,1872],{"className":12726,"style":2027},[1907,1911,1945],[1807,12728,1963],{"className":12729},[1962],[1807,12731,12733],{"className":12732},[1925],[1807,12734,12737],{"className":12735,"style":12736},[1929],"height:0.2481em;",[1807,12738],{},"，在此基础上我们定义若干常见绩效指标。",[12741,12742,12744],"h3",{"id":12743},"_41-年化收益率与波动率","4.1 年化收益率与波动率",[1792,12746,12747,12748,12833,12834,12914],{},"设日度收益率为 ",[1807,12749,12751,12775],{"className":12750},[1814],[1807,12752,12754],{"className":12753},[1818],[1820,12755,12756],{"xmlns":1822},[1825,12757,12758,12772],{},[1828,12759,12760],{},[1836,12761,12762,12764],{},[1839,12763,1841],{},[1828,12765,12766,12768,12770],{},[1839,12767,1792],{},[1831,12769,1849],{"separator":1848},[1839,12771,1852],{},[1883,12773,12774],{"encoding":1885},"r_{p,t}",[1807,12776,12778],{"className":12777,"ariaHidden":1848},[1890],[1807,12779,12781,12784],{"className":12780},[1894],[1807,12782],{"className":12783,"style":4728},[1898],[1807,12785,12787,12790],{"className":12786},[1907],[1807,12788,1841],{"className":12789,"style":1912},[1907,1911],[1807,12791,12793],{"className":12792},[1916],[1807,12794,12796,12825],{"className":12795},[1920,1921],[1807,12797,12799,12822],{"className":12798},[1925],[1807,12800,12802],{"className":12801,"style":1930},[1929],[1807,12803,12804,12807],{"style":1933},[1807,12805],{"className":12806,"style":1938},[1937],[1807,12808,12810],{"className":12809},[1942,1943,1944,1945],[1807,12811,12813,12816,12819],{"className":12812},[1907,1945],[1807,12814,1792],{"className":12815},[1907,1911,1945],[1807,12817,1849],{"className":12818},[1955,1945],[1807,12820,1852],{"className":12821},[1907,1911,1945],[1807,12823,1963],{"className":12824},[1962],[1807,12826,12828],{"className":12827},[1925],[1807,12829,12831],{"className":12830,"style":1970},[1929],[1807,12832],{},"，",[1807,12835,12837,12863],{"className":12836},[1814],[1807,12838,12840],{"className":12839},[1818],[1820,12841,12842],{"xmlns":1822},[1825,12843,12844,12860],{},[1828,12845,12846,12848,12850,12852,12854,12856,12858],{},[1839,12847,1852],{},[1831,12849,1865],{},[1867,12851,1869],{},[1831,12853,1849],{"separator":1848},[1831,12855,5344],{},[1831,12857,1849],{"separator":1848},[1839,12859,1872],{},[1883,12861,12862],{"encoding":1885},"t=1,\\dots,T",[1807,12864,12866,12884],{"className":12865,"ariaHidden":1848},[1890],[1807,12867,12869,12872,12875,12878,12881],{"className":12868},[1894],[1807,12870],{"className":12871,"style":2110},[1898],[1807,12873,1852],{"className":12874},[1907,1911],[1807,12876],{"className":12877,"style":2044},[2043],[1807,12879,1865],{"className":12880},[2011],[1807,12882],{"className":12883,"style":2044},[2043],[1807,12885,12887,12890,12893,12896,12899,12902,12905,12908,12911],{"className":12886},[1894],[1807,12888],{"className":12889,"style":11186},[1898],[1807,12891,1869],{"className":12892},[1907],[1807,12894,1849],{"className":12895},[1955],[1807,12897],{"className":12898,"style":2553},[2043],[1807,12900,5344],{"className":12901},[5495],[1807,12903],{"className":12904,"style":2553},[2043],[1807,12906,1849],{"className":12907},[1955],[1807,12909],{"className":12910,"style":2553},[2043],[1807,12912,1872],{"className":12913,"style":2027},[1907,1911],"。定义累计收益：",[1807,12916,12918],{"className":12917},[1810],[1807,12919,12921,12983],{"className":12920},[1814],[1807,12922,12924],{"className":12923},[1818],[1820,12925,12926],{"xmlns":1822,"display":1823},[1825,12927,12928,12980],{},[1828,12929,12930,12938,12940,12955,12957,12959,12961,12973,12975,12977],{},[1836,12931,12932,12935],{},[1839,12933,12934],{},"R",[1877,12936,12937],{},"tot",[1831,12939,1865],{},[8523,12941,12942,12945,12953],{},[1831,12943,12944],{},"∏",[1828,12946,12947,12949,12951],{},[1839,12948,1852],{},[1831,12950,1865],{},[1867,12952,1869],{},[1839,12954,1872],{},[1831,12956,2282],{"stretchy":1833},[1867,12958,1869],{},[1831,12960,2209],{},[1836,12962,12963,12965],{},[1839,12964,1841],{},[1828,12966,12967,12969,12971],{},[1839,12968,1792],{},[1831,12970,1849],{"separator":1848},[1839,12972,1852],{},[1831,12974,2291],{"stretchy":1833},[1831,12976,3649],{},[1867,12978,12979],{},"1.",[1883,12981,12982],{"encoding":1885}," R_{\\text{tot}} = \\prod_{t=1}^T (1 + r_{p,t}) - 1.",[1807,12984,12986,13049,13134,13201],{"className":12985,"ariaHidden":1848},[1890],[1807,12987,12989,12992,13040,13043,13046],{"className":12988},[1894],[1807,12990],{"className":12991,"style":2147},[1898],[1807,12993,12995,12999],{"className":12994},[1907],[1807,12996,12934],{"className":12997,"style":12998},[1907,1911],"margin-right:0.0077em;",[1807,13000,13002],{"className":13001},[1916],[1807,13003,13005,13032],{"className":13004},[1920,1921],[1807,13006,13008,13029],{"className":13007},[1925],[1807,13009,13011],{"className":13010,"style":1930},[1929],[1807,13012,13014,13017],{"style":13013},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[1807,13015],{"className":13016,"style":1938},[1937],[1807,13018,13020],{"className":13019},[1942,1943,1944,1945],[1807,13021,13023],{"className":13022},[1907,1945],[1807,13024,13026],{"className":13025},[1907,2061,1945],[1807,13027,12937],{"className":13028},[1907,1945],[1807,13030,1963],{"className":13031},[1962],[1807,13033,13035],{"className":13034},[1925],[1807,13036,13038],{"className":13037,"style":2189},[1929],[1807,13039],{},[1807,13041],{"className":13042,"style":2044},[2043],[1807,13044,1865],{"className":13045},[2011],[1807,13047],{"className":13048,"style":2044},[2043],[1807,13050,13052,13055,13119,13122,13125,13128,13131],{"className":13051},[1894],[1807,13053],{"className":13054,"style":9578},[1898],[1807,13056,13058],{"className":13057},[3687,3688],[1807,13059,13061,13111],{"className":13060},[1920,1921],[1807,13062,13064,13108],{"className":13063},[1925],[1807,13065,13067,13087,13097],{"className":13066,"style":8747},[1929],[1807,13068,13069,13072],{"style":9659},[1807,13070],{"className":13071,"style":8754},[1937],[1807,13073,13075],{"className":13074},[1942,1943,1944,1945],[1807,13076,13078,13081,13084],{"className":13077},[1907,1945],[1807,13079,1852],{"className":13080},[1907,1911,1945],[1807,13082,1865],{"className":13083},[2011,1945],[1807,13085,1869],{"className":13086},[1907,1945],[1807,13088,13089,13092],{"style":8773},[1807,13090],{"className":13091,"style":8754},[1937],[1807,13093,13094],{},[1807,13095,12944],{"className":13096},[3687,5655,8782],[1807,13098,13099,13102],{"style":8785},[1807,13100],{"className":13101,"style":8754},[1937],[1807,13103,13105],{"className":13104},[1942,1943,1944,1945],[1807,13106,1872],{"className":13107,"style":2027},[1907,1911,1945],[1807,13109,1963],{"className":13110},[1962],[1807,13112,13114],{"className":13113},[1925],[1807,13115,13117],{"className":13116,"style":9708},[1929],[1807,13118],{},[1807,13120,2282],{"className":13121},[1903],[1807,13123,1869],{"className":13124},[1907],[1807,13126],{"className":13127,"style":2231},[2043],[1807,13129,2209],{"className":13130},[2235],[1807,13132],{"className":13133,"style":2231},[2043],[1807,13135,13137,13140,13189,13192,13195,13198],{"className":13136},[1894],[1807,13138],{"className":13139,"style":4418},[1898],[1807,13141,13143,13146],{"className":13142},[1907],[1807,13144,1841],{"className":13145,"style":1912},[1907,1911],[1807,13147,13149],{"className":13148},[1916],[1807,13150,13152,13181],{"className":13151},[1920,1921],[1807,13153,13155,13178],{"className":13154},[1925],[1807,13156,13158],{"className":13157,"style":1930},[1929],[1807,13159,13160,13163],{"style":1933},[1807,13161],{"className":13162,"style":1938},[1937],[1807,13164,13166],{"className":13165},[1942,1943,1944,1945],[1807,13167,13169,13172,13175],{"className":13168},[1907,1945],[1807,13170,1792],{"className":13171},[1907,1911,1945],[1807,13173,1849],{"className":13174},[1955,1945],[1807,13176,1852],{"className":13177},[1907,1911,1945],[1807,13179,1963],{"className":13180},[1962],[1807,13182,13184],{"className":13183},[1925],[1807,13185,13187],{"className":13186,"style":1970},[1929],[1807,13188],{},[1807,13190,2291],{"className":13191},[1976],[1807,13193],{"className":13194,"style":2231},[2043],[1807,13196,3649],{"className":13197},[2235],[1807,13199],{"className":13200,"style":2231},[2043],[1807,13202,13204,13207],{"className":13203},[1894],[1807,13205],{"className":13206,"style":2245},[1898],[1807,13208,12979],{"className":13209},[1907],[1792,13211,13212,13213,13241,13242,13294,13295,13298],{},"若一年有 ",[1807,13214,13216,13229],{"className":13215},[1814],[1807,13217,13219],{"className":13218},[1818],[1820,13220,13221],{"xmlns":1822},[1825,13222,13223,13227],{},[1828,13224,13225],{},[1839,13226,5355],{},[1883,13228,5355],{"encoding":1885},[1807,13230,13232],{"className":13231,"ariaHidden":1848},[1890],[1807,13233,13235,13238],{"className":13234},[1894],[1807,13236],{"className":13237,"style":3587},[1898],[1807,13239,5355],{"className":13240,"style":5538},[1907,1911]," 个交易日（例如 ",[1807,13243,13245,13264],{"className":13244},[1814],[1807,13246,13248],{"className":13247},[1818],[1820,13249,13250],{"xmlns":1822},[1825,13251,13252,13261],{},[1828,13253,13254,13256,13258],{},[1839,13255,5355],{},[1831,13257,1865],{},[1867,13259,13260],{},"252",[1883,13262,13263],{"encoding":1885},"N=252",[1807,13265,13267,13285],{"className":13266,"ariaHidden":1848},[1890],[1807,13268,13270,13273,13276,13279,13282],{"className":13269},[1894],[1807,13271],{"className":13272,"style":3587},[1898],[1807,13274,5355],{"className":13275,"style":5538},[1907,1911],[1807,13277],{"className":13278,"style":2044},[2043],[1807,13280,1865],{"className":13281},[2011],[1807,13283],{"className":13284,"style":2044},[2043],[1807,13286,13288,13291],{"className":13287},[1894],[1807,13289],{"className":13290,"style":2245},[1898],[1807,13292,13260],{"className":13293},[1907],"），则",[6070,13296,13297],{},"年化收益率","常定义为：",[1807,13300,13302],{"className":13301},[1810],[1807,13303,13305,13355],{"className":13304},[1814],[1807,13306,13308],{"className":13307},[1818],[1820,13309,13310],{"xmlns":1822,"display":1823},[1825,13311,13312,13352],{},[1828,13313,13314,13321,13323,13325,13327,13329,13335,13348,13350],{},[1836,13315,13316,13318],{},[1839,13317,12934],{},[1877,13319,13320],{},"ann",[1831,13322,1865],{},[1831,13324,2282],{"stretchy":1833},[1867,13326,1869],{},[1831,13328,2209],{},[1836,13330,13331,13333],{},[1839,13332,12934],{},[1877,13334,12937],{},[3639,13336,13337,13339],{},[1831,13338,2291],{"stretchy":1833},[1828,13340,13341,13343,13346],{},[1839,13342,5355],{},[1839,13344,13345],{"mathvariant":2361},"\u002F",[1839,13347,1872],{},[1831,13349,3649],{},[1867,13351,12979],{},[1883,13353,13354],{"encoding":1885}," R_{\\text{ann}} = (1 + R_{\\text{tot}})^{N\u002FT} - 1.",[1807,13356,13358,13419,13440,13541],{"className":13357,"ariaHidden":1848},[1890],[1807,13359,13361,13364,13410,13413,13416],{"className":13360},[1894],[1807,13362],{"className":13363,"style":2147},[1898],[1807,13365,13367,13370],{"className":13366},[1907],[1807,13368,12934],{"className":13369,"style":12998},[1907,1911],[1807,13371,13373],{"className":13372},[1916],[1807,13374,13376,13402],{"className":13375},[1920,1921],[1807,13377,13379,13399],{"className":13378},[1925],[1807,13380,13382],{"className":13381,"style":7919},[1929],[1807,13383,13384,13387],{"style":13013},[1807,13385],{"className":13386,"style":1938},[1937],[1807,13388,13390],{"className":13389},[1942,1943,1944,1945],[1807,13391,13393],{"className":13392},[1907,1945],[1807,13394,13396],{"className":13395},[1907,2061,1945],[1807,13397,13320],{"className":13398},[1907,1945],[1807,13400,1963],{"className":13401},[1962],[1807,13403,13405],{"className":13404},[1925],[1807,13406,13408],{"className":13407,"style":2189},[1929],[1807,13409],{},[1807,13411],{"className":13412,"style":2044},[2043],[1807,13414,1865],{"className":13415},[2011],[1807,13417],{"className":13418,"style":2044},[2043],[1807,13420,13422,13425,13428,13431,13434,13437],{"className":13421},[1894],[1807,13423],{"className":13424,"style":2057},[1898],[1807,13426,2282],{"className":13427},[1903],[1807,13429,1869],{"className":13430},[1907],[1807,13432],{"className":13433,"style":2231},[2043],[1807,13435,2209],{"className":13436},[2235],[1807,13438],{"className":13439,"style":2231},[2043],[1807,13441,13443,13447,13493,13532,13535,13538],{"className":13442},[1894],[1807,13444],{"className":13445,"style":13446},[1898],"height:1.188em;vertical-align:-0.25em;",[1807,13448,13450,13453],{"className":13449},[1907],[1807,13451,12934],{"className":13452,"style":12998},[1907,1911],[1807,13454,13456],{"className":13455},[1916],[1807,13457,13459,13485],{"className":13458},[1920,1921],[1807,13460,13462,13482],{"className":13461},[1925],[1807,13463,13465],{"className":13464,"style":1930},[1929],[1807,13466,13467,13470],{"style":13013},[1807,13468],{"className":13469,"style":1938},[1937],[1807,13471,13473],{"className":13472},[1942,1943,1944,1945],[1807,13474,13476],{"className":13475},[1907,1945],[1807,13477,13479],{"className":13478},[1907,2061,1945],[1807,13480,12937],{"className":13481},[1907,1945],[1807,13483,1963],{"className":13484},[1962],[1807,13486,13488],{"className":13487},[1925],[1807,13489,13491],{"className":13490,"style":2189},[1929],[1807,13492],{},[1807,13494,13496,13499],{"className":13495},[1976],[1807,13497,2291],{"className":13498},[1976],[1807,13500,13502],{"className":13501},[1916],[1807,13503,13505],{"className":13504},[1920],[1807,13506,13508],{"className":13507},[1925],[1807,13509,13512],{"className":13510,"style":13511},[1929],"height:0.938em;",[1807,13513,13514,13517],{"style":2017},[1807,13515],{"className":13516,"style":1938},[1937],[1807,13518,13520],{"className":13519},[1942,1943,1944,1945],[1807,13521,13523,13526,13529],{"className":13522},[1907,1945],[1807,13524,5355],{"className":13525,"style":5538},[1907,1911,1945],[1807,13527,13345],{"className":13528},[1907,1945],[1807,13530,1872],{"className":13531,"style":2027},[1907,1911,1945],[1807,13533],{"className":13534,"style":2231},[2043],[1807,13536,3649],{"className":13537},[2235],[1807,13539],{"className":13540,"style":2231},[2043],[1807,13542,13544,13547],{"className":13543},[1894],[1807,13545],{"className":13546,"style":2245},[1898],[1807,13548,12979],{"className":13549},[1907],[1792,13551,13552],{},"样本平均收益率为",[1807,13554,13556],{"className":13555},[1810],[1807,13557,13559,13613],{"className":13558},[1814],[1807,13560,13562],{"className":13561},[1818],[1820,13563,13564],{"xmlns":1822,"display":1823},[1825,13565,13566,13610],{},[1828,13567,13568,13574,13576,13582,13596,13608],{},[2300,13569,13570,13572],{"accent":1848},[1839,13571,1841],{},[1831,13573,9443],{},[1831,13575,1865],{},[3651,13577,13578,13580],{},[1867,13579,1869],{},[1839,13581,1872],{},[8523,13583,13584,13586,13594],{},[1831,13585,5609],{},[1828,13587,13588,13590,13592],{},[1839,13589,1852],{},[1831,13591,1865],{},[1867,13593,1869],{},[1839,13595,1872],{},[1836,13597,13598,13600],{},[1839,13599,1841],{},[1828,13601,13602,13604,13606],{},[1839,13603,1792],{},[1831,13605,1849],{"separator":1848},[1839,13607,1852],{},[1831,13609,1849],{"separator":1848},[1883,13611,13612],{"encoding":1885}," \\bar{r} = \\frac{1}{T} \\sum_{t=1}^T 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s = \\sqrt{\\frac{1}{T-1} \\sum_{t=1}^T (r_{p,t} - \\bar{r})^2}.",[1807,13941,13943,13961],{"className":13942,"ariaHidden":1848},[1890],[1807,13944,13946,13949,13952,13955,13958],{"className":13945},[1894],[1807,13947],{"className":13948,"style":3698},[1898],[1807,13950,2272],{"className":13951},[1907,1911],[1807,13953],{"className":13954,"style":2044},[2043],[1807,13956,1865],{"className":13957},[2011],[1807,13959],{"className":13960,"style":2044},[2043],[1807,13962,13964,13968,14294],{"className":13963},[1894],[1807,13965],{"className":13966,"style":13967},[1898],"height:3.3232em;vertical-align:-1.2671em;",[1807,13969,13972],{"className":13970},[1907,13971],"sqrt",[1807,13973,13975,14286],{"className":13974},[1920,1921],[1807,13976,13978,14283],{"className":13977},[1925],[1807,13979,13982,14260],{"className":13980,"style":13981},[1929],"height:2.0561em;",[1807,13983,13987,13991],{"className":13984,"style":13986},[13985],"svg-align","top:-5.2832em;",[1807,13988],{"className":13989,"style":13990},[1937],"height:5.2832em;",[1807,13992,13995,14070,14073,14137,14140,14189,14192,14195,14198,14229],{"className":13993,"style":13994},[1907],"padding-left:1.056em;",[1807,13996,13998,14001,14067],{"className":13997},[1907],[1807,13999],{"className":14000},[1903,3793],[1807,14002,14004],{"className":14003},[3651],[1807,14005,14007,14058],{"className":14006},[1920,1921],[1807,14008,14010,14055],{"className":14009},[1925],[1807,14011,14013,14036,14044],{"className":14012,"style":9597},[1929],[1807,14014,14015,14018],{"style":3809},[1807,14016],{"className":14017,"style":2577},[1937],[1807,14019,14021,14024,14027,14030,14033],{"className":14020},[1907],[1807,14022,1872],{"className":14023,"style":2027},[1907,1911],[1807,14025],{"className":14026,"style":2231},[2043],[1807,14028,3649],{"className":14029},[2235],[1807,14031],{"className":14032,"style":2231},[2043],[1807,14034,1869],{"className":14035},[1907],[1807,14037,14038,14041],{"style":3821},[1807,14039],{"className":14040,"style":2577},[1937],[1807,14042],{"className":14043,"style":3829},[3828],[1807,14045,14046,14049],{"style":3832},[1807,14047],{"className":14048,"style":2577},[1937],[1807,14050,14052],{"className":14051},[1907],[1807,14053,1869],{"className":14054},[1907],[1807,14056,1963],{"className":14057},[1962],[1807,14059,14061],{"className":14060},[1925],[1807,14062,14065],{"className":14063,"style":14064},[1929],"height:0.7693em;",[1807,14066],{},[1807,14068],{"className":14069},[1976,3793],[1807,14071],{"className":14072,"style":2553},[2043],[1807,14074,14076],{"className":14075},[3687,3688],[1807,14077,14079,14129],{"className":14078},[1920,1921],[1807,14080,14082,14126],{"className":14081},[1925],[1807,14083,14085,14105,14115],{"className":14084,"style":8747},[1929],[1807,14086,14087,14090],{"style":9659},[1807,14088],{"className":14089,"style":8754},[1937],[1807,14091,14093],{"className":14092},[1942,1943,1944,1945],[1807,14094,14096,14099,14102],{"className":14095},[1907,1945],[1807,14097,1852],{"className":14098},[1907,1911,1945],[1807,14100,1865],{"className":14101},[2011,1945],[1807,14103,1869],{"className":14104},[1907,1945],[1807,14106,14107,14110],{"style":8773},[1807,14108],{"className":14109,"style":8754},[1937],[1807,14111,14112],{},[1807,14113,5609],{"className":14114},[3687,5655,8782],[1807,14116,14117,14120],{"style":8785},[1807,14118],{"className":14119,"style":8754},[1937],[1807,14121,14123],{"className":14122},[1942,1943,1944,1945],[1807,14124,1872],{"className":14125,"style":2027},[1907,1911,1945],[1807,14127,1963],{"className":14128},[1962],[1807,14130,14132],{"className":14131},[1925],[1807,14133,14135],{"className":14134,"style":9708},[1929],[1807,14136],{},[1807,14138,2282],{"className":14139},[1903],[1807,14141,14143,14146],{"className":14142},[1907],[1807,14144,1841],{"className":14145,"style":1912},[1907,1911],[1807,14147,14149],{"className":14148},[1916],[1807,14150,14152,14181],{"className":14151},[1920,1921],[1807,14153,14155,14178],{"className":14154},[1925],[1807,14156,14158],{"className":14157,"style":1930},[1929],[1807,14159,14160,14163],{"style":1933},[1807,14161],{"className":14162,"style":1938},[1937],[1807,14164,14166],{"className":14165},[1942,1943,1944,1945],[1807,14167,14169,14172,14175],{"className":14168},[1907,1945],[1807,14170,1792],{"className":14171},[1907,1911,1945],[1807,14173,1849],{"className":14174},[1955,1945],[1807,14176,1852],{"className":14177},[1907,1911,1945],[1807,14179,1963],{"className":14180},[1962],[1807,14182,14184],{"className":14183},[1925],[1807,14185,14187],{"className":14186,"style":1970},[1929],[1807,14188],{},[1807,14190],{"className":14191,"style":2231},[2043],[1807,14193,3649],{"className":14194},[2235],[1807,14196],{"className":14197,"style":2231},[2043],[1807,14199,14201],{"className":14200},[1907,2560],[1807,14202,14204],{"className":14203},[1920],[1807,14205,14207],{"className":14206},[1925],[1807,14208,14210,14218],{"className":14209,"style":13622},[1929],[1807,14211,14212,14215],{"style":2573},[1807,14213],{"className":14214,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0 400000 3363","xMinYMin slice",[14280,14281],"path",{"d":14282},"M702 80H40000040\nH742v3229l-4 4-4 4c-.667.7 -2 1.5-4 2.5s-4.167 1.833-6.5 2.5-5.5 1-9.5 1\nh-12l-28-84c-16.667-52-96.667 -294.333-240-727l-212 -643 -85 170\nc-4-3.333-8.333-7.667-13 -13l-13-13l77-155 77-156c66 199.333 139 419.667\n219 661 l218 661zM702 80H400000v40H742z",[1807,14284,1963],{"className":14285},[1962],[1807,14287,14289],{"className":14288},[1925],[1807,14290,14292],{"className":14291,"style":9708},[1929],[1807,14293],{},[1807,14295,2423],{"className":14296},[1907],[1792,14298,14299,14300,14303],{},"则",[6070,14301,14302],{},"年化波动率","为：",[1807,14305,14307],{"className":14306},[1810],[1807,14308,14310,14339],{"className":14309},[1814],[1807,14311,14313],{"className":14312},[1818],[1820,14314,14315],{"xmlns":1822,"display":1823},[1825,14316,14317,14336],{},[1828,14318,14319,14326,14328,14330,14334],{},[1836,14320,14321,14324],{},[1839,14322,14323],{},"σ",[1877,14325,13320],{},[1831,14327,1865],{},[1839,14329,2272],{},[13877,14331,14332],{},[1839,14333,5355],{},[1839,14335,2423],{"mathvariant":2361},[1883,14337,14338],{"encoding":1885}," \\sigma_{\\text{ann}} = s \\sqrt{N}.",[1807,14340,14342,14404],{"className":14341,"ariaHidden":1848},[1890],[1807,14343,14345,14348,14395,14398,14401],{"className":14344},[1894],[1807,14346],{"className":14347,"style":2436},[1898],[1807,14349,14351,14354],{"className":14350},[1907],[1807,14352,14323],{"className":14353,"style":6803},[1907,1911],[1807,14355,14357],{"className":14356},[1916],[1807,14358,14360,14387],{"className":14359},[1920,1921],[1807,14361,14363,14384],{"className":14362},[1925],[1807,14364,14366],{"className":14365,"style":7919},[1929],[1807,14367,14369,14372],{"style":14368},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1807,14370],{"className":14371,"style":1938},[1937],[1807,14373,14375],{"className":14374},[1942,1943,1944,1945],[1807,14376,14378],{"className":14377},[1907,1945],[1807,14379,14381],{"className":14380},[1907,2061,1945],[1807,14382,13320],{"className":14383},[1907,1945],[1807,14385,1963],{"className":14386},[1962],[1807,14388,14390],{"className":14389},[1925],[1807,14391,14393],{"className":14392,"style":2189},[1929],[1807,14394],{},[1807,14396],{"className":14397,"style":2044},[2043],[1807,14399,1865],{"className":14400},[2011],[1807,14402],{"className":14403,"style":2044},[2043],[1807,14405,14407,14411,14414,14469],{"className":14406},[1894],[1807,14408],{"className":14409,"style":14410},[1898],"height:1.04em;vertical-align:-0.0645em;",[1807,14412,2272],{"className":14413},[1907,1911],[1807,14415,14417],{"className":14416},[1907,13971],[1807,14418,14420,14460],{"className":14419},[1920,1921],[1807,14421,14423,14457],{"className":14422},[1925],[1807,14424,14427,14440],{"className":14425,"style":14426},[1929],"height:0.9755em;",[1807,14428,14430,14433],{"className":14429,"style":2573},[13985],[1807,14431],{"className":14432,"style":2577},[1937],[1807,14434,14437],{"className":14435,"style":14436},[1907],"padding-left:0.833em;",[1807,14438,5355],{"className":14439,"style":5538},[1907,1911],[1807,14441,14443,14446],{"style":14442},"top:-2.9355em;",[1807,14444],{"className":14445,"style":2577},[1937],[1807,14447,14450],{"className":14448,"style":14449},[14269],"min-width:0.853em;height:1.08em;",[14272,14451,14454],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},"1.08em","0 0 400000 1080",[14280,14455],{"d":14456},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[1807,14458,1963],{"className":14459},[1962],[1807,14461,14463],{"className":14462},[1925],[1807,14464,14467],{"className":14465,"style":14466},[1929],"height:0.0645em;",[1807,14468],{},[1807,14470,2423],{"className":14471},[1907],[1792,14473,14474,14475,14554],{},"以上假设收益近似独立同分布。在实际策略中，收益往往存在自相关，此时简单的 ",[1807,14476,14478,14494],{"className":14477},[1814],[1807,14479,14481],{"className":14480},[1818],[1820,14482,14483],{"xmlns":1822},[1825,14484,14485,14491],{},[1828,14486,14487],{},[13877,14488,14489],{},[1839,14490,5355],{},[1883,14492,14493],{"encoding":1885},"\\sqrt{N}",[1807,14495,14497],{"className":14496,"ariaHidden":1848},[1890],[1807,14498,14500,14504],{"className":14499},[1894],[1807,14501],{"className":14502,"style":14503},[1898],"height:1.04em;vertical-align:-0.1133em;",[1807,14505,14507],{"className":14506},[1907,13971],[1807,14508,14510,14545],{"className":14509},[1920,1921],[1807,14511,14513,14542],{"className":14512},[1925],[1807,14514,14517,14529],{"className":14515,"style":14516},[1929],"height:0.9267em;",[1807,14518,14520,14523],{"className":14519,"style":2573},[13985],[1807,14521],{"className":14522,"style":2577},[1937],[1807,14524,14526],{"className":14525,"style":14436},[1907],[1807,14527,5355],{"className":14528,"style":5538},[1907,1911],[1807,14530,14532,14535],{"style":14531},"top:-2.8867em;",[1807,14533],{"className":14534,"style":2577},[1937],[1807,14536,14538],{"className":14537,"style":14449},[14269],[14272,14539,14540],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},[14280,14541],{"d":14456},[1807,14543,1963],{"className":14544},[1962],[1807,14546,14548],{"className":14547},[1925],[1807,14549,14552],{"className":14550,"style":14551},[1929],"height:0.1133em;",[1807,14553],{}," 放大可能低估风险，需要更复杂的建模（例如 HAC 协方差估计）。",[1792,14556,14557,14558,14629],{},"若考虑收益的一阶自相关 ",[1807,14559,14561,14580],{"className":14560},[1814],[1807,14562,14564],{"className":14563},[1818],[1820,14565,14566],{"xmlns":1822},[1825,14567,14568,14577],{},[1828,14569,14570],{},[1836,14571,14572,14575],{},[1839,14573,14574],{},"ρ",[1867,14576,1869],{},[1883,14578,14579],{"encoding":1885},"\\rho_1",[1807,14581,14583],{"className":14582,"ariaHidden":1848},[1890],[1807,14584,14586,14589],{"className":14585},[1894],[1807,14587],{"className":14588,"style":3925},[1898],[1807,14590,14592,14595],{"className":14591},[1907],[1807,14593,14574],{"className":14594},[1907,1911],[1807,14596,14598],{"className":14597},[1916],[1807,14599,14601,14621],{"className":14600},[1920,1921],[1807,14602,14604,14618],{"className":14603},[1925],[1807,14605,14607],{"className":14606,"style":3009},[1929],[1807,14608,14609,14612],{"style":2457},[1807,14610],{"className":14611,"style":1938},[1937],[1807,14613,14615],{"className":14614},[1942,1943,1944,1945],[1807,14616,1869],{"className":14617},[1907,1945],[1807,14619,1963],{"className":14620},[1962],[1807,14622,14624],{"className":14623},[1925],[1807,14625,14627],{"className":14626,"style":2189},[1929],[1807,14628],{},"，简单的年化波动率调整可以写作：",[1807,14631,14633],{"className":14632},[1810],[1807,14634,14636,14699],{"className":14635},[1814],[1807,14637,14639],{"className":14638},[1818],[1820,14640,14641],{"xmlns":1822,"display":1823},[1825,14642,14643,14696],{},[1828,14644,14645,14652,14655,14657,14661,14664,14694],{},[1836,14646,14647,14649],{},[1839,14648,14323],{},[1877,14650,14651],{},"ann, adj",[1831,14653,14654],{},"≈",[1839,14656,2272],{},[13877,14658,14659],{},[1839,14660,5355],{},[1831,14662,14663],{},"×",[13877,14665,14666],{},[1828,14667,14668,14670,14672,14674,14688],{},[1867,14669,1869],{},[1831,14671,2209],{},[1867,14673,3658],{},[8523,14675,14676,14678,14686],{},[1831,14677,5609],{},[1828,14679,14680,14682,14684],{},[1839,14681,8531],{},[1831,14683,1865],{},[1867,14685,1869],{},[1839,14687,8538],{},[1836,14689,14690,14692],{},[1839,14691,14574],{},[1839,14693,8531],{},[1831,14695,1849],{"separator":1848},[1883,14697,14698],{"encoding":1885},"\\sigma_{\\text{ann, adj}} \\approx s \\sqrt{N} \\times \\sqrt{1 + 2 \\sum_{k=1}^{K} \\rho_k},",[1807,14700,14702,14764,14830],{"className":14701,"ariaHidden":1848},[1890],[1807,14703,14705,14709,14755,14758,14761],{"className":14704},[1894],[1807,14706],{"className":14707,"style":14708},[1898],"height:0.7692em;vertical-align:-0.2861em;",[1807,14710,14712,14715],{"className":14711},[1907],[1807,14713,14323],{"className":14714,"style":6803},[1907,1911],[1807,14716,14718],{"className":14717},[1916],[1807,14719,14721,14747],{"className":14720},[1920,1921],[1807,14722,14724,14744],{"className":14723},[1925],[1807,14725,14727],{"className":14726,"style":7848},[1929],[1807,14728,14729,14732],{"style":14368},[1807,14730],{"className":14731,"style":1938},[1937],[1807,14733,14735],{"className":14734},[1942,1943,1944,1945],[1807,14736,14738],{"className":14737},[1907,1945],[1807,14739,14741],{"className":14740},[1907,2061,1945],[1807,14742,14651],{"className":14743},[1907,1945],[1807,14745,1963],{"className":14746},[1962],[1807,14748,14750],{"className":14749},[1925],[1807,14751,14753],{"className":14752,"style":1970},[1929],[1807,14754],{},[1807,14756],{"className":14757,"style":2044},[2043],[1807,14759,14654],{"className":14760},[2011],[1807,14762],{"className":14763,"style":2044},[2043],[1807,14765,14767,14771,14774,14821,14824,14827],{"className":14766},[1894],[1807,14768],{"className":14769,"style":14770},[1898],"height:1.0589em;vertical-align:-0.0833em;",[1807,14772,2272],{"className":14773},[1907,1911],[1807,14775,14777],{"className":14776},[1907,13971],[1807,14778,14780,14813],{"className":14779},[1920,1921],[1807,14781,14783,14810],{"className":14782},[1925],[1807,14784,14786,14798],{"className":14785,"style":14426},[1929],[1807,14787,14789,14792],{"className":14788,"style":2573},[13985],[1807,14790],{"className":14791,"style":2577},[1937],[1807,14793,14795],{"className":14794,"style":14436},[1907],[1807,14796,5355],{"className":14797,"style":5538},[1907,1911],[1807,14799,14800,14803],{"style":14442},[1807,14801],{"className":14802,"style":2577},[1937],[1807,14804,14806],{"className":14805,"style":14449},[14269],[14272,14807,14808],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},[14280,14809],{"d":14456},[1807,14811,1963],{"className":14812},[1962],[1807,14814,14816],{"className":14815},[1925],[1807,14817,14819],{"className":14818,"style":14466},[1929],[1807,14820],{},[1807,14822],{"className":14823,"style":2231},[2043],[1807,14825,14663],{"className":14826},[2235],[1807,14828],{"className":14829,"style":2231},[2043],[1807,14831,14833,14837,15015],{"className":14832},[1894],[1807,14834],{"className":14835,"style":14836},[1898],"height:3.3582em;vertical-align:-1.3021em;",[1807,14838,14840],{"className":14839},[1907,13971],[1807,14841,14843,15007],{"className":14842},[1920,1921],[1807,14844,14846,15004],{"className":14845},[1925],[1807,14847,14849,14988],{"className":14848,"style":13981},[1929],[1807,14850,14853,14857],{"className":14851,"style":14852},[13985],"top:-5.3182em;",[1807,14854],{"className":14855,"style":14856},[1937],"height:5.3182em;",[1807,14858,14860,14863,14866,14869,14872,14875,14878,14945,14948],{"className":14859,"style":13994},[1907],[1807,14861,1869],{"className":14862},[1907],[1807,14864],{"className":14865,"style":2231},[2043],[1807,14867,2209],{"className":14868},[2235],[1807,14870],{"className":14871,"style":2231},[2043],[1807,14873,3658],{"className":14874},[1907],[1807,14876],{"className":14877,"style":2553},[2043],[1807,14879,14881],{"className":14880},[3687,3688],[1807,14882,14884,14937],{"className":14883},[1920,1921],[1807,14885,14887,14934],{"className":14886},[1925],[1807,14888,14890,14910,14920],{"className":14889,"style":8747},[1929],[1807,14891,14892,14895],{"style":8750},[1807,14893],{"className":14894,"style":8754},[1937],[1807,14896,14898],{"className":14897},[1942,1943,1944,1945],[1807,14899,14901,14904,14907],{"className":14900},[1907,1945],[1807,14902,8531],{"className":14903,"style":8764},[1907,1911,1945],[1807,14905,1865],{"className":14906},[2011,1945],[1807,14908,1869],{"className":14909},[1907,1945],[1807,14911,14912,14915],{"style":8773},[1807,14913],{"className":14914,"style":8754},[1937],[1807,14916,14917],{},[1807,14918,5609],{"className":14919},[3687,5655,8782],[1807,14921,14922,14925],{"style":8785},[1807,14923],{"className":14924,"style":8754},[1937],[1807,14926,14928],{"className":14927},[1942,1943,1944,1945],[1807,14929,14931],{"className":14930},[1907,1945],[1807,14932,8538],{"className":14933,"style":8795},[1907,1911,1945],[1807,14935,1963],{"className":14936},[1962],[1807,14938,14940],{"className":14939},[1925],[1807,14941,14943],{"className":14942,"style":8805},[1929],[1807,14944],{},[1807,14946],{"className":14947,"style":2553},[2043],[1807,14949,14951,14954],{"className":14950},[1907],[1807,14952,14574],{"className":14953},[1907,1911],[1807,14955,14957],{"className":14956},[1916],[1807,14958,14960,14980],{"className":14959},[1920,1921],[1807,14961,14963,14977],{"className":14962},[1925],[1807,14964,14966],{"className":14965,"style":7848},[1929],[1807,14967,14968,14971],{"style":2457},[1807,14969],{"className":14970,"style":1938},[1937],[1807,14972,14974],{"className":14973},[1942,1943,1944,1945],[1807,14975,8531],{"className":14976,"style":8764},[1907,1911,1945],[1807,14978,1963],{"className":14979},[1962],[1807,14981,14983],{"className":14982},[1925],[1807,14984,14986],{"className":14985,"style":2189},[1929],[1807,14987],{},[1807,14989,14990,14993],{"style":14262},[1807,14991],{"className":14992,"style":14856},[1937],[1807,14994,14997],{"className":14995,"style":14996},[14269],"min-width:0.742em;height:3.3982em;",[14272,14998,15001],{"xmlns":14274,"width":14275,"height":14999,"viewBox":15000,"preserveAspectRatio":14278},"3.3982em","0 0 400000 3398",[14280,15002],{"d":15003},"M702 80H40000040\nH742v3264l-4 4-4 4c-.667.7 -2 1.5-4 2.5s-4.167 1.833-6.5 2.5-5.5 1-9.5 1\nh-12l-28-84c-16.667-52-96.667 -294.333-240-727l-212 -643 -85 170\nc-4-3.333-8.333-7.667-13 -13l-13-13l77-155 77-156c66 199.333 139 419.667\n219 661 l218 661zM702 80H400000v40H742z",[1807,15005,1963],{"className":15006},[1962],[1807,15008,15010],{"className":15009},[1925],[1807,15011,15013],{"className":15012,"style":8805},[1929],[1807,15014],{},[1807,15016,1849],{"className":15017},[1955],[1792,15019,5090,15020,15090,15091,15119,15120,15148],{},[1807,15021,15023,15041],{"className":15022},[1814],[1807,15024,15026],{"className":15025},[1818],[1820,15027,15028],{"xmlns":1822},[1825,15029,15030,15038],{},[1828,15031,15032],{},[1836,15033,15034,15036],{},[1839,15035,14574],{},[1839,15037,8531],{},[1883,15039,15040],{"encoding":1885},"\\rho_k",[1807,15042,15044],{"className":15043,"ariaHidden":1848},[1890],[1807,15045,15047,15050],{"className":15046},[1894],[1807,15048],{"className":15049,"style":3925},[1898],[1807,15051,15053,15056],{"className":15052},[1907],[1807,15054,14574],{"className":15055},[1907,1911],[1807,15057,15059],{"className":15058},[1916],[1807,15060,15062,15082],{"className":15061},[1920,1921],[1807,15063,15065,15079],{"className":15064},[1925],[1807,15066,15068],{"className":15067,"style":7848},[1929],[1807,15069,15070,15073],{"style":2457},[1807,15071],{"className":15072,"style":1938},[1937],[1807,15074,15076],{"className":15075},[1942,1943,1944,1945],[1807,15077,8531],{"className":15078,"style":8764},[1907,1911,1945],[1807,15080,1963],{"className":15081},[1962],[1807,15083,15085],{"className":15084},[1925],[1807,15086,15088],{"className":15087,"style":2189},[1929],[1807,15089],{}," 是滞后 ",[1807,15092,15094,15107],{"className":15093},[1814],[1807,15095,15097],{"className":15096},[1818],[1820,15098,15099],{"xmlns":1822},[1825,15100,15101,15105],{},[1828,15102,15103],{},[1839,15104,8531],{},[1883,15106,8531],{"encoding":1885},[1807,15108,15110],{"className":15109,"ariaHidden":1848},[1890],[1807,15111,15113,15116],{"className":15112},[1894],[1807,15114],{"className":15115,"style":2570},[1898],[1807,15117,8531],{"className":15118,"style":8764},[1907,1911]," 期的自相关系数，",[1807,15121,15123,15136],{"className":15122},[1814],[1807,15124,15126],{"className":15125},[1818],[1820,15127,15128],{"xmlns":1822},[1825,15129,15130,15134],{},[1828,15131,15132],{},[1839,15133,8538],{},[1883,15135,8538],{"encoding":1885},[1807,15137,15139],{"className":15138,"ariaHidden":1848},[1890],[1807,15140,15142,15145],{"className":15141},[1894],[1807,15143],{"className":15144,"style":3587},[1898],[1807,15146,8538],{"className":15147,"style":8795},[1907,1911]," 为截断阶数。更系统的处理方式是采用 Newey–West 类型的长期方差估计器，这在“计量方法”章节会专门讨论。",[12741,15150,15152],{"id":15151},"_42-夏普比率sharpe-ratio","4.2 夏普比率（Sharpe Ratio）",[1792,15154,15155,15156,15226,15227,15230],{},"设无风险利率为 ",[1807,15157,15159,15177],{"className":15158},[1814],[1807,15160,15162],{"className":15161},[1818],[1820,15163,15164],{"xmlns":1822},[1825,15165,15166,15174],{},[1828,15167,15168],{},[1836,15169,15170,15172],{},[1839,15171,1841],{},[1839,15173,2279],{},[1883,15175,15176],{"encoding":1885},"r_f",[1807,15178,15180],{"className":15179,"ariaHidden":1848},[1890],[1807,15181,15183,15186],{"className":15182},[1894],[1807,15184],{"className":15185,"style":4728},[1898],[1807,15187,15189,15192],{"className":15188},[1907],[1807,15190,1841],{"className":15191,"style":1912},[1907,1911],[1807,15193,15195],{"className":15194},[1916],[1807,15196,15198,15218],{"className":15197},[1920,1921],[1807,15199,15201,15215],{"className":15200},[1925],[1807,15202,15204],{"className":15203,"style":7848},[1929],[1807,15205,15206,15209],{"style":1933},[1807,15207],{"className":15208,"style":1938},[1937],[1807,15210,15212],{"className":15211},[1942,1943,1944,1945],[1807,15213,2279],{"className":15214,"style":2496},[1907,1911,1945],[1807,15216,1963],{"className":15217},[1962],[1807,15219,15221],{"className":15220},[1925],[1807,15222,15224],{"className":15223,"style":1970},[1929],[1807,15225],{},"（若忽略，可视为 0），则",[6070,15228,15229],{},"年化夏普比率","定义为：",[1807,15232,15234],{"className":15233},[1810],[1807,15235,15237,15280],{"className":15236},[1814],[1807,15238,15240],{"className":15239},[1818],[1820,15241,15242],{"xmlns":1822,"display":1823},[1825,15243,15244,15277],{},[1828,15245,15246,15249,15251,15275],{},[1877,15247,15248],{},"Sharpe",[1831,15250,1865],{},[3651,15252,15253,15269],{},[1828,15254,15255,15261,15263],{},[1836,15256,15257,15259],{},[1839,15258,12934],{},[1877,15260,13320],{},[1831,15262,3649],{},[1836,15264,15265,15267],{},[1839,15266,1841],{},[1839,15268,2279],{},[1836,15270,15271,15273],{},[1839,15272,14323],{},[1877,15274,13320],{},[1839,15276,2423],{"mathvariant":2361},[1883,15278,15279],{"encoding":1885}," \\text{Sharpe} = \\frac{R_{\\text{ann}} - r_f}{\\sigma_{\\text{ann}}}.",[1807,15281,15283,15304],{"className":15282,"ariaHidden":1848},[1890],[1807,15284,15286,15289,15295,15298,15301],{"className":15285},[1894],[1807,15287],{"className":15288,"style":3277},[1898],[1807,15290,15292],{"className":15291},[1907,2061],[1807,15293,15248],{"className":15294},[1907],[1807,15296],{"className":15297,"style":2044},[2043],[1807,15299,1865],{"className":15300},[2011],[1807,15302],{"className":15303,"style":2044},[2043],[1807,15305,15307,15311,15509],{"className":15306},[1894],[1807,15308],{"className":15309,"style":15310},[1898],"height:2.1963em;vertical-align:-0.836em;",[1807,15312,15314,15317,15506],{"className":15313},[1907],[1807,15315],{"className":15316},[1903,3793],[1807,15318,15320],{"className":15319},[3651],[1807,15321,15323,15497],{"className":15322},[1920,1921],[1807,15324,15326,15494],{"className":15325},[1925],[1807,15327,15329,15383,15391],{"className":15328,"style":4818},[1929],[1807,15330,15331,15334],{"style":3809},[1807,15332],{"className":15333,"style":2577},[1937],[1807,15335,15337],{"className":15336},[1907],[1807,15338,15340,15343],{"className":15339},[1907],[1807,15341,14323],{"className":15342,"style":6803},[1907,1911],[1807,15344,15346],{"className":15345},[1916],[1807,15347,15349,15375],{"className":15348},[1920,1921],[1807,15350,15352,15372],{"className":15351},[1925],[1807,15353,15355],{"className":15354,"style":7919},[1929],[1807,15356,15357,15360],{"style":14368},[1807,15358],{"className":15359,"style":1938},[1937],[1807,15361,15363],{"className":15362},[1942,1943,1944,1945],[1807,15364,15366],{"className":15365},[1907,1945],[1807,15367,15369],{"className":15368},[1907,2061,1945],[1807,15370,13320],{"className":15371},[1907,1945],[1807,15373,1963],{"className":15374},[1962],[1807,15376,15378],{"className":15377},[1925],[1807,15379,15381],{"className":15380,"style":2189},[1929],[1807,15382],{},[1807,15384,15385,15388],{"style":3821},[1807,15386],{"className":15387,"style":2577},[1937],[1807,15389],{"className":15390,"style":3829},[3828],[1807,15392,15393,15396],{"style":3832},[1807,15394],{"className":15395,"style":2577},[1937],[1807,15397,15399,15445,15448,15451,15454],{"className":15398},[1907],[1807,15400,15402,15405],{"className":15401},[1907],[1807,15403,12934],{"className":15404,"style":12998},[1907,1911],[1807,15406,15408],{"className":15407},[1916],[1807,15409,15411,15437],{"className":15410},[1920,1921],[1807,15412,15414,15434],{"className":15413},[1925],[1807,15415,15417],{"className":15416,"style":7919},[1929],[1807,15418,15419,15422],{"style":13013},[1807,15420],{"className":15421,"style":1938},[1937],[1807,15423,15425],{"className":15424},[1942,1943,1944,1945],[1807,15426,15428],{"className":15427},[1907,1945],[1807,15429,15431],{"className":15430},[1907,2061,1945],[1807,15432,13320],{"className":15433},[1907,1945],[1807,15435,1963],{"className":15436},[1962],[1807,15438,15440],{"className":15439},[1925],[1807,15441,15443],{"className":15442,"style":2189},[1929],[1807,15444],{},[1807,15446],{"className":15447,"style":2231},[2043],[1807,15449,3649],{"className":15450},[2235],[1807,15452],{"className":15453,"style":2231},[2043],[1807,15455,15457,15460],{"className":15456},[1907],[1807,15458,1841],{"className":15459,"style":1912},[1907,1911],[1807,15461,15463],{"className":15462},[1916],[1807,15464,15466,15486],{"className":15465},[1920,1921],[1807,15467,15469,15483],{"className":15468},[1925],[1807,15470,15472],{"className":15471,"style":7848},[1929],[1807,15473,15474,15477],{"style":1933},[1807,15475],{"className":15476,"style":1938},[1937],[1807,15478,15480],{"className":15479},[1942,1943,1944,1945],[1807,15481,2279],{"className":15482,"style":2496},[1907,1911,1945],[1807,15484,1963],{"className":15485},[1962],[1807,15487,15489],{"className":15488},[1925],[1807,15490,15492],{"className":15491,"style":1970},[1929],[1807,15493],{},[1807,15495,1963],{"className":15496},[1962],[1807,15498,15500],{"className":15499},[1925],[1807,15501,15504],{"className":15502,"style":15503},[1929],"height:0.836em;",[1807,15505],{},[1807,15507],{"className":15508},[1976,3793],[1807,15510,2423],{"className":15511},[1907],[1792,15513,15514,15515,15584],{},"在日度数据上，若 ",[1807,15516,15518,15535],{"className":15517},[1814],[1807,15519,15521],{"className":15520},[1818],[1820,15522,15523],{"xmlns":1822},[1825,15524,15525,15533],{},[1828,15526,15527],{},[1836,15528,15529,15531],{},[1839,15530,1841],{},[1839,15532,2279],{},[1883,15534,15176],{"encoding":1885},[1807,15536,15538],{"className":15537,"ariaHidden":1848},[1890],[1807,15539,15541,15544],{"className":15540},[1894],[1807,15542],{"className":15543,"style":4728},[1898],[1807,15545,15547,15550],{"className":15546},[1907],[1807,15548,1841],{"className":15549,"style":1912},[1907,1911],[1807,15551,15553],{"className":15552},[1916],[1807,15554,15556,15576],{"className":15555},[1920,1921],[1807,15557,15559,15573],{"className":15558},[1925],[1807,15560,15562],{"className":15561,"style":7848},[1929],[1807,15563,15564,15567],{"style":1933},[1807,15565],{"className":15566,"style":1938},[1937],[1807,15568,15570],{"className":15569},[1942,1943,1944,1945],[1807,15571,2279],{"className":15572,"style":2496},[1907,1911,1945],[1807,15574,1963],{"className":15575},[1962],[1807,15577,15579],{"className":15578},[1925],[1807,15580,15582],{"className":15581,"style":1970},[1929],[1807,15583],{}," 很小，可以使用近似形式：",[1807,15586,15588],{"className":15587},[1810],[1807,15589,15591,15623],{"className":15590},[1814],[1807,15592,15594],{"className":15593},[1818],[1820,15595,15596],{"xmlns":1822,"display":1823},[1825,15597,15598,15620],{},[1828,15599,15600,15602,15604,15614,15618],{},[1877,15601,15248],{},[1831,15603,14654],{},[3651,15605,15606,15612],{},[2300,15607,15608,15610],{"accent":1848},[1839,15609,1841],{},[1831,15611,9443],{},[1839,15613,2272],{},[13877,15615,15616],{},[1839,15617,5355],{},[1839,15619,2423],{"mathvariant":2361},[1883,15621,15622],{"encoding":1885}," \\text{Sharpe} \\approx \\frac{\\bar{r}}{s} \\sqrt{N}.",[1807,15624,15626,15647],{"className":15625,"ariaHidden":1848},[1890],[1807,15627,15629,15632,15638,15641,15644],{"className":15628},[1894],[1807,15630],{"className":15631,"style":3277},[1898],[1807,15633,15635],{"className":15634},[1907,2061],[1807,15636,15248],{"className":15637},[1907],[1807,15639],{"className":15640,"style":2044},[2043],[1807,15642,14654],{"className":15643},[2011],[1807,15645],{"className":15646,"style":2044},[2043],[1807,15648,15650,15654,15745,15792],{"className":15649},[1894],[1807,15651],{"className":15652,"style":15653},[1898],"height:1.9308em;vertical-align:-0.686em;",[1807,15655,15657,15660,15742],{"className":15656},[1907],[1807,15658],{"className":15659},[1903,3793],[1807,15661,15663],{"className":15662},[3651],[1807,15664,15666,15734],{"className":15665},[1920,1921],[1807,15667,15669,15731],{"className":15668},[1925],[1807,15670,15673,15684,15692],{"className":15671,"style":15672},[1929],"height:1.2448em;",[1807,15674,15675,15678],{"style":3809},[1807,15676],{"className":15677,"style":2577},[1937],[1807,15679,15681],{"className":15680},[1907],[1807,15682,2272],{"className":15683},[1907,1911],[1807,15685,15686,15689],{"style":3821},[1807,15687],{"className":15688,"style":2577},[1937],[1807,15690],{"className":15691,"style":3829},[3828],[1807,15693,15694,15697],{"style":3832},[1807,15695],{"className":15696,"style":2577},[1937],[1807,15698,15700],{"className":15699},[1907],[1807,15701,15703],{"className":15702},[1907,2560],[1807,15704,15706],{"className":15705},[1920],[1807,15707,15709],{"className":15708},[1925],[1807,15710,15712,15720],{"className":15711,"style":13622},[1929],[1807,15713,15714,15717],{"style":2573},[1807,15715],{"className":15716,"style":2577},[1937],[1807,15718,1841],{"className":15719,"style":1912},[1907,1911],[1807,15721,15722,15725],{"style":2573},[1807,15723],{"className":15724,"style":2577},[1937],[1807,15726,15728],{"className":15727,"style":13651},[2589],[1807,15729,9443],{"className":15730},[1907],[1807,15732,1963],{"className":15733},[1962],[1807,15735,15737],{"className":15736},[1925],[1807,15738,15740],{"className":15739,"style":3852},[1929],[1807,15741],{},[1807,15743],{"className":15744},[1976,3793],[1807,15746,15748],{"className":15747},[1907,13971],[1807,15749,15751,15784],{"className":15750},[1920,1921],[1807,15752,15754,15781],{"className":15753},[1925],[1807,15755,15757,15769],{"className":15756,"style":14426},[1929],[1807,15758,15760,15763],{"className":15759,"style":2573},[13985],[1807,15761],{"className":15762,"style":2577},[1937],[1807,15764,15766],{"className":15765,"style":14436},[1907],[1807,15767,5355],{"className":15768,"style":5538},[1907,1911],[1807,15770,15771,15774],{"style":14442},[1807,15772],{"className":15773,"style":2577},[1937],[1807,15775,15777],{"className":15776,"style":14449},[14269],[14272,15778,15779],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},[14280,15780],{"d":14456},[1807,15782,1963],{"className":15783},[1962],[1807,15785,15787],{"className":15786},[1925],[1807,15788,15790],{"className":15789,"style":14466},[1929],[1807,15791],{},[1807,15793,2423],{"className":15794},[1907],[1792,15796,15797],{},"学术上，夏普比率是对“单位风险获取多少超额收益”的度量；在 Grinold & Kahn (2000) 视角下，它也可以由信息系数和交易规模分解出来，用于评估一个 Alpha 源的质量。",[1792,15799,15800],{},"在假设收益独立同分布且近似正态的前提下，样本夏普比率的 t 统计量可以近似写作：",[1807,15802,15804],{"className":15803},[1810],[1807,15805,15807,15860],{"className":15806},[1814],[1807,15808,15810],{"className":15809},[1818],[1820,15811,15812],{"xmlns":1822,"display":1823},[1825,15813,15814,15857],{},[1828,15815,15816,15822,15824,15851,15855],{},[1836,15817,15818,15820],{},[1839,15819,1852],{},[1877,15821,15248],{},[1831,15823,14654],{},[3651,15825,15826,15828],{},[1877,15827,15248],{},[13877,15829,15830],{},[1828,15831,15832,15834,15836,15842,15845],{},[1867,15833,1869],{},[1831,15835,2209],{},[3651,15837,15838,15840],{},[1867,15839,1869],{},[1867,15841,3658],{},[1877,15843,15844],{}," ",[3639,15846,15847,15849],{},[1877,15848,15248],{},[1867,15850,3658],{},[13877,15852,15853],{},[1839,15854,1872],{},[1831,15856,1849],{"separator":1848},[1883,15858,15859],{"encoding":1885},"t_{\\text{Sharpe}} \\approx \\frac{\\text{Sharpe}}{\\sqrt{1 + \\frac{1}{2}\\,\\text{Sharpe}^2}} \\sqrt{T},",[1807,15861,15863,15925],{"className":15862,"ariaHidden":1848},[1890],[1807,15864,15866,15870,15916,15919,15922],{"className":15865},[1894],[1807,15867],{"className":15868,"style":15869},[1898],"height:0.9012em;vertical-align:-0.2861em;",[1807,15871,15873,15876],{"className":15872},[1907],[1807,15874,1852],{"className":15875},[1907,1911],[1807,15877,15879],{"className":15878},[1916],[1807,15880,15882,15908],{"className":15881},[1920,1921],[1807,15883,15885,15905],{"className":15884},[1925],[1807,15886,15888],{"className":15887,"style":7848},[1929],[1807,15889,15890,15893],{"style":2457},[1807,15891],{"className":15892,"style":1938},[1937],[1807,15894,15896],{"className":15895},[1942,1943,1944,1945],[1807,15897,15899],{"className":15898},[1907,1945],[1807,15900,15902],{"className":15901},[1907,2061,1945],[1807,15903,15248],{"className":15904},[1907,1945],[1807,15906,1963],{"className":15907},[1962],[1807,15909,15911],{"className":15910},[1925],[1807,15912,15914],{"className":15913,"style":1970},[1929],[1807,15915],{},[1807,15917],{"className":15918,"style":2044},[2043],[1807,15920,14654],{"className":15921},[2011],[1807,15923],{"className":15924,"style":2044},[2043],[1807,15926,15928,15932,16175,16222],{"className":15927},[1894],[1807,15929],{"className":15930,"style":15931},[1898],"height:3.1014em;vertical-align:-1.73em;",[1807,15933,15935,15938,16172],{"className":15934},[1907],[1807,15936],{"className":15937},[1903,3793],[1807,15939,15941],{"className":15940},[3651],[1807,15942,15944,16163],{"className":15943},[1920,1921],[1807,15945,15947,16160],{"className":15946},[1925],[1807,15948,15951,16136,16145],{"className":15949,"style":15950},[1929],"height:1.3714em;",[1807,15952,15954,15958],{"style":15953},"top:-2.11em;",[1807,15955],{"className":15956,"style":15957},[1937],"height:3.2617em;",[1807,15959,15961],{"className":15960},[1907],[1807,15962,15964],{"className":15963},[1907,13971],[1807,15965,15967,16127],{"className":15966},[1920,1921],[1807,15968,15970,16124],{"className":15969},[1925],[1807,15971,15974,16107],{"className":15972,"style":15973},[1929],"height:1.2617em;",[1807,15975,15978,15982],{"className":15976,"style":15977},[13985],"top:-3.8em;",[1807,15979],{"className":15980,"style":15981},[1937],"height:3.8em;",[1807,15983,15986,15989,15992,15995,15998,16070,16073],{"className":15984,"style":15985},[1907],"padding-left:1em;",[1807,15987,1869],{"className":15988},[1907],[1807,15990],{"className":15991,"style":2231},[2043],[1807,15993,2209],{"className":15994},[2235],[1807,15996],{"className":15997,"style":2231},[2043],[1807,15999,16001,16004,16067],{"className":16000},[1907],[1807,16002],{"className":16003},[1903,3793],[1807,16005,16007],{"className":16006},[3651],[1807,16008,16010,16058],{"className":16009},[1920,1921],[1807,16011,16013,16055],{"className":16012},[1925],[1807,16014,16017,16032,16040],{"className":16015,"style":16016},[1929],"height:0.8451em;",[1807,16018,16020,16023],{"style":16019},"top:-2.655em;",[1807,16021],{"className":16022,"style":2577},[1937],[1807,16024,16026],{"className":16025},[1942,1943,1944,1945],[1807,16027,16029],{"className":16028},[1907,1945],[1807,16030,3658],{"className":16031},[1907,1945],[1807,16033,16034,16037],{"style":3821},[1807,16035],{"className":16036,"style":2577},[1937],[1807,16038],{"className":16039,"style":3829},[3828],[1807,16041,16043,16046],{"style":16042},"top:-3.394em;",[1807,16044],{"className":16045,"style":2577},[1937],[1807,16047,16049],{"className":16048},[1942,1943,1944,1945],[1807,16050,16052],{"className":16051},[1907,1945],[1807,16053,1869],{"className":16054},[1907,1945],[1807,16056,1963],{"className":16057},[1962],[1807,16059,16061],{"className":16060},[1925],[1807,16062,16065],{"className":16063,"style":16064},[1929],"height:0.345em;",[1807,16066],{},[1807,16068],{"className":16069},[1976,3793],[1807,16071],{"className":16072,"style":2553},[2043],[1807,16074,16076,16082],{"className":16075},[1907],[1807,16077,16079],{"className":16078},[1907,2061],[1807,16080,15248],{"className":16081},[1907],[1807,16083,16085],{"className":16084},[1916],[1807,16086,16088],{"className":16087},[1920],[1807,16089,16091],{"className":16090},[1925],[1807,16092,16095],{"className":16093,"style":16094},[1929],"height:0.8984em;",[1807,16096,16098,16101],{"style":16097},"top:-3.1473em;margin-right:0.05em;",[1807,16099],{"className":16100,"style":1938},[1937],[1807,16102,16104],{"className":16103},[1942,1943,1944,1945],[1807,16105,3658],{"className":16106},[1907,1945],[1807,16108,16110,16113],{"style":16109},"top:-3.2217em;",[1807,16111],{"className":16112,"style":15981},[1937],[1807,16114,16117],{"className":16115,"style":16116},[14269],"min-width:1.02em;height:1.88em;",[14272,16118,16121],{"xmlns":14274,"width":14275,"height":16119,"viewBox":16120,"preserveAspectRatio":14278},"1.88em","0 0 400000 1944",[14280,16122],{"d":16123},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[1807,16125,1963],{"className":16126},[1962],[1807,16128,16130],{"className":16129},[1925],[1807,16131,16134],{"className":16132,"style":16133},[1929],"height:0.5783em;",[1807,16135],{},[1807,16137,16139,16142],{"style":16138},"top:-3.4917em;",[1807,16140],{"className":16141,"style":15957},[1937],[1807,16143],{"className":16144,"style":3829},[3828],[1807,16146,16148,16151],{"style":16147},"top:-3.9387em;",[1807,16149],{"className":16150,"style":15957},[1937],[1807,16152,16154],{"className":16153},[1907],[1807,16155,16157],{"className":16156},[1907,2061],[1807,16158,15248],{"className":16159},[1907],[1807,16161,1963],{"className":16162},[1962],[1807,16164,16166],{"className":16165},[1925],[1807,16167,16170],{"className":16168,"style":16169},[1929],"height:1.73em;",[1807,16171],{},[1807,16173],{"className":16174},[1976,3793],[1807,16176,16178],{"className":16177},[1907,13971],[1807,16179,16181,16214],{"className":16180},[1920,1921],[1807,16182,16184,16211],{"className":16183},[1925],[1807,16185,16187,16199],{"className":16186,"style":14426},[1929],[1807,16188,16190,16193],{"className":16189,"style":2573},[13985],[1807,16191],{"className":16192,"style":2577},[1937],[1807,16194,16196],{"className":16195,"style":14436},[1907],[1807,16197,1872],{"className":16198,"style":2027},[1907,1911],[1807,16200,16201,16204],{"style":14442},[1807,16202],{"className":16203,"style":2577},[1937],[1807,16205,16207],{"className":16206,"style":14449},[14269],[14272,16208,16209],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},[14280,16210],{"d":14456},[1807,16212,1963],{"className":16213},[1962],[1807,16215,16217],{"className":16216},[1925],[1807,16218,16220],{"className":16219,"style":14466},[1929],[1807,16221],{},[1807,16223,1849],{"className":16224},[1955],[1792,16226,16227],{},"这一近似有助于在学术研究中评估某一策略夏普比率的统计显著性（见 Jobson & Korkie, 1981；Lo, 2002）。在实务中，更重要的是比较不同策略在相同数据窗口下的夏普差异，而不是孤立看单一策略的绝对数值。",[12741,16229,16231],{"id":16230},"_43-最大回撤与-calmar-比率","4.3 最大回撤与 Calmar 比率",[1792,16233,16234,16235,16305,16306,16334],{},"设策略净值为 ",[1807,16236,16238,16256],{"className":16237},[1814],[1807,16239,16241],{"className":16240},[1818],[1820,16242,16243],{"xmlns":1822},[1825,16244,16245,16253],{},[1828,16246,16247],{},[1836,16248,16249,16251],{},[1839,16250,11063],{},[1839,16252,1852],{},[1883,16254,16255],{"encoding":1885},"V_t",[1807,16257,16259],{"className":16258,"ariaHidden":1848},[1890],[1807,16260,16262,16265],{"className":16261},[1894],[1807,16263],{"className":16264,"style":2147},[1898],[1807,16266,16268,16271],{"className":16267},[1907],[1807,16269,11063],{"className":16270,"style":2231},[1907,1911],[1807,16272,16274],{"className":16273},[1916],[1807,16275,16277,16297],{"className":16276},[1920,1921],[1807,16278,16280,16294],{"className":16279},[1925],[1807,16281,16283],{"className":16282,"style":1930},[1929],[1807,16284,16285,16288],{"style":11098},[1807,16286],{"className":16287,"style":1938},[1937],[1807,16289,16291],{"className":16290},[1942,1943,1944,1945],[1807,16292,1852],{"className":16293},[1907,1911,1945],[1807,16295,1963],{"className":16296},[1962],[1807,16298,16300],{"className":16299},[1925],[1807,16301,16303],{"className":16302,"style":2189},[1929],[1807,16304],{},"。定义直到时点 ",[1807,16307,16309,16322],{"className":16308},[1814],[1807,16310,16312],{"className":16311},[1818],[1820,16313,16314],{"xmlns":1822},[1825,16315,16316,16320],{},[1828,16317,16318],{},[1839,16319,1852],{},[1883,16321,1852],{"encoding":1885},[1807,16323,16325],{"className":16324,"ariaHidden":1848},[1890],[1807,16326,16328,16331],{"className":16327},[1894],[1807,16329],{"className":16330,"style":2110},[1898],[1807,16332,1852],{"className":16333},[1907,1911]," 的历史最高净值：",[1807,16336,16338],{"className":16337},[1810],[1807,16339,16341,16391],{"className":16340},[1814],[1807,16342,16344],{"className":16343},[1818],[1820,16345,16346],{"xmlns":1822,"display":1823},[1825,16347,16348,16388],{},[1828,16349,16350,16357,16359,16380,16386],{},[1836,16351,16352,16355],{},[1839,16353,16354],{},"M",[1839,16356,1852],{},[1831,16358,1865],{},[3623,16360,16361,16367],{},[1828,16362,16363,16365],{},[1839,16364,3629],{},[1831,16366,3632],{},[1828,16368,16369,16371,16374,16376,16378],{},[1867,16370,5905],{},[1831,16372,16373],{},"≤",[1839,16375,2272],{},[1831,16377,16373],{},[1839,16379,1852],{},[1836,16381,16382,16384],{},[1839,16383,11063],{},[1839,16385,2272],{},[1839,16387,2423],{"mathvariant":2361},[1883,16389,16390],{"encoding":1885}," M_t = \\max_{0 \\le s \\le t} V_s.",[1807,16392,16394,16450],{"className":16393,"ariaHidden":1848},[1890],[1807,16395,16397,16400,16441,16444,16447],{"className":16396},[1894],[1807,16398],{"className":16399,"style":2147},[1898],[1807,16401,16403,16406],{"className":16402},[1907],[1807,16404,16354],{"className":16405,"style":5538},[1907,1911],[1807,16407,16409],{"className":16408},[1916],[1807,16410,16412,16433],{"className":16411},[1920,1921],[1807,16413,16415,16430],{"className":16414},[1925],[1807,16416,16418],{"className":16417,"style":1930},[1929],[1807,16419,16421,16424],{"style":16420},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1807,16422],{"className":16423,"style":1938},[1937],[1807,16425,16427],{"className":16426},[1942,1943,1944,1945],[1807,16428,1852],{"className":16429},[1907,1911,1945],[1807,16431,1963],{"className":16432},[1962],[1807,16434,16436],{"className":16435},[1925],[1807,16437,16439],{"className":16438,"style":2189},[1929],[1807,16440],{},[1807,16442],{"className":16443,"style":2044},[2043],[1807,16445,1865],{"className":16446},[2011],[1807,16448],{"className":16449,"style":2044},[2043],[1807,16451,16453,16457,16518,16521,16561],{"className":16452},[1894],[1807,16454],{"className":16455,"style":16456},[1898],"height:1.4956em;vertical-align:-0.8123em;",[1807,16458,16460],{"className":16459},[3687,3688],[1807,16461,16463,16509],{"className":16462},[1920,1921],[1807,16464,16466,16506],{"className":16465},[1925],[1807,16467,16469,16496],{"className":16468,"style":3698},[1929],[1807,16470,16472,16475],{"style":16471},"top:-2.3829em;margin-left:0em;",[1807,16473],{"className":16474,"style":2577},[1937],[1807,16476,16478],{"className":16477},[1942,1943,1944,1945],[1807,16479,16481,16484,16487,16490,16493],{"className":16480},[1907,1945],[1807,16482,5905],{"className":16483},[1907,1945],[1807,16485,16373],{"className":16486},[2011,1945],[1807,16488,2272],{"className":16489},[1907,1911,1945],[1807,16491,16373],{"className":16492},[2011,1945],[1807,16494,1852],{"className":16495},[1907,1911,1945],[1807,16497,16498,16501],{"style":2573},[1807,16499],{"className":16500,"style":2577},[1937],[1807,16502,16503],{},[1807,16504,3629],{"className":16505},[3687],[1807,16507,1963],{"className":16508},[1962],[1807,16510,16512],{"className":16511},[1925],[1807,16513,16516],{"className":16514,"style":16515},[1929],"height:0.8123em;",[1807,16517],{},[1807,16519],{"className":16520,"style":2553},[2043],[1807,16522,16524,16527],{"className":16523},[1907],[1807,16525,11063],{"className":16526,"style":2231},[1907,1911],[1807,16528,16530],{"className":16529},[1916],[1807,16531,16533,16553],{"className":16532},[1920,1921],[1807,16534,16536,16550],{"className":16535},[1925],[1807,16537,16539],{"className":16538,"style":7919},[1929],[1807,16540,16541,16544],{"style":11098},[1807,16542],{"className":16543,"style":1938},[1937],[1807,16545,16547],{"className":16546},[1942,1943,1944,1945],[1807,16548,2272],{"className":16549},[1907,1911,1945],[1807,16551,1963],{"className":16552},[1962],[1807,16554,16556],{"className":16555},[1925],[1807,16557,16559],{"className":16558,"style":2189},[1929],[1807,16560],{},[1807,16562,2423],{"className":16563},[1907],[1792,16565,16566,16567,16595],{},"则时点 ",[1807,16568,16570,16583],{"className":16569},[1814],[1807,16571,16573],{"className":16572},[1818],[1820,16574,16575],{"xmlns":1822},[1825,16576,16577,16581],{},[1828,16578,16579],{},[1839,16580,1852],{},[1883,16582,1852],{"encoding":1885},[1807,16584,16586],{"className":16585,"ariaHidden":1848},[1890],[1807,16587,16589,16592],{"className":16588},[1894],[1807,16590],{"className":16591,"style":2110},[1898],[1807,16593,1852],{"className":16594},[1907,1911]," 的回撤为：",[1807,16597,16599],{"className":16598},[1810],[1807,16600,16602,16642],{"className":16601},[1814],[1807,16603,16605],{"className":16604},[1818],[1820,16606,16607],{"xmlns":1822,"display":1823},[1825,16608,16609,16639],{},[1828,16610,16611,16617,16619,16621,16623,16637],{},[1836,16612,16613,16615],{},[1839,16614,4689],{},[1839,16616,1852],{},[1831,16618,1865],{},[1867,16620,1869],{},[1831,16622,3649],{},[3651,16624,16625,16631],{},[1836,16626,16627,16629],{},[1839,16628,11063],{},[1839,16630,1852],{},[1836,16632,16633,16635],{},[1839,16634,16354],{},[1839,16636,1852],{},[1839,16638,2423],{"mathvariant":2361},[1883,16640,16641],{"encoding":1885}," D_t = 1 - \\frac{V_t}{M_t}.",[1807,16643,16645,16700,16719],{"className":16644,"ariaHidden":1848},[1890],[1807,16646,16648,16651,16691,16694,16697],{"className":16647},[1894],[1807,16649],{"className":16650,"style":2147},[1898],[1807,16652,16654,16657],{"className":16653},[1907],[1807,16655,4689],{"className":16656,"style":1912},[1907,1911],[1807,16658,16660],{"className":16659},[1916],[1807,16661,16663,16683],{"className":16662},[1920,1921],[1807,16664,16666,16680],{"className":16665},[1925],[1807,16667,16669],{"className":16668,"style":1930},[1929],[1807,16670,16671,16674],{"style":1933},[1807,16672],{"className":16673,"style":1938},[1937],[1807,16675,16677],{"className":16676},[1942,1943,1944,1945],[1807,16678,1852],{"className":16679},[1907,1911,1945],[1807,16681,1963],{"className":16682},[1962],[1807,16684,16686],{"className":16685},[1925],[1807,16687,16689],{"className":16688,"style":2189},[1929],[1807,16690],{},[1807,16692],{"className":16693,"style":2044},[2043],[1807,16695,1865],{"className":16696},[2011],[1807,16698],{"className":16699,"style":2044},[2043],[1807,16701,16703,16707,16710,16713,16716],{"className":16702},[1894],[1807,16704],{"className":16705,"style":16706},[1898],"height:0.7278em;vertical-align:-0.0833em;",[1807,16708,1869],{"className":16709},[1907],[1807,16711],{"className":16712,"style":2231},[2043],[1807,16714,3649],{"className":16715},[2235],[1807,16717],{"className":16718,"style":2231},[2043],[1807,16720,16722,16725,16861],{"className":16721},[1894],[1807,16723],{"className":16724,"style":15310},[1898],[1807,16726,16728,16731,16858],{"className":16727},[1907],[1807,16729],{"className":16730},[1903,3793],[1807,16732,16734],{"className":16733},[3651],[1807,16735,16737,16850],{"className":16736},[1920,1921],[1807,16738,16740,16847],{"className":16739},[1925],[1807,16741,16743,16791,16799],{"className":16742,"style":4818},[1929],[1807,16744,16745,16748],{"style":3809},[1807,16746],{"className":16747,"style":2577},[1937],[1807,16749,16751],{"className":16750},[1907],[1807,16752,16754,16757],{"className":16753},[1907],[1807,16755,16354],{"className":16756,"style":5538},[1907,1911],[1807,16758,16760],{"className":16759},[1916],[1807,16761,16763,16783],{"className":16762},[1920,1921],[1807,16764,16766,16780],{"className":16765},[1925],[1807,16767,16769],{"className":16768,"style":1930},[1929],[1807,16770,16771,16774],{"style":16420},[1807,16772],{"className":16773,"style":1938},[1937],[1807,16775,16777],{"className":16776},[1942,1943,1944,1945],[1807,16778,1852],{"className":16779},[1907,1911,1945],[1807,16781,1963],{"className":16782},[1962],[1807,16784,16786],{"className":16785},[1925],[1807,16787,16789],{"className":16788,"style":2189},[1929],[1807,16790],{},[1807,16792,16793,16796],{"style":3821},[1807,16794],{"className":16795,"style":2577},[1937],[1807,16797],{"className":16798,"style":3829},[3828],[1807,16800,16801,16804],{"style":3832},[1807,16802],{"className":16803,"style":2577},[1937],[1807,16805,16807],{"className":16806},[1907],[1807,16808,16810,16813],{"className":16809},[1907],[1807,16811,11063],{"className":16812,"style":2231},[1907,1911],[1807,16814,16816],{"className":16815},[1916],[1807,16817,16819,16839],{"className":16818},[1920,1921],[1807,16820,16822,16836],{"className":16821},[1925],[1807,16823,16825],{"className":16824,"style":1930},[1929],[1807,16826,16827,16830],{"style":11098},[1807,16828],{"className":16829,"style":1938},[1937],[1807,16831,16833],{"className":16832},[1942,1943,1944,1945],[1807,16834,1852],{"className":16835},[1907,1911,1945],[1807,16837,1963],{"className":16838},[1962],[1807,16840,16842],{"className":16841},[1925],[1807,16843,16845],{"className":16844,"style":2189},[1929],[1807,16846],{},[1807,16848,1963],{"className":16849},[1962],[1807,16851,16853],{"className":16852},[1925],[1807,16854,16856],{"className":16855,"style":15503},[1929],[1807,16857],{},[1807,16859],{"className":16860},[1976,3793],[1807,16862,2423],{"className":16863},[1907],[1792,16865,16866,16867,14303],{},"整个样本期的",[6070,16868,16869],{},"最大回撤",[1807,16871,16873],{"className":16872},[1810],[1807,16874,16876,16926],{"className":16875},[1814],[1807,16877,16879],{"className":16878},[1818],[1820,16880,16881],{"xmlns":1822,"display":1823},[1825,16882,16883,16923],{},[1828,16884,16885,16893,16895,16915,16921],{},[1836,16886,16887,16889,16891],{},[1839,16888,4689],{},[1839,16890,3629],{},[1831,16892,3632],{},[1831,16894,1865],{},[3623,16896,16897,16903],{},[1828,16898,16899,16901],{},[1839,16900,3629],{},[1831,16902,3632],{},[1828,16904,16905,16907,16909,16911,16913],{},[1867,16906,5905],{},[1831,16908,16373],{},[1839,16910,1852],{},[1831,16912,16373],{},[1839,16914,1872],{},[1836,16916,16917,16919],{},[1839,16918,4689],{},[1839,16920,1852],{},[1839,16922,2423],{"mathvariant":2361},[1883,16924,16925],{"encoding":1885}," D_{\\max} = \\max_{0 \\le t \\le T} D_t.",[1807,16927,16929,16997],{"className":16928,"ariaHidden":1848},[1890],[1807,16930,16932,16935,16988,16991,16994],{"className":16931},[1894],[1807,16933],{"className":16934,"style":2147},[1898],[1807,16936,16938,16941],{"className":16937},[1907],[1807,16939,4689],{"className":16940,"style":1912},[1907,1911],[1807,16942,16944],{"className":16943},[1916],[1807,16945,16947,16980],{"className":16946},[1920,1921],[1807,16948,16950,16977],{"className":16949},[1925],[1807,16951,16953],{"className":16952,"style":7919},[1929],[1807,16954,16955,16958],{"style":1933},[1807,16956],{"className":16957,"style":1938},[1937],[1807,16959,16961],{"className":16960},[1942,1943,1944,1945],[1807,16962,16964],{"className":16963},[1907,1945],[1807,16965,16967,16971,16974],{"className":16966},[3687,1945],[1807,16968,16970],{"className":16969},[1945],"m",[1807,16972,3595],{"className":16973},[1945],[1807,16975,6728],{"className":16976},[1945],[1807,16978,1963],{"className":16979},[1962],[1807,16981,16983],{"className":16982},[1925],[1807,16984,16986],{"className":16985,"style":2189},[1929],[1807,16987],{},[1807,16989],{"className":16990,"style":2044},[2043],[1807,16992,1865],{"className":16993},[2011],[1807,16995],{"className":16996,"style":2044},[2043],[1807,16998,17000,17004,17065,17068,17108],{"className":16999},[1894],[1807,17001],{"className":17002,"style":17003},[1898],"height:1.5228em;vertical-align:-0.8395em;",[1807,17005,17007],{"className":17006},[3687,3688],[1807,17008,17010,17056],{"className":17009},[1920,1921],[1807,17011,17013,17053],{"className":17012},[1925],[1807,17014,17016,17043],{"className":17015,"style":3698},[1929],[1807,17017,17019,17022],{"style":17018},"top:-2.3557em;margin-left:0em;",[1807,17020],{"className":17021,"style":2577},[1937],[1807,17023,17025],{"className":17024},[1942,1943,1944,1945],[1807,17026,17028,17031,17034,17037,17040],{"className":17027},[1907,1945],[1807,17029,5905],{"className":17030},[1907,1945],[1807,17032,16373],{"className":17033},[2011,1945],[1807,17035,1852],{"className":17036},[1907,1911,1945],[1807,17038,16373],{"className":17039},[2011,1945],[1807,17041,1872],{"className":17042,"style":2027},[1907,1911,1945],[1807,17044,17045,17048],{"style":2573},[1807,17046],{"className":17047,"style":2577},[1937],[1807,17049,17050],{},[1807,17051,3629],{"className":17052},[3687],[1807,17054,1963],{"className":17055},[1962],[1807,17057,17059],{"className":17058},[1925],[1807,17060,17063],{"className":17061,"style":17062},[1929],"height:0.8395em;",[1807,17064],{},[1807,17066],{"className":17067,"style":2553},[2043],[1807,17069,17071,17074],{"className":17070},[1907],[1807,17072,4689],{"className":17073,"style":1912},[1907,1911],[1807,17075,17077],{"className":17076},[1916],[1807,17078,17080,17100],{"className":17079},[1920,1921],[1807,17081,17083,17097],{"className":17082},[1925],[1807,17084,17086],{"className":17085,"style":1930},[1929],[1807,17087,17088,17091],{"style":1933},[1807,17089],{"className":17090,"style":1938},[1937],[1807,17092,17094],{"className":17093},[1942,1943,1944,1945],[1807,17095,1852],{"className":17096},[1907,1911,1945],[1807,17098,1963],{"className":17099},[1962],[1807,17101,17103],{"className":17102},[1925],[1807,17104,17106],{"className":17105,"style":2189},[1929],[1807,17107],{},[1807,17109,2423],{"className":17110},[1907],[1792,17112,17113],{},"Calmar 比率常定义为：",[1807,17115,17117],{"className":17116},[1810],[1807,17118,17120,17155],{"className":17119},[1814],[1807,17121,17123],{"className":17122},[1818],[1820,17124,17125],{"xmlns":1822,"display":1823},[1825,17126,17127,17152],{},[1828,17128,17129,17132,17134,17150],{},[1877,17130,17131],{},"Calmar",[1831,17133,1865],{},[3651,17135,17136,17142],{},[1836,17137,17138,17140],{},[1839,17139,12934],{},[1877,17141,13320],{},[1836,17143,17144,17146,17148],{},[1839,17145,4689],{},[1839,17147,3629],{},[1831,17149,3632],{},[1839,17151,2423],{"mathvariant":2361},[1883,17153,17154],{"encoding":1885}," \\text{Calmar} = \\frac{R_{\\text{ann}}}{D_{\\max}}.",[1807,17156,17158,17179],{"className":17157,"ariaHidden":1848},[1890],[1807,17159,17161,17164,17170,17173,17176],{"className":17160},[1894],[1807,17162],{"className":17163,"style":2570},[1898],[1807,17165,17167],{"className":17166},[1907,2061],[1807,17168,17131],{"className":17169},[1907],[1807,17171],{"className":17172,"style":2044},[2043],[1807,17174,1865],{"className":17175},[2011],[1807,17177],{"className":17178,"style":2044},[2043],[1807,17180,17182,17185,17339],{"className":17181},[1894],[1807,17183],{"className":17184,"style":15310},[1898],[1807,17186,17188,17191,17336],{"className":17187},[1907],[1807,17189],{"className":17190},[1903,3793],[1807,17192,17194],{"className":17193},[3651],[1807,17195,17197,17328],{"className":17196},[1920,1921],[1807,17198,17200,17325],{"className":17199},[1925],[1807,17201,17203,17263,17271],{"className":17202,"style":4818},[1929],[1807,17204,17205,17208],{"style":3809},[1807,17206],{"className":17207,"style":2577},[1937],[1807,17209,17211],{"className":17210},[1907],[1807,17212,17214,17217],{"className":17213},[1907],[1807,17215,4689],{"className":17216,"style":1912},[1907,1911],[1807,17218,17220],{"className":17219},[1916],[1807,17221,17223,17255],{"className":17222},[1920,1921],[1807,17224,17226,17252],{"className":17225},[1925],[1807,17227,17229],{"className":17228,"style":7919},[1929],[1807,17230,17231,17234],{"style":1933},[1807,17232],{"className":17233,"style":1938},[1937],[1807,17235,17237],{"className":17236},[1942,1943,1944,1945],[1807,17238,17240],{"className":17239},[1907,1945],[1807,17241,17243,17246,17249],{"className":17242},[3687,1945],[1807,17244,16970],{"className":17245},[1945],[1807,17247,3595],{"className":17248},[1945],[1807,17250,6728],{"className":17251},[1945],[1807,17253,1963],{"className":17254},[1962],[1807,17256,17258],{"className":17257},[1925],[1807,17259,17261],{"className":17260,"style":2189},[1929],[1807,17262],{},[1807,17264,17265,17268],{"style":3821},[1807,17266],{"className":17267,"style":2577},[1937],[1807,17269],{"className":17270,"style":3829},[3828],[1807,17272,17273,17276],{"style":3832},[1807,17274],{"className":17275,"style":2577},[1937],[1807,17277,17279],{"className":17278},[1907],[1807,17280,17282,17285],{"className":17281},[1907],[1807,17283,12934],{"className":17284,"style":12998},[1907,1911],[1807,17286,17288],{"className":17287},[1916],[1807,17289,17291,17317],{"className":17290},[1920,1921],[1807,17292,17294,17314],{"className":17293},[1925],[1807,17295,17297],{"className":17296,"style":7919},[1929],[1807,17298,17299,17302],{"style":13013},[1807,17300],{"className":17301,"style":1938},[1937],[1807,17303,17305],{"className":17304},[1942,1943,1944,1945],[1807,17306,17308],{"className":17307},[1907,1945],[1807,17309,17311],{"className":17310},[1907,2061,1945],[1807,17312,13320],{"className":17313},[1907,1945],[1807,17315,1963],{"className":17316},[1962],[1807,17318,17320],{"className":17319},[1925],[1807,17321,17323],{"className":17322,"style":2189},[1929],[1807,17324],{},[1807,17326,1963],{"className":17327},[1962],[1807,17329,17331],{"className":17330},[1925],[1807,17332,17334],{"className":17333,"style":15503},[1929],[1807,17335],{},[1807,17337],{"className":17338},[1976,3793],[1807,17340,2423],{"className":17341},[1907],[1792,17343,17344],{},"它强调“在遭受多大历史损失的情况下实现了多少年化收益”，在某些偏主观的基金评价中比夏普更直观。",[1792,17346,17347],{},"在偏“风险管理”的视角下，还可以考虑下行风险相关度量，例如半标准差、下行偏差以及基于分位数的 VaR\u002FCVaR（后续章节会详细介绍）。这些指标与回撤结合使用，可以更全面地刻画策略的尾部风险特征。",[17349,17350],"model-curve-chart",{"props64":17351},"eyJ0aXRsZSI6IuWHgOWAvOOAgeWOhuWPsumrmOeCueS4juWbnuaSpCIsInN1YnRpdGxlIjoi5YeA5YC85puy57q\u002F5Zue562U6LWa5LqG5aSa5bCR77yb5Zue5pKk5puy57q\u002F5Zue562U6L+H56iL5Lit6ZyA6KaB5om\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\u002Fpg6jnvbLmgKflsLHpnIDopoHph43mlrDor4TkvLDjgIIifQ==",[1792,17353,17354],{},"回撤图的价值在于把“亏过多少”从最终收益里单独拿出来。很多策略期末净值看起来不错，但中途可能经历了投资者很难承受的压力期；这也是为什么实盘评估不能只看年化收益和夏普比率。Calmar 比率把年化收益放在最大回撤的背景下看，更贴近资金管理里的生存问题。",[2078,17356,17358],{"id":17357},"_5-回测频率与持仓更新","5. 回测频率与持仓更新",[12741,17360,17362],{"id":17361},"_51-日度回测","5.1 日度回测",[1792,17364,17365],{},"适用于中低频策略，例如：",[5589,17367,17368,17371],{},[4352,17369,17370],{},"按日、按周或按月调仓的股票多因子策略；",[4352,17372,17373],{},"中低频 CTA 策略。",[1792,17375,17376],{},"此时，时间索引可以理解为交易日，持仓在每个调仓日更新：",[5589,17378,17379,17760],{},[4352,17380,17381,17382,17410,17411,17480,17481,17759],{},"若每 ",[1807,17383,17385,17398],{"className":17384},[1814],[1807,17386,17388],{"className":17387},[1818],[1820,17389,17390],{"xmlns":1822},[1825,17391,17392,17396],{},[1828,17393,17394],{},[1839,17395,8538],{},[1883,17397,8538],{"encoding":1885},[1807,17399,17401],{"className":17400,"ariaHidden":1848},[1890],[1807,17402,17404,17407],{"className":17403},[1894],[1807,17405],{"className":17406,"style":3587},[1898],[1807,17408,8538],{"className":17409,"style":8795},[1907,1911]," 日调仓一次，则 ",[1807,17412,17414,17431],{"className":17413},[1814],[1807,17415,17417],{"className":17416},[1818],[1820,17418,17419],{"xmlns":1822},[1825,17420,17421,17429],{},[1828,17422,17423],{},[1836,17424,17425,17427],{},[1839,17426,2333],{},[1839,17428,1852],{},[1883,17430,6648],{"encoding":1885},[1807,17432,17434],{"className":17433,"ariaHidden":1848},[1890],[1807,17435,17437,17440],{"className":17436},[1894],[1807,17438],{"className":17439,"style":2436},[1898],[1807,17441,17443,17446],{"className":17442},[1907],[1807,17444,2333],{"className":17445,"style":2719},[1907,1911],[1807,17447,17449],{"className":17448},[1916],[1807,17450,17452,17472],{"className":17451},[1920,1921],[1807,17453,17455,17469],{"className":17454},[1925],[1807,17456,17458],{"className":17457,"style":1930},[1929],[1807,17459,17460,17463],{"style":2734},[1807,17461],{"className":17462,"style":1938},[1937],[1807,17464,17466],{"className":17465},[1942,1943,1944,1945],[1807,17467,1852],{"className":17468},[1907,1911,1945],[1807,17470,1963],{"className":17471},[1962],[1807,17473,17475],{"className":17474},[1925],[1807,17476,17478],{"className":17477,"style":2189},[1929],[1807,17479],{}," 只有在 ",[1807,17482,17484,17542],{"className":17483},[1814],[1807,17485,17487],{"className":17486},[1818],[1820,17488,17489],{"xmlns":1822},[1825,17490,17491,17539],{},[1828,17492,17493,17495,17497,17499,17505,17507,17513,17515,17517,17519,17525,17527,17529,17531,17533,17535,17537],{},[1839,17494,1852],{},[1831,17496,12204],{},[1831,17498,1834],{"stretchy":1833},[1836,17500,17501,17503],{},[1839,17502,1852],{},[1867,17504,5905],{},[1831,17506,1849],{"separator":1848},[1836,17508,17509,17511],{},[1839,17510,1852],{},[1867,17512,5905],{},[1831,17514,2209],{},[1839,17516,8538],{},[1831,17518,1849],{"separator":1848},[1836,17520,17521,17523],{},[1839,17522,1852],{},[1867,17524,5905],{},[1831,17526,2209],{},[1867,17528,3658],{},[1839,17530,8538],{},[1831,17532,1849],{"separator":1848},[1831,17534,5344],{},[1877,17536,15844],{},[1831,17538,1858],{"stretchy":1833},[1883,17540,17541],{"encoding":1885},"t \\in \\{t_0, t_0+K, t_0+2K, \\dots\\}",[1807,17543,17545,17564,17668,17732],{"className":17544,"ariaHidden":1848},[1890],[1807,17546,17548,17552,17555,17558,17561],{"className":17547},[1894],[1807,17549],{"className":17550,"style":17551},[1898],"height:0.6542em;vertical-align:-0.0391em;",[1807,17553,1852],{"className":17554},[1907,1911],[1807,17556],{"className":17557,"style":2044},[2043],[1807,17559,12204],{"className":17560},[2011],[1807,17562],{"className":17563,"style":2044},[2043],[1807,17565,17567,17570,17573,17613,17616,17619,17659,17662,17665],{"className":17566},[1894],[1807,17568],{"className":17569,"style":2057},[1898],[1807,17571,1834],{"className":17572},[1903],[1807,17574,17576,17579],{"className":17575},[1907],[1807,17577,1852],{"className":17578},[1907,1911],[1807,17580,17582],{"className":17581},[1916],[1807,17583,17585,17605],{"className":17584},[1920,1921],[1807,17586,17588,17602],{"className":17587},[1925],[1807,17589,17591],{"className":17590,"style":3009},[1929],[1807,17592,17593,17596],{"style":2457},[1807,17594],{"className":17595,"style":1938},[1937],[1807,17597,17599],{"className":17598},[1942,1943,1944,1945],[1807,17600,5905],{"className":17601},[1907,1945],[1807,17603,1963],{"className":17604},[1962],[1807,17606,17608],{"className":17607},[1925],[1807,17609,17611],{"className":17610,"style":2189},[1929],[1807,17612],{},[1807,17614,1849],{"className":17615},[1955],[1807,17617],{"className":17618,"style":2553},[2043],[1807,17620,17622,17625],{"className":17621},[1907],[1807,17623,1852],{"className":17624},[1907,1911],[1807,17626,17628],{"className":17627},[1916],[1807,17629,17631,17651],{"className":17630},[1920,1921],[1807,17632,17634,17648],{"className":17633},[1925],[1807,17635,17637],{"className":17636,"style":3009},[1929],[1807,17638,17639,17642],{"style":2457},[1807,17640],{"className":17641,"style":1938},[1937],[1807,17643,17645],{"className":17644},[1942,1943,1944,1945],[1807,17646,5905],{"className":17647},[1907,1945],[1807,17649,1963],{"className":17650},[1962],[1807,17652,17654],{"className":17653},[1925],[1807,17655,17657],{"className":17656,"style":2189},[1929],[1807,17658],{},[1807,17660],{"className":17661,"style":2231},[2043],[1807,17663,2209],{"className":17664},[2235],[1807,17666],{"className":17667,"style":2231},[2043],[1807,17669,17671,17674,17677,17680,17683,17723,17726,17729],{"className":17670},[1894],[1807,17672],{"className":17673,"style":11186},[1898],[1807,17675,8538],{"className":17676,"style":8795},[1907,1911],[1807,17678,1849],{"className":17679},[1955],[1807,17681],{"className":17682,"style":2553},[2043],[1807,17684,17686,17689],{"className":17685},[1907],[1807,17687,1852],{"className":17688},[1907,1911],[1807,17690,17692],{"className":17691},[1916],[1807,17693,17695,17715],{"className":17694},[1920,1921],[1807,17696,17698,17712],{"className":17697},[1925],[1807,17699,17701],{"className":17700,"style":3009},[1929],[1807,17702,17703,17706],{"style":2457},[1807,17704],{"className":17705,"style":1938},[1937],[1807,17707,17709],{"className":17708},[1942,1943,1944,1945],[1807,17710,5905],{"className":17711},[1907,1945],[1807,17713,1963],{"className":17714},[1962],[1807,17716,17718],{"className":17717},[1925],[1807,17719,17721],{"className":17720,"style":2189},[1929],[1807,17722],{},[1807,17724],{"className":17725,"style":2231},[2043],[1807,17727,2209],{"className":17728},[2235],[1807,17730],{"className":17731,"style":2231},[2043],[1807,17733,17735,17738,17741,17744,17747,17750,17753,17756],{"className":17734},[1894],[1807,17736],{"className":17737,"style":2057},[1898],[1807,17739,3658],{"className":17740},[1907],[1807,17742,8538],{"className":17743,"style":8795},[1907,1911],[1807,17745,1849],{"className":17746},[1955],[1807,17748],{"className":17749,"style":2553},[2043],[1807,17751,5344],{"className":17752},[5495],[1807,17754],{"className":17755,"style":2553},[2043],[1807,17757,1858],{"className":17758},[1976]," 时发生变化，其余时间保持不变；",[4352,17761,17762,17763],{},"回测引擎需要正确处理“信号生成日与成交日的对应关系”，例如：\n",[5589,17764,17765],{},[4352,17766,17767],{},"用 T 日收盘数据生成 T+1 日盘中或收盘的交易指令。",[12741,17769,17771],{"id":17770},"_52-事件驱动与高频回测概览","5.2 事件驱动与高频回测（概览）",[1792,17773,17774],{},"对于日内或高频策略，时间步不再是固定日历，而是由事件（订单、成交、价格跳变）触发：",[5589,17776,17777,17780,17783],{},[4352,17778,17779],{},"事件可以是“收到新的行情 tick”、“订单部分成交”或“到达某个时间阈值”；",[4352,17781,17782],{},"策略逻辑在这些事件发生时被调用，根据当前状态和信息集做出决策；",[4352,17784,17785],{},"回测需要模拟订单簿、排队与撮合规则，这在市场微结构章节会进一步讨论。",[1792,17787,17788],{},"研究导向的角度，事件驱动回测可以被视为对一个连续时间随机过程的离散近似，其难点在于：",[5589,17790,17791,17794],{},[4352,17792,17793],{},"如何在有限的历史数据下合理逼近真实的订单簿动力学；",[4352,17795,17796],{},"如何处理“反馈效应”（策略本身对价格形成的影响）。",[1792,17798,17799],{},"从数学金融的角度，高频回测可以与鞅理论、伊藤过程等连续时间模型建立联系，但在实际工程实现中，更多依赖经验建模（例如基于 Hawkes 过程或简化的限价订单簿模型）而非完全解析的闭式解。这也是微结构研究与高频量化中的一个重要交叉领域。",[2078,17801,17803],{"id":17802},"_6-回测中的常见偏差与陷阱","6. 回测中的常见偏差与陷阱",[1792,17805,17806],{},"尽管前一章在数据层面已经讨论了幸存者偏差和前视偏差，在回测实现时仍有大量技术细节会重新引入这些问题。",[12741,17808,17810],{"id":17809},"_61-幸存者偏差与样本构建","6.1 幸存者偏差与样本构建",[5589,17812,17813,17816],{},[4352,17814,17815],{},"只使用当前仍在指数中的成分股来做历史回测，会漏掉历史上被剔除或退市的资产；",[4352,17817,17818,17819],{},"要避免这一点，需要：\n",[5589,17820,17821,17824],{},[4352,17822,17823],{},"使用历史成分列表重构当期可投资标的池；",[4352,17825,17826],{},"对退市资产保留其最后报价和退市相关处理（现金替代、估值方式等）。",[12741,17828,17830],{"id":17829},"_62-前视偏差再次强调","6.2 前视偏差（再次强调）",[1792,17832,17833],{},"代码层面最常见的前视偏差包括：",[5589,17835,17836,17839,17842],{},[4352,17837,17838],{},"使用了“未来日期”的数据列（例如用 T+1 日的开盘价来计算 T 日信号）；",[4352,17840,17841],{},"使用了“最后一次已经调整好的财报数值”来构建 T 之前的因子，而不是使用“当时已披露版本”；",[4352,17843,17844],{},"在排序或截面统计时，不小心引入了后验的样本信息。",[1792,17846,17847,17848,17876,17877,17922,17923,18007,18008,18093,18094,18163],{},"更形式化地说，若我们在 ",[1807,17849,17851,17864],{"className":17850},[1814],[1807,17852,17854],{"className":17853},[1818],[1820,17855,17856],{"xmlns":1822},[1825,17857,17858,17862],{},[1828,17859,17860],{},[1839,17861,1852],{},[1883,17863,1852],{"encoding":1885},[1807,17865,17867],{"className":17866,"ariaHidden":1848},[1890],[1807,17868,17870,17873],{"className":17869},[1894],[1807,17871],{"className":17872,"style":2110},[1898],[1807,17874,1852],{"className":17875},[1907,1911]," 时刻的决策函数 ",[1807,17878,17880,17901],{"className":17879},[1814],[1807,17881,17883],{"className":17882},[1818],[1820,17884,17885],{"xmlns":1822},[1825,17886,17887,17898],{},[1828,17888,17889,17891,17893,17896],{},[1839,17890,6721],{},[1831,17892,2282],{"stretchy":1833},[1831,17894,17895],{},"⋅",[1831,17897,2291],{"stretchy":1833},[1883,17899,17900],{"encoding":1885},"g(\\cdot)",[1807,17902,17904],{"className":17903,"ariaHidden":1848},[1890],[1807,17905,17907,17910,17913,17916,17919],{"className":17906},[1894],[1807,17908],{"className":17909,"style":2057},[1898],[1807,17911,6721],{"className":17912,"style":6803},[1907,1911],[1807,17914,2282],{"className":17915},[1903],[1807,17917,17895],{"className":17918},[1907],[1807,17920,2291],{"className":17921},[1976]," 使用了 ",[1807,17924,17926,17949],{"className":17925},[1814],[1807,17927,17929],{"className":17928},[1818],[1820,17930,17931],{"xmlns":1822},[1825,17932,17933,17947],{},[1828,17934,17935],{},[1836,17936,17937,17939],{},[1839,17938,1841],{},[1828,17940,17941,17943,17945],{},[1839,17942,1852],{},[1831,17944,2209],{},[1867,17946,1869],{},[1883,17948,11726],{"encoding":1885},[1807,17950,17952],{"className":17951,"ariaHidden":1848},[1890],[1807,17953,17955,17958],{"className":17954},[1894],[1807,17956],{"className":17957,"style":6400},[1898],[1807,17959,17961,17964],{"className":17960},[1907],[1807,17962,1841],{"className":17963,"style":1912},[1907,1911],[1807,17965,17967],{"className":17966},[1916],[1807,17968,17970,17999],{"className":17969},[1920,1921],[1807,17971,17973,17996],{"className":17972},[1925],[1807,17974,17976],{"className":17975,"style":3009},[1929],[1807,17977,17978,17981],{"style":1933},[1807,17979],{"className":17980,"style":1938},[1937],[1807,17982,17984],{"className":17983},[1942,1943,1944,1945],[1807,17985,17987,17990,17993],{"className":17986},[1907,1945],[1807,17988,1852],{"className":17989},[1907,1911,1945],[1807,17991,2209],{"className":17992},[2235,1945],[1807,17994,1869],{"className":17995},[1907,1945],[1807,17997,1963],{"className":17998},[1962],[1807,18000,18002],{"className":18001},[1925],[1807,18003,18005],{"className":18004,"style":3163},[1929],[1807,18006],{}," 或 ",[1807,18009,18011,18035],{"className":18010},[1814],[1807,18012,18014],{"className":18013},[1818],[1820,18015,18016],{"xmlns":1822},[1825,18017,18018,18032],{},[1828,18019,18020],{},[1836,18021,18022,18024],{},[1839,18023,6728],{},[1828,18025,18026,18028,18030],{},[1839,18027,1852],{},[1831,18029,2209],{},[1867,18031,1869],{},[1883,18033,18034],{"encoding":1885},"x_{t+1}",[1807,18036,18038],{"className":18037,"ariaHidden":1848},[1890],[1807,18039,18041,18044],{"className":18040},[1894],[1807,18042],{"className":18043,"style":6400},[1898],[1807,18045,18047,18050],{"className":18046},[1907],[1807,18048,6728],{"className":18049},[1907,1911],[1807,18051,18053],{"className":18052},[1916],[1807,18054,18056,18085],{"className":18055},[1920,1921],[1807,18057,18059,18082],{"className":18058},[1925],[1807,18060,18062],{"className":18061,"style":3009},[1929],[1807,18063,18064,18067],{"style":2457},[1807,18065],{"className":18066,"style":1938},[1937],[1807,18068,18070],{"className":18069},[1942,1943,1944,1945],[1807,18071,18073,18076,18079],{"className":18072},[1907,1945],[1807,18074,1852],{"className":18075},[1907,1911,1945],[1807,18077,2209],{"className":18078},[2235,1945],[1807,18080,1869],{"className":18081},[1907,1945],[1807,18083,1963],{"className":18084},[1962],[1807,18086,18088],{"className":18087},[1925],[1807,18089,18091],{"className":18090,"style":3163},[1929],[1807,18092],{}," 中的信息，就违反了自洽的信息集假设 ",[1807,18095,18097,18114],{"className":18096},[1814],[1807,18098,18100],{"className":18099},[1818],[1820,18101,18102],{"xmlns":1822},[1825,18103,18104,18112],{},[1828,18105,18106],{},[1836,18107,18108,18110],{},[1839,18109,2132],{"mathvariant":2131},[1839,18111,1852],{},[1883,18113,2137],{"encoding":1885},[1807,18115,18117],{"className":18116,"ariaHidden":1848},[1890],[1807,18118,18120,18123],{"className":18119},[1894],[1807,18121],{"className":18122,"style":2147},[1898],[1807,18124,18126,18129],{"className":18125},[1907],[1807,18127,2132],{"className":18128,"style":2155},[1907,2154],[1807,18130,18132],{"className":18131},[1916],[1807,18133,18135,18155],{"className":18134},[1920,1921],[1807,18136,18138,18152],{"className":18137},[1925],[1807,18139,18141],{"className":18140,"style":1930},[1929],[1807,18142,18143,18146],{"style":2170},[1807,18144],{"className":18145,"style":1938},[1937],[1807,18147,18149],{"className":18148},[1942,1943,1944,1945],[1807,18150,1852],{"className":18151},[1907,1911,1945],[1807,18153,1963],{"className":18154},[1962],[1807,18156,18158],{"className":18157},[1925],[1807,18159,18161],{"className":18160,"style":2189},[1929],[1807,18162],{},"，从而导致回测结果对未来信息敏感，具有不可实现性。",[12741,18165,18167],{"id":18166},"_63-交易成本与成交模型过于乐观","6.3 交易成本与成交模型过于乐观",[1792,18169,18170],{},"简单的“按收盘价成交且无成本”假设在学术教学上尚可，但在研究导向的实务环境中会造成显著偏差：",[5589,18172,18173,18176,18179],{},[4352,18174,18175],{},"忽略显性成本（佣金、印花税、挂牌费等）；",[4352,18177,18178],{},"忽略隐性成本（冲击成本、机会成本、价差损失）；",[4352,18180,18181],{},"假设任意规模都能瞬间以某个理想价格成交，忽略了流动性约束。",[1792,18183,18184],{},"更精细的模型通常会：",[5589,18186,18187,18190,18193],{},[4352,18188,18189],{},"将价差（bid–ask spread）的一半作为基础成本；",[4352,18191,18192],{},"将成交量的某个比例与价格冲击函数结合，模拟大额交易的价格影响；",[4352,18194,18195],{},"使用成交量加权平均价（VWAP）或区间价格作为更接近真实的成交价近似。",[12741,18197,18199],{"id":18198},"_64-参数过拟合与多重检验","6.4 参数过拟合与多重检验",[1792,18201,18202],{},"在同一份数据上反复测试大量策略、频繁调参，会严重放大小样本中的偶然性：",[5589,18204,18205,18208],{},[4352,18206,18207],{},"样本内表现极好的策略，在样本外很可能迅速失效；",[4352,18209,18210],{},"多重检验问题使得传统 t 检验和 p 值不再可靠。",[1792,18212,18213],{},"研究导向的解决方案包括：",[5589,18215,18216,18219,18222],{},[4352,18217,18218],{},"严格的训练\u002F验证\u002F测试集划分；",[4352,18220,18221],{},"使用滚动窗口和“跨时间交叉验证”方法；",[4352,18223,18224],{},"使用 White’s Reality Check 或 SPA 检验等更高级的统计方法评估策略显著性（White, 2000; Hansen, 2005）。",[1792,18226,18227],{},"在更精细的设置中，还可以考虑引入“模型复杂度惩罚”，例如通过信息准则（AIC\u002FBIC）或 VC 维、Rademacher 复杂度等概念，从理论层面约束可接受的模型族复杂度，从而降低过拟合风险。这部分思想与统计学习理论和机器学习中的结构风险最小化是一致的。",[2078,18229,18231],{"id":18230},"_7-简单线性回测模型的数学小结","7. 简单线性回测模型的数学小结",[1792,18233,18234],{},"将上述内容抽象成一个简化的线性模型，可以写作：",[4349,18236,18237,18567,18757],{},[4352,18238,18239,18240,18397,5090,18399,18468,18469,18497,18498,5986],{},"因子生成：",[1807,18241,18243],{"className":18242},[1810],[1807,18244,18246,18281],{"className":18245},[1814],[1807,18247,18249],{"className":18248},[1818],[1820,18250,18251],{"xmlns":1822,"display":1823},[1825,18252,18253,18278],{},[1828,18254,18255,18261,18263,18266,18268,18274,18276],{},[1836,18256,18257,18259],{},[1839,18258,6728],{},[1839,18260,1852],{},[1831,18262,1865],{},[1839,18264,18265],{},"F",[1831,18267,2282],{"stretchy":1833},[1836,18269,18270,18272],{},[1839,18271,2132],{"mathvariant":2131},[1839,18273,1852],{},[1831,18275,2291],{"stretchy":1833},[1831,18277,1849],{"separator":1848},[1883,18279,18280],{"encoding":1885},"x_t = F(\\mathcal{I}_t),",[1807,18282,18284,18339],{"className":18283,"ariaHidden":1848},[1890],[1807,18285,18287,18290,18330,18333,18336],{"className":18286},[1894],[1807,18288],{"className":18289,"style":2436},[1898],[1807,18291,18293,18296],{"className":18292},[1907],[1807,18294,6728],{"className":18295},[1907,1911],[1807,18297,18299],{"className":18298},[1916],[1807,18300,18302,18322],{"className":18301},[1920,1921],[1807,18303,18305,18319],{"className":18304},[1925],[1807,18306,18308],{"className":18307,"style":1930},[1929],[1807,18309,18310,18313],{"style":2457},[1807,18311],{"className":18312,"style":1938},[1937],[1807,18314,18316],{"className":18315},[1942,1943,1944,1945],[1807,18317,1852],{"className":18318},[1907,1911,1945],[1807,18320,1963],{"className":18321},[1962],[1807,18323,18325],{"className":18324},[1925],[1807,18326,18328],{"className":18327,"style":2189},[1929],[1807,18329],{},[1807,18331],{"className":18332,"style":2044},[2043],[1807,18334,1865],{"className":18335},[2011],[1807,18337],{"className":18338,"style":2044},[2043],[1807,18340,18342,18345,18348,18351,18391,18394],{"className":18341},[1894],[1807,18343],{"className":18344,"style":2057},[1898],[1807,18346,18265],{"className":18347,"style":2027},[1907,1911],[1807,18349,2282],{"className":18350},[1903],[1807,18352,18354,18357],{"className":18353},[1907],[1807,18355,2132],{"className":18356,"style":2155},[1907,2154],[1807,18358,18360],{"className":18359},[1916],[1807,18361,18363,18383],{"className":18362},[1920,1921],[1807,18364,18366,18380],{"className":18365},[1925],[1807,18367,18369],{"className":18368,"style":1930},[1929],[1807,18370,18371,18374],{"style":2170},[1807,18372],{"className":18373,"style":1938},[1937],[1807,18375,18377],{"className":18376},[1942,1943,1944,1945],[1807,18378,1852],{"className":18379},[1907,1911,1945],[1807,18381,1963],{"className":18382},[1962],[1807,18384,18386],{"className":18385},[1925],[1807,18387,18389],{"className":18388,"style":2189},[1929],[1807,18390],{},[1807,18392,2291],{"className":18393},[1976],[1807,18395,1849],{"className":18396},[1955],[9924,18398],{},[1807,18400,18402,18419],{"className":18401},[1814],[1807,18403,18405],{"className":18404},[1818],[1820,18406,18407],{"xmlns":1822},[1825,18408,18409,18417],{},[1828,18410,18411],{},[1836,18412,18413,18415],{},[1839,18414,6728],{},[1839,18416,1852],{},[1883,18418,6871],{"encoding":1885},[1807,18420,18422],{"className":18421,"ariaHidden":1848},[1890],[1807,18423,18425,18428],{"className":18424},[1894],[1807,18426],{"className":18427,"style":2436},[1898],[1807,18429,18431,18434],{"className":18430},[1907],[1807,18432,6728],{"className":18433},[1907,1911],[1807,18435,18437],{"className":18436},[1916],[1807,18438,18440,18460],{"className":18439},[1920,1921],[1807,18441,18443,18457],{"className":18442},[1925],[1807,18444,18446],{"className":18445,"style":1930},[1929],[1807,18447,18448,18451],{"style":2457},[1807,18449],{"className":18450,"style":1938},[1937],[1807,18452,18454],{"className":18453},[1942,1943,1944,1945],[1807,18455,1852],{"className":18456},[1907,1911,1945],[1807,18458,1963],{"className":18459},[1962],[1807,18461,18463],{"className":18462},[1925],[1807,18464,18466],{"className":18465,"style":2189},[1929],[1807,18467],{}," 是因子向量，",[1807,18470,18472,18485],{"className":18471},[1814],[1807,18473,18475],{"className":18474},[1818],[1820,18476,18477],{"xmlns":1822},[1825,18478,18479,18483],{},[1828,18480,18481],{},[1839,18482,18265],{},[1883,18484,18265],{"encoding":1885},[1807,18486,18488],{"className":18487,"ariaHidden":1848},[1890],[1807,18489,18491,18494],{"className":18490},[1894],[1807,18492],{"className":18493,"style":3587},[1898],[1807,18495,18265],{"className":18496,"style":2027},[1907,1911]," 为一个映射，只依赖于已知信息集 ",[1807,18499,18501,18518],{"className":18500},[1814],[1807,18502,18504],{"className":18503},[1818],[1820,18505,18506],{"xmlns":1822},[1825,18507,18508,18516],{},[1828,18509,18510],{},[1836,18511,18512,18514],{},[1839,18513,2132],{"mathvariant":2131},[1839,18515,1852],{},[1883,18517,2137],{"encoding":1885},[1807,18519,18521],{"className":18520,"ariaHidden":1848},[1890],[1807,18522,18524,18527],{"className":18523},[1894],[1807,18525],{"className":18526,"style":2147},[1898],[1807,18528,18530,18533],{"className":18529},[1907],[1807,18531,2132],{"className":18532,"style":2155},[1907,2154],[1807,18534,18536],{"className":18535},[1916],[1807,18537,18539,18559],{"className":18538},[1920,1921],[1807,18540,18542,18556],{"className":18541},[1925],[1807,18543,18545],{"className":18544,"style":1930},[1929],[1807,18546,18547,18550],{"style":2170},[1807,18548],{"className":18549,"style":1938},[1937],[1807,18551,18553],{"className":18552},[1942,1943,1944,1945],[1807,18554,1852],{"className":18555},[1907,1911,1945],[1807,18557,1963],{"className":18558},[1962],[1807,18560,18562],{"className":18561},[1925],[1807,18563,18565],{"className":18564,"style":2189},[1929],[1807,18566],{},[4352,18568,18569,18570,18726,18728,18756],{},"信号与权重：",[1807,18571,18573],{"className":18572},[1810],[1807,18574,18576,18610],{"className":18575},[1814],[1807,18577,18579],{"className":18578},[1818],[1820,18580,18581],{"xmlns":1822,"display":1823},[1825,18582,18583,18607],{},[1828,18584,18585,18591,18593,18595,18597,18603,18605],{},[1836,18586,18587,18589],{},[1839,18588,2333],{},[1839,18590,1852],{},[1831,18592,1865],{},[1839,18594,2340],{},[1831,18596,2282],{"stretchy":1833},[1836,18598,18599,18601],{},[1839,18600,6728],{},[1839,18602,1852],{},[1831,18604,2291],{"stretchy":1833},[1831,18606,1849],{"separator":1848},[1883,18608,18609],{"encoding":1885},"w_t = G(x_t),",[1807,18611,18613,18668],{"className":18612,"ariaHidden":1848},[1890],[1807,18614,18616,18619,18659,18662,18665],{"className":18615},[1894],[1807,18617],{"className":18618,"style":2436},[1898],[1807,18620,18622,18625],{"className":18621},[1907],[1807,18623,2333],{"className":18624,"style":2719},[1907,1911],[1807,18626,18628],{"className":18627},[1916],[1807,18629,18631,18651],{"className":18630},[1920,1921],[1807,18632,18634,18648],{"className":18633},[1925],[1807,18635,18637],{"className":18636,"style":1930},[1929],[1807,18638,18639,18642],{"style":2734},[1807,18640],{"className":18641,"style":1938},[1937],[1807,18643,18645],{"className":18644},[1942,1943,1944,1945],[1807,18646,1852],{"className":18647},[1907,1911,1945],[1807,18649,1963],{"className":18650},[1962],[1807,18652,18654],{"className":18653},[1925],[1807,18655,18657],{"className":18656,"style":2189},[1929],[1807,18658],{},[1807,18660],{"className":18661,"style":2044},[2043],[1807,18663,1865],{"className":18664},[2011],[1807,18666],{"className":18667,"style":2044},[2043],[1807,18669,18671,18674,18677,18680,18720,18723],{"className":18670},[1894],[1807,18672],{"className":18673,"style":2057},[1898],[1807,18675,2340],{"className":18676},[1907,1911],[1807,18678,2282],{"className":18679},[1903],[1807,18681,18683,18686],{"className":18682},[1907],[1807,18684,6728],{"className":18685},[1907,1911],[1807,18687,18689],{"className":18688},[1916],[1807,18690,18692,18712],{"className":18691},[1920,1921],[1807,18693,18695,18709],{"className":18694},[1925],[1807,18696,18698],{"className":18697,"style":1930},[1929],[1807,18699,18700,18703],{"style":2457},[1807,18701],{"className":18702,"style":1938},[1937],[1807,18704,18706],{"className":18705},[1942,1943,1944,1945],[1807,18707,1852],{"className":18708},[1907,1911,1945],[1807,18710,1963],{"className":18711},[1962],[1807,18713,18715],{"className":18714},[1925],[1807,18716,18718],{"className":18717,"style":2189},[1929],[1807,18719],{},[1807,18721,2291],{"className":18722},[1976],[1807,18724,1849],{"className":18725},[1955],[9924,18727],{},[1807,18729,18731,18744],{"className":18730},[1814],[1807,18732,18734],{"className":18733},[1818],[1820,18735,18736],{"xmlns":1822},[1825,18737,18738,18742],{},[1828,18739,18740],{},[1839,18741,2340],{},[1883,18743,2340],{"encoding":1885},[1807,18745,18747],{"className":18746,"ariaHidden":1848},[1890],[1807,18748,18750,18753],{"className":18749},[1894],[1807,18751],{"className":18752,"style":3587},[1898],[1807,18754,2340],{"className":18755},[1907,1911]," 可以是线性函数（如多因子线性打分）或非线性模型（如树模型）。",[4352,18758,18759,18760,19148,5090,19150,19194,19195,19343],{},"策略收益：",[1807,18761,18763],{"className":18762},[1810],[1807,18764,18766,18847],{"className":18765},[1814],[1807,18767,18769],{"className":18768},[1818],[1820,18770,18771],{"xmlns":1822,"display":1823},[1825,18772,18773,18844],{},[1828,18774,18775,18791,18793,18801,18813,18815,18818,18820,18826,18828,18840,18842],{},[1836,18776,18777,18779],{},[1839,18778,1841],{},[1828,18780,18781,18783,18785,18787,18789],{},[1839,18782,1792],{},[1831,18784,1849],{"separator":1848},[1839,18786,1852],{},[1831,18788,2209],{},[1867,18790,1869],{},[1831,18792,1865],{},[1854,18794,18795,18797,18799],{},[1839,18796,2333],{},[1839,18798,1852],{},[1839,18800,2408],{"mathvariant":2361},[1836,18802,18803,18805],{},[1839,18804,1841],{},[1828,18806,18807,18809,18811],{},[1839,18808,1852],{},[1831,18810,2209],{},[1867,18812,1869],{},[1831,18814,3649],{},[1839,18816,18817],{},"C",[1831,18819,2282],{"stretchy":1833},[1836,18821,18822,18824],{},[1839,18823,2333],{},[1839,18825,1852],{},[1831,18827,1849],{"separator":1848},[1836,18829,18830,18832],{},[1839,18831,2333],{},[1828,18833,18834,18836,18838],{},[1839,18835,1852],{},[1831,18837,3649],{},[1867,18839,1869],{},[1831,18841,2291],{"stretchy":1833},[1831,18843,1849],{"separator":1848},[1883,18845,18846],{"encoding":1885},"r_{p,t+1} = w_t^\\top r_{t+1} - C(w_t, w_{t-1}),",[1807,18848,18850,18920,19035],{"className":18849,"ariaHidden":1848},[1890],[1807,18851,18853,18856,18911,18914,18917],{"className":18852},[1894],[1807,18854],{"className":18855,"style":4728},[1898],[1807,18857,18859,18862],{"className":18858},[1907],[1807,18860,1841],{"className":18861,"style":1912},[1907,1911],[1807,18863,18865],{"className":18864},[1916],[1807,18866,18868,18903],{"className":18867},[1920,1921],[1807,18869,18871,18900],{"className":18870},[1925],[1807,18872,18874],{"className":18873,"style":3009},[1929],[1807,18875,18876,18879],{"style":1933},[1807,18877],{"className":18878,"style":1938},[1937],[1807,18880,18882],{"className":18881},[1942,1943,1944,1945],[1807,18883,18885,18888,18891,18894,18897],{"className":18884},[1907,1945],[1807,18886,1792],{"className":18887},[1907,1911,1945],[1807,18889,1849],{"className":18890},[1955,1945],[1807,18892,1852],{"className":18893},[1907,1911,1945],[1807,18895,2209],{"className":18896},[2235,1945],[1807,18898,1869],{"className":18899},[1907,1945],[1807,18901,1963],{"className":18902},[1962],[1807,18904,18906],{"className":18905},[1925],[1807,18907,18909],{"className":18908,"style":1970},[1929],[1807,18910],{},[1807,18912],{"className":18913,"style":2044},[2043],[1807,18915,1865],{"className":18916},[2011],[1807,18918],{"className":18919,"style":2044},[2043],[1807,18921,18923,18926,18977,19026,19029,19032],{"className":18922},[1894],[1807,18924],{"className":18925,"style":3062},[1898],[1807,18927,18929,18932],{"className":18928},[1907],[1807,18930,2333],{"className":18931,"style":2719},[1907,1911],[1807,18933,18935],{"className":18934},[1916],[1807,18936,18938,18969],{"className":18937},[1920,1921],[1807,18939,18941,18966],{"className":18940},[1925],[1807,18942,18944,18955],{"className":18943,"style":3081},[1929],[1807,18945,18946,18949],{"style":3084},[1807,18947],{"className":18948,"style":1938},[1937],[1807,18950,18952],{"className":18951},[1942,1943,1944,1945],[1807,18953,1852],{"className":18954},[1907,1911,1945],[1807,18956,18957,18960],{"style":2017},[1807,18958],{"className":18959,"style":1938},[1937],[1807,18961,18963],{"className":18962},[1942,1943,1944,1945],[1807,18964,2408],{"className":18965},[1907,1945],[1807,18967,1963],{"className":18968},[1962],[1807,18970,18972],{"className":18971},[1925],[1807,18973,18975],{"className":18974,"style":2037},[1929],[1807,18976],{},[1807,18978,18980,18983],{"className":18979},[1907],[1807,18981,1841],{"className":18982,"style":1912},[1907,1911],[1807,18984,18986],{"className":18985},[1916],[1807,18987,18989,19018],{"className":18988},[1920,1921],[1807,18990,18992,19015],{"className":18991},[1925],[1807,18993,18995],{"className":18994,"style":3009},[1929],[1807,18996,18997,19000],{"style":1933},[1807,18998],{"className":18999,"style":1938},[1937],[1807,19001,19003],{"className":19002},[1942,1943,1944,1945],[1807,19004,19006,19009,19012],{"className":19005},[1907,1945],[1807,19007,1852],{"className":19008},[1907,1911,1945],[1807,19010,2209],{"className":19011},[2235,1945],[1807,19013,1869],{"className":19014},[1907,1945],[1807,19016,1963],{"className":19017},[1962],[1807,19019,19021],{"className":19020},[1925],[1807,19022,19024],{"className":19023,"style":3163},[1929],[1807,19025],{},[1807,19027],{"className":19028,"style":2231},[2043],[1807,19030,3649],{"className":19031},[2235],[1807,19033],{"className":19034,"style":2231},[2043],[1807,19036,19038,19041,19044,19047,19087,19090,19093,19142,19145],{"className":19037},[1894],[1807,19039],{"className":19040,"style":2057},[1898],[1807,19042,18817],{"className":19043,"style":8795},[1907,1911],[1807,19045,2282],{"className":19046},[1903],[1807,19048,19050,19053],{"className":19049},[1907],[1807,19051,2333],{"className":19052,"style":2719},[1907,1911],[1807,19054,19056],{"className":19055},[1916],[1807,19057,19059,19079],{"className":19058},[1920,1921],[1807,19060,19062,19076],{"className":19061},[1925],[1807,19063,19065],{"className":19064,"style":1930},[1929],[1807,19066,19067,19070],{"style":2734},[1807,19068],{"className":19069,"style":1938},[1937],[1807,19071,19073],{"className":19072},[1942,1943,1944,1945],[1807,19074,1852],{"className":19075},[1907,1911,1945],[1807,19077,1963],{"className":19078},[1962],[1807,19080,19082],{"className":19081},[1925],[1807,19083,19085],{"className":19084,"style":2189},[1929],[1807,19086],{},[1807,19088,1849],{"className":19089},[1955],[1807,19091],{"className":19092,"style":2553},[2043],[1807,19094,19096,19099],{"className":19095},[1907],[1807,19097,2333],{"className":19098,"style":2719},[1907,1911],[1807,19100,19102],{"className":19101},[1916],[1807,19103,19105,19134],{"className":19104},[1920,1921],[1807,19106,19108,19131],{"className":19107},[1925],[1807,19109,19111],{"className":19110,"style":3009},[1929],[1807,19112,19113,19116],{"style":2734},[1807,19114],{"className":19115,"style":1938},[1937],[1807,19117,19119],{"className":19118},[1942,1943,1944,1945],[1807,19120,19122,19125,19128],{"className":19121},[1907,1945],[1807,19123,1852],{"className":19124},[1907,1911,1945],[1807,19126,3649],{"className":19127},[2235,1945],[1807,19129,1869],{"className":19130},[1907,1945],[1807,19132,1963],{"className":19133},[1962],[1807,19135,19137],{"className":19136},[1925],[1807,19138,19140],{"className":19139,"style":3163},[1929],[1807,19141],{},[1807,19143,2291],{"className":19144},[1976],[1807,19146,1849],{"className":19147},[1955],[9924,19149],{},[1807,19151,19153,19173],{"className":19152},[1814],[1807,19154,19156],{"className":19155},[1818],[1820,19157,19158],{"xmlns":1822},[1825,19159,19160,19170],{},[1828,19161,19162,19164,19166,19168],{},[1839,19163,18817],{},[1831,19165,2282],{"stretchy":1833},[1831,19167,17895],{},[1831,19169,2291],{"stretchy":1833},[1883,19171,19172],{"encoding":1885},"C(\\cdot)",[1807,19174,19176],{"className":19175,"ariaHidden":1848},[1890],[1807,19177,19179,19182,19185,19188,19191],{"className":19178},[1894],[1807,19180],{"className":19181,"style":2057},[1898],[1807,19183,18817],{"className":19184,"style":8795},[1907,1911],[1807,19186,2282],{"className":19187},[1903],[1807,19189,17895],{"className":19190},[1907],[1807,19192,2291],{"className":19193},[1976]," 是交易成本函数，通常依赖于权重变化 ",[1807,19196,19198,19230],{"className":19197},[1814],[1807,19199,19201],{"className":19200},[1818],[1820,19202,19203],{"xmlns":1822},[1825,19204,19205,19227],{},[1828,19206,19207,19213,19215],{},[1836,19208,19209,19211],{},[1839,19210,2333],{},[1839,19212,1852],{},[1831,19214,3649],{},[1836,19216,19217,19219],{},[1839,19218,2333],{},[1828,19220,19221,19223,19225],{},[1839,19222,1852],{},[1831,19224,3649],{},[1867,19226,1869],{},[1883,19228,19229],{"encoding":1885},"w_t - w_{t-1}",[1807,19231,19233,19288],{"className":19232,"ariaHidden":1848},[1890],[1807,19234,19236,19239,19279,19282,19285],{"className":19235},[1894],[1807,19237],{"className":19238,"style":7120},[1898],[1807,19240,19242,19245],{"className":19241},[1907],[1807,19243,2333],{"className":19244,"style":2719},[1907,1911],[1807,19246,19248],{"className":19247},[1916],[1807,19249,19251,19271],{"className":19250},[1920,1921],[1807,19252,19254,19268],{"className":19253},[1925],[1807,19255,19257],{"className":19256,"style":1930},[1929],[1807,19258,19259,19262],{"style":2734},[1807,19260],{"className":19261,"style":1938},[1937],[1807,19263,19265],{"className":19264},[1942,1943,1944,1945],[1807,19266,1852],{"className":19267},[1907,1911,1945],[1807,19269,1963],{"className":19270},[1962],[1807,19272,19274],{"className":19273},[1925],[1807,19275,19277],{"className":19276,"style":2189},[1929],[1807,19278],{},[1807,19280],{"className":19281,"style":2231},[2043],[1807,19283,3649],{"className":19284},[2235],[1807,19286],{"className":19287,"style":2231},[2043],[1807,19289,19291,19294],{"className":19290},[1894],[1807,19292],{"className":19293,"style":6400},[1898],[1807,19295,19297,19300],{"className":19296},[1907],[1807,19298,2333],{"className":19299,"style":2719},[1907,1911],[1807,19301,19303],{"className":19302},[1916],[1807,19304,19306,19335],{"className":19305},[1920,1921],[1807,19307,19309,19332],{"className":19308},[1925],[1807,19310,19312],{"className":19311,"style":3009},[1929],[1807,19313,19314,19317],{"style":2734},[1807,19315],{"className":19316,"style":1938},[1937],[1807,19318,19320],{"className":19319},[1942,1943,1944,1945],[1807,19321,19323,19326,19329],{"className":19322},[1907,1945],[1807,19324,1852],{"className":19325},[1907,1911,1945],[1807,19327,3649],{"className":19328},[2235,1945],[1807,19330,1869],{"className":19331},[1907,1945],[1807,19333,1963],{"className":19334},[1962],[1807,19336,19338],{"className":19337},[1925],[1807,19339,19341],{"className":19340,"style":3163},[1929],[1807,19342],{}," 及市场流动性。",[1792,19345,19346],{},"理论上，我们希望在某个意义下最大化",[1807,19348,19350],{"className":19349},[1810],[1807,19351,19353,19439],{"className":19352},[1814],[1807,19354,19356],{"className":19355},[1818],[1820,19357,19358],{"xmlns":1822,"display":1823},[1825,19359,19360,19436],{},[1828,19361,19362,19372,19375,19379,19382,19398,19401,19403,19409,19412,19414,19416,19432,19434],{},[3623,19363,19364,19370],{},[1828,19365,19366,19368],{},[1839,19367,3629],{},[1831,19369,3632],{},[1839,19371,2340],{},[1877,19373,19374],{}," ",[1839,19376,19378],{"mathvariant":19377},"double-struck","E",[1831,19380,19381],{"stretchy":1833},"[",[1836,19383,19384,19386],{},[1839,19385,1841],{},[1828,19387,19388,19390,19392,19394,19396],{},[1839,19389,1792],{},[1831,19391,1849],{"separator":1848},[1839,19393,1852],{},[1831,19395,2209],{},[1867,19397,1869],{},[1831,19399,19400],{"stretchy":1833},"]",[1831,19402,3649],{},[3651,19404,19405,19407],{},[1839,19406,8511],{},[1867,19408,3658],{},[1839,19410,19411],{"mathvariant":2361},"Var",[1831,19413,3632],{},[1831,19415,2282],{"stretchy":1833},[1836,19417,19418,19420],{},[1839,19419,1841],{},[1828,19421,19422,19424,19426,19428,19430],{},[1839,19423,1792],{},[1831,19425,1849],{"separator":1848},[1839,19427,1852],{},[1831,19429,2209],{},[1867,19431,1869],{},[1831,19433,2291],{"stretchy":1833},[1831,19435,1849],{"separator":1848},[1883,19437,19438],{"encoding":1885}," \\max_G \\ \\mathbb{E}[r_{p,t+1}] - \\frac{\\lambda}{2} \\operatorname{Var}(r_{p,t+1}),",[1807,19440,19442,19574],{"className":19441,"ariaHidden":1848},[1890],[1807,19443,19445,19449,19494,19497,19500,19504,19507,19562,19565,19568,19571],{"className":19444},[1894],[1807,19446],{"className":19447,"style":19448},[1898],"height:1.4943em;vertical-align:-0.7443em;",[1807,19450,19452],{"className":19451},[3687,3688],[1807,19453,19455,19485],{"className":19454},[1920,1921],[1807,19456,19458,19482],{"className":19457},[1925],[1807,19459,19461,19472],{"className":19460,"style":3698},[1929],[1807,19462,19463,19466],{"style":17018},[1807,19464],{"className":19465,"style":2577},[1937],[1807,19467,19469],{"className":19468},[1942,1943,1944,1945],[1807,19470,2340],{"className":19471},[1907,1911,1945],[1807,19473,19474,19477],{"style":2573},[1807,19475],{"className":19476,"style":2577},[1937],[1807,19478,19479],{},[1807,19480,3629],{"className":19481},[3687],[1807,19483,1963],{"className":19484},[1962],[1807,19486,19488],{"className":19487},[1925],[1807,19489,19492],{"className":19490,"style":19491},[1929],"height:0.7443em;",[1807,19493],{},[1807,19495,19374],{"className":19496},[2043],[1807,19498],{"className":19499,"style":2553},[2043],[1807,19501,19378],{"className":19502},[1907,19503],"mathbb",[1807,19505,19381],{"className":19506},[1903],[1807,19508,19510,19513],{"className":19509},[1907],[1807,19511,1841],{"className":19512,"style":1912},[1907,1911],[1807,19514,19516],{"className":19515},[1916],[1807,19517,19519,19554],{"className":19518},[1920,1921],[1807,19520,19522,19551],{"className":19521},[1925],[1807,19523,19525],{"className":19524,"style":3009},[1929],[1807,19526,19527,19530],{"style":1933},[1807,19528],{"className":19529,"style":1938},[1937],[1807,19531,19533],{"className":19532},[1942,1943,1944,1945],[1807,19534,19536,19539,19542,19545,19548],{"className":19535},[1907,1945],[1807,19537,1792],{"className":19538},[1907,1911,1945],[1807,19540,1849],{"className":19541},[1955,1945],[1807,19543,1852],{"className":19544},[1907,1911,1945],[1807,19546,2209],{"className":19547},[2235,1945],[1807,19549,1869],{"className":19550},[1907,1945],[1807,19552,1963],{"className":19553},[1962],[1807,19555,19557],{"className":19556},[1925],[1807,19558,19560],{"className":19559,"style":1970},[1929],[1807,19561],{},[1807,19563,19400],{"className":19564},[1976],[1807,19566],{"className":19567,"style":2231},[2043],[1807,19569,3649],{"className":19570},[2235],[1807,19572],{"className":19573,"style":2231},[2043],[1807,19575,19577,19581,19643,19646,19653,19656,19711,19714],{"className":19576},[1894],[1807,19578],{"className":19579,"style":19580},[1898],"height:2.0574em;vertical-align:-0.686em;",[1807,19582,19584,19587,19640],{"className":19583},[1907],[1807,19585],{"className":19586},[1903,3793],[1807,19588,19590],{"className":19589},[3651],[1807,19591,19593,19632],{"className":19592},[1920,1921],[1807,19594,19596,19629],{"className":19595},[1925],[1807,19597,19599,19610,19618],{"className":19598,"style":15950},[1929],[1807,19600,19601,19604],{"style":3809},[1807,19602],{"className":19603,"style":2577},[1937],[1807,19605,19607],{"className":19606},[1907],[1807,19608,3658],{"className":19609},[1907],[1807,19611,19612,19615],{"style":3821},[1807,19613],{"className":19614,"style":2577},[1937],[1807,19616],{"className":19617,"style":3829},[3828],[1807,19619,19620,19623],{"style":3832},[1807,19621],{"className":19622,"style":2577},[1937],[1807,19624,19626],{"className":19625},[1907],[1807,19627,8511],{"className":19628},[1907,1911],[1807,19630,1963],{"className":19631},[1962],[1807,19633,19635],{"className":19634},[1925],[1807,19636,19638],{"className":19637,"style":3852},[1929],[1807,19639],{},[1807,19641],{"className":19642},[1976,3793],[1807,19644],{"className":19645,"style":2553},[2043],[1807,19647,19649],{"className":19648},[3687],[1807,19650,19411],{"className":19651},[1907,19652],"mathrm",[1807,19654,2282],{"className":19655},[1903],[1807,19657,19659,19662],{"className":19658},[1907],[1807,19660,1841],{"className":19661,"style":1912},[1907,1911],[1807,19663,19665],{"className":19664},[1916],[1807,19666,19668,19703],{"className":19667},[1920,1921],[1807,19669,19671,19700],{"className":19670},[1925],[1807,19672,19674],{"className":19673,"style":3009},[1929],[1807,19675,19676,19679],{"style":1933},[1807,19677],{"className":19678,"style":1938},[1937],[1807,19680,19682],{"className":19681},[1942,1943,1944,1945],[1807,19683,19685,19688,19691,19694,19697],{"className":19684},[1907,1945],[1807,19686,1792],{"className":19687},[1907,1911,1945],[1807,19689,1849],{"className":19690},[1955,1945],[1807,19692,1852],{"className":19693},[1907,1911,1945],[1807,19695,2209],{"className":19696},[2235,1945],[1807,19698,1869],{"className":19699},[1907,1945],[1807,19701,1963],{"className":19702},[1962],[1807,19704,19706],{"className":19705},[1925],[1807,19707,19709],{"className":19708,"style":1970},[1929],[1807,19710],{},[1807,19712,2291],{"className":19713},[1976],[1807,19715,1849],{"className":19716},[1955],[1792,19718,19719,19720,19827],{},"或更一般地，最大化某个效用函数 ",[1807,19721,19723,19758],{"className":19722},[1814],[1807,19724,19726],{"className":19725},[1818],[1820,19727,19728],{"xmlns":1822},[1825,19729,19730,19755],{},[1828,19731,19732,19735,19737,19739,19751,19753],{},[1839,19733,19734],{},"U",[1831,19736,2282],{"stretchy":1833},[1831,19738,1834],{"stretchy":1833},[1836,19740,19741,19743],{},[1839,19742,1841],{},[1828,19744,19745,19747,19749],{},[1839,19746,1792],{},[1831,19748,1849],{"separator":1848},[1839,19750,1852],{},[1831,19752,1858],{"stretchy":1833},[1831,19754,2291],{"stretchy":1833},[1883,19756,19757],{"encoding":1885},"U(\\{r_{p,t}\\})",[1807,19759,19761],{"className":19760,"ariaHidden":1848},[1890],[1807,19762,19764,19767,19770,19774,19823],{"className":19763},[1894],[1807,19765],{"className":19766,"style":4418},[1898],[1807,19768,19734],{"className":19769,"style":5538},[1907,1911],[1807,19771,19773],{"className":19772},[1903],"({",[1807,19775,19777,19780],{"className":19776},[1907],[1807,19778,1841],{"className":19779,"style":1912},[1907,1911],[1807,19781,19783],{"className":19782},[1916],[1807,19784,19786,19815],{"className":19785},[1920,1921],[1807,19787,19789,19812],{"className":19788},[1925],[1807,19790,19792],{"className":19791,"style":1930},[1929],[1807,19793,19794,19797],{"style":1933},[1807,19795],{"className":19796,"style":1938},[1937],[1807,19798,19800],{"className":19799},[1942,1943,1944,1945],[1807,19801,19803,19806,19809],{"className":19802},[1907,1945],[1807,19804,1792],{"className":19805},[1907,1911,1945],[1807,19807,1849],{"className":19808},[1955,1945],[1807,19810,1852],{"className":19811},[1907,1911,1945],[1807,19813,1963],{"className":19814},[1962],[1807,19816,19818],{"className":19817},[1925],[1807,19819,19821],{"className":19820,"style":1970},[1929],[1807,19822],{},[1807,19824,19826],{"className":19825},[1976],"})","。这与均值–方差优化、效用最大化、甚至强化学习框架都有直接联系。",[19829,19830],"hr",{},[2078,19832,19834],{"id":19833},"_8-自学手册搭建一个可信的最小回测","8. 自学手册：搭建一个可信的最小回测",[12741,19836,19838],{"id":19837},"_81-学习目标","8.1 学习目标",[1792,19840,19841],{},"学完本章后，你应当能够：",[4349,19843,19844,19993,19996,19999,20002],{},[4352,19845,19846,19847,19992],{},"用 ",[1807,19848,19850,19882],{"className":19849},[1814],[1807,19851,19853],{"className":19852},[1818],[1820,19854,19855],{"xmlns":1822},[1825,19856,19857,19879],{},[1828,19858,19859,19867],{},[1854,19860,19861,19863,19865],{},[1839,19862,2333],{},[1839,19864,1852],{},[1839,19866,2408],{"mathvariant":2361},[1836,19868,19869,19871],{},[1839,19870,1841],{},[1828,19872,19873,19875,19877],{},[1839,19874,1852],{},[1831,19876,2209],{},[1867,19878,1869],{},[1883,19880,19881],{"encoding":1885},"w_t^\\top r_{t+1}",[1807,19883,19885],{"className":19884,"ariaHidden":1848},[1890],[1807,19886,19888,19892,19943],{"className":19887},[1894],[1807,19889],{"className":19890,"style":19891},[1898],"height:1.0961em;vertical-align:-0.247em;",[1807,19893,19895,19898],{"className":19894},[1907],[1807,19896,2333],{"className":19897,"style":2719},[1907,1911],[1807,19899,19901],{"className":19900},[1916],[1807,19902,19904,19935],{"className":19903},[1920,1921],[1807,19905,19907,19932],{"className":19906},[1925],[1807,19908,19910,19921],{"className":19909,"style":5574},[1929],[1807,19911,19912,19915],{"style":3084},[1807,19913],{"className":19914,"style":1938},[1937],[1807,19916,19918],{"className":19917},[1942,1943,1944,1945],[1807,19919,1852],{"className":19920},[1907,1911,1945],[1807,19922,19923,19926],{"style":5577},[1807,19924],{"className":19925,"style":1938},[1937],[1807,19927,19929],{"className":19928},[1942,1943,1944,1945],[1807,19930,2408],{"className":19931},[1907,1945],[1807,19933,1963],{"className":19934},[1962],[1807,19936,19938],{"className":19937},[1925],[1807,19939,19941],{"className":19940,"style":2037},[1929],[1807,19942],{},[1807,19944,19946,19949],{"className":19945},[1907],[1807,19947,1841],{"className":19948,"style":1912},[1907,1911],[1807,19950,19952],{"className":19951},[1916],[1807,19953,19955,19984],{"className":19954},[1920,1921],[1807,19956,19958,19981],{"className":19957},[1925],[1807,19959,19961],{"className":19960,"style":3009},[1929],[1807,19962,19963,19966],{"style":1933},[1807,19964],{"className":19965,"style":1938},[1937],[1807,19967,19969],{"className":19968},[1942,1943,1944,1945],[1807,19970,19972,19975,19978],{"className":19971},[1907,1945],[1807,19973,1852],{"className":19974},[1907,1911,1945],[1807,19976,2209],{"className":19977},[2235,1945],[1807,19979,1869],{"className":19980},[1907,1945],[1807,19982,1963],{"className":19983},[1962],[1807,19985,19987],{"className":19986},[1925],[1807,19988,19990],{"className":19989,"style":3163},[1929],[1807,19991],{}," 描述策略收益，并说明权重与收益的时间错位；",[4352,19994,19995],{},"写出一个不看未来的日度或月度回测循环；",[4352,19997,19998],{},"计算年化收益、波动、夏普、最大回撤和换手率；",[4352,20000,20001],{},"识别回测中常见的时序错误、成本低估和参数过拟合；",[4352,20003,20004],{},"把回测结果拆成样本内、验证期和样本外评估。",[12741,20006,20008],{"id":20007},"_82-研究场景","8.2 研究场景",[1792,20010,20011,20012,20015],{},"你已经从第 02 章得到一个月度多因子打分 ",[1799,20013,20014],{},"Score_{i,t}","。现在需要回答：如果每月末根据打分调仓，这个信号是否能在 2017-2024 年样本外获得正信息比率？研究经理希望看到的不是一张漂亮净值图，而是一份可审计的回测说明：",[5589,20017,20018,20021,20024,20027,20030],{},[4352,20019,20020],{},"信号在什么时候生成？",[4352,20022,20023],{},"订单在什么时候成交？",[4352,20025,20026],{},"成本和冲击如何扣除？",[4352,20028,20029],{},"参数是否在测试期前固定？",[4352,20031,20032],{},"表现是否来自少数极端月份？",[12741,20034,20036],{"id":20035},"_83-定义与工作流逻辑","8.3 定义与工作流逻辑",[4072,20038,20039,20052],{},[4075,20040,20041],{},[4078,20042,20043,20046,20049],{},[4081,20044,20045],{},"模块",[4081,20047,20048],{},"需要固定的定义",[4081,20050,20051],{},"常见检查",[4091,20053,20054,20219,20428,20551,20716,20977],{},[4078,20055,20056,20059,20131],{},[4096,20057,20058],{},"信息集",[4096,20060,20061,20130],{},[1807,20062,20064,20081],{"className":20063},[1814],[1807,20065,20067],{"className":20066},[1818],[1820,20068,20069],{"xmlns":1822},[1825,20070,20071,20079],{},[1828,20072,20073],{},[1836,20074,20075,20077],{},[1839,20076,2132],{"mathvariant":2131},[1839,20078,1852],{},[1883,20080,2137],{"encoding":1885},[1807,20082,20084],{"className":20083,"ariaHidden":1848},[1890],[1807,20085,20087,20090],{"className":20086},[1894],[1807,20088],{"className":20089,"style":2147},[1898],[1807,20091,20093,20096],{"className":20092},[1907],[1807,20094,2132],{"className":20095,"style":2155},[1907,2154],[1807,20097,20099],{"className":20098},[1916],[1807,20100,20102,20122],{"className":20101},[1920,1921],[1807,20103,20105,20119],{"className":20104},[1925],[1807,20106,20108],{"className":20107,"style":1930},[1929],[1807,20109,20110,20113],{"style":2170},[1807,20111],{"className":20112,"style":1938},[1937],[1807,20114,20116],{"className":20115},[1942,1943,1944,1945],[1807,20117,1852],{"className":20118},[1907,1911,1945],[1807,20120,1963],{"className":20121},[1962],[1807,20123,20125],{"className":20124},[1925],[1807,20126,20128],{"className":20127,"style":2189},[1929],[1807,20129],{}," 包含哪些当时可见字段",[4096,20132,20133,20134,20218],{},"禁止使用 ",[1807,20135,20137,20160],{"className":20136},[1814],[1807,20138,20140],{"className":20139},[1818],[1820,20141,20142],{"xmlns":1822},[1825,20143,20144,20158],{},[1828,20145,20146],{},[1836,20147,20148,20150],{},[1839,20149,1841],{},[1828,20151,20152,20154,20156],{},[1839,20153,1852],{},[1831,20155,2209],{},[1867,20157,1869],{},[1883,20159,11726],{"encoding":1885},[1807,20161,20163],{"className":20162,"ariaHidden":1848},[1890],[1807,20164,20166,20169],{"className":20165},[1894],[1807,20167],{"className":20168,"style":6400},[1898],[1807,20170,20172,20175],{"className":20171},[1907],[1807,20173,1841],{"className":20174,"style":1912},[1907,1911],[1807,20176,20178],{"className":20177},[1916],[1807,20179,20181,20210],{"className":20180},[1920,1921],[1807,20182,20184,20207],{"className":20183},[1925],[1807,20185,20187],{"className":20186,"style":3009},[1929],[1807,20188,20189,20192],{"style":1933},[1807,20190],{"className":20191,"style":1938},[1937],[1807,20193,20195],{"className":20194},[1942,1943,1944,1945],[1807,20196,20198,20201,20204],{"className":20197},[1907,1945],[1807,20199,1852],{"className":20200},[1907,1911,1945],[1807,20202,2209],{"className":20203},[2235,1945],[1807,20205,1869],{"className":20206},[1907,1945],[1807,20208,1963],{"className":20209},[1962],[1807,20211,20213],{"className":20212},[1925],[1807,20214,20216],{"className":20215,"style":3163},[1929],[1807,20217],{}," 或未来财报",[4078,20220,20221,20224,20425],{},[4096,20222,20223],{},"信号",[4096,20225,20226],{},[1807,20227,20229,20284],{"className":20228},[1814],[1807,20230,20232],{"className":20231},[1818],[1820,20233,20234],{"xmlns":1822},[1825,20235,20236,20281],{},[1828,20237,20238,20241,20243,20246,20248,20260,20262,20264,20266,20279],{},[1839,20239,20240],{},"S",[1839,20242,2373],{},[1839,20244,20245],{},"o",[1839,20247,1841],{},[1836,20249,20250,20252],{},[1839,20251,11344],{},[1828,20253,20254,20256,20258],{},[1839,20255,4399],{},[1831,20257,1849],{"separator":1848},[1839,20259,1852],{},[1831,20261,1865],{},[1839,20263,2340],{},[1831,20265,2282],{"stretchy":1833},[1836,20267,20268,20271],{},[1839,20269,20270],{},"X",[1828,20272,20273,20275,20277],{},[1839,20274,4399],{},[1831,20276,1849],{"separator":1848},[1839,20278,1852],{},[1831,20280,2291],{"stretchy":1833},[1883,20282,20283],{"encoding":1885},"Score_{i,t}=G(X_{i,t})",[1807,20285,20287,20359],{"className":20286,"ariaHidden":1848},[1890],[1807,20288,20290,20293,20297,20301,20350,20353,20356],{"className":20289},[1894],[1807,20291],{"className":20292,"style":5127},[1898],[1807,20294,20240],{"className":20295,"style":20296},[1907,1911],"margin-right:0.0576em;",[1807,20298,20300],{"className":20299,"style":1912},[1907,1911],"cor",[1807,20302,20304,20307],{"className":20303},[1907],[1807,20305,11344],{"className":20306},[1907,1911],[1807,20308,20310],{"className":20309},[1916],[1807,20311,20313,20342],{"className":20312},[1920,1921],[1807,20314,20316,20339],{"className":20315},[1925],[1807,20317,20319],{"className":20318,"style":4440},[1929],[1807,20320,20321,20324],{"style":2457},[1807,20322],{"className":20323,"style":1938},[1937],[1807,20325,20327],{"className":20326},[1942,1943,1944,1945],[1807,20328,20330,20333,20336],{"className":20329},[1907,1945],[1807,20331,4399],{"className":20332},[1907,1911,1945],[1807,20334,1849],{"className":20335},[1955,1945],[1807,20337,1852],{"className":20338},[1907,1911,1945],[1807,20340,1963],{"className":20341},[1962],[1807,20343,20345],{"className":20344},[1925],[1807,20346,20348],{"className":20347,"style":1970},[1929],[1807,20349],{},[1807,20351],{"className":20352,"style":2044},[2043],[1807,20354,1865],{"className":20355},[2011],[1807,20357],{"className":20358,"style":2044},[2043],[1807,20360,20362,20365,20368,20371,20422],{"className":20361},[1894],[1807,20363],{"className":20364,"style":4418},[1898],[1807,20366,2340],{"className":20367},[1907,1911],[1807,20369,2282],{"className":20370},[1903],[1807,20372,20374,20378],{"className":20373},[1907],[1807,20375,20270],{"className":20376,"style":20377},[1907,1911],"margin-right:0.0785em;",[1807,20379,20381],{"className":20380},[1916],[1807,20382,20384,20414],{"className":20383},[1920,1921],[1807,20385,20387,20411],{"className":20386},[1925],[1807,20388,20390],{"className":20389,"style":4440},[1929],[1807,20391,20393,20396],{"style":20392},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1807,20394],{"className":20395,"style":1938},[1937],[1807,20397,20399],{"className":20398},[1942,1943,1944,1945],[1807,20400,20402,20405,20408],{"className":20401},[1907,1945],[1807,20403,4399],{"className":20404},[1907,1911,1945],[1807,20406,1849],{"className":20407},[1955,1945],[1807,20409,1852],{"className":20410},[1907,1911,1945],[1807,20412,1963],{"className":20413},[1962],[1807,20415,20417],{"className":20416},[1925],[1807,20418,20420],{"className":20419,"style":1970},[1929],[1807,20421],{},[1807,20423,2291],{"className":20424},[1976],[4096,20426,20427],{},"是否与第 02 章因子口径一致",[4078,20429,20430,20433,20548],{},[4096,20431,20432],{},"调仓",[4096,20434,20435,20436],{},"何时从信号生成 ",[1807,20437,20439,20470],{"className":20438},[1814],[1807,20440,20442],{"className":20441},[1818],[1820,20443,20444],{"xmlns":1822},[1825,20445,20446,20468],{},[1828,20447,20448],{},[1854,20449,20450,20452,20454],{},[1839,20451,2333],{},[1839,20453,1852],{},[1828,20455,20456,20458,20460,20462,20464,20466],{},[1839,20457,1852],{},[1839,20459,3595],{},[1839,20461,1841],{},[1839,20463,6721],{},[1839,20465,11344],{},[1839,20467,1852],{},[1883,20469,11349],{"encoding":1885},[1807,20471,20473],{"className":20472,"ariaHidden":1848},[1890],[1807,20474,20476,20479],{"className":20475},[1894],[1807,20477],{"className":20478,"style":11359},[1898],[1807,20480,20482,20485],{"className":20481},[1907],[1807,20483,2333],{"className":20484,"style":2719},[1907,1911],[1807,20486,20488],{"className":20487},[1916],[1807,20489,20491,20540],{"className":20490},[1920,1921],[1807,20492,20494,20537],{"className":20493},[1925],[1807,20495,20497,20508],{"className":20496,"style":11378},[1929],[1807,20498,20499,20502],{"style":11381},[1807,20500],{"className":20501,"style":1938},[1937],[1807,20503,20505],{"className":20504},[1942,1943,1944,1945],[1807,20506,1852],{"className":20507},[1907,1911,1945],[1807,20509,20510,20513],{"style":11393},[1807,20511],{"className":20512,"style":1938},[1937],[1807,20514,20516],{"className":20515},[1942,1943,1944,1945],[1807,20517,20519,20522,20525,20528,20531,20534],{"className":20518},[1907,1945],[1807,20520,1852],{"className":20521},[1907,1911,1945],[1807,20523,3595],{"className":20524},[1907,1911,1945],[1807,20526,1841],{"className":20527,"style":1912},[1907,1911,1945],[1807,20529,6721],{"className":20530,"style":6803},[1907,1911,1945],[1807,20532,11344],{"className":20533},[1907,1911,1945],[1807,20535,1852],{"className":20536},[1907,1911,1945],[1807,20538,1963],{"className":20539},[1962],[1807,20541,20543],{"className":20542},[1925],[1807,20544,20546],{"className":20545,"style":11430},[1929],[1807,20547],{},[4096,20549,20550],{},"月末信号、下月首日成交",[4078,20552,20553,20556,20713],{},[4096,20554,20555],{},"成本",[4096,20557,20558,20712],{},[1807,20559,20561,20599],{"className":20560},[1814],[1807,20562,20564],{"className":20563},[1818],[1820,20565,20566],{"xmlns":1822},[1825,20567,20568,20596],{},[1828,20569,20570,20572,20574,20580,20582,20594],{},[1839,20571,18817],{},[1831,20573,2282],{"stretchy":1833},[1836,20575,20576,20578],{},[1839,20577,2333],{},[1839,20579,1852],{},[1831,20581,1849],{"separator":1848},[1836,20583,20584,20586],{},[1839,20585,2333],{},[1828,20587,20588,20590,20592],{},[1839,20589,1852],{},[1831,20591,3649],{},[1867,20593,1869],{},[1831,20595,2291],{"stretchy":1833},[1883,20597,20598],{"encoding":1885},"C(w_t,w_{t-1})",[1807,20600,20602],{"className":20601,"ariaHidden":1848},[1890],[1807,20603,20605,20608,20611,20614,20654,20657,20660,20709],{"className":20604},[1894],[1807,20606],{"className":20607,"style":2057},[1898],[1807,20609,18817],{"className":20610,"style":8795},[1907,1911],[1807,20612,2282],{"className":20613},[1903],[1807,20615,20617,20620],{"className":20616},[1907],[1807,20618,2333],{"className":20619,"style":2719},[1907,1911],[1807,20621,20623],{"className":20622},[1916],[1807,20624,20626,20646],{"className":20625},[1920,1921],[1807,20627,20629,20643],{"className":20628},[1925],[1807,20630,20632],{"className":20631,"style":1930},[1929],[1807,20633,20634,20637],{"style":2734},[1807,20635],{"className":20636,"style":1938},[1937],[1807,20638,20640],{"className":20639},[1942,1943,1944,1945],[1807,20641,1852],{"className":20642},[1907,1911,1945],[1807,20644,1963],{"className":20645},[1962],[1807,20647,20649],{"className":20648},[1925],[1807,20650,20652],{"className":20651,"style":2189},[1929],[1807,20653],{},[1807,20655,1849],{"className":20656},[1955],[1807,20658],{"className":20659,"style":2553},[2043],[1807,20661,20663,20666],{"className":20662},[1907],[1807,20664,2333],{"className":20665,"style":2719},[1907,1911],[1807,20667,20669],{"className":20668},[1916],[1807,20670,20672,20701],{"className":20671},[1920,1921],[1807,20673,20675,20698],{"className":20674},[1925],[1807,20676,20678],{"className":20677,"style":3009},[1929],[1807,20679,20680,20683],{"style":2734},[1807,20681],{"className":20682,"style":1938},[1937],[1807,20684,20686],{"className":20685},[1942,1943,1944,1945],[1807,20687,20689,20692,20695],{"className":20688},[1907,1945],[1807,20690,1852],{"className":20691},[1907,1911,1945],[1807,20693,3649],{"className":20694},[2235,1945],[1807,20696,1869],{"className":20697},[1907,1945],[1807,20699,1963],{"className":20700},[1962],[1807,20702,20704],{"className":20703},[1925],[1807,20705,20707],{"className":20706,"style":3163},[1929],[1807,20708],{},[1807,20710,2291],{"className":20711},[1976]," 如何估计",[4096,20714,20715],{},"半价差、佣金、冲击、拒单",[4078,20717,20718,20721,20974],{},[4096,20719,20720],{},"净值",[4096,20722,20723],{},[1807,20724,20726,20782],{"className":20725},[1814],[1807,20727,20729],{"className":20728},[1818],[1820,20730,20731],{"xmlns":1822},[1825,20732,20733,20779],{},[1828,20734,20735,20747,20749,20755,20757,20759,20761,20777],{},[1836,20736,20737,20739],{},[1839,20738,11063],{},[1828,20740,20741,20743,20745],{},[1839,20742,1852],{},[1831,20744,2209],{},[1867,20746,1869],{},[1831,20748,1865],{},[1836,20750,20751,20753],{},[1839,20752,11063],{},[1839,20754,1852],{},[1831,20756,2282],{"stretchy":1833},[1867,20758,1869],{},[1831,20760,2209],{},[1836,20762,20763,20765],{},[1839,20764,1841],{},[1828,20766,20767,20769,20771,20773,20775],{},[1839,20768,1792],{},[1831,20770,1849],{"separator":1848},[1839,20772,1852],{},[1831,20774,2209],{},[1867,20776,1869],{},[1831,20778,2291],{"stretchy":1833},[1883,20780,20781],{"encoding":1885},"V_{t+1}=V_t(1+r_{p,t+1})",[1807,20783,20785,20849,20910],{"className":20784,"ariaHidden":1848},[1890],[1807,20786,20788,20791,20840,20843,20846],{"className":20787},[1894],[1807,20789],{"className":20790,"style":11856},[1898],[1807,20792,20794,20797],{"className":20793},[1907],[1807,20795,11063],{"className":20796,"style":2231},[1907,1911],[1807,20798,20800],{"className":20799},[1916],[1807,20801,20803,20832],{"className":20802},[1920,1921],[1807,20804,20806,20829],{"className":20805},[1925],[1807,20807,20809],{"className":20808,"style":3009},[1929],[1807,20810,20811,20814],{"style":11098},[1807,20812],{"className":20813,"style":1938},[1937],[1807,20815,20817],{"className":20816},[1942,1943,1944,1945],[1807,20818,20820,20823,20826],{"className":20819},[1907,1945],[1807,20821,1852],{"className":20822},[1907,1911,1945],[1807,20824,2209],{"className":20825},[2235,1945],[1807,20827,1869],{"className":20828},[1907,1945],[1807,20830,1963],{"className":20831},[1962],[1807,20833,20835],{"className":20834},[1925],[1807,20836,20838],{"className":20837,"style":3163},[1929],[1807,20839],{},[1807,20841],{"className":20842,"style":2044},[2043],[1807,20844,1865],{"className":20845},[2011],[1807,20847],{"className":20848,"style":2044},[2043],[1807,20850,20852,20855,20895,20898,20901,20904,20907],{"className":20851},[1894],[1807,20853],{"className":20854,"style":2057},[1898],[1807,20856,20858,20861],{"className":20857},[1907],[1807,20859,11063],{"className":20860,"style":2231},[1907,1911],[1807,20862,20864],{"className":20863},[1916],[1807,20865,20867,20887],{"className":20866},[1920,1921],[1807,20868,20870,20884],{"className":20869},[1925],[1807,20871,20873],{"className":20872,"style":1930},[1929],[1807,20874,20875,20878],{"style":11098},[1807,20876],{"className":20877,"style":1938},[1937],[1807,20879,20881],{"className":20880},[1942,1943,1944,1945],[1807,20882,1852],{"className":20883},[1907,1911,1945],[1807,20885,1963],{"className":20886},[1962],[1807,20888,20890],{"className":20889},[1925],[1807,20891,20893],{"className":20892,"style":2189},[1929],[1807,20894],{},[1807,20896,2282],{"className":20897},[1903],[1807,20899,1869],{"className":20900},[1907],[1807,20902],{"className":20903,"style":2231},[2043],[1807,20905,2209],{"className":20906},[2235],[1807,20908],{"className":20909,"style":2231},[2043],[1807,20911,20913,20916,20971],{"className":20912},[1894],[1807,20914],{"className":20915,"style":4418},[1898],[1807,20917,20919,20922],{"className":20918},[1907],[1807,20920,1841],{"className":20921,"style":1912},[1907,1911],[1807,20923,20925],{"className":20924},[1916],[1807,20926,20928,20963],{"className":20927},[1920,1921],[1807,20929,20931,20960],{"className":20930},[1925],[1807,20932,20934],{"className":20933,"style":3009},[1929],[1807,20935,20936,20939],{"style":1933},[1807,20937],{"className":20938,"style":1938},[1937],[1807,20940,20942],{"className":20941},[1942,1943,1944,1945],[1807,20943,20945,20948,20951,20954,20957],{"className":20944},[1907,1945],[1807,20946,1792],{"className":20947},[1907,1911,1945],[1807,20949,1849],{"className":20950},[1955,1945],[1807,20952,1852],{"className":20953},[1907,1911,1945],[1807,20955,2209],{"className":20956},[2235,1945],[1807,20958,1869],{"className":20959},[1907,1945],[1807,20961,1963],{"className":20962},[1962],[1807,20964,20966],{"className":20965},[1925],[1807,20967,20969],{"className":20968,"style":1970},[1929],[1807,20970],{},[1807,20972,2291],{"className":20973},[1976],[4096,20975,20976],{},"现金、分红、退市处理",[4078,20978,20979,20982,20985],{},[4096,20980,20981],{},"评估",[4096,20983,20984],{},"指标和检验窗口",[4096,20986,20987],{},"样本内\u002F外分离、稳健标准误",[1792,20989,20990],{},"最小可信回测可以按下面顺序执行：",[4349,20992,20993,20996,21098,21101,21104,21107,21110],{},[4352,20994,20995],{},"固定数据版本、标的池、调仓日历和参数；",[4352,20997,20998,20999,21027,21028,21097],{},"在每个 ",[1807,21000,21002,21015],{"className":21001},[1814],[1807,21003,21005],{"className":21004},[1818],[1820,21006,21007],{"xmlns":1822},[1825,21008,21009,21013],{},[1828,21010,21011],{},[1839,21012,1852],{},[1883,21014,1852],{"encoding":1885},[1807,21016,21018],{"className":21017,"ariaHidden":1848},[1890],[1807,21019,21021,21024],{"className":21020},[1894],[1807,21022],{"className":21023,"style":2110},[1898],[1807,21025,1852],{"className":21026},[1907,1911]," 只读取 ",[1807,21029,21031,21048],{"className":21030},[1814],[1807,21032,21034],{"className":21033},[1818],[1820,21035,21036],{"xmlns":1822},[1825,21037,21038,21046],{},[1828,21039,21040],{},[1836,21041,21042,21044],{},[1839,21043,2132],{"mathvariant":2131},[1839,21045,1852],{},[1883,21047,2137],{"encoding":1885},[1807,21049,21051],{"className":21050,"ariaHidden":1848},[1890],[1807,21052,21054,21057],{"className":21053},[1894],[1807,21055],{"className":21056,"style":2147},[1898],[1807,21058,21060,21063],{"className":21059},[1907],[1807,21061,2132],{"className":21062,"style":2155},[1907,2154],[1807,21064,21066],{"className":21065},[1916],[1807,21067,21069,21089],{"className":21068},[1920,1921],[1807,21070,21072,21086],{"className":21071},[1925],[1807,21073,21075],{"className":21074,"style":1930},[1929],[1807,21076,21077,21080],{"style":2170},[1807,21078],{"className":21079,"style":1938},[1937],[1807,21081,21083],{"className":21082},[1942,1943,1944,1945],[1807,21084,1852],{"className":21085},[1907,1911,1945],[1807,21087,1963],{"className":21088},[1962],[1807,21090,21092],{"className":21091},[1925],[1807,21093,21095],{"className":21094,"style":2189},[1929],[1807,21096],{}," 内可见数据；",[4352,21099,21100],{},"生成目标权重，并应用组合约束；",[4352,21102,21103],{},"用下一可交易时点的可实现价格成交；",[4352,21105,21106],{},"扣除交易成本和冲击成本；",[4352,21108,21109],{},"记录净值、持仓、交易、风险暴露和异常事件；",[4352,21111,21112],{},"分窗口输出绩效与诊断指标。",[12741,21114,21116],{"id":21115},"_84-迷你案例月度调仓时间线","8.4 迷你案例：月度调仓时间线",[1792,21118,21119],{},"一个常见的正确时间线如下：",[4072,21121,21122,21135],{},[4075,21123,21124],{},[4078,21125,21126,21129,21132],{},[4081,21127,21128],{},"日期",[4081,21130,21131],{},"动作",[4081,21133,21134],{},"可使用信息",[4091,21136,21137,21148,21159,21170],{},[4078,21138,21139,21142,21145],{},[4096,21140,21141],{},"2024-04-30 收盘后",[4096,21143,21144],{},"计算因子和打分",[4096,21146,21147],{},"截至 2024-04-30 已披露、已落库的数据",[4078,21149,21150,21153,21156],{},[4096,21151,21152],{},"2024-05-01 或下一交易日前",[4096,21154,21155],{},"生成目标权重",[4096,21157,21158],{},"固定后的打分、风险模型和约束",[4078,21160,21161,21164,21167],{},[4096,21162,21163],{},"2024-05-02 开盘\u002F区间 VWAP",[4096,21165,21166],{},"模拟成交",[4096,21168,21169],{},"不能用 2024-05-02 收盘后才知道的信息",[4078,21171,21172,21175,21178],{},[4096,21173,21174],{},"2024-05-31",[4096,21176,21177],{},"计算本月收益",[4096,21179,21180],{},"用持仓期间真实收益和成本更新净值",[1792,21182,21183],{},"若你在 2024-04-30 收盘前就假设能使用 2024-04-30 收盘价计算信号并按同一收盘价成交，需要明确这是否符合真实交易流程；多数中低频研究会更保守地设为“收盘后生成信号，下一交易日成交”。",[21185,21186],"pyodide",{"code64":21187,"layout":21188,"locale":7,"title":21189},"bW9udGhseV9yZXR1cm5zID0gWzAuMDMwLCAtMC4wMjAsIDAuMDEwLCAwLjA0MCwgLTAuMDMwLCAwLjAyMCwKICAgICAgICAgICAgICAgICAgIC0wLjAxMCwgMC4wNTAsIC0wLjAyMCwgMC4wMTAsIDAuMDMwLCAtMC4wMTVdCgojIOaciOacq+inguWvn+acrOaciOaUtuebiu+8jOaWueWQkeS\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","vertical","比较正确错位与同月泄漏",[1792,21191,21192,21193,21196,21197,21200,21201,21204],{},"静态结果：正确错位的毛收益合计为 ",[6070,21194,21195],{},"−11.50%","，加入示意成本后为 ",[6070,21198,21199],{},"−12.35%","；泄漏版本却显示 ",[6070,21202,21203],{},"+25.50%","。泄漏版本几乎必然显得优秀，因为仓位由待预测收益本身决定。真实回测还应复利、处理现金和公司行动；这里故意只保留时间错位这一件事。",[12741,21206,21208],{"id":21207},"_85-常见错误与研究陷阱","8.5 常见错误与研究陷阱",[5589,21210,21211,21388,21394,21400,21406],{},[4352,21212,21213,21216,21217,21302,21303,21387],{},[6070,21214,21215],{},"权重和收益同日对齐错误","：用 ",[1807,21218,21220,21244],{"className":21219},[1814],[1807,21221,21223],{"className":21222},[1818],[1820,21224,21225],{"xmlns":1822},[1825,21226,21227,21241],{},[1828,21228,21229],{},[1836,21230,21231,21233],{},[1839,21232,2333],{},[1828,21234,21235,21237,21239],{},[1839,21236,1852],{},[1831,21238,2209],{},[1867,21240,1869],{},[1883,21242,21243],{"encoding":1885},"w_{t+1}",[1807,21245,21247],{"className":21246,"ariaHidden":1848},[1890],[1807,21248,21250,21253],{"className":21249},[1894],[1807,21251],{"className":21252,"style":6400},[1898],[1807,21254,21256,21259],{"className":21255},[1907],[1807,21257,2333],{"className":21258,"style":2719},[1907,1911],[1807,21260,21262],{"className":21261},[1916],[1807,21263,21265,21294],{"className":21264},[1920,1921],[1807,21266,21268,21291],{"className":21267},[1925],[1807,21269,21271],{"className":21270,"style":3009},[1929],[1807,21272,21273,21276],{"style":2734},[1807,21274],{"className":21275,"style":1938},[1937],[1807,21277,21279],{"className":21278},[1942,1943,1944,1945],[1807,21280,21282,21285,21288],{"className":21281},[1907,1945],[1807,21283,1852],{"className":21284},[1907,1911,1945],[1807,21286,2209],{"className":21287},[2235,1945],[1807,21289,1869],{"className":21290},[1907,1945],[1807,21292,1963],{"className":21293},[1962],[1807,21295,21297],{"className":21296},[1925],[1807,21298,21300],{"className":21299,"style":3163},[1929],[1807,21301],{}," 乘 ",[1807,21304,21306,21329],{"className":21305},[1814],[1807,21307,21309],{"className":21308},[1818],[1820,21310,21311],{"xmlns":1822},[1825,21312,21313,21327],{},[1828,21314,21315],{},[1836,21316,21317,21319],{},[1839,21318,1841],{},[1828,21320,21321,21323,21325],{},[1839,21322,1852],{},[1831,21324,2209],{},[1867,21326,1869],{},[1883,21328,11726],{"encoding":1885},[1807,21330,21332],{"className":21331,"ariaHidden":1848},[1890],[1807,21333,21335,21338],{"className":21334},[1894],[1807,21336],{"className":21337,"style":6400},[1898],[1807,21339,21341,21344],{"className":21340},[1907],[1807,21342,1841],{"className":21343,"style":1912},[1907,1911],[1807,21345,21347],{"className":21346},[1916],[1807,21348,21350,21379],{"className":21349},[1920,1921],[1807,21351,21353,21376],{"className":21352},[1925],[1807,21354,21356],{"className":21355,"style":3009},[1929],[1807,21357,21358,21361],{"style":1933},[1807,21359],{"className":21360,"style":1938},[1937],[1807,21362,21364],{"className":21363},[1942,1943,1944,1945],[1807,21365,21367,21370,21373],{"className":21366},[1907,1945],[1807,21368,1852],{"className":21369},[1907,1911,1945],[1807,21371,2209],{"className":21372},[2235,1945],[1807,21374,1869],{"className":21375},[1907,1945],[1807,21377,1963],{"className":21378},[1962],[1807,21380,21382],{"className":21381},[1925],[1807,21383,21385],{"className":21384,"style":3163},[1929],[1807,21386],{},"，等于拿未来信号交易过去收益。",[4352,21389,21390,21393],{},[6070,21391,21392],{},"成本模型只扣佣金","：多因子策略的换手率往往较高，半价差和冲击成本可能吞掉大部分 alpha。",[4352,21395,21396,21399],{},[6070,21397,21398],{},"把测试期用于调参","：每次看样本外结果后再改参数，测试期就变成了训练集。",[4352,21401,21402,21405],{},[6070,21403,21404],{},"忽略不可成交资产","：涨跌停、停牌、流动性枯竭会让理想回测无法落地。",[4352,21407,21408,21411],{},[6070,21409,21410],{},"只展示全样本夏普","：隐藏了策略在不同市场状态下的退化、回撤和尾部风险。",[12741,21413,21415],{"id":21414},"_86-自测题与答案提示","8.6 自测题与答案提示",[4349,21417,21418,21631,21634,21637],{},[4352,21419,21420,21421,21490,21491,21560,21561,21630],{},"为什么 ",[1807,21422,21424,21441],{"className":21423},[1814],[1807,21425,21427],{"className":21426},[1818],[1820,21428,21429],{"xmlns":1822},[1825,21430,21431,21439],{},[1828,21432,21433],{},[1836,21434,21435,21437],{},[1839,21436,2333],{},[1839,21438,1852],{},[1883,21440,6648],{"encoding":1885},[1807,21442,21444],{"className":21443,"ariaHidden":1848},[1890],[1807,21445,21447,21450],{"className":21446},[1894],[1807,21448],{"className":21449,"style":2436},[1898],[1807,21451,21453,21456],{"className":21452},[1907],[1807,21454,2333],{"className":21455,"style":2719},[1907,1911],[1807,21457,21459],{"className":21458},[1916],[1807,21460,21462,21482],{"className":21461},[1920,1921],[1807,21463,21465,21479],{"className":21464},[1925],[1807,21466,21468],{"className":21467,"style":1930},[1929],[1807,21469,21470,21473],{"style":2734},[1807,21471],{"className":21472,"style":1938},[1937],[1807,21474,21476],{"className":21475},[1942,1943,1944,1945],[1807,21477,1852],{"className":21478},[1907,1911,1945],[1807,21480,1963],{"className":21481},[1962],[1807,21483,21485],{"className":21484},[1925],[1807,21486,21488],{"className":21487,"style":2189},[1929],[1807,21489],{}," 必须只依赖 ",[1807,21492,21494,21511],{"className":21493},[1814],[1807,21495,21497],{"className":21496},[1818],[1820,21498,21499],{"xmlns":1822},[1825,21500,21501,21509],{},[1828,21502,21503],{},[1836,21504,21505,21507],{},[1839,21506,2132],{"mathvariant":2131},[1839,21508,1852],{},[1883,21510,2137],{"encoding":1885},[1807,21512,21514],{"className":21513,"ariaHidden":1848},[1890],[1807,21515,21517,21520],{"className":21516},[1894],[1807,21518],{"className":21519,"style":2147},[1898],[1807,21521,21523,21526],{"className":21522},[1907],[1807,21524,2132],{"className":21525,"style":2155},[1907,2154],[1807,21527,21529],{"className":21528},[1916],[1807,21530,21532,21552],{"className":21531},[1920,1921],[1807,21533,21535,21549],{"className":21534},[1925],[1807,21536,21538],{"className":21537,"style":1930},[1929],[1807,21539,21540,21543],{"style":2170},[1807,21541],{"className":21542,"style":1938},[1937],[1807,21544,21546],{"className":21545},[1942,1943,1944,1945],[1807,21547,1852],{"className":21548},[1907,1911,1945],[1807,21550,1963],{"className":21551},[1962],[1807,21553,21555],{"className":21554},[1925],[1807,21556,21558],{"className":21557,"style":2189},[1929],[1807,21559],{},"？\n答案提示：这是可实现性的核心。若 ",[1807,21562,21564,21581],{"className":21563},[1814],[1807,21565,21567],{"className":21566},[1818],[1820,21568,21569],{"xmlns":1822},[1825,21570,21571,21579],{},[1828,21572,21573],{},[1836,21574,21575,21577],{},[1839,21576,2333],{},[1839,21578,1852],{},[1883,21580,6648],{"encoding":1885},[1807,21582,21584],{"className":21583,"ariaHidden":1848},[1890],[1807,21585,21587,21590],{"className":21586},[1894],[1807,21588],{"className":21589,"style":2436},[1898],[1807,21591,21593,21596],{"className":21592},[1907],[1807,21594,2333],{"className":21595,"style":2719},[1907,1911],[1807,21597,21599],{"className":21598},[1916],[1807,21600,21602,21622],{"className":21601},[1920,1921],[1807,21603,21605,21619],{"className":21604},[1925],[1807,21606,21608],{"className":21607,"style":1930},[1929],[1807,21609,21610,21613],{"style":2734},[1807,21611],{"className":21612,"style":1938},[1937],[1807,21614,21616],{"className":21615},[1942,1943,1944,1945],[1807,21617,1852],{"className":21618},[1907,1911,1945],[1807,21620,1963],{"className":21621},[1962],[1807,21623,21625],{"className":21624},[1925],[1807,21626,21628],{"className":21627,"style":2189},[1929],[1807,21629],{}," 使用未来收益或未来数据，回测收益不可能在实盘复制。",[4352,21632,21633],{},"回测中“无成本表现”还有什么价值？\n答案提示：它可视为理论上界，用于判断信号毛收益是否足够大；但不能作为部署依据。",[4352,21635,21636],{},"参数在训练期、验证期、测试期中应如何使用？\n答案提示：训练期拟合，验证期选择和冻结参数，测试期只做一次最终评估。",[4352,21638,21639,21640,21714],{},"为什么收益自相关会影响夏普显著性？\n答案提示：自相关降低独立观测数量，简单 ",[1807,21641,21643,21658],{"className":21642},[1814],[1807,21644,21646],{"className":21645},[1818],[1820,21647,21648],{"xmlns":1822},[1825,21649,21650,21656],{},[1828,21651,21652],{},[13877,21653,21654],{},[1839,21655,5355],{},[1883,21657,14493],{"encoding":1885},[1807,21659,21661],{"className":21660,"ariaHidden":1848},[1890],[1807,21662,21664,21667],{"className":21663},[1894],[1807,21665],{"className":21666,"style":14503},[1898],[1807,21668,21670],{"className":21669},[1907,13971],[1807,21671,21673,21706],{"className":21672},[1920,1921],[1807,21674,21676,21703],{"className":21675},[1925],[1807,21677,21679,21691],{"className":21678,"style":14516},[1929],[1807,21680,21682,21685],{"className":21681,"style":2573},[13985],[1807,21683],{"className":21684,"style":2577},[1937],[1807,21686,21688],{"className":21687,"style":14436},[1907],[1807,21689,5355],{"className":21690,"style":5538},[1907,1911],[1807,21692,21693,21696],{"style":14531},[1807,21694],{"className":21695,"style":2577},[1937],[1807,21697,21699],{"className":21698,"style":14449},[14269],[14272,21700,21701],{"xmlns":14274,"width":14275,"height":14452,"viewBox":14453,"preserveAspectRatio":14278},[14280,21702],{"d":14456},[1807,21704,1963],{"className":21705},[1962],[1807,21707,21709],{"className":21708},[1925],[1807,21710,21712],{"className":21711,"style":14551},[1929],[1807,21713],{}," 年化和普通 t 检验会高估显著性。",[12741,21716,21718],{"id":21717},"_87-小结与过渡","8.7 小结与过渡",[1792,21720,21721],{},"回测不是把信号套进历史价格，而是一次严格的“可实现性模拟”。本章要求你把信息集、成交时点、成本、约束和绩效检验全部写清楚。下一章会进一步讨论：在信号和回测通过初筛后，如何把预期收益、风险模型和现实约束合成一个可管理的投资组合。",[19829,21723],{},[1792,21725,21726,9922],{},[6070,21727,21728],{},"参考文献（节选）",[5589,21730,21731,21737,21743,21750,21756],{},[4352,21732,21733,21734],{},"Fama, E. F., & MacBeth, J. D. (1973). \"Risk, return, and equilibrium: Empirical tests.\" ",[3603,21735,21736],{},"Journal of Political Economy.",[4352,21738,21739,21740],{},"Fama, E. F., & French, K. R. (1993). \"Common risk factors in the returns on stocks and bonds.\" ",[3603,21741,21742],{},"Journal of Financial Economics.",[4352,21744,21745,21746,21749],{},"Grinold, R. C., & Kahn, R. N. (2000). ",[3603,21747,21748],{},"Active Portfolio Management."," McGraw-Hill.",[4352,21751,21752,21753],{},"White, H. (2000). \"A reality check for data snooping.\" ",[3603,21754,21755],{},"Econometrica.",[4352,21757,21758,21759],{},"Hansen, P. R. (2005). \"A test for superior predictive ability.\" ",[3603,21760,21761],{},"Journal of Business & Economic Statistics.",{"title":10,"searchDepth":21763,"depth":21763,"links":21764},2,[21765,21766,21767,21768,21769,21775,21779,21785,21786],{"id":2080,"depth":21763,"text":2081},{"id":4372,"depth":21763,"text":4373},{"id":8469,"depth":21763,"text":8470},{"id":11037,"depth":21763,"text":11038},{"id":12566,"depth":21763,"text":12567,"children":21770},[21771,21773,21774],{"id":12743,"depth":21772,"text":12744},3,{"id":15151,"depth":21772,"text":15152},{"id":16230,"depth":21772,"text":16231},{"id":17357,"depth":21763,"text":17358,"children":21776},[21777,21778],{"id":17361,"depth":21772,"text":17362},{"id":17770,"depth":21772,"text":17771},{"id":17802,"depth":21763,"text":17803,"children":21780},[21781,21782,21783,21784],{"id":17809,"depth":21772,"text":17810},{"id":17829,"depth":21772,"text":17830},{"id":18166,"depth":21772,"text":18167},{"id":18198,"depth":21772,"text":18199},{"id":18230,"depth":21763,"text":18231},{"id":19833,"depth":21763,"text":19834,"children":21787},[21788,21789,21790,21791,21792,21793,21794],{"id":19837,"depth":21772,"text":19838},{"id":20007,"depth":21772,"text":20008},{"id":20035,"depth":21772,"text":20036},{"id":21115,"depth":21772,"text":21116},{"id":21207,"depth":21772,"text":21208},{"id":21414,"depth":21772,"text":21415},{"id":21717,"depth":21772,"text":21718},"用时间有效的训练、验证和测试窗口完成包含基准、成本与偏差审计的回测。","md",{"sidebar":21798},{"order":21772},true,{"title":1751,"description":21795},"lATHcaIkmCTK50gRdAP1bL84fzyHVlkKGIDzVWS9L8I",[21803,21805],{"title":1747,"path":1748,"stem":1749,"description":21804,"children":-1},"从经济假设构造、标准化、中性化并验证横截面因子和可交易信号。",{"title":1755,"path":1756,"stem":1757,"description":21806,"children":-1},"在估计误差、风险暴露、换手、流动性和容量约束下把 alpha 分数转化为组合。",1785754759014]