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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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Fama–French 三因子模型、五因子模型等多因子框架，用以刻画价值、规模、盈利能力等系统性风险暴露（见 Fama & French, 1993, 2015）。在量化实务中，我们通常会在这些“已知”因子基础上，进一步挖掘新的 alpha 因子。",[1792,1799,1800],{},"形式化一点，我们可以在横截面上写出经典的线性因子模型：",[1802,1803,1806],"span",{"className":1804},[1805],"katex-display",[1802,1807,1810,1915],{"className":1808},[1809],"katex",[1802,1811,1814],{"className":1812},[1813],"katex-mathml",[1815,1816,1819],"math",{"xmlns":1817,"display":1818},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1820,1821,1822,1910],"semantics",{},[1823,1824,1825,1852,1855,1862,1864,1876,1889,1891,1908],"mrow",{},[1826,1827,1828,1832],"msub",{},[1829,1830,1831],"mi",{},"r",[1823,1833,1834,1837,1842,1845,1848],{},[1829,1835,1836],{},"i",[1838,1839,1841],"mo",{"separator":1840},"true",",",[1829,1843,1844],{},"t",[1838,1846,1847],{},"+",[1849,1850,1851],"mn",{},"1",[1838,1853,1854],{},"=",[1826,1856,1857,1860],{},[1829,1858,1859],{},"α",[1829,1861,1836],{},[1838,1863,1847],{},[1865,1866,1867,1870,1872],"msubsup",{},[1829,1868,1869],{},"β",[1829,1871,1836],{},[1829,1873,1875],{"mathvariant":1874},"normal","⊤",[1826,1877,1878,1881],{},[1829,1879,1880],{},"f",[1823,1882,1883,1885,1887],{},[1829,1884,1844],{},[1838,1886,1847],{},[1849,1888,1851],{},[1838,1890,1847],{},[1826,1892,1893,1896],{},[1829,1894,1895],{},"ϵ",[1823,1897,1898,1900,1902,1904,1906],{},[1829,1899,1836],{},[1838,1901,1841],{"separator":1840},[1829,1903,1844],{},[1838,1905,1847],{},[1849,1907,1851],{},[1838,1909,1841],{"separator":1840},[1911,1912,1914],"annotation",{"encoding":1913},"application\u002Fx-tex","r_{i,t+1} = \\alpha_i + \\beta_i^\\top f_{t+1} + \\epsilon_{i,t+1},",[1802,1916,1919,2016,2076,2201],{"className":1917,"ariaHidden":1840},[1918],"katex-html",[1802,1920,1923,1928,2004,2009,2013],{"className":1921},[1922],"base",[1802,1924],{"className":1925,"style":1927},[1926],"strut","height:0.7167em;vertical-align:-0.2861em;",[1802,1929,1932,1937],{"className":1930},[1931],"mord",[1802,1933,1831],{"className":1934,"style":1936},[1931,1935],"mathnormal","margin-right:0.0278em;",[1802,1938,1941],{"className":1939},[1940],"msupsub",[1802,1942,1946,1995],{"className":1943},[1944,1945],"vlist-t","vlist-t2",[1802,1947,1950,1990],{"className":1948},[1949],"vlist-r",[1802,1951,1955],{"className":1952,"style":1954},[1953],"vlist","height:0.3117em;",[1802,1956,1958,1963],{"style":1957},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1802,1959],{"className":1960,"style":1962},[1961],"pstrut","height:2.7em;",[1802,1964,1970],{"className":1965},[1966,1967,1968,1969],"sizing","reset-size6","size3","mtight",[1802,1971,1973,1976,1980,1983,1987],{"className":1972},[1931,1969],[1802,1974,1836],{"className":1975},[1931,1935,1969],[1802,1977,1841],{"className":1978},[1979,1969],"mpunct",[1802,1981,1844],{"className":1982},[1931,1935,1969],[1802,1984,1847],{"className":1985},[1986,1969],"mbin",[1802,1988,1851],{"className":1989},[1931,1969],[1802,1991,1994],{"className":1992},[1993],"vlist-s","​",[1802,1996,1998],{"className":1997},[1949],[1802,1999,2002],{"className":2000,"style":2001},[1953],"height:0.2861em;",[1802,2003],{},[1802,2005],{"className":2006,"style":2008},[2007],"mspace","margin-right:0.2778em;",[1802,2010,1854],{"className":2011},[2012],"mrel",[1802,2014],{"className":2015,"style":2008},[2007],[1802,2017,2019,2023,2066,2070,2073],{"className":2018},[1922],[1802,2020],{"className":2021,"style":2022},[1926],"height:0.7333em;vertical-align:-0.15em;",[1802,2024,2026,2030],{"className":2025},[1931],[1802,2027,1859],{"className":2028,"style":2029},[1931,1935],"margin-right:0.0037em;",[1802,2031,2033],{"className":2032},[1940],[1802,2034,2036,2057],{"className":2035},[1944,1945],[1802,2037,2039,2054],{"className":2038},[1949],[1802,2040,2042],{"className":2041,"style":1954},[1953],[1802,2043,2045,2048],{"style":2044},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1802,2046],{"className":2047,"style":1962},[1961],[1802,2049,2051],{"className":2050},[1966,1967,1968,1969],[1802,2052,1836],{"className":2053},[1931,1935,1969],[1802,2055,1994],{"className":2056},[1993],[1802,2058,2060],{"className":2059},[1949],[1802,2061,2064],{"className":2062,"style":2063},[1953],"height:0.15em;",[1802,2065],{},[1802,2067],{"className":2068,"style":2069},[2007],"margin-right:0.2222em;",[1802,2071,1847],{"className":2072},[1986],[1802,2074],{"className":2075,"style":2069},[2007],[1802,2077,2079,2083,2139,2192,2195,2198],{"className":2078},[1922],[1802,2080],{"className":2081,"style":2082},[1926],"height:1.1461em;vertical-align:-0.247em;",[1802,2084,2086,2090],{"className":2085},[1931],[1802,2087,1869],{"className":2088,"style":2089},[1931,1935],"margin-right:0.0528em;",[1802,2091,2093],{"className":2092},[1940],[1802,2094,2096,2130],{"className":2095},[1944,1945],[1802,2097,2099,2127],{"className":2098},[1949],[1802,2100,2103,2115],{"className":2101,"style":2102},[1953],"height:0.8991em;",[1802,2104,2106,2109],{"style":2105},"top:-2.453em;margin-left:-0.0528em;margin-right:0.05em;",[1802,2107],{"className":2108,"style":1962},[1961],[1802,2110,2112],{"className":2111},[1966,1967,1968,1969],[1802,2113,1836],{"className":2114},[1931,1935,1969],[1802,2116,2118,2121],{"style":2117},"top:-3.113em;margin-right:0.05em;",[1802,2119],{"className":2120,"style":1962},[1961],[1802,2122,2124],{"className":2123},[1966,1967,1968,1969],[1802,2125,1875],{"className":2126},[1931,1969],[1802,2128,1994],{"className":2129},[1993],[1802,2131,2133],{"className":2132},[1949],[1802,2134,2137],{"className":2135,"style":2136},[1953],"height:0.247em;",[1802,2138],{},[1802,2140,2142,2146],{"className":2141},[1931],[1802,2143,1880],{"className":2144,"style":2145},[1931,1935],"margin-right:0.1076em;",[1802,2147,2149],{"className":2148},[1940],[1802,2150,2152,2183],{"className":2151},[1944,1945],[1802,2153,2155,2180],{"className":2154},[1949],[1802,2156,2159],{"className":2157,"style":2158},[1953],"height:0.3011em;",[1802,2160,2162,2165],{"style":2161},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1802,2163],{"className":2164,"style":1962},[1961],[1802,2166,2168],{"className":2167},[1966,1967,1968,1969],[1802,2169,2171,2174,2177],{"className":2170},[1931,1969],[1802,2172,1844],{"className":2173},[1931,1935,1969],[1802,2175,1847],{"className":2176},[1986,1969],[1802,2178,1851],{"className":2179},[1931,1969],[1802,2181,1994],{"className":2182},[1993],[1802,2184,2186],{"className":2185},[1949],[1802,2187,2190],{"className":2188,"style":2189},[1953],"height:0.2083em;",[1802,2191],{},[1802,2193],{"className":2194,"style":2069},[2007],[1802,2196,1847],{"className":2197},[1986],[1802,2199],{"className":2200,"style":2069},[2007],[1802,2202,2204,2207,2263],{"className":2203},[1922],[1802,2205],{"className":2206,"style":1927},[1926],[1802,2208,2210,2213],{"className":2209},[1931],[1802,2211,1895],{"className":2212},[1931,1935],[1802,2214,2216],{"className":2215},[1940],[1802,2217,2219,2255],{"className":2218},[1944,1945],[1802,2220,2222,2252],{"className":2221},[1949],[1802,2223,2225],{"className":2224,"style":1954},[1953],[1802,2226,2228,2231],{"style":2227},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1802,2229],{"className":2230,"style":1962},[1961],[1802,2232,2234],{"className":2233},[1966,1967,1968,1969],[1802,2235,2237,2240,2243,2246,2249],{"className":2236},[1931,1969],[1802,2238,1836],{"className":2239},[1931,1935,1969],[1802,2241,1841],{"className":2242},[1979,1969],[1802,2244,1844],{"className":2245},[1931,1935,1969],[1802,2247,1847],{"className":2248},[1986,1969],[1802,2250,1851],{"className":2251},[1931,1969],[1802,2253,1994],{"className":2254},[1993],[1802,2256,2258],{"className":2257},[1949],[1802,2259,2261],{"className":2260,"style":2001},[1953],[1802,2262],{},[1802,2264,1841],{"className":2265},[1979],[1792,2267,2268],{},"其中：",[2270,2271,2272,2485,2574,2677],"ul",{},[2273,2274,2275,2370,2371,2400,2401,2430,2431,2484],"li",{},[1802,2276,2278,2306],{"className":2277},[1809],[1802,2279,2281],{"className":2280},[1813],[1815,2282,2283],{"xmlns":1817},[1820,2284,2285,2303],{},[1823,2286,2287],{},[1826,2288,2289,2291],{},[1829,2290,1831],{},[1823,2292,2293,2295,2297,2299,2301],{},[1829,2294,1836],{},[1838,2296,1841],{"separator":1840},[1829,2298,1844],{},[1838,2300,1847],{},[1849,2302,1851],{},[1911,2304,2305],{"encoding":1913},"r_{i,t+1}",[1802,2307,2309],{"className":2308,"ariaHidden":1840},[1918],[1802,2310,2312,2315],{"className":2311},[1922],[1802,2313],{"className":2314,"style":1927},[1926],[1802,2316,2318,2321],{"className":2317},[1931],[1802,2319,1831],{"className":2320,"style":1936},[1931,1935],[1802,2322,2324],{"className":2323},[1940],[1802,2325,2327,2362],{"className":2326},[1944,1945],[1802,2328,2330,2359],{"className":2329},[1949],[1802,2331,2333],{"className":2332,"style":1954},[1953],[1802,2334,2335,2338],{"style":1957},[1802,2336],{"className":2337,"style":1962},[1961],[1802,2339,2341],{"className":2340},[1966,1967,1968,1969],[1802,2342,2344,2347,2350,2353,2356],{"className":2343},[1931,1969],[1802,2345,1836],{"className":2346},[1931,1935,1969],[1802,2348,1841],{"className":2349},[1979,1969],[1802,2351,1844],{"className":2352},[1931,1935,1969],[1802,2354,1847],{"className":2355},[1986,1969],[1802,2357,1851],{"className":2358},[1931,1969],[1802,2360,1994],{"className":2361},[1993],[1802,2363,2365],{"className":2364},[1949],[1802,2366,2368],{"className":2367,"style":2001},[1953],[1802,2369],{}," 是资产 ",[1802,2372,2374,2387],{"className":2373},[1809],[1802,2375,2377],{"className":2376},[1813],[1815,2378,2379],{"xmlns":1817},[1820,2380,2381,2385],{},[1823,2382,2383],{},[1829,2384,1836],{},[1911,2386,1836],{"encoding":1913},[1802,2388,2390],{"className":2389,"ariaHidden":1840},[1918],[1802,2391,2393,2397],{"className":2392},[1922],[1802,2394],{"className":2395,"style":2396},[1926],"height:0.6595em;",[1802,2398,1836],{"className":2399},[1931,1935]," 在 ",[1802,2402,2404,2417],{"className":2403},[1809],[1802,2405,2407],{"className":2406},[1813],[1815,2408,2409],{"xmlns":1817},[1820,2410,2411,2415],{},[1823,2412,2413],{},[1829,2414,1844],{},[1911,2416,1844],{"encoding":1913},[1802,2418,2420],{"className":2419,"ariaHidden":1840},[1918],[1802,2421,2423,2427],{"className":2422},[1922],[1802,2424],{"className":2425,"style":2426},[1926],"height:0.6151em;",[1802,2428,1844],{"className":2429},[1931,1935]," 到 ",[1802,2432,2434,2452],{"className":2433},[1809],[1802,2435,2437],{"className":2436},[1813],[1815,2438,2439],{"xmlns":1817},[1820,2440,2441,2449],{},[1823,2442,2443,2445,2447],{},[1829,2444,1844],{},[1838,2446,1847],{},[1849,2448,1851],{},[1911,2450,2451],{"encoding":1913},"t+1",[1802,2453,2455,2474],{"className":2454,"ariaHidden":1840},[1918],[1802,2456,2458,2462,2465,2468,2471],{"className":2457},[1922],[1802,2459],{"className":2460,"style":2461},[1926],"height:0.6984em;vertical-align:-0.0833em;",[1802,2463,1844],{"className":2464},[1931,1935],[1802,2466],{"className":2467,"style":2069},[2007],[1802,2469,1847],{"className":2470},[1986],[1802,2472],{"className":2473,"style":2069},[2007],[1802,2475,2477,2481],{"className":2476},[1922],[1802,2478],{"className":2479,"style":2480},[1926],"height:0.6444em;",[1802,2482,1851],{"className":2483},[1931]," 的超额收益；",[2273,2486,2487,2573],{},[1802,2488,2490,2514],{"className":2489},[1809],[1802,2491,2493],{"className":2492},[1813],[1815,2494,2495],{"xmlns":1817},[1820,2496,2497,2511],{},[1823,2498,2499],{},[1826,2500,2501,2503],{},[1829,2502,1880],{},[1823,2504,2505,2507,2509],{},[1829,2506,1844],{},[1838,2508,1847],{},[1849,2510,1851],{},[1911,2512,2513],{"encoding":1913},"f_{t+1}",[1802,2515,2517],{"className":2516,"ariaHidden":1840},[1918],[1802,2518,2520,2524],{"className":2519},[1922],[1802,2521],{"className":2522,"style":2523},[1926],"height:0.9028em;vertical-align:-0.2083em;",[1802,2525,2527,2530],{"className":2526},[1931],[1802,2528,1880],{"className":2529,"style":2145},[1931,1935],[1802,2531,2533],{"className":2532},[1940],[1802,2534,2536,2565],{"className":2535},[1944,1945],[1802,2537,2539,2562],{"className":2538},[1949],[1802,2540,2542],{"className":2541,"style":2158},[1953],[1802,2543,2544,2547],{"style":2161},[1802,2545],{"className":2546,"style":1962},[1961],[1802,2548,2550],{"className":2549},[1966,1967,1968,1969],[1802,2551,2553,2556,2559],{"className":2552},[1931,1969],[1802,2554,1844],{"className":2555},[1931,1935,1969],[1802,2557,1847],{"className":2558},[1986,1969],[1802,2560,1851],{"className":2561},[1931,1969],[1802,2563,1994],{"className":2564},[1993],[1802,2566,2568],{"className":2567},[1949],[1802,2569,2571],{"className":2570,"style":2189},[1953],[1802,2572],{}," 是一组系统性因子（如市场、规模、价值、动量等）的收益向量；",[2273,2575,2576,2370,2648,2676],{},[1802,2577,2579,2597],{"className":2578},[1809],[1802,2580,2582],{"className":2581},[1813],[1815,2583,2584],{"xmlns":1817},[1820,2585,2586,2594],{},[1823,2587,2588],{},[1826,2589,2590,2592],{},[1829,2591,1869],{},[1829,2593,1836],{},[1911,2595,2596],{"encoding":1913},"\\beta_i",[1802,2598,2600],{"className":2599,"ariaHidden":1840},[1918],[1802,2601,2603,2607],{"className":2602},[1922],[1802,2604],{"className":2605,"style":2606},[1926],"height:0.8889em;vertical-align:-0.1944em;",[1802,2608,2610,2613],{"className":2609},[1931],[1802,2611,1869],{"className":2612,"style":2089},[1931,1935],[1802,2614,2616],{"className":2615},[1940],[1802,2617,2619,2640],{"className":2618},[1944,1945],[1802,2620,2622,2637],{"className":2621},[1949],[1802,2623,2625],{"className":2624,"style":1954},[1953],[1802,2626,2628,2631],{"style":2627},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1802,2629],{"className":2630,"style":1962},[1961],[1802,2632,2634],{"className":2633},[1966,1967,1968,1969],[1802,2635,1836],{"className":2636},[1931,1935,1969],[1802,2638,1994],{"className":2639},[1993],[1802,2641,2643],{"className":2642},[1949],[1802,2644,2646],{"className":2645,"style":2063},[1953],[1802,2647],{},[1802,2649,2651,2664],{"className":2650},[1809],[1802,2652,2654],{"className":2653},[1813],[1815,2655,2656],{"xmlns":1817},[1820,2657,2658,2662],{},[1823,2659,2660],{},[1829,2661,1836],{},[1911,2663,1836],{"encoding":1913},[1802,2665,2667],{"className":2666,"ariaHidden":1840},[1918],[1802,2668,2670,2673],{"className":2669},[1922],[1802,2671],{"className":2672,"style":2396},[1926],[1802,2674,1836],{"className":2675},[1931,1935]," 对这些因子的暴露；",[2273,2678,2679,2750],{},[1802,2680,2682,2700],{"className":2681},[1809],[1802,2683,2685],{"className":2684},[1813],[1815,2686,2687],{"xmlns":1817},[1820,2688,2689,2697],{},[1823,2690,2691],{},[1826,2692,2693,2695],{},[1829,2694,1859],{},[1829,2696,1836],{},[1911,2698,2699],{"encoding":1913},"\\alpha_i",[1802,2701,2703],{"className":2702,"ariaHidden":1840},[1918],[1802,2704,2706,2710],{"className":2705},[1922],[1802,2707],{"className":2708,"style":2709},[1926],"height:0.5806em;vertical-align:-0.15em;",[1802,2711,2713,2716],{"className":2712},[1931],[1802,2714,1859],{"className":2715,"style":2029},[1931,1935],[1802,2717,2719],{"className":2718},[1940],[1802,2720,2722,2742],{"className":2721},[1944,1945],[1802,2723,2725,2739],{"className":2724},[1949],[1802,2726,2728],{"className":2727,"style":1954},[1953],[1802,2729,2730,2733],{"style":2044},[1802,2731],{"className":2732,"style":1962},[1961],[1802,2734,2736],{"className":2735},[1966,1967,1968,1969],[1802,2737,1836],{"className":2738},[1931,1935,1969],[1802,2740,1994],{"className":2741},[1993],[1802,2743,2745],{"className":2744},[1949],[1802,2746,2748],{"className":2747,"style":2063},[1953],[1802,2749],{}," 是无法被这些因子解释的超额收益（通常被视为“纯 alpha”）。",[1792,2752,2753,2754,2838,2839,2908,2909,2978,2979,3048,3049,3133,3134,3203],{},"在资产定价的视角下，我们关心的是 ",[1802,2755,2757,2780],{"className":2756},[1809],[1802,2758,2760],{"className":2759},[1813],[1815,2761,2762],{"xmlns":1817},[1820,2763,2764,2778],{},[1823,2765,2766],{},[1826,2767,2768,2770],{},[1829,2769,1880],{},[1823,2771,2772,2774,2776],{},[1829,2773,1844],{},[1838,2775,1847],{},[1849,2777,1851],{},[1911,2779,2513],{"encoding":1913},[1802,2781,2783],{"className":2782,"ariaHidden":1840},[1918],[1802,2784,2786,2789],{"className":2785},[1922],[1802,2787],{"className":2788,"style":2523},[1926],[1802,2790,2792,2795],{"className":2791},[1931],[1802,2793,1880],{"className":2794,"style":2145},[1931,1935],[1802,2796,2798],{"className":2797},[1940],[1802,2799,2801,2830],{"className":2800},[1944,1945],[1802,2802,2804,2827],{"className":2803},[1949],[1802,2805,2807],{"className":2806,"style":2158},[1953],[1802,2808,2809,2812],{"style":2161},[1802,2810],{"className":2811,"style":1962},[1961],[1802,2813,2815],{"className":2814},[1966,1967,1968,1969],[1802,2816,2818,2821,2824],{"className":2817},[1931,1969],[1802,2819,1844],{"className":2820},[1931,1935,1969],[1802,2822,1847],{"className":2823},[1986,1969],[1802,2825,1851],{"className":2826},[1931,1969],[1802,2828,1994],{"className":2829},[1993],[1802,2831,2833],{"className":2832},[1949],[1802,2834,2836],{"className":2835,"style":2189},[1953],[1802,2837],{}," 的风险溢价是否存在、",[1802,2840,2842,2859],{"className":2841},[1809],[1802,2843,2845],{"className":2844},[1813],[1815,2846,2847],{"xmlns":1817},[1820,2848,2849,2857],{},[1823,2850,2851],{},[1826,2852,2853,2855],{},[1829,2854,1869],{},[1829,2856,1836],{},[1911,2858,2596],{"encoding":1913},[1802,2860,2862],{"className":2861,"ariaHidden":1840},[1918],[1802,2863,2865,2868],{"className":2864},[1922],[1802,2866],{"className":2867,"style":2606},[1926],[1802,2869,2871,2874],{"className":2870},[1931],[1802,2872,1869],{"className":2873,"style":2089},[1931,1935],[1802,2875,2877],{"className":2876},[1940],[1802,2878,2880,2900],{"className":2879},[1944,1945],[1802,2881,2883,2897],{"className":2882},[1949],[1802,2884,2886],{"className":2885,"style":1954},[1953],[1802,2887,2888,2891],{"style":2627},[1802,2889],{"className":2890,"style":1962},[1961],[1802,2892,2894],{"className":2893},[1966,1967,1968,1969],[1802,2895,1836],{"className":2896},[1931,1935,1969],[1802,2898,1994],{"className":2899},[1993],[1802,2901,2903],{"className":2902},[1949],[1802,2904,2906],{"className":2905,"style":2063},[1953],[1802,2907],{}," 是否能解释截面上的收益差异；而在量化策略的视角下，我们既关心 ",[1802,2910,2912,2929],{"className":2911},[1809],[1802,2913,2915],{"className":2914},[1813],[1815,2916,2917],{"xmlns":1817},[1820,2918,2919,2927],{},[1823,2920,2921],{},[1826,2922,2923,2925],{},[1829,2924,1869],{},[1829,2926,1836],{},[1911,2928,2596],{"encoding":1913},[1802,2930,2932],{"className":2931,"ariaHidden":1840},[1918],[1802,2933,2935,2938],{"className":2934},[1922],[1802,2936],{"className":2937,"style":2606},[1926],[1802,2939,2941,2944],{"className":2940},[1931],[1802,2942,1869],{"className":2943,"style":2089},[1931,1935],[1802,2945,2947],{"className":2946},[1940],[1802,2948,2950,2970],{"className":2949},[1944,1945],[1802,2951,2953,2967],{"className":2952},[1949],[1802,2954,2956],{"className":2955,"style":1954},[1953],[1802,2957,2958,2961],{"style":2627},[1802,2959],{"className":2960,"style":1962},[1961],[1802,2962,2964],{"className":2963},[1966,1967,1968,1969],[1802,2965,1836],{"className":2966},[1931,1935,1969],[1802,2968,1994],{"className":2969},[1993],[1802,2971,2973],{"className":2972},[1949],[1802,2974,2976],{"className":2975,"style":2063},[1953],[1802,2977],{},"（因为它影响组合风险），也关心 ",[1802,2980,2982,2999],{"className":2981},[1809],[1802,2983,2985],{"className":2984},[1813],[1815,2986,2987],{"xmlns":1817},[1820,2988,2989,2997],{},[1823,2990,2991],{},[1826,2992,2993,2995],{},[1829,2994,1859],{},[1829,2996,1836],{},[1911,2998,2699],{"encoding":1913},[1802,3000,3002],{"className":3001,"ariaHidden":1840},[1918],[1802,3003,3005,3008],{"className":3004},[1922],[1802,3006],{"className":3007,"style":2709},[1926],[1802,3009,3011,3014],{"className":3010},[1931],[1802,3012,1859],{"className":3013,"style":2029},[1931,1935],[1802,3015,3017],{"className":3016},[1940],[1802,3018,3020,3040],{"className":3019},[1944,1945],[1802,3021,3023,3037],{"className":3022},[1949],[1802,3024,3026],{"className":3025,"style":1954},[1953],[1802,3027,3028,3031],{"style":2044},[1802,3029],{"className":3030,"style":1962},[1961],[1802,3032,3034],{"className":3033},[1966,1967,1968,1969],[1802,3035,1836],{"className":3036},[1931,1935,1969],[1802,3038,1994],{"className":3039},[1993],[1802,3041,3043],{"className":3042},[1949],[1802,3044,3046],{"className":3045,"style":2063},[1953],[1802,3047],{},"（因为它是主动收益的来源）。本章讨论的“因子”和“信号”，可以理解为对 ",[1802,3050,3052,3075],{"className":3051},[1809],[1802,3053,3055],{"className":3054},[1813],[1815,3056,3057],{"xmlns":1817},[1820,3058,3059,3073],{},[1823,3060,3061],{},[1826,3062,3063,3065],{},[1829,3064,1880],{},[1823,3066,3067,3069,3071],{},[1829,3068,1844],{},[1838,3070,1847],{},[1849,3072,1851],{},[1911,3074,2513],{"encoding":1913},[1802,3076,3078],{"className":3077,"ariaHidden":1840},[1918],[1802,3079,3081,3084],{"className":3080},[1922],[1802,3082],{"className":3083,"style":2523},[1926],[1802,3085,3087,3090],{"className":3086},[1931],[1802,3088,1880],{"className":3089,"style":2145},[1931,1935],[1802,3091,3093],{"className":3092},[1940],[1802,3094,3096,3125],{"className":3095},[1944,1945],[1802,3097,3099,3122],{"className":3098},[1949],[1802,3100,3102],{"className":3101,"style":2158},[1953],[1802,3103,3104,3107],{"style":2161},[1802,3105],{"className":3106,"style":1962},[1961],[1802,3108,3110],{"className":3109},[1966,1967,1968,1969],[1802,3111,3113,3116,3119],{"className":3112},[1931,1969],[1802,3114,1844],{"className":3115},[1931,1935,1969],[1802,3117,1847],{"className":3118},[1986,1969],[1802,3120,1851],{"className":3121},[1931,1969],[1802,3123,1994],{"className":3124},[1993],[1802,3126,3128],{"className":3127},[1949],[1802,3129,3131],{"className":3130,"style":2189},[1953],[1802,3132],{}," 和 ",[1802,3135,3137,3154],{"className":3136},[1809],[1802,3138,3140],{"className":3139},[1813],[1815,3141,3142],{"xmlns":1817},[1820,3143,3144,3152],{},[1823,3145,3146],{},[1826,3147,3148,3150],{},[1829,3149,1859],{},[1829,3151,1836],{},[1911,3153,2699],{"encoding":1913},[1802,3155,3157],{"className":3156,"ariaHidden":1840},[1918],[1802,3158,3160,3163],{"className":3159},[1922],[1802,3161],{"className":3162,"style":2709},[1926],[1802,3164,3166,3169],{"className":3165},[1931],[1802,3167,1859],{"className":3168,"style":2029},[1931,1935],[1802,3170,3172],{"className":3171},[1940],[1802,3173,3175,3195],{"className":3174},[1944,1945],[1802,3176,3178,3192],{"className":3177},[1949],[1802,3179,3181],{"className":3180,"style":1954},[1953],[1802,3182,3183,3186],{"style":2044},[1802,3184],{"className":3185,"style":1962},[1961],[1802,3187,3189],{"className":3188},[1966,1967,1968,1969],[1802,3190,1836],{"className":3191},[1931,1935,1969],[1802,3193,1994],{"className":3194},[1993],[1802,3196,3198],{"className":3197},[1949],[1802,3199,3201],{"className":3200,"style":2063},[1953],[1802,3202],{}," 的进一步细化和工程化实现。",[3205,3206,3208],"h2",{"id":3207},"_1-因子与信号的基本概念","1. 因子与信号的基本概念",[2270,3210,3211,3218],{},[2273,3212,3213,3217],{},[3214,3215,3216],"strong",{},"因子（Factor）","：刻画资产某一“特征”的数值，例如估值水平、盈利能力、价格动量等。",[2273,3219,3220,3223],{},[3214,3221,3222],{},"交易信号（Signal）","：给出具体操作方向和强度的信息，例如某只股票明天应该“加仓 2%”或“减仓 1%”。",[1792,3225,3226],{},"通常的流程是：",[3228,3229,3230,3233,3236,3239],"ol",{},[2273,3231,3232],{},"从原始数据构建多个因子；",[2273,3234,3235],{},"检验因子的预测能力（比如是否能预测未来收益率）；",[2273,3237,3238],{},"将一个或多个因子组合成交易信号；",[2273,3240,3241],{},"将信号转化为实际仓位或订单，进入回测或真实交易。",[3205,3243,3245],{"id":3244},"_2-常见因子类型","2. 常见因子类型",[1792,3247,3248],{},"这里按较常见的分类方法进行概览，仅列举典型例子，具体实现会根据市场和策略而变化。",[3250,3251,3253],"h3",{"id":3252},"_21-估值因子value","2.1 估值因子（Value）",[1792,3255,3256],{},"描述资产当前价格相对于其基本面是否“便宜”或“贵”。常见指标：",[2270,3258,3259,3418,3554],{},[2273,3260,3261,3262],{},"市盈率 PE（Price-to-Earnings）：\n",[1802,3263,3265],{"className":3264},[1805],[1802,3266,3268,3298],{"className":3267},[1809],[1802,3269,3271],{"className":3270},[1813],[1815,3272,3273],{"xmlns":1817,"display":1818},[1820,3274,3275,3295],{},[1823,3276,3277,3280,3283,3285],{},[1829,3278,3279],{},"P",[1829,3281,3282],{},"E",[1838,3284,1854],{},[3286,3287,3288,3292],"mfrac",{},[3289,3290,3291],"mtext",{},"股价",[3289,3293,3294],{},"每股收益(EPS)",[1911,3296,3297],{"encoding":1913},"PE = \\frac{\\text{股价}}{\\text{每股收益(EPS)}}",[1802,3299,3301,3325],{"className":3300,"ariaHidden":1840},[1918],[1802,3302,3304,3308,3312,3316,3319,3322],{"className":3303},[1922],[1802,3305],{"className":3306,"style":3307},[1926],"height:0.6833em;",[1802,3309,3279],{"className":3310,"style":3311},[1931,1935],"margin-right:0.1389em;",[1802,3313,3282],{"className":3314,"style":3315},[1931,1935],"margin-right:0.0576em;",[1802,3317],{"className":3318,"style":2008},[2007],[1802,3320,1854],{"className":3321},[2012],[1802,3323],{"className":3324,"style":2008},[2007],[1802,3326,3328,3332],{"className":3327},[1922],[1802,3329],{"className":3330,"style":3331},[1926],"height:2.2963em;vertical-align:-0.936em;",[1802,3333,3335,3340,3414],{"className":3334},[1931],[1802,3336],{"className":3337},[3338,3339],"mopen","nulldelimiter",[1802,3341,3343],{"className":3342},[3286],[1802,3344,3346,3405],{"className":3345},[1944,1945],[1802,3347,3349,3402],{"className":3348},[1949],[1802,3350,3353,3376,3387],{"className":3351,"style":3352},[1953],"height:1.3603em;",[1802,3354,3356,3360],{"style":3355},"top:-2.314em;",[1802,3357],{"className":3358,"style":3359},[1961],"height:3em;",[1802,3361,3363],{"className":3362},[1931],[1802,3364,3367,3372],{"className":3365},[1931,3366],"text",[1802,3368,3371],{"className":3369},[1931,3370],"cjk_fallback","每股收益",[1802,3373,3375],{"className":3374},[1931],"(EPS)",[1802,3377,3379,3382],{"style":3378},"top:-3.23em;",[1802,3380],{"className":3381,"style":3359},[1961],[1802,3383],{"className":3384,"style":3386},[3385],"frac-line","border-bottom-width:0.04em;",[1802,3388,3390,3393],{"style":3389},"top:-3.677em;",[1802,3391],{"className":3392,"style":3359},[1961],[1802,3394,3396],{"className":3395},[1931],[1802,3397,3399],{"className":3398},[1931,3366],[1802,3400,3291],{"className":3401},[1931,3370],[1802,3403,1994],{"className":3404},[1993],[1802,3406,3408],{"className":3407},[1949],[1802,3409,3412],{"className":3410,"style":3411},[1953],"height:0.936em;",[1802,3413],{},[1802,3415],{"className":3416},[3417,3339],"mclose",[2273,3419,3420,3421],{},"市净率 PB（Price-to-Book）：\n",[1802,3422,3424],{"className":3423},[1805],[1802,3425,3427,3453],{"className":3426},[1809],[1802,3428,3430],{"className":3429},[1813],[1815,3431,3432],{"xmlns":1817,"display":1818},[1820,3433,3434,3450],{},[1823,3435,3436,3438,3441,3443],{},[1829,3437,3279],{},[1829,3439,3440],{},"B",[1838,3442,1854],{},[3286,3444,3445,3447],{},[3289,3446,3291],{},[3289,3448,3449],{},"每股净资产",[1911,3451,3452],{"encoding":1913},"PB = \\frac{\\text{股价}}{\\text{每股净资产}}",[1802,3454,3456,3478],{"className":3455,"ariaHidden":1840},[1918],[1802,3457,3459,3462,3465,3469,3472,3475],{"className":3458},[1922],[1802,3460],{"className":3461,"style":3307},[1926],[1802,3463,3279],{"className":3464,"style":3311},[1931,1935],[1802,3466,3440],{"className":3467,"style":3468},[1931,1935],"margin-right:0.0502em;",[1802,3470],{"className":3471,"style":2008},[2007],[1802,3473,1854],{"className":3474},[2012],[1802,3476],{"className":3477,"style":2008},[2007],[1802,3479,3481,3485],{"className":3480},[1922],[1802,3482],{"className":3483,"style":3484},[1926],"height:2.0463em;vertical-align:-0.686em;",[1802,3486,3488,3491,3551],{"className":3487},[1931],[1802,3489],{"className":3490},[3338,3339],[1802,3492,3494],{"className":3493},[3286],[1802,3495,3497,3542],{"className":3496},[1944,1945],[1802,3498,3500,3539],{"className":3499},[1949],[1802,3501,3503,3517,3525],{"className":3502,"style":3352},[1953],[1802,3504,3505,3508],{"style":3355},[1802,3506],{"className":3507,"style":3359},[1961],[1802,3509,3511],{"className":3510},[1931],[1802,3512,3514],{"className":3513},[1931,3366],[1802,3515,3449],{"className":3516},[1931,3370],[1802,3518,3519,3522],{"style":3378},[1802,3520],{"className":3521,"style":3359},[1961],[1802,3523],{"className":3524,"style":3386},[3385],[1802,3526,3527,3530],{"style":3389},[1802,3528],{"className":3529,"style":3359},[1961],[1802,3531,3533],{"className":3532},[1931],[1802,3534,3536],{"className":3535},[1931,3366],[1802,3537,3291],{"className":3538},[1931,3370],[1802,3540,1994],{"className":3541},[1993],[1802,3543,3545],{"className":3544},[1949],[1802,3546,3549],{"className":3547,"style":3548},[1953],"height:0.686em;",[1802,3550],{},[1802,3552],{"className":3553},[3417,3339],[2273,3555,3556,3557],{},"股息率 Dividend Yield：\n",[1802,3558,3560],{"className":3559},[1805],[1802,3561,3563,3591],{"className":3562},[1809],[1802,3564,3566],{"className":3565},[1813],[1815,3567,3568],{"xmlns":1817,"display":1818},[1820,3569,3570,3588],{},[1823,3571,3572,3575,3578,3580],{},[1829,3573,3574],{},"D",[1829,3576,3577],{},"Y",[1838,3579,1854],{},[3286,3581,3582,3585],{},[3289,3583,3584],{},"过去一年的股息",[3289,3586,3587],{},"当前股价",[1911,3589,3590],{"encoding":1913},"DY = \\frac{\\text{过去一年的股息}}{\\text{当前股价}}",[1802,3592,3594,3615],{"className":3593,"ariaHidden":1840},[1918],[1802,3595,3597,3600,3603,3606,3609,3612],{"className":3596},[1922],[1802,3598],{"className":3599,"style":3307},[1926],[1802,3601,3574],{"className":3602,"style":1936},[1931,1935],[1802,3604,3577],{"className":3605,"style":2069},[1931,1935],[1802,3607],{"className":3608,"style":2008},[2007],[1802,3610,1854],{"className":3611},[2012],[1802,3613],{"className":3614,"style":2008},[2007],[1802,3616,3618,3621],{"className":3617},[1922],[1802,3619],{"className":3620,"style":3484},[1926],[1802,3622,3624,3627,3686],{"className":3623},[1931],[1802,3625],{"className":3626},[3338,3339],[1802,3628,3630],{"className":3629},[3286],[1802,3631,3633,3678],{"className":3632},[1944,1945],[1802,3634,3636,3675],{"className":3635},[1949],[1802,3637,3639,3653,3661],{"className":3638,"style":3352},[1953],[1802,3640,3641,3644],{"style":3355},[1802,3642],{"className":3643,"style":3359},[1961],[1802,3645,3647],{"className":3646},[1931],[1802,3648,3650],{"className":3649},[1931,3366],[1802,3651,3587],{"className":3652},[1931,3370],[1802,3654,3655,3658],{"style":3378},[1802,3656],{"className":3657,"style":3359},[1961],[1802,3659],{"className":3660,"style":3386},[3385],[1802,3662,3663,3666],{"style":3389},[1802,3664],{"className":3665,"style":3359},[1961],[1802,3667,3669],{"className":3668},[1931],[1802,3670,3672],{"className":3671},[1931,3366],[1802,3673,3584],{"className":3674},[1931,3370],[1802,3676,1994],{"className":3677},[1993],[1802,3679,3681],{"className":3680},[1949],[1802,3682,3684],{"className":3683,"style":3548},[1953],[1802,3685],{},[1802,3687],{"className":3688},[3417,3339],[1792,3690,3691,3692,3695],{},"估值因子的典型假设：",[3214,3693,3694],{},"低估值资产未来预期收益更高","，对应于学术文献中的“价值溢价”（value premium）。例如 Fama & French (1993) 通过构建高账面市值比减去低账面市值比组合（HML），验证价值因子在股票回报中的重要性。",[3250,3697,3699],{"id":3698},"_22-成长因子growth","2.2 成长因子（Growth）",[1792,3701,3702],{},"刻画公司盈利和规模的成长性：",[2270,3704,3705,3708,3711,3714],{},[2273,3706,3707],{},"营业收入增长率；",[2273,3709,3710],{},"净利润增长率；",[2273,3712,3713],{},"EPS 增长率；",[2273,3715,3716],{},"现金流增长情况等。",[1792,3718,3719,3720,3723],{},"典型假设：",[3214,3721,3722],{},"高成长公司未来盈利和股价有更高的上行空间","（成长溢价）。",[3250,3725,3727],{"id":3726},"_23-质量因子quality","2.3 质量因子（Quality）",[1792,3729,3730],{},"刻画公司盈利质量、财务稳健程度：",[2270,3732,3733,3736,3739,3742],{},[2273,3734,3735],{},"ROE（净资产收益率）；",[2273,3737,3738],{},"毛利率、净利率；",[2273,3740,3741],{},"资产负债率、流动比率；",[2273,3743,3744],{},"盈利的稳定性（利润波动率较小）。",[1792,3746,3719,3747],{},[3214,3748,3749],{},"高质量公司在长期具有更稳健的收益表现和相对较低的风险。",[3250,3751,3753],{"id":3752},"_24-动量与反转因子momentum-reversal","2.4 动量与反转因子（Momentum & Reversal）",[1792,3755,3756],{},"根据历史价格走势构建因子：",[2270,3758,3759,4427],{},[2273,3760,3761,3764,3765],{},[3214,3762,3763],{},"动量因子","：\n",[2270,3766,3767,4080,4420],{},[2273,3768,3769,3770],{},"例如过去 3~12 个月的累积收益：\n",[1802,3771,3773],{"className":3772},[1805],[1802,3774,3776,3831],{"className":3775},[1809],[1802,3777,3779],{"className":3778},[1813],[1815,3780,3781],{"xmlns":1817,"display":1818},[1820,3782,3783,3828],{},[1823,3784,3785,3788,3791,3797,3799,3824,3826],{},[1829,3786,3787],{},"M",[1829,3789,3790],{},"O",[1826,3792,3793,3795],{},[1829,3794,3787],{},[1829,3796,1844],{},[1838,3798,1854],{},[3286,3800,3801,3807],{},[1826,3802,3803,3805],{},[1829,3804,3279],{},[1829,3806,1844],{},[1826,3808,3809,3811],{},[1829,3810,3279],{},[1823,3812,3813,3815,3818,3821],{},[1829,3814,1844],{},[1838,3816,3817],{},"−",[1849,3819,3820],{},"12",[1829,3822,3823],{},"m",[1838,3825,3817],{},[1849,3827,1851],{},[1911,3829,3830],{"encoding":1913},"MOM_{t} = \\frac{P_{t}}{P_{t-12m}} - 1",[1802,3832,3834,3902,4071],{"className":3833,"ariaHidden":1840},[1918],[1802,3835,3837,3841,3845,3848,3893,3896,3899],{"className":3836},[1922],[1802,3838],{"className":3839,"style":3840},[1926],"height:0.8333em;vertical-align:-0.15em;",[1802,3842,3787],{"className":3843,"style":3844},[1931,1935],"margin-right:0.109em;",[1802,3846,3790],{"className":3847,"style":1936},[1931,1935],[1802,3849,3851,3854],{"className":3850},[1931],[1802,3852,3787],{"className":3853,"style":3844},[1931,1935],[1802,3855,3857],{"className":3856},[1940],[1802,3858,3860,3885],{"className":3859},[1944,1945],[1802,3861,3863,3882],{"className":3862},[1949],[1802,3864,3867],{"className":3865,"style":3866},[1953],"height:0.2806em;",[1802,3868,3870,3873],{"style":3869},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[1802,3871],{"className":3872,"style":1962},[1961],[1802,3874,3876],{"className":3875},[1966,1967,1968,1969],[1802,3877,3879],{"className":3878},[1931,1969],[1802,3880,1844],{"className":3881},[1931,1935,1969],[1802,3883,1994],{"className":3884},[1993],[1802,3886,3888],{"className":3887},[1949],[1802,3889,3891],{"className":3890,"style":2063},[1953],[1802,3892],{},[1802,3894],{"className":3895,"style":2008},[2007],[1802,3897,1854],{"className":3898},[2012],[1802,3900],{"className":3901,"style":2008},[2007],[1802,3903,3905,3909,4062,4065,4068],{"className":3904},[1922],[1802,3906],{"className":3907,"style":3908},[1926],"height:2.2547em;vertical-align:-0.8943em;",[1802,3910,3912,3915,4059],{"className":3911},[1931],[1802,3913],{"className":3914},[3338,3339],[1802,3916,3918],{"className":3917},[3286],[1802,3919,3921,4050],{"className":3920},[1944,1945],[1802,3922,3924,4047],{"className":3923},[1949],[1802,3925,3927,3988,3996],{"className":3926,"style":3352},[1953],[1802,3928,3929,3932],{"style":3355},[1802,3930],{"className":3931,"style":3359},[1961],[1802,3933,3935],{"className":3934},[1931],[1802,3936,3938,3941],{"className":3937},[1931],[1802,3939,3279],{"className":3940,"style":3311},[1931,1935],[1802,3942,3944],{"className":3943},[1940],[1802,3945,3947,3980],{"className":3946},[1944,1945],[1802,3948,3950,3977],{"className":3949},[1949],[1802,3951,3953],{"className":3952,"style":2158},[1953],[1802,3954,3956,3959],{"style":3955},"top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;",[1802,3957],{"className":3958,"style":1962},[1961],[1802,3960,3962],{"className":3961},[1966,1967,1968,1969],[1802,3963,3965,3968,3971,3974],{"className":3964},[1931,1969],[1802,3966,1844],{"className":3967},[1931,1935,1969],[1802,3969,3817],{"className":3970},[1986,1969],[1802,3972,3820],{"className":3973},[1931,1969],[1802,3975,3823],{"className":3976},[1931,1935,1969],[1802,3978,1994],{"className":3979},[1993],[1802,3981,3983],{"className":3982},[1949],[1802,3984,3986],{"className":3985,"style":2189},[1953],[1802,3987],{},[1802,3989,3990,3993],{"style":3378},[1802,3991],{"className":3992,"style":3359},[1961],[1802,3994],{"className":3995,"style":3386},[3385],[1802,3997,3998,4001],{"style":3389},[1802,3999],{"className":4000,"style":3359},[1961],[1802,4002,4004],{"className":4003},[1931],[1802,4005,4007,4010],{"className":4006},[1931],[1802,4008,3279],{"className":4009,"style":3311},[1931,1935],[1802,4011,4013],{"className":4012},[1940],[1802,4014,4016,4039],{"className":4015},[1944,1945],[1802,4017,4019,4036],{"className":4018},[1949],[1802,4020,4022],{"className":4021,"style":3866},[1953],[1802,4023,4024,4027],{"style":3955},[1802,4025],{"className":4026,"style":1962},[1961],[1802,4028,4030],{"className":4029},[1966,1967,1968,1969],[1802,4031,4033],{"className":4032},[1931,1969],[1802,4034,1844],{"className":4035},[1931,1935,1969],[1802,4037,1994],{"className":4038},[1993],[1802,4040,4042],{"className":4041},[1949],[1802,4043,4045],{"className":4044,"style":2063},[1953],[1802,4046],{},[1802,4048,1994],{"className":4049},[1993],[1802,4051,4053],{"className":4052},[1949],[1802,4054,4057],{"className":4055,"style":4056},[1953],"height:0.8943em;",[1802,4058],{},[1802,4060],{"className":4061},[3417,3339],[1802,4063],{"className":4064,"style":2069},[2007],[1802,4066,3817],{"className":4067},[1986],[1802,4069],{"className":4070,"style":2069},[2007],[1802,4072,4074,4077],{"className":4073},[1922],[1802,4075],{"className":4076,"style":2480},[1926],[1802,4078,1851],{"className":4079},[1931],[2273,4081,4082,4083],{},"更接近文献的定义是去掉最近一个月的收益（即“12-2” 动量），以避免短期反转的干扰（参见 Jegadeesh & Titman, 1993）：\n",[1802,4084,4086],{"className":4085},[1805],[1802,4087,4089,4166],{"className":4088},[1809],[1802,4090,4092],{"className":4091},[1813],[1815,4093,4094],{"xmlns":1817,"display":1818},[1820,4095,4096,4163],{},[1823,4097,4098,4100,4102,4108,4110,4142,4146,4148,4150,4156,4159,4161],{},[1829,4099,3787],{},[1829,4101,3790],{},[1826,4103,4104,4106],{},[1829,4105,3787],{},[1829,4107,1844],{},[1838,4109,1854],{},[4111,4112,4113,4116,4131],"munderover",{},[1838,4114,4115],{},"∏",[1823,4117,4118,4121,4123,4125,4127,4129],{},[1829,4119,4120],{},"τ",[1838,4122,1854],{},[1829,4124,1844],{},[1838,4126,3817],{},[1849,4128,3820],{},[1829,4130,3823],{},[1823,4132,4133,4135,4137,4140],{},[1829,4134,1844],{},[1838,4136,3817],{},[1849,4138,4139],{},"2",[1829,4141,3823],{},[1838,4143,4145],{"stretchy":4144},"false","(",[1849,4147,1851],{},[1838,4149,1847],{},[1826,4151,4152,4154],{},[1829,4153,1831],{},[1829,4155,4120],{},[1838,4157,4158],{"stretchy":4144},")",[1838,4160,3817],{},[1849,4162,1851],{},[1911,4164,4165],{"encoding":1913},"MOM_{t} = \\prod_{\\tau=t-12m}^{t-2m} (1 + r_\\tau) - 1",[1802,4167,4169,4233,4351,4411],{"className":4168,"ariaHidden":1840},[1918],[1802,4170,4172,4175,4178,4181,4224,4227,4230],{"className":4171},[1922],[1802,4173],{"className":4174,"style":3840},[1926],[1802,4176,3787],{"className":4177,"style":3844},[1931,1935],[1802,4179,3790],{"className":4180,"style":1936},[1931,1935],[1802,4182,4184,4187],{"className":4183},[1931],[1802,4185,3787],{"className":4186,"style":3844},[1931,1935],[1802,4188,4190],{"className":4189},[1940],[1802,4191,4193,4216],{"className":4192},[1944,1945],[1802,4194,4196,4213],{"className":4195},[1949],[1802,4197,4199],{"className":4198,"style":3866},[1953],[1802,4200,4201,4204],{"style":3869},[1802,4202],{"className":4203,"style":1962},[1961],[1802,4205,4207],{"className":4206},[1966,1967,1968,1969],[1802,4208,4210],{"className":4209},[1931,1969],[1802,4211,1844],{"className":4212},[1931,1935,1969],[1802,4214,1994],{"className":4215},[1993],[1802,4217,4219],{"className":4218},[1949],[1802,4220,4222],{"className":4221,"style":2063},[1953],[1802,4223],{},[1802,4225],{"className":4226,"style":2008},[2007],[1802,4228,1854],{"className":4229},[2012],[1802,4231],{"className":4232,"style":2008},[2007],[1802,4234,4236,4240,4336,4339,4342,4345,4348],{"className":4235},[1922],[1802,4237],{"className":4238,"style":4239},[1926],"height:3.1266em;vertical-align:-1.3254em;",[1802,4241,4245],{"className":4242},[4243,4244],"mop","op-limits",[1802,4246,4248,4327],{"className":4247},[1944,1945],[1802,4249,4251,4324],{"className":4250},[1949],[1802,4252,4255,4287,4300],{"className":4253,"style":4254},[1953],"height:1.8011em;",[1802,4256,4258,4262],{"style":4257},"top:-1.8829em;margin-left:0em;",[1802,4259],{"className":4260,"style":4261},[1961],"height:3.05em;",[1802,4263,4265],{"className":4264},[1966,1967,1968,1969],[1802,4266,4268,4272,4275,4278,4281,4284],{"className":4267},[1931,1969],[1802,4269,4120],{"className":4270,"style":4271},[1931,1935,1969],"margin-right:0.1132em;",[1802,4273,1854],{"className":4274},[2012,1969],[1802,4276,1844],{"className":4277},[1931,1935,1969],[1802,4279,3817],{"className":4280},[1986,1969],[1802,4282,3820],{"className":4283},[1931,1969],[1802,4285,3823],{"className":4286},[1931,1935,1969],[1802,4288,4290,4293],{"style":4289},"top:-3.05em;",[1802,4291],{"className":4292,"style":4261},[1961],[1802,4294,4295],{},[1802,4296,4115],{"className":4297},[4243,4298,4299],"op-symbol","large-op",[1802,4301,4303,4306],{"style":4302},"top:-4.3em;margin-left:0em;",[1802,4304],{"className":4305,"style":4261},[1961],[1802,4307,4309],{"className":4308},[1966,1967,1968,1969],[1802,4310,4312,4315,4318,4321],{"className":4311},[1931,1969],[1802,4313,1844],{"className":4314},[1931,1935,1969],[1802,4316,3817],{"className":4317},[1986,1969],[1802,4319,4139],{"className":4320},[1931,1969],[1802,4322,3823],{"className":4323},[1931,1935,1969],[1802,4325,1994],{"className":4326},[1993],[1802,4328,4330],{"className":4329},[1949],[1802,4331,4334],{"className":4332,"style":4333},[1953],"height:1.3254em;",[1802,4335],{},[1802,4337,4145],{"className":4338},[3338],[1802,4340,1851],{"className":4341},[1931],[1802,4343],{"className":4344,"style":2069},[2007],[1802,4346,1847],{"className":4347},[1986],[1802,4349],{"className":4350,"style":2069},[2007],[1802,4352,4354,4358,4399,4402,4405,4408],{"className":4353},[1922],[1802,4355],{"className":4356,"style":4357},[1926],"height:1em;vertical-align:-0.25em;",[1802,4359,4361,4364],{"className":4360},[1931],[1802,4362,1831],{"className":4363,"style":1936},[1931,1935],[1802,4365,4367],{"className":4366},[1940],[1802,4368,4370,4391],{"className":4369},[1944,1945],[1802,4371,4373,4388],{"className":4372},[1949],[1802,4374,4377],{"className":4375,"style":4376},[1953],"height:0.1514em;",[1802,4378,4379,4382],{"style":1957},[1802,4380],{"className":4381,"style":1962},[1961],[1802,4383,4385],{"className":4384},[1966,1967,1968,1969],[1802,4386,4120],{"className":4387,"style":4271},[1931,1935,1969],[1802,4389,1994],{"className":4390},[1993],[1802,4392,4394],{"className":4393},[1949],[1802,4395,4397],{"className":4396,"style":2063},[1953],[1802,4398],{},[1802,4400,4158],{"className":4401},[3417],[1802,4403],{"className":4404,"style":2069},[2007],[1802,4406,3817],{"className":4407},[1986],[1802,4409],{"className":4410,"style":2069},[2007],[1802,4412,4414,4417],{"className":4413},[1922],[1802,4415],{"className":4416,"style":2480},[1926],[1802,4418,1851],{"className":4419},[1931],[2273,4421,4422,4423,4426],{},"假设：",[3214,4424,4425],{},"涨得多的继续涨，跌得多的继续跌","（趋势延续）。",[2273,4428,4429,3764,4432],{},[3214,4430,4431],{},"短期反转因子",[2270,4433,4434,4697],{},[2273,4435,4436,4437],{},"例如过去 1~5 日的收益率：\n",[1802,4438,4440],{"className":4439},[1805],[1802,4441,4443,4500],{"className":4442},[1809],[1802,4444,4446],{"className":4445},[1813],[1815,4447,4448],{"xmlns":1817,"display":1818},[1820,4449,4450,4497],{},[1823,4451,4452,4455,4457,4464,4466,4468,4470,4476,4479,4491,4493,4495],{},[1829,4453,4454],{},"R",[1829,4456,3282],{},[1826,4458,4459,4462],{},[1829,4460,4461],{},"V",[1829,4463,1844],{},[1838,4465,1854],{},[1838,4467,3817],{},[1838,4469,4145],{"stretchy":4144},[1826,4471,4472,4474],{},[1829,4473,3279],{},[1829,4475,1844],{},[1829,4477,4478],{"mathvariant":1874},"\u002F",[1826,4480,4481,4483],{},[1829,4482,3279],{},[1823,4484,4485,4487,4489],{},[1829,4486,1844],{},[1838,4488,3817],{},[1849,4490,1851],{},[1838,4492,3817],{},[1849,4494,1851],{},[1838,4496,4158],{"stretchy":4144},[1911,4498,4499],{"encoding":1913},"REV_{t} = - (P_{t} \u002F P_{t-1} - 1)",[1802,4501,4503,4569,4685],{"className":4502,"ariaHidden":1840},[1918],[1802,4504,4506,4509,4513,4516,4560,4563,4566],{"className":4505},[1922],[1802,4507],{"className":4508,"style":3840},[1926],[1802,4510,4454],{"className":4511,"style":4512},[1931,1935],"margin-right:0.0077em;",[1802,4514,3282],{"className":4515,"style":3315},[1931,1935],[1802,4517,4519,4522],{"className":4518},[1931],[1802,4520,4461],{"className":4521,"style":2069},[1931,1935],[1802,4523,4525],{"className":4524},[1940],[1802,4526,4528,4552],{"className":4527},[1944,1945],[1802,4529,4531,4549],{"className":4530},[1949],[1802,4532,4534],{"className":4533,"style":3866},[1953],[1802,4535,4537,4540],{"style":4536},"top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;",[1802,4538],{"className":4539,"style":1962},[1961],[1802,4541,4543],{"className":4542},[1966,1967,1968,1969],[1802,4544,4546],{"className":4545},[1931,1969],[1802,4547,1844],{"className":4548},[1931,1935,1969],[1802,4550,1994],{"className":4551},[1993],[1802,4553,4555],{"className":4554},[1949],[1802,4556,4558],{"className":4557,"style":2063},[1953],[1802,4559],{},[1802,4561],{"className":4562,"style":2008},[2007],[1802,4564,1854],{"className":4565},[2012],[1802,4567],{"className":4568,"style":2008},[2007],[1802,4570,4572,4575,4578,4581,4624,4627,4676,4679,4682],{"className":4571},[1922],[1802,4573],{"className":4574,"style":4357},[1926],[1802,4576,3817],{"className":4577},[1931],[1802,4579,4145],{"className":4580},[3338],[1802,4582,4584,4587],{"className":4583},[1931],[1802,4585,3279],{"className":4586,"style":3311},[1931,1935],[1802,4588,4590],{"className":4589},[1940],[1802,4591,4593,4616],{"className":4592},[1944,1945],[1802,4594,4596,4613],{"className":4595},[1949],[1802,4597,4599],{"className":4598,"style":3866},[1953],[1802,4600,4601,4604],{"style":3955},[1802,4602],{"className":4603,"style":1962},[1961],[1802,4605,4607],{"className":4606},[1966,1967,1968,1969],[1802,4608,4610],{"className":4609},[1931,1969],[1802,4611,1844],{"className":4612},[1931,1935,1969],[1802,4614,1994],{"className":4615},[1993],[1802,4617,4619],{"className":4618},[1949],[1802,4620,4622],{"className":4621,"style":2063},[1953],[1802,4623],{},[1802,4625,4478],{"className":4626},[1931],[1802,4628,4630,4633],{"className":4629},[1931],[1802,4631,3279],{"className":4632,"style":3311},[1931,1935],[1802,4634,4636],{"className":4635},[1940],[1802,4637,4639,4668],{"className":4638},[1944,1945],[1802,4640,4642,4665],{"className":4641},[1949],[1802,4643,4645],{"className":4644,"style":2158},[1953],[1802,4646,4647,4650],{"style":3955},[1802,4648],{"className":4649,"style":1962},[1961],[1802,4651,4653],{"className":4652},[1966,1967,1968,1969],[1802,4654,4656,4659,4662],{"className":4655},[1931,1969],[1802,4657,1844],{"className":4658},[1931,1935,1969],[1802,4660,3817],{"className":4661},[1986,1969],[1802,4663,1851],{"className":4664},[1931,1969],[1802,4666,1994],{"className":4667},[1993],[1802,4669,4671],{"className":4670},[1949],[1802,4672,4674],{"className":4673,"style":2189},[1953],[1802,4675],{},[1802,4677],{"className":4678,"style":2069},[2007],[1802,4680,3817],{"className":4681},[1986],[1802,4683],{"className":4684,"style":2069},[2007],[1802,4686,4688,4691,4694],{"className":4687},[1922],[1802,4689],{"className":4690,"style":4357},[1926],[1802,4692,1851],{"className":4693},[1931],[1802,4695,4158],{"className":4696},[3417],[2273,4698,4422,4699],{},[3214,4700,4701],{},"短期内价格有过度反应，存在均值回归。",[3250,4703,4705],{"id":4704},"_25-情绪与流动性因子sentiment-liquidity","2.5 情绪与流动性因子（Sentiment & Liquidity）",[2270,4707,4708,4711],{},[2273,4709,4710],{},"换手率、成交量、买卖盘不平衡等；",[2273,4712,4713],{},"研报推荐、新闻情绪、舆情指标；",[1792,4715,3719],{},[2270,4717,4718,4721],{},[2273,4719,4720],{},"投资者情绪会在短期内驱动资产价格偏离基本面；",[2273,4722,4723],{},"流动性较好的资产更易交易，但过高的换手也可能意味着噪声较多。",[3205,4725,4727],{"id":4726},"_3-因子构建的一般流程","3. 因子构建的一般流程",[1792,4729,4730],{},"从工程和研究的角度，一个规范的因子构建流程大致如下：",[3228,4732,4733,4744,4754,4764,4777],{},[2273,4734,4735,4738,4739],{},[3214,4736,4737],{},"定义经济\u002F金融含义","：",[2270,4740,4741],{},[2273,4742,4743],{},"因子应该有清晰的经济解释，而不仅仅是“机器自动筛出来的公式”。",[2273,4745,4746,4738,4749],{},[3214,4747,4748],{},"确定计算公式和频率",[2270,4750,4751],{},[2273,4752,4753],{},"例如：PE 按滚动 12 个月盈利计算；动量按过去 12 个月收益率但去掉最近 1 个月。",[2273,4755,4756,4738,4759],{},[3214,4757,4758],{},"处理原始指标的缺失和异常值",[2270,4760,4761],{},[2273,4762,4763],{},"参考上一章的数据清洗方法。",[2273,4765,4766,4738,4769],{},[3214,4767,4768],{},"标准化与中性化处理",[2270,4770,4771,4774],{},[2273,4772,4773],{},"将不同量纲的因子转化到可比较的尺度；",[2273,4775,4776],{},"对行业、市值等进行中性化，避免因子只是“伪装的行业\u002F市值效应”。",[2273,4778,4779,4738,4782],{},[3214,4780,4781],{},"因子存储与版本管理",[2270,4783,4784],{},[2273,4785,4786],{},"对于生产环境，需要对因子值进行版本控制和回溯，确保回测和实盘的一致性。",[3205,4788,4790],{"id":4789},"_4-标准化与中性化","4. 标准化与中性化",[3250,4792,4794],{"id":4793},"_41-标准化standardization","4.1 标准化（Standardization）",[1792,4796,4797],{},"一个常见做法是对因子在每个截面（例如每天）上进行 z-score 标准化：",[1802,4799,4801],{"className":4800},[1805],[1802,4802,4804,4844],{"className":4803},[1809],[1802,4805,4807],{"className":4806},[1813],[1815,4808,4809],{"xmlns":1817,"display":1818},[1820,4810,4811,4841],{},[1823,4812,4813,4820,4822],{},[1826,4814,4815,4818],{},[1829,4816,4817],{},"z",[1829,4819,1836],{},[1838,4821,1854],{},[3286,4823,4824,4838],{},[1823,4825,4826,4833,4835],{},[1826,4827,4828,4831],{},[1829,4829,4830],{},"x",[1829,4832,1836],{},[1838,4834,3817],{},[1829,4836,4837],{},"μ",[1829,4839,4840],{},"σ",[1911,4842,4843],{"encoding":1913}," z_i = \\frac{x_i - \\mu}{\\sigma}",[1802,4845,4847,4904],{"className":4846,"ariaHidden":1840},[1918],[1802,4848,4850,4853,4895,4898,4901],{"className":4849},[1922],[1802,4851],{"className":4852,"style":2709},[1926],[1802,4854,4856,4860],{"className":4855},[1931],[1802,4857,4817],{"className":4858,"style":4859},[1931,1935],"margin-right:0.044em;",[1802,4861,4863],{"className":4862},[1940],[1802,4864,4866,4887],{"className":4865},[1944,1945],[1802,4867,4869,4884],{"className":4868},[1949],[1802,4870,4872],{"className":4871,"style":1954},[1953],[1802,4873,4875,4878],{"style":4874},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[1802,4876],{"className":4877,"style":1962},[1961],[1802,4879,4881],{"className":4880},[1966,1967,1968,1969],[1802,4882,1836],{"className":4883},[1931,1935,1969],[1802,4885,1994],{"className":4886},[1993],[1802,4888,4890],{"className":4889},[1949],[1802,4891,4893],{"className":4892,"style":2063},[1953],[1802,4894],{},[1802,4896],{"className":4897,"style":2008},[2007],[1802,4899,1854],{"className":4900},[2012],[1802,4902],{"className":4903,"style":2008},[2007],[1802,4905,4907,4911],{"className":4906},[1922],[1802,4908],{"className":4909,"style":4910},[1926],"height:1.9463em;vertical-align:-0.686em;",[1802,4912,4914,4917,5021],{"className":4913},[1931],[1802,4915],{"className":4916},[3338,3339],[1802,4918,4920],{"className":4919},[3286],[1802,4921,4923,5013],{"className":4922},[1944,1945],[1802,4924,4926,5010],{"className":4925},[1949],[1802,4927,4930,4942,4950],{"className":4928,"style":4929},[1953],"height:1.2603em;",[1802,4931,4932,4935],{"style":3355},[1802,4933],{"className":4934,"style":3359},[1961],[1802,4936,4938],{"className":4937},[1931],[1802,4939,4840],{"className":4940,"style":4941},[1931,1935],"margin-right:0.0359em;",[1802,4943,4944,4947],{"style":3378},[1802,4945],{"className":4946,"style":3359},[1961],[1802,4948],{"className":4949,"style":3386},[3385],[1802,4951,4952,4955],{"style":3389},[1802,4953],{"className":4954,"style":3359},[1961],[1802,4956,4958,4998,5001,5004,5007],{"className":4957},[1931],[1802,4959,4961,4964],{"className":4960},[1931],[1802,4962,4830],{"className":4963},[1931,1935],[1802,4965,4967],{"className":4966},[1940],[1802,4968,4970,4990],{"className":4969},[1944,1945],[1802,4971,4973,4987],{"className":4972},[1949],[1802,4974,4976],{"className":4975,"style":1954},[1953],[1802,4977,4978,4981],{"style":2227},[1802,4979],{"className":4980,"style":1962},[1961],[1802,4982,4984],{"className":4983},[1966,1967,1968,1969],[1802,4985,1836],{"className":4986},[1931,1935,1969],[1802,4988,1994],{"className":4989},[1993],[1802,4991,4993],{"className":4992},[1949],[1802,4994,4996],{"className":4995,"style":2063},[1953],[1802,4997],{},[1802,4999],{"className":5000,"style":2069},[2007],[1802,5002,3817],{"className":5003},[1986],[1802,5005],{"className":5006,"style":2069},[2007],[1802,5008,4837],{"className":5009},[1931,1935],[1802,5011,1994],{"className":5012},[1993],[1802,5014,5016],{"className":5015},[1949],[1802,5017,5019],{"className":5018,"style":3548},[1953],[1802,5020],{},[1802,5022],{"className":5023},[3417,3339],[1792,5025,2268],{},[2270,5027,5028,5130,5163],{},[2273,5029,5030,5100,5101,5129],{},[1802,5031,5033,5051],{"className":5032},[1809],[1802,5034,5036],{"className":5035},[1813],[1815,5037,5038],{"xmlns":1817},[1820,5039,5040,5048],{},[1823,5041,5042],{},[1826,5043,5044,5046],{},[1829,5045,4830],{},[1829,5047,1836],{},[1911,5049,5050],{"encoding":1913},"x_i",[1802,5052,5054],{"className":5053,"ariaHidden":1840},[1918],[1802,5055,5057,5060],{"className":5056},[1922],[1802,5058],{"className":5059,"style":2709},[1926],[1802,5061,5063,5066],{"className":5062},[1931],[1802,5064,4830],{"className":5065},[1931,1935],[1802,5067,5069],{"className":5068},[1940],[1802,5070,5072,5092],{"className":5071},[1944,1945],[1802,5073,5075,5089],{"className":5074},[1949],[1802,5076,5078],{"className":5077,"style":1954},[1953],[1802,5079,5080,5083],{"style":2227},[1802,5081],{"className":5082,"style":1962},[1961],[1802,5084,5086],{"className":5085},[1966,1967,1968,1969],[1802,5087,1836],{"className":5088},[1931,1935,1969],[1802,5090,1994],{"className":5091},[1993],[1802,5093,5095],{"className":5094},[1949],[1802,5096,5098],{"className":5097,"style":2063},[1953],[1802,5099],{}," 为第 ",[1802,5102,5104,5117],{"className":5103},[1809],[1802,5105,5107],{"className":5106},[1813],[1815,5108,5109],{"xmlns":1817},[1820,5110,5111,5115],{},[1823,5112,5113],{},[1829,5114,1836],{},[1911,5116,1836],{"encoding":1913},[1802,5118,5120],{"className":5119,"ariaHidden":1840},[1918],[1802,5121,5123,5126],{"className":5122},[1922],[1802,5124],{"className":5125,"style":2396},[1926],[1802,5127,1836],{"className":5128},[1931,1935]," 只资产的原始因子值；",[2273,5131,5132,5162],{},[1802,5133,5135,5149],{"className":5134},[1809],[1802,5136,5138],{"className":5137},[1813],[1815,5139,5140],{"xmlns":1817},[1820,5141,5142,5146],{},[1823,5143,5144],{},[1829,5145,4837],{},[1911,5147,5148],{"encoding":1913},"\\mu",[1802,5150,5152],{"className":5151,"ariaHidden":1840},[1918],[1802,5153,5155,5159],{"className":5154},[1922],[1802,5156],{"className":5157,"style":5158},[1926],"height:0.625em;vertical-align:-0.1944em;",[1802,5160,4837],{"className":5161},[1931,1935]," 为当期截面因子值的均值；",[2273,5164,5165,5195],{},[1802,5166,5168,5182],{"className":5167},[1809],[1802,5169,5171],{"className":5170},[1813],[1815,5172,5173],{"xmlns":1817},[1820,5174,5175,5179],{},[1823,5176,5177],{},[1829,5178,4840],{},[1911,5180,5181],{"encoding":1913},"\\sigma",[1802,5183,5185],{"className":5184,"ariaHidden":1840},[1918],[1802,5186,5188,5192],{"className":5187},[1922],[1802,5189],{"className":5190,"style":5191},[1926],"height:0.4306em;",[1802,5193,4840],{"className":5194,"style":4941},[1931,1935]," 为当期截面因子值的标准差。",[1792,5197,5198],{},"标准化后的因子：",[2270,5200,5201,5204,5207],{},[2273,5202,5203],{},"均值约为 0，标准差约为 1；",[2273,5205,5206],{},"便于不同因子的组合和比较；",[2273,5208,5209],{},"对极端值的影响相对更可控（通常会配合去极值）。",[3250,5211,5213],{"id":5212},"_42-中性化neutralization","4.2 中性化（Neutralization）",[1792,5215,5216],{},"假设我们构建了一个“质量因子”，但在截面回归中发现：",[2270,5218,5219,5222],{},[2273,5220,5221],{},"质量因子与市值因子高度相关；",[2273,5223,5224],{},"质量因子与某些行业权重高度重叠。",[1792,5226,5227],{},"这时，如果不做中性化，回测看到的“质量因子收益”可能实际上是市值或行业暴露带来的。",[1792,5229,5230],{},"常见做法是通过截面回归将因子对指定变量（如市值、行业哑变量）回归，保留残差部分作为“中性化因子”：",[1802,5232,5234],{"className":5233},[1805],[1802,5235,5237,5336],{"className":5236},[1809],[1802,5238,5240],{"className":5239},[1813],[1815,5241,5242],{"xmlns":1817,"display":1818},[1820,5243,5244,5333],{},[1823,5245,5246,5252,5254,5256,5258,5264,5267,5269,5275,5277,5286,5293,5295,5298,5301,5304,5307,5310,5312,5314,5325,5327],{},[1826,5247,5248,5250],{},[1829,5249,4830],{},[1829,5251,1836],{},[1838,5253,1854],{},[1829,5255,1859],{},[1838,5257,1847],{},[1826,5259,5260,5262],{},[1829,5261,1869],{},[1849,5263,1851],{},[1838,5265,5266],{},"⋅",[1829,5268,3787],{},[1826,5270,5271,5273],{},[1829,5272,4461],{},[1829,5274,1836],{},[1838,5276,1847],{},[5278,5279,5280,5283],"munder",{},[1838,5281,5282],{},"∑",[1829,5284,5285],{},"k",[1826,5287,5288,5291],{},[1829,5289,5290],{},"γ",[1829,5292,5285],{},[1838,5294,5266],{},[1829,5296,5297],{},"I",[1829,5299,5300],{},"n",[1829,5302,5303],{},"d",[1829,5305,5306],{},"u",[1829,5308,5309],{},"s",[1829,5311,1844],{},[1829,5313,1831],{},[1826,5315,5316,5319],{},[1829,5317,5318],{},"y",[1823,5320,5321,5323],{},[1829,5322,1836],{},[1829,5324,5285],{},[1838,5326,1847],{},[1826,5328,5329,5331],{},[1829,5330,1895],{},[1829,5332,1836],{},[1911,5334,5335],{"encoding":1913}," x_{i} = \\alpha + \\beta_1 \\cdot MV_i + \\sum_k \\gamma_k \\cdot Industry_{ik} + \\epsilon_i",[1802,5337,5339,5397,5416,5471,5529,5640,5722],{"className":5338,"ariaHidden":1840},[1918],[1802,5340,5342,5345,5388,5391,5394],{"className":5341},[1922],[1802,5343],{"className":5344,"style":2709},[1926],[1802,5346,5348,5351],{"className":5347},[1931],[1802,5349,4830],{"className":5350},[1931,1935],[1802,5352,5354],{"className":5353},[1940],[1802,5355,5357,5380],{"className":5356},[1944,1945],[1802,5358,5360,5377],{"className":5359},[1949],[1802,5361,5363],{"className":5362,"style":1954},[1953],[1802,5364,5365,5368],{"style":2227},[1802,5366],{"className":5367,"style":1962},[1961],[1802,5369,5371],{"className":5370},[1966,1967,1968,1969],[1802,5372,5374],{"className":5373},[1931,1969],[1802,5375,1836],{"className":5376},[1931,1935,1969],[1802,5378,1994],{"className":5379},[1993],[1802,5381,5383],{"className":5382},[1949],[1802,5384,5386],{"className":5385,"style":2063},[1953],[1802,5387],{},[1802,5389],{"className":5390,"style":2008},[2007],[1802,5392,1854],{"className":5393},[2012],[1802,5395],{"className":5396,"style":2008},[2007],[1802,5398,5400,5404,5407,5410,5413],{"className":5399},[1922],[1802,5401],{"className":5402,"style":5403},[1926],"height:0.6667em;vertical-align:-0.0833em;",[1802,5405,1859],{"className":5406,"style":2029},[1931,1935],[1802,5408],{"className":5409,"style":2069},[2007],[1802,5411,1847],{"className":5412},[1986],[1802,5414],{"className":5415,"style":2069},[2007],[1802,5417,5419,5422,5462,5465,5468],{"className":5418},[1922],[1802,5420],{"className":5421,"style":2606},[1926],[1802,5423,5425,5428],{"className":5424},[1931],[1802,5426,1869],{"className":5427,"style":2089},[1931,1935],[1802,5429,5431],{"className":5430},[1940],[1802,5432,5434,5454],{"className":5433},[1944,1945],[1802,5435,5437,5451],{"className":5436},[1949],[1802,5438,5440],{"className":5439,"style":2158},[1953],[1802,5441,5442,5445],{"style":2627},[1802,5443],{"className":5444,"style":1962},[1961],[1802,5446,5448],{"className":5447},[1966,1967,1968,1969],[1802,5449,1851],{"className":5450},[1931,1969],[1802,5452,1994],{"className":5453},[1993],[1802,5455,5457],{"className":5456},[1949],[1802,5458,5460],{"className":5459,"style":2063},[1953],[1802,5461],{},[1802,5463],{"className":5464,"style":2069},[2007],[1802,5466,5266],{"className":5467},[1986],[1802,5469],{"className":5470,"style":2069},[2007],[1802,5472,5474,5477,5480,5520,5523,5526],{"className":5473},[1922],[1802,5475],{"className":5476,"style":3840},[1926],[1802,5478,3787],{"className":5479,"style":3844},[1931,1935],[1802,5481,5483,5486],{"className":5482},[1931],[1802,5484,4461],{"className":5485,"style":2069},[1931,1935],[1802,5487,5489],{"className":5488},[1940],[1802,5490,5492,5512],{"className":5491},[1944,1945],[1802,5493,5495,5509],{"className":5494},[1949],[1802,5496,5498],{"className":5497,"style":1954},[1953],[1802,5499,5500,5503],{"style":4536},[1802,5501],{"className":5502,"style":1962},[1961],[1802,5504,5506],{"className":5505},[1966,1967,1968,1969],[1802,5507,1836],{"className":5508},[1931,1935,1969],[1802,5510,1994],{"className":5511},[1993],[1802,5513,5515],{"className":5514},[1949],[1802,5516,5518],{"className":5517,"style":2063},[1953],[1802,5519],{},[1802,5521],{"className":5522,"style":2069},[2007],[1802,5524,1847],{"className":5525},[1986],[1802,5527],{"className":5528,"style":2069},[2007],[1802,5530,5532,5536,5584,5588,5631,5634,5637],{"className":5531},[1922],[1802,5533],{"className":5534,"style":5535},[1926],"height:2.3521em;vertical-align:-1.3021em;",[1802,5537,5539],{"className":5538},[4243,4244],[1802,5540,5542,5575],{"className":5541},[1944,1945],[1802,5543,5545,5572],{"className":5544},[1949],[1802,5546,5549,5562],{"className":5547,"style":5548},[1953],"height:1.05em;",[1802,5550,5552,5555],{"style":5551},"top:-1.8479em;margin-left:0em;",[1802,5553],{"className":5554,"style":4261},[1961],[1802,5556,5558],{"className":5557},[1966,1967,1968,1969],[1802,5559,5285],{"className":5560,"style":5561},[1931,1935,1969],"margin-right:0.0315em;",[1802,5563,5564,5567],{"style":4289},[1802,5565],{"className":5566,"style":4261},[1961],[1802,5568,5569],{},[1802,5570,5282],{"className":5571},[4243,4298,4299],[1802,5573,1994],{"className":5574},[1993],[1802,5576,5578],{"className":5577},[1949],[1802,5579,5582],{"className":5580,"style":5581},[1953],"height:1.3021em;",[1802,5583],{},[1802,5585],{"className":5586,"style":5587},[2007],"margin-right:0.1667em;",[1802,5589,5591,5595],{"className":5590},[1931],[1802,5592,5290],{"className":5593,"style":5594},[1931,1935],"margin-right:0.0556em;",[1802,5596,5598],{"className":5597},[1940],[1802,5599,5601,5623],{"className":5600},[1944,1945],[1802,5602,5604,5620],{"className":5603},[1949],[1802,5605,5608],{"className":5606,"style":5607},[1953],"height:0.3361em;",[1802,5609,5611,5614],{"style":5610},"top:-2.55em;margin-left:-0.0556em;margin-right:0.05em;",[1802,5612],{"className":5613,"style":1962},[1961],[1802,5615,5617],{"className":5616},[1966,1967,1968,1969],[1802,5618,5285],{"className":5619,"style":5561},[1931,1935,1969],[1802,5621,1994],{"className":5622},[1993],[1802,5624,5626],{"className":5625},[1949],[1802,5627,5629],{"className":5628,"style":2063},[1953],[1802,5630],{},[1802,5632],{"className":5633,"style":2069},[2007],[1802,5635,5266],{"className":5636},[1986],[1802,5638],{"className":5639,"style":2069},[2007],[1802,5641,5643,5646,5650,5653,5656,5659,5662,5665,5668,5713,5716,5719],{"className":5642},[1922],[1802,5644],{"className":5645,"style":2606},[1926],[1802,5647,5297],{"className":5648,"style":5649},[1931,1935],"margin-right:0.0785em;",[1802,5651,5300],{"className":5652},[1931,1935],[1802,5654,5303],{"className":5655},[1931,1935],[1802,5657,5306],{"className":5658},[1931,1935],[1802,5660,5309],{"className":5661},[1931,1935],[1802,5663,1844],{"className":5664},[1931,1935],[1802,5666,1831],{"className":5667,"style":1936},[1931,1935],[1802,5669,5671,5674],{"className":5670},[1931],[1802,5672,5318],{"className":5673,"style":4941},[1931,1935],[1802,5675,5677],{"className":5676},[1940],[1802,5678,5680,5705],{"className":5679},[1944,1945],[1802,5681,5683,5702],{"className":5682},[1949],[1802,5684,5686],{"className":5685,"style":5607},[1953],[1802,5687,5689,5692],{"style":5688},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1802,5690],{"className":5691,"style":1962},[1961],[1802,5693,5695],{"className":5694},[1966,1967,1968,1969],[1802,5696,5698],{"className":5697},[1931,1969],[1802,5699,5701],{"className":5700,"style":5561},[1931,1935,1969],"ik",[1802,5703,1994],{"className":5704},[1993],[1802,5706,5708],{"className":5707},[1949],[1802,5709,5711],{"className":5710,"style":2063},[1953],[1802,5712],{},[1802,5714],{"className":5715,"style":2069},[2007],[1802,5717,1847],{"className":5718},[1986],[1802,5720],{"className":5721,"style":2069},[2007],[1802,5723,5725,5728],{"className":5724},[1922],[1802,5726],{"className":5727,"style":2709},[1926],[1802,5729,5731,5734],{"className":5730},[1931],[1802,5732,1895],{"className":5733},[1931,1935],[1802,5735,5737],{"className":5736},[1940],[1802,5738,5740,5760],{"className":5739},[1944,1945],[1802,5741,5743,5757],{"className":5742},[1949],[1802,5744,5746],{"className":5745,"style":1954},[1953],[1802,5747,5748,5751],{"style":2227},[1802,5749],{"className":5750,"style":1962},[1961],[1802,5752,5754],{"className":5753},[1966,1967,1968,1969],[1802,5755,1836],{"className":5756},[1931,1935,1969],[1802,5758,1994],{"className":5759},[1993],[1802,5761,5763],{"className":5762},[1949],[1802,5764,5766],{"className":5765,"style":2063},[1953],[1802,5767],{},[2270,5769,5770,5842,5920,6035],{},[2273,5771,5772,5841],{},[1802,5773,5775,5792],{"className":5774},[1809],[1802,5776,5778],{"className":5777},[1813],[1815,5779,5780],{"xmlns":1817},[1820,5781,5782,5790],{},[1823,5783,5784],{},[1826,5785,5786,5788],{},[1829,5787,4830],{},[1829,5789,1836],{},[1911,5791,5050],{"encoding":1913},[1802,5793,5795],{"className":5794,"ariaHidden":1840},[1918],[1802,5796,5798,5801],{"className":5797},[1922],[1802,5799],{"className":5800,"style":2709},[1926],[1802,5802,5804,5807],{"className":5803},[1931],[1802,5805,4830],{"className":5806},[1931,1935],[1802,5808,5810],{"className":5809},[1940],[1802,5811,5813,5833],{"className":5812},[1944,1945],[1802,5814,5816,5830],{"className":5815},[1949],[1802,5817,5819],{"className":5818,"style":1954},[1953],[1802,5820,5821,5824],{"style":2227},[1802,5822],{"className":5823,"style":1962},[1961],[1802,5825,5827],{"className":5826},[1966,1967,1968,1969],[1802,5828,1836],{"className":5829},[1931,1935,1969],[1802,5831,1994],{"className":5832},[1993],[1802,5834,5836],{"className":5835},[1949],[1802,5837,5839],{"className":5838,"style":2063},[1953],[1802,5840],{},"：原始因子值；",[2273,5843,5844,5919],{},[1802,5845,5847,5867],{"className":5846},[1809],[1802,5848,5850],{"className":5849},[1813],[1815,5851,5852],{"xmlns":1817},[1820,5853,5854,5864],{},[1823,5855,5856,5858],{},[1829,5857,3787],{},[1826,5859,5860,5862],{},[1829,5861,4461],{},[1829,5863,1836],{},[1911,5865,5866],{"encoding":1913},"MV_i",[1802,5868,5870],{"className":5869,"ariaHidden":1840},[1918],[1802,5871,5873,5876,5879],{"className":5872},[1922],[1802,5874],{"className":5875,"style":3840},[1926],[1802,5877,3787],{"className":5878,"style":3844},[1931,1935],[1802,5880,5882,5885],{"className":5881},[1931],[1802,5883,4461],{"className":5884,"style":2069},[1931,1935],[1802,5886,5888],{"className":5887},[1940],[1802,5889,5891,5911],{"className":5890},[1944,1945],[1802,5892,5894,5908],{"className":5893},[1949],[1802,5895,5897],{"className":5896,"style":1954},[1953],[1802,5898,5899,5902],{"style":4536},[1802,5900],{"className":5901,"style":1962},[1961],[1802,5903,5905],{"className":5904},[1966,1967,1968,1969],[1802,5906,1836],{"className":5907},[1931,1935,1969],[1802,5909,1994],{"className":5910},[1993],[1802,5912,5914],{"className":5913},[1949],[1802,5915,5917],{"className":5916,"style":2063},[1953],[1802,5918],{},"：市值（可取对数）；",[2273,5921,5922,6034],{},[1802,5923,5925,5961],{"className":5924},[1809],[1802,5926,5928],{"className":5927},[1813],[1815,5929,5930],{"xmlns":1817},[1820,5931,5932,5958],{},[1823,5933,5934,5936,5938,5940,5942,5944,5946,5948],{},[1829,5935,5297],{},[1829,5937,5300],{},[1829,5939,5303],{},[1829,5941,5306],{},[1829,5943,5309],{},[1829,5945,1844],{},[1829,5947,1831],{},[1826,5949,5950,5952],{},[1829,5951,5318],{},[1823,5953,5954,5956],{},[1829,5955,1836],{},[1829,5957,5285],{},[1911,5959,5960],{"encoding":1913},"Industry_{ik}",[1802,5962,5964],{"className":5963,"ariaHidden":1840},[1918],[1802,5965,5967,5970,5973,5976,5979,5982,5985,5988,5991],{"className":5966},[1922],[1802,5968],{"className":5969,"style":2606},[1926],[1802,5971,5297],{"className":5972,"style":5649},[1931,1935],[1802,5974,5300],{"className":5975},[1931,1935],[1802,5977,5303],{"className":5978},[1931,1935],[1802,5980,5306],{"className":5981},[1931,1935],[1802,5983,5309],{"className":5984},[1931,1935],[1802,5986,1844],{"className":5987},[1931,1935],[1802,5989,1831],{"className":5990,"style":1936},[1931,1935],[1802,5992,5994,5997],{"className":5993},[1931],[1802,5995,5318],{"className":5996,"style":4941},[1931,1935],[1802,5998,6000],{"className":5999},[1940],[1802,6001,6003,6026],{"className":6002},[1944,1945],[1802,6004,6006,6023],{"className":6005},[1949],[1802,6007,6009],{"className":6008,"style":5607},[1953],[1802,6010,6011,6014],{"style":5688},[1802,6012],{"className":6013,"style":1962},[1961],[1802,6015,6017],{"className":6016},[1966,1967,1968,1969],[1802,6018,6020],{"className":6019},[1931,1969],[1802,6021,5701],{"className":6022,"style":5561},[1931,1935,1969],[1802,6024,1994],{"className":6025},[1993],[1802,6027,6029],{"className":6028},[1949],[1802,6030,6032],{"className":6031,"style":2063},[1953],[1802,6033],{},"：行业虚拟变量（1 表示属于该行业，0 表示不属于）；",[2273,6036,6037,6107],{},[1802,6038,6040,6058],{"className":6039},[1809],[1802,6041,6043],{"className":6042},[1813],[1815,6044,6045],{"xmlns":1817},[1820,6046,6047,6055],{},[1823,6048,6049],{},[1826,6050,6051,6053],{},[1829,6052,1895],{},[1829,6054,1836],{},[1911,6056,6057],{"encoding":1913},"\\epsilon_i",[1802,6059,6061],{"className":6060,"ariaHidden":1840},[1918],[1802,6062,6064,6067],{"className":6063},[1922],[1802,6065],{"className":6066,"style":2709},[1926],[1802,6068,6070,6073],{"className":6069},[1931],[1802,6071,1895],{"className":6072},[1931,1935],[1802,6074,6076],{"className":6075},[1940],[1802,6077,6079,6099],{"className":6078},[1944,1945],[1802,6080,6082,6096],{"className":6081},[1949],[1802,6083,6085],{"className":6084,"style":1954},[1953],[1802,6086,6087,6090],{"style":2227},[1802,6088],{"className":6089,"style":1962},[1961],[1802,6091,6093],{"className":6092},[1966,1967,1968,1969],[1802,6094,1836],{"className":6095},[1931,1935,1969],[1802,6097,1994],{"className":6098},[1993],[1802,6100,6102],{"className":6101},[1949],[1802,6103,6105],{"className":6104,"style":2063},[1953],[1802,6106],{},"：回归残差，被视为剔除了市值和行业影响后的“纯因子”。",[1792,6109,6110],{},"在实践中，大多数多因子模型都会使用中性化因子进行组合，以提高可解释性和稳定性。",[6112,6113],"pyodide",{"code64":6114,"layout":6115,"locale":7,"title":6116},"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","vertical","用组内去均值看清行业中性化",[1792,6118,6119,6120,6123],{},"静态结果为 A\u002FC\u002FE 做多、B\u002FD\u002FF 做空，权重绝对值之和为 1，下一期多空收益为 ",[3214,6121,6122],{},"0.88%","。这个六只股票的算例只展示“剔除组均值”的机械含义。真实行业中性化还要处理行业内样本数、连续市值暴露、权重和异方差；中性化也会改变目标信号，不能作为默认仪式。",[3205,6125,6127],{"id":6126},"_5-因子有效性的初步检验","5. 因子有效性的初步检验",[1792,6129,6130,6131,6134,6135,6138],{},"构建好因子后，需要检验其是否具有预测未来收益的能力。最常见的两个工具是",[3214,6132,6133],{},"排序分组法","和 ",[3214,6136,6137],{},"IC\u002FRank IC","。",[3250,6140,6142],{"id":6141},"_51-排序分组回测portfolio-sorts","5.1 排序分组回测（Portfolio Sorts）",[1792,6144,6145],{},"基本步骤：",[3228,6147,6148,6151,6154,6157],{},[2273,6149,6150],{},"在每个截面（如每月末），按因子值从低到高对所有资产排序；",[2273,6152,6153],{},"将资产分成若干组（如 5 组或 10 组）；",[2273,6155,6156],{},"计算每一组在下期的平均收益率；",[2273,6158,6159],{},"比较高因子组与低因子组之间的收益差异。",[1792,6161,6162],{},"如果该因子有效，通常会观察到：",[2270,6164,6165,6168,6171],{},[2273,6166,6167],{},"高因子组（如最高分组 Q5）的平均收益率显著高于低因子组（如最低分组 Q1）；",[2273,6169,6170],{},"“多高因子组、空低因子组”的多空组合收益显著为正；",[2273,6172,6173],{},"这一特征在较长时间范围、不同市场环境下具有一定稳健性。",[1792,6175,6176],{},"从更偏“资产定价实证”的角度看，分组回测也可以被视为一种非参数的横截面检验：",[2270,6178,6179,6182],{},[2273,6180,6181],{},"将因子值视为对未来收益率的排序指标；",[2273,6183,6184],{},"若因子具有单调性和稳定性，则高分组与低分组之间的收益差可以视为对该因子“价格”的估计。",[6186,6187],"model-curve-chart",{"props64":6188},"eyJ0aXRsZSI6IuWIhue7hOaUtuebiuWNleiwg+aAp++8muWboOWtkOaYr+WQpuecn+eahOiDveaOkuW6j+acquadpeaUtuebiiIsInN1YnRpdGxlIjoi5o6S5bqP5YiG57uE5YWI55yLIFExIOWIsCBRNSDnmoTmlbTkvZPlvaLnirbvvIzlho3nnIvlpJrnqbrnu4TlkIjnmoTmlLbnm4rmmK\u002FlkKbnqLPlrprjgIIiLCJ4TGFiZWwiOiLlm6DlrZDliIbnu4TvvIhRMSDkvY7vvIxRNSDpq5jvvIkiLCJ5TGFiZWwiOiLkuIvmnJ\u002FlubPlnYfmlLbnm4ogKCUpIiwiaGVpZ2h0IjozOTAsIm1pblgiOjEsIm1heFgiOjUsIm1pblkiOi0wLjQ1LCJtYXhZIjowLjg1LCJzZXJpZXMiOlt7Im5hbWUiOiLljp\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",[1792,6190,6191],{},"分组回测首先看的是排序关系，而不是某一组是否碰巧赚钱。如果 Q1 到 Q5 的收益大体单调上升，Q5-Q1 的多空收益才更像来自因子信息；如果收益只在某一个分组突然跳起，就要警惕极端样本、行业暴露或数据挖掘。中性化后的曲线仍然向上，才更有资格进入下一步的稳健性检验。",[1792,6193,6194],{},"对分组组合本身，还可以进一步做时间序列回归，例如检验多空组合收益对 Fama–French 因子是否具有正的截距：",[1802,6196,6198],{"className":6197},[1805],[1802,6199,6201,6276],{"className":6200},[1809],[1802,6202,6204],{"className":6203},[1813],[1815,6205,6206],{"xmlns":1817,"display":1818},[1820,6207,6208,6273],{},[1823,6209,6210,6244,6246,6248,6250,6257,6263,6265,6271],{},[1826,6211,6212,6214],{},[1829,6213,1831],{},[1823,6215,6216,6219,6222,6224,6227,6229,6231,6234,6236,6238,6240,6242],{},[1829,6217,6218],{},"l",[1829,6220,6221],{},"o",[1829,6223,5300],{},[1829,6225,6226],{},"g",[1838,6228,3817],{},[1829,6230,5309],{},[1829,6232,6233],{},"h",[1829,6235,6221],{},[1829,6237,1831],{},[1829,6239,1844],{},[1838,6241,1841],{"separator":1840},[1829,6243,1844],{},[1838,6245,1854],{},[1829,6247,1859],{},[1838,6249,1847],{},[6251,6252,6253,6255],"msup",{},[1829,6254,1869],{},[1829,6256,1875],{"mathvariant":1874},[1826,6258,6259,6261],{},[1829,6260,1880],{},[1829,6262,1844],{},[1838,6264,1847],{},[1826,6266,6267,6269],{},[1829,6268,5306],{},[1829,6270,1844],{},[1838,6272,1841],{"separator":1840},[1911,6274,6275],{"encoding":1913},"r_{long-short,t} = \\alpha + \\beta^\\top f_t + u_t,",[1802,6277,6279,6369,6387,6472],{"className":6278,"ariaHidden":1840},[1918],[1802,6280,6282,6285,6360,6363,6366],{"className":6281},[1922],[1802,6283],{"className":6284,"style":1927},[1926],[1802,6286,6288,6291],{"className":6287},[1931],[1802,6289,1831],{"className":6290,"style":1936},[1931,1935],[1802,6292,6294],{"className":6293},[1940],[1802,6295,6297,6352],{"className":6296},[1944,1945],[1802,6298,6300,6349],{"className":6299},[1949],[1802,6301,6303],{"className":6302,"style":5607},[1953],[1802,6304,6305,6308],{"style":1957},[1802,6306],{"className":6307,"style":1962},[1961],[1802,6309,6311],{"className":6310},[1966,1967,1968,1969],[1802,6312,6314,6318,6321,6324,6327,6330,6333,6336,6340,6343,6346],{"className":6313},[1931,1969],[1802,6315,6218],{"className":6316,"style":6317},[1931,1935,1969],"margin-right:0.0197em;",[1802,6319,6221],{"className":6320},[1931,1935,1969],[1802,6322,5300],{"className":6323},[1931,1935,1969],[1802,6325,6226],{"className":6326,"style":4941},[1931,1935,1969],[1802,6328,3817],{"className":6329},[1986,1969],[1802,6331,5309],{"className":6332},[1931,1935,1969],[1802,6334,6233],{"className":6335},[1931,1935,1969],[1802,6337,6339],{"className":6338,"style":1936},[1931,1935,1969],"or",[1802,6341,1844],{"className":6342},[1931,1935,1969],[1802,6344,1841],{"className":6345},[1979,1969],[1802,6347,1844],{"className":6348},[1931,1935,1969],[1802,6350,1994],{"className":6351},[1993],[1802,6353,6355],{"className":6354},[1949],[1802,6356,6358],{"className":6357,"style":2001},[1953],[1802,6359],{},[1802,6361],{"className":6362,"style":2008},[2007],[1802,6364,1854],{"className":6365},[2012],[1802,6367],{"className":6368,"style":2008},[2007],[1802,6370,6372,6375,6378,6381,6384],{"className":6371},[1922],[1802,6373],{"className":6374,"style":5403},[1926],[1802,6376,1859],{"className":6377,"style":2029},[1931,1935],[1802,6379],{"className":6380,"style":2069},[2007],[1802,6382,1847],{"className":6383},[1986],[1802,6385],{"className":6386,"style":2069},[2007],[1802,6388,6390,6394,6423,6463,6466,6469],{"className":6389},[1922],[1802,6391],{"className":6392,"style":6393},[1926],"height:1.0935em;vertical-align:-0.1944em;",[1802,6395,6397,6400],{"className":6396},[1931],[1802,6398,1869],{"className":6399,"style":2089},[1931,1935],[1802,6401,6403],{"className":6402},[1940],[1802,6404,6406],{"className":6405},[1944],[1802,6407,6409],{"className":6408},[1949],[1802,6410,6412],{"className":6411,"style":2102},[1953],[1802,6413,6414,6417],{"style":2117},[1802,6415],{"className":6416,"style":1962},[1961],[1802,6418,6420],{"className":6419},[1966,1967,1968,1969],[1802,6421,1875],{"className":6422},[1931,1969],[1802,6424,6426,6429],{"className":6425},[1931],[1802,6427,1880],{"className":6428,"style":2145},[1931,1935],[1802,6430,6432],{"className":6431},[1940],[1802,6433,6435,6455],{"className":6434},[1944,1945],[1802,6436,6438,6452],{"className":6437},[1949],[1802,6439,6441],{"className":6440,"style":3866},[1953],[1802,6442,6443,6446],{"style":2161},[1802,6444],{"className":6445,"style":1962},[1961],[1802,6447,6449],{"className":6448},[1966,1967,1968,1969],[1802,6450,1844],{"className":6451},[1931,1935,1969],[1802,6453,1994],{"className":6454},[1993],[1802,6456,6458],{"className":6457},[1949],[1802,6459,6461],{"className":6460,"style":2063},[1953],[1802,6462],{},[1802,6464],{"className":6465,"style":2069},[2007],[1802,6467,1847],{"className":6468},[1986],[1802,6470],{"className":6471,"style":2069},[2007],[1802,6473,6475,6478,6518],{"className":6474},[1922],[1802,6476],{"className":6477,"style":5158},[1926],[1802,6479,6481,6484],{"className":6480},[1931],[1802,6482,5306],{"className":6483},[1931,1935],[1802,6485,6487],{"className":6486},[1940],[1802,6488,6490,6510],{"className":6489},[1944,1945],[1802,6491,6493,6507],{"className":6492},[1949],[1802,6494,6496],{"className":6495,"style":3866},[1953],[1802,6497,6498,6501],{"style":2227},[1802,6499],{"className":6500,"style":1962},[1961],[1802,6502,6504],{"className":6503},[1966,1967,1968,1969],[1802,6505,1844],{"className":6506},[1931,1935,1969],[1802,6508,1994],{"className":6509},[1993],[1802,6511,6513],{"className":6512},[1949],[1802,6514,6516],{"className":6515,"style":2063},[1953],[1802,6517],{},[1802,6519,1841],{"className":6520},[1979],[1792,6522,6523,6524,6553],{},"若 ",[1802,6525,6527,6541],{"className":6526},[1809],[1802,6528,6530],{"className":6529},[1813],[1815,6531,6532],{"xmlns":1817},[1820,6533,6534,6538],{},[1823,6535,6536],{},[1829,6537,1859],{},[1911,6539,6540],{"encoding":1913},"\\alpha",[1802,6542,6544],{"className":6543,"ariaHidden":1840},[1918],[1802,6545,6547,6550],{"className":6546},[1922],[1802,6548],{"className":6549,"style":5191},[1926],[1802,6551,1859],{"className":6552,"style":2029},[1931,1935]," 显著大于 0，说明该因子在控制传统风险因子后仍然具有独立的超额收益贡献。",[3250,6555,6557],{"id":6556},"_52-icinformation-coefficient与-rank-ic","5.2 IC（Information Coefficient）与 Rank IC",[1792,6559,6560],{},"在截面上计算因子与下期收益率之间的相关性：",[2270,6562,6563,6808],{},[2273,6564,6565,6568,6569],{},[3214,6566,6567],{},"IC","：使用皮尔逊相关系数，度量线性相关：",[1802,6570,6572],{"className":6571},[1805],[1802,6573,6575,6631],{"className":6574},[1809],[1802,6576,6578],{"className":6577},[1813],[1815,6579,6580],{"xmlns":1817,"display":1818},[1820,6581,6582,6628],{},[1823,6583,6584,6586,6593,6595,6598,6600,6602,6604,6606,6612,6614,6626],{},[1829,6585,5297],{},[1826,6587,6588,6591],{},[1829,6589,6590],{},"C",[1829,6592,1844],{},[1838,6594,1854],{},[1829,6596,6597],{},"c",[1829,6599,6221],{},[1829,6601,1831],{},[1829,6603,1831],{},[1838,6605,4145],{"stretchy":4144},[1826,6607,6608,6610],{},[1829,6609,4830],{},[1829,6611,1844],{},[1838,6613,1841],{"separator":1840},[1826,6615,6616,6618],{},[1829,6617,1831],{},[1823,6619,6620,6622,6624],{},[1829,6621,1844],{},[1838,6623,1847],{},[1849,6625,1851],{},[1838,6627,4158],{"stretchy":4144},[1911,6629,6630],{"encoding":1913},"IC_t = corr(x_t, r_{t+1})",[1802,6632,6634,6694],{"className":6633,"ariaHidden":1840},[1918],[1802,6635,6637,6640,6643,6685,6688,6691],{"className":6636},[1922],[1802,6638],{"className":6639,"style":3840},[1926],[1802,6641,5297],{"className":6642,"style":5649},[1931,1935],[1802,6644,6646,6650],{"className":6645},[1931],[1802,6647,6590],{"className":6648,"style":6649},[1931,1935],"margin-right:0.0715em;",[1802,6651,6653],{"className":6652},[1940],[1802,6654,6656,6677],{"className":6655},[1944,1945],[1802,6657,6659,6674],{"className":6658},[1949],[1802,6660,6662],{"className":6661,"style":3866},[1953],[1802,6663,6665,6668],{"style":6664},"top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;",[1802,6666],{"className":6667,"style":1962},[1961],[1802,6669,6671],{"className":6670},[1966,1967,1968,1969],[1802,6672,1844],{"className":6673},[1931,1935,1969],[1802,6675,1994],{"className":6676},[1993],[1802,6678,6680],{"className":6679},[1949],[1802,6681,6683],{"className":6682,"style":2063},[1953],[1802,6684],{},[1802,6686],{"className":6687,"style":2008},[2007],[1802,6689,1854],{"className":6690},[2012],[1802,6692],{"className":6693,"style":2008},[2007],[1802,6695,6697,6700,6704,6707,6710,6750,6753,6756,6805],{"className":6696},[1922],[1802,6698],{"className":6699,"style":4357},[1926],[1802,6701,6703],{"className":6702,"style":1936},[1931,1935],"cor",[1802,6705,1831],{"className":6706,"style":1936},[1931,1935],[1802,6708,4145],{"className":6709},[3338],[1802,6711,6713,6716],{"className":6712},[1931],[1802,6714,4830],{"className":6715},[1931,1935],[1802,6717,6719],{"className":6718},[1940],[1802,6720,6722,6742],{"className":6721},[1944,1945],[1802,6723,6725,6739],{"className":6724},[1949],[1802,6726,6728],{"className":6727,"style":3866},[1953],[1802,6729,6730,6733],{"style":2227},[1802,6731],{"className":6732,"style":1962},[1961],[1802,6734,6736],{"className":6735},[1966,1967,1968,1969],[1802,6737,1844],{"className":6738},[1931,1935,1969],[1802,6740,1994],{"className":6741},[1993],[1802,6743,6745],{"className":6744},[1949],[1802,6746,6748],{"className":6747,"style":2063},[1953],[1802,6749],{},[1802,6751,1841],{"className":6752},[1979],[1802,6754],{"className":6755,"style":5587},[2007],[1802,6757,6759,6762],{"className":6758},[1931],[1802,6760,1831],{"className":6761,"style":1936},[1931,1935],[1802,6763,6765],{"className":6764},[1940],[1802,6766,6768,6797],{"className":6767},[1944,1945],[1802,6769,6771,6794],{"className":6770},[1949],[1802,6772,6774],{"className":6773,"style":2158},[1953],[1802,6775,6776,6779],{"style":1957},[1802,6777],{"className":6778,"style":1962},[1961],[1802,6780,6782],{"className":6781},[1966,1967,1968,1969],[1802,6783,6785,6788,6791],{"className":6784},[1931,1969],[1802,6786,1844],{"className":6787},[1931,1935,1969],[1802,6789,1847],{"className":6790},[1986,1969],[1802,6792,1851],{"className":6793},[1931,1969],[1802,6795,1994],{"className":6796},[1993],[1802,6798,6800],{"className":6799},[1949],[1802,6801,6803],{"className":6802,"style":2189},[1953],[1802,6804],{},[1802,6806,4158],{"className":6807},[3417],[2273,6809,6810,6813,6814],{},[3214,6811,6812],{},"Rank IC","：使用秩相关（如 Spearman 相关），度量排序的一致性：",[1802,6815,6817],{"className":6816},[1805],[1802,6818,6820,6907],{"className":6819},[1809],[1802,6821,6823],{"className":6822},[1813],[1815,6824,6825],{"xmlns":1817,"display":1818},[1820,6826,6827,6904],{},[1823,6828,6829,6831,6834,6836,6838,6840,6846,6848,6850,6852,6854,6856,6858,6860,6862,6864,6866,6868,6874,6876,6878,6880,6882,6884,6886,6888,6900,6902],{},[1829,6830,4454],{},[1829,6832,6833],{},"a",[1829,6835,5300],{},[1829,6837,5285],{},[1829,6839,5297],{},[1826,6841,6842,6844],{},[1829,6843,6590],{},[1829,6845,1844],{},[1838,6847,1854],{},[1829,6849,6597],{},[1829,6851,6221],{},[1829,6853,1831],{},[1829,6855,1831],{},[1838,6857,4145],{"stretchy":4144},[1829,6859,1831],{},[1829,6861,6833],{},[1829,6863,5300],{},[1829,6865,5285],{},[1838,6867,4145],{"stretchy":4144},[1826,6869,6870,6872],{},[1829,6871,4830],{},[1829,6873,1844],{},[1838,6875,4158],{"stretchy":4144},[1838,6877,1841],{"separator":1840},[1829,6879,1831],{},[1829,6881,6833],{},[1829,6883,5300],{},[1829,6885,5285],{},[1838,6887,4145],{"stretchy":4144},[1826,6889,6890,6892],{},[1829,6891,1831],{},[1823,6893,6894,6896,6898],{},[1829,6895,1844],{},[1838,6897,1847],{},[1849,6899,1851],{},[1838,6901,4158],{"stretchy":4144},[1838,6903,4158],{"stretchy":4144},[1911,6905,6906],{"encoding":1913},"RankIC_t = corr(rank(x_t), rank(r_{t+1}))",[1802,6908,6910,6976],{"className":6909,"ariaHidden":1840},[1918],[1802,6911,6913,6917,6920,6924,6927,6967,6970,6973],{"className":6912},[1922],[1802,6914],{"className":6915,"style":6916},[1926],"height:0.8444em;vertical-align:-0.15em;",[1802,6918,4454],{"className":6919,"style":4512},[1931,1935],[1802,6921,6923],{"className":6922,"style":5561},[1931,1935],"ank",[1802,6925,5297],{"className":6926,"style":5649},[1931,1935],[1802,6928,6930,6933],{"className":6929},[1931],[1802,6931,6590],{"className":6932,"style":6649},[1931,1935],[1802,6934,6936],{"className":6935},[1940],[1802,6937,6939,6959],{"className":6938},[1944,1945],[1802,6940,6942,6956],{"className":6941},[1949],[1802,6943,6945],{"className":6944,"style":3866},[1953],[1802,6946,6947,6950],{"style":6664},[1802,6948],{"className":6949,"style":1962},[1961],[1802,6951,6953],{"className":6952},[1966,1967,1968,1969],[1802,6954,1844],{"className":6955},[1931,1935,1969],[1802,6957,1994],{"className":6958},[1993],[1802,6960,6962],{"className":6961},[1949],[1802,6963,6965],{"className":6964,"style":2063},[1953],[1802,6966],{},[1802,6968],{"className":6969,"style":2008},[2007],[1802,6971,1854],{"className":6972},[2012],[1802,6974],{"className":6975,"style":2008},[2007],[1802,6977,6979,6982,6985,6988,6991,6994,6997,7000,7040,7043,7046,7049,7052,7055,7058,7107],{"className":6978},[1922],[1802,6980],{"className":6981,"style":4357},[1926],[1802,6983,6703],{"className":6984,"style":1936},[1931,1935],[1802,6986,1831],{"className":6987,"style":1936},[1931,1935],[1802,6989,4145],{"className":6990},[3338],[1802,6992,1831],{"className":6993,"style":1936},[1931,1935],[1802,6995,6923],{"className":6996,"style":5561},[1931,1935],[1802,6998,4145],{"className":6999},[3338],[1802,7001,7003,7006],{"className":7002},[1931],[1802,7004,4830],{"className":7005},[1931,1935],[1802,7007,7009],{"className":7008},[1940],[1802,7010,7012,7032],{"className":7011},[1944,1945],[1802,7013,7015,7029],{"className":7014},[1949],[1802,7016,7018],{"className":7017,"style":3866},[1953],[1802,7019,7020,7023],{"style":2227},[1802,7021],{"className":7022,"style":1962},[1961],[1802,7024,7026],{"className":7025},[1966,1967,1968,1969],[1802,7027,1844],{"className":7028},[1931,1935,1969],[1802,7030,1994],{"className":7031},[1993],[1802,7033,7035],{"className":7034},[1949],[1802,7036,7038],{"className":7037,"style":2063},[1953],[1802,7039],{},[1802,7041,4158],{"className":7042},[3417],[1802,7044,1841],{"className":7045},[1979],[1802,7047],{"className":7048,"style":5587},[2007],[1802,7050,1831],{"className":7051,"style":1936},[1931,1935],[1802,7053,6923],{"className":7054,"style":5561},[1931,1935],[1802,7056,4145],{"className":7057},[3338],[1802,7059,7061,7064],{"className":7060},[1931],[1802,7062,1831],{"className":7063,"style":1936},[1931,1935],[1802,7065,7067],{"className":7066},[1940],[1802,7068,7070,7099],{"className":7069},[1944,1945],[1802,7071,7073,7096],{"className":7072},[1949],[1802,7074,7076],{"className":7075,"style":2158},[1953],[1802,7077,7078,7081],{"style":1957},[1802,7079],{"className":7080,"style":1962},[1961],[1802,7082,7084],{"className":7083},[1966,1967,1968,1969],[1802,7085,7087,7090,7093],{"className":7086},[1931,1969],[1802,7088,1844],{"className":7089},[1931,1935,1969],[1802,7091,1847],{"className":7092},[1986,1969],[1802,7094,1851],{"className":7095},[1931,1969],[1802,7097,1994],{"className":7098},[1993],[1802,7100,7102],{"className":7101},[1949],[1802,7103,7105],{"className":7104,"style":2189},[1953],[1802,7106],{},[1802,7108,7110],{"className":7109},[3417],"))",[1792,7112,2268],{},[2270,7114,7115,7217],{},[2273,7116,7117,7187,7188,7216],{},[1802,7118,7120,7138],{"className":7119},[1809],[1802,7121,7123],{"className":7122},[1813],[1815,7124,7125],{"xmlns":1817},[1820,7126,7127,7135],{},[1823,7128,7129],{},[1826,7130,7131,7133],{},[1829,7132,4830],{},[1829,7134,1844],{},[1911,7136,7137],{"encoding":1913},"x_t",[1802,7139,7141],{"className":7140,"ariaHidden":1840},[1918],[1802,7142,7144,7147],{"className":7143},[1922],[1802,7145],{"className":7146,"style":2709},[1926],[1802,7148,7150,7153],{"className":7149},[1931],[1802,7151,4830],{"className":7152},[1931,1935],[1802,7154,7156],{"className":7155},[1940],[1802,7157,7159,7179],{"className":7158},[1944,1945],[1802,7160,7162,7176],{"className":7161},[1949],[1802,7163,7165],{"className":7164,"style":3866},[1953],[1802,7166,7167,7170],{"style":2227},[1802,7168],{"className":7169,"style":1962},[1961],[1802,7171,7173],{"className":7172},[1966,1967,1968,1969],[1802,7174,1844],{"className":7175},[1931,1935,1969],[1802,7177,1994],{"className":7178},[1993],[1802,7180,7182],{"className":7181},[1949],[1802,7183,7185],{"className":7184,"style":2063},[1953],[1802,7186],{}," 是时点 ",[1802,7189,7191,7204],{"className":7190},[1809],[1802,7192,7194],{"className":7193},[1813],[1815,7195,7196],{"xmlns":1817},[1820,7197,7198,7202],{},[1823,7199,7200],{},[1829,7201,1844],{},[1911,7203,1844],{"encoding":1913},[1802,7205,7207],{"className":7206,"ariaHidden":1840},[1918],[1802,7208,7210,7213],{"className":7209},[1922],[1802,7211],{"className":7212,"style":2426},[1926],[1802,7214,1844],{"className":7215},[1931,1935]," 的因子截面向量；",[2273,7218,7219,7305,7306,2430,7334,7384],{},[1802,7220,7222,7246],{"className":7221},[1809],[1802,7223,7225],{"className":7224},[1813],[1815,7226,7227],{"xmlns":1817},[1820,7228,7229,7243],{},[1823,7230,7231],{},[1826,7232,7233,7235],{},[1829,7234,1831],{},[1823,7236,7237,7239,7241],{},[1829,7238,1844],{},[1838,7240,1847],{},[1849,7242,1851],{},[1911,7244,7245],{"encoding":1913},"r_{t+1}",[1802,7247,7249],{"className":7248,"ariaHidden":1840},[1918],[1802,7250,7252,7256],{"className":7251},[1922],[1802,7253],{"className":7254,"style":7255},[1926],"height:0.6389em;vertical-align:-0.2083em;",[1802,7257,7259,7262],{"className":7258},[1931],[1802,7260,1831],{"className":7261,"style":1936},[1931,1935],[1802,7263,7265],{"className":7264},[1940],[1802,7266,7268,7297],{"className":7267},[1944,1945],[1802,7269,7271,7294],{"className":7270},[1949],[1802,7272,7274],{"className":7273,"style":2158},[1953],[1802,7275,7276,7279],{"style":1957},[1802,7277],{"className":7278,"style":1962},[1961],[1802,7280,7282],{"className":7281},[1966,1967,1968,1969],[1802,7283,7285,7288,7291],{"className":7284},[1931,1969],[1802,7286,1844],{"className":7287},[1931,1935,1969],[1802,7289,1847],{"className":7290},[1986,1969],[1802,7292,1851],{"className":7293},[1931,1969],[1802,7295,1994],{"className":7296},[1993],[1802,7298,7300],{"className":7299},[1949],[1802,7301,7303],{"className":7302,"style":2189},[1953],[1802,7304],{}," 是从 ",[1802,7307,7309,7322],{"className":7308},[1809],[1802,7310,7312],{"className":7311},[1813],[1815,7313,7314],{"xmlns":1817},[1820,7315,7316,7320],{},[1823,7317,7318],{},[1829,7319,1844],{},[1911,7321,1844],{"encoding":1913},[1802,7323,7325],{"className":7324,"ariaHidden":1840},[1918],[1802,7326,7328,7331],{"className":7327},[1922],[1802,7329],{"className":7330,"style":2426},[1926],[1802,7332,1844],{"className":7333},[1931,1935],[1802,7335,7337,7354],{"className":7336},[1809],[1802,7338,7340],{"className":7339},[1813],[1815,7341,7342],{"xmlns":1817},[1820,7343,7344,7352],{},[1823,7345,7346,7348,7350],{},[1829,7347,1844],{},[1838,7349,1847],{},[1849,7351,1851],{},[1911,7353,2451],{"encoding":1913},[1802,7355,7357,7375],{"className":7356,"ariaHidden":1840},[1918],[1802,7358,7360,7363,7366,7369,7372],{"className":7359},[1922],[1802,7361],{"className":7362,"style":2461},[1926],[1802,7364,1844],{"className":7365},[1931,1935],[1802,7367],{"className":7368,"style":2069},[2007],[1802,7370,1847],{"className":7371},[1986],[1802,7373],{"className":7374,"style":2069},[2007],[1802,7376,7378,7381],{"className":7377},[1922],[1802,7379],{"className":7380,"style":2480},[1926],[1802,7382,1851],{"className":7383},[1931]," 的收益率向量。",[1792,7386,7387],{},"统计量：",[2270,7389,7390,7486,7571],{},[2273,7391,7392,7393,7485],{},"IC 的时间序列均值 ",[1802,7394,7396,7424],{"className":7395},[1809],[1802,7397,7399],{"className":7398},[1813],[1815,7400,7401],{"xmlns":1817},[1820,7402,7403,7421],{},[1823,7404,7405,7407,7410,7412,7418],{},[1829,7406,3282],{},[1838,7408,7409],{"stretchy":4144},"[",[1829,7411,5297],{},[1826,7413,7414,7416],{},[1829,7415,6590],{},[1829,7417,1844],{},[1838,7419,7420],{"stretchy":4144},"]",[1911,7422,7423],{"encoding":1913},"E[IC_t]",[1802,7425,7427],{"className":7426,"ariaHidden":1840},[1918],[1802,7428,7430,7433,7436,7439,7442,7482],{"className":7429},[1922],[1802,7431],{"className":7432,"style":4357},[1926],[1802,7434,3282],{"className":7435,"style":3315},[1931,1935],[1802,7437,7409],{"className":7438},[3338],[1802,7440,5297],{"className":7441,"style":5649},[1931,1935],[1802,7443,7445,7448],{"className":7444},[1931],[1802,7446,6590],{"className":7447,"style":6649},[1931,1935],[1802,7449,7451],{"className":7450},[1940],[1802,7452,7454,7474],{"className":7453},[1944,1945],[1802,7455,7457,7471],{"className":7456},[1949],[1802,7458,7460],{"className":7459,"style":3866},[1953],[1802,7461,7462,7465],{"style":6664},[1802,7463],{"className":7464,"style":1962},[1961],[1802,7466,7468],{"className":7467},[1966,1967,1968,1969],[1802,7469,1844],{"className":7470},[1931,1935,1969],[1802,7472,1994],{"className":7473},[1993],[1802,7475,7477],{"className":7476},[1949],[1802,7478,7480],{"className":7479,"style":2063},[1953],[1802,7481],{},[1802,7483,7420],{"className":7484},[3417],"：衡量平均预测能力；",[2273,7487,7488,7489,7570],{},"IC 的标准差 ",[1802,7490,7492,7514],{"className":7491},[1809],[1802,7493,7495],{"className":7494},[1813],[1815,7496,7497],{"xmlns":1817},[1820,7498,7499,7511],{},[1823,7500,7501],{},[1826,7502,7503,7505],{},[1829,7504,4840],{},[1823,7506,7507,7509],{},[1829,7508,5297],{},[1829,7510,6590],{},[1911,7512,7513],{"encoding":1913},"\\sigma_{IC}",[1802,7515,7517],{"className":7516,"ariaHidden":1840},[1918],[1802,7518,7520,7523],{"className":7519},[1922],[1802,7521],{"className":7522,"style":2709},[1926],[1802,7524,7526,7529],{"className":7525},[1931],[1802,7527,4840],{"className":7528,"style":4941},[1931,1935],[1802,7530,7532],{"className":7531},[1940],[1802,7533,7535,7562],{"className":7534},[1944,1945],[1802,7536,7538,7559],{"className":7537},[1949],[1802,7539,7542],{"className":7540,"style":7541},[1953],"height:0.3283em;",[1802,7543,7544,7547],{"style":5688},[1802,7545],{"className":7546,"style":1962},[1961],[1802,7548,7550],{"className":7549},[1966,1967,1968,1969],[1802,7551,7553,7556],{"className":7552},[1931,1969],[1802,7554,5297],{"className":7555,"style":5649},[1931,1935,1969],[1802,7557,6590],{"className":7558,"style":6649},[1931,1935,1969],[1802,7560,1994],{"className":7561},[1993],[1802,7563,7565],{"className":7564},[1949],[1802,7566,7568],{"className":7567,"style":2063},[1953],[1802,7569],{}," 和 t 统计：衡量显著性；",[2273,7572,7573,7574],{},"IC 的信息比率（IR）：\n",[1802,7575,7577],{"className":7576},[1805],[1802,7578,7580,7626],{"className":7579},[1809],[1802,7581,7583],{"className":7582},[1813],[1815,7584,7585],{"xmlns":1817,"display":1818},[1820,7586,7587,7623],{},[1823,7588,7589,7591,7593,7595],{},[1829,7590,5297],{},[1829,7592,4454],{},[1838,7594,1854],{},[3286,7596,7597,7613],{},[1823,7598,7599,7601,7603,7605,7611],{},[1829,7600,3282],{},[1838,7602,7409],{"stretchy":4144},[1829,7604,5297],{},[1826,7606,7607,7609],{},[1829,7608,6590],{},[1829,7610,1844],{},[1838,7612,7420],{"stretchy":4144},[1826,7614,7615,7617],{},[1829,7616,4840],{},[1823,7618,7619,7621],{},[1829,7620,5297],{},[1829,7622,6590],{},[1911,7624,7625],{"encoding":1913},"IR = \\frac{E[IC_t]}{\\sigma_{IC}}",[1802,7627,7629,7650],{"className":7628,"ariaHidden":1840},[1918],[1802,7630,7632,7635,7638,7641,7644,7647],{"className":7631},[1922],[1802,7633],{"className":7634,"style":3307},[1926],[1802,7636,5297],{"className":7637,"style":5649},[1931,1935],[1802,7639,4454],{"className":7640,"style":4512},[1931,1935],[1802,7642],{"className":7643,"style":2008},[2007],[1802,7645,1854],{"className":7646},[2012],[1802,7648],{"className":7649,"style":2008},[2007],[1802,7651,7653,7657],{"className":7652},[1922],[1802,7654],{"className":7655,"style":7656},[1926],"height:2.263em;vertical-align:-0.836em;",[1802,7658,7660,7663,7810],{"className":7659},[1931],[1802,7661],{"className":7662},[3338,3339],[1802,7664,7666],{"className":7665},[3286],[1802,7667,7669,7801],{"className":7668},[1944,1945],[1802,7670,7672,7798],{"className":7671},[1949],[1802,7673,7676,7730,7738],{"className":7674,"style":7675},[1953],"height:1.427em;",[1802,7677,7678,7681],{"style":3355},[1802,7679],{"className":7680,"style":3359},[1961],[1802,7682,7684],{"className":7683},[1931],[1802,7685,7687,7690],{"className":7686},[1931],[1802,7688,4840],{"className":7689,"style":4941},[1931,1935],[1802,7691,7693],{"className":7692},[1940],[1802,7694,7696,7722],{"className":7695},[1944,1945],[1802,7697,7699,7719],{"className":7698},[1949],[1802,7700,7702],{"className":7701,"style":7541},[1953],[1802,7703,7704,7707],{"style":5688},[1802,7705],{"className":7706,"style":1962},[1961],[1802,7708,7710],{"className":7709},[1966,1967,1968,1969],[1802,7711,7713,7716],{"className":7712},[1931,1969],[1802,7714,5297],{"className":7715,"style":5649},[1931,1935,1969],[1802,7717,6590],{"className":7718,"style":6649},[1931,1935,1969],[1802,7720,1994],{"className":7721},[1993],[1802,7723,7725],{"className":7724},[1949],[1802,7726,7728],{"className":7727,"style":2063},[1953],[1802,7729],{},[1802,7731,7732,7735],{"style":3378},[1802,7733],{"className":7734,"style":3359},[1961],[1802,7736],{"className":7737,"style":3386},[3385],[1802,7739,7740,7743],{"style":3389},[1802,7741],{"className":7742,"style":3359},[1961],[1802,7744,7746,7749,7752,7755,7795],{"className":7745},[1931],[1802,7747,3282],{"className":7748,"style":3315},[1931,1935],[1802,7750,7409],{"className":7751},[3338],[1802,7753,5297],{"className":7754,"style":5649},[1931,1935],[1802,7756,7758,7761],{"className":7757},[1931],[1802,7759,6590],{"className":7760,"style":6649},[1931,1935],[1802,7762,7764],{"className":7763},[1940],[1802,7765,7767,7787],{"className":7766},[1944,1945],[1802,7768,7770,7784],{"className":7769},[1949],[1802,7771,7773],{"className":7772,"style":3866},[1953],[1802,7774,7775,7778],{"style":6664},[1802,7776],{"className":7777,"style":1962},[1961],[1802,7779,7781],{"className":7780},[1966,1967,1968,1969],[1802,7782,1844],{"className":7783},[1931,1935,1969],[1802,7785,1994],{"className":7786},[1993],[1802,7788,7790],{"className":7789},[1949],[1802,7791,7793],{"className":7792,"style":2063},[1953],[1802,7794],{},[1802,7796,7420],{"className":7797},[3417],[1802,7799,1994],{"className":7800},[1993],[1802,7802,7804],{"className":7803},[1949],[1802,7805,7808],{"className":7806,"style":7807},[1953],"height:0.836em;",[1802,7809],{},[1802,7811],{"className":7812},[3417,3339],[1792,7814,7815],{},"在许多学术和实务研究中（例如 Grinold & Kahn, 2000），Rank IC 被视为“信息系数”，其大小与预期的 Alpha 信息含量和可实现的信息比率紧密相关，是构造多因子模型和组合优化的关键输入之一。",[1792,7817,7818],{},"不要把某个 IC 数值当成跨市场阈值。同样的 0.03 会因资产数量、持有期重叠、换手、衰减速度、横截面依赖和成本而具有完全不同的经济价值。报告 IC 的时间序列分布、有效样本量、分组单调性、成本后组合增量，并与冻结的基准模型比较。",[1792,7820,7821,7822,7897,7898,7978,7979,8058],{},"在假设 ",[1802,7823,7825,7845],{"className":7824},[1809],[1802,7826,7828],{"className":7827},[1813],[1815,7829,7830],{"xmlns":1817},[1820,7831,7832,7842],{},[1823,7833,7834,7836],{},[1829,7835,5297],{},[1826,7837,7838,7840],{},[1829,7839,6590],{},[1829,7841,1844],{},[1911,7843,7844],{"encoding":1913},"IC_t",[1802,7846,7848],{"className":7847,"ariaHidden":1840},[1918],[1802,7849,7851,7854,7857],{"className":7850},[1922],[1802,7852],{"className":7853,"style":3840},[1926],[1802,7855,5297],{"className":7856,"style":5649},[1931,1935],[1802,7858,7860,7863],{"className":7859},[1931],[1802,7861,6590],{"className":7862,"style":6649},[1931,1935],[1802,7864,7866],{"className":7865},[1940],[1802,7867,7869,7889],{"className":7868},[1944,1945],[1802,7870,7872,7886],{"className":7871},[1949],[1802,7873,7875],{"className":7874,"style":3866},[1953],[1802,7876,7877,7880],{"style":6664},[1802,7878],{"className":7879,"style":1962},[1961],[1802,7881,7883],{"className":7882},[1966,1967,1968,1969],[1802,7884,1844],{"className":7885},[1931,1935,1969],[1802,7887,1994],{"className":7888},[1993],[1802,7890,7892],{"className":7891},[1949],[1802,7893,7895],{"className":7894,"style":2063},[1953],[1802,7896],{}," 独立同分布且均值为 ",[1802,7899,7901,7923],{"className":7900},[1809],[1802,7902,7904],{"className":7903},[1813],[1815,7905,7906],{"xmlns":1817},[1820,7907,7908,7920],{},[1823,7909,7910],{},[1826,7911,7912,7914],{},[1829,7913,4837],{},[1823,7915,7916,7918],{},[1829,7917,5297],{},[1829,7919,6590],{},[1911,7921,7922],{"encoding":1913},"\\mu_{IC}",[1802,7924,7926],{"className":7925,"ariaHidden":1840},[1918],[1802,7927,7929,7932],{"className":7928},[1922],[1802,7930],{"className":7931,"style":5158},[1926],[1802,7933,7935,7938],{"className":7934},[1931],[1802,7936,4837],{"className":7937},[1931,1935],[1802,7939,7941],{"className":7940},[1940],[1802,7942,7944,7970],{"className":7943},[1944,1945],[1802,7945,7947,7967],{"className":7946},[1949],[1802,7948,7950],{"className":7949,"style":7541},[1953],[1802,7951,7952,7955],{"style":2227},[1802,7953],{"className":7954,"style":1962},[1961],[1802,7956,7958],{"className":7957},[1966,1967,1968,1969],[1802,7959,7961,7964],{"className":7960},[1931,1969],[1802,7962,5297],{"className":7963,"style":5649},[1931,1935,1969],[1802,7965,6590],{"className":7966,"style":6649},[1931,1935,1969],[1802,7968,1994],{"className":7969},[1993],[1802,7971,7973],{"className":7972},[1949],[1802,7974,7976],{"className":7975,"style":2063},[1953],[1802,7977],{},"、标准差为 ",[1802,7980,7982,8003],{"className":7981},[1809],[1802,7983,7985],{"className":7984},[1813],[1815,7986,7987],{"xmlns":1817},[1820,7988,7989,8001],{},[1823,7990,7991],{},[1826,7992,7993,7995],{},[1829,7994,4840],{},[1823,7996,7997,7999],{},[1829,7998,5297],{},[1829,8000,6590],{},[1911,8002,7513],{"encoding":1913},[1802,8004,8006],{"className":8005,"ariaHidden":1840},[1918],[1802,8007,8009,8012],{"className":8008},[1922],[1802,8010],{"className":8011,"style":2709},[1926],[1802,8013,8015,8018],{"className":8014},[1931],[1802,8016,4840],{"className":8017,"style":4941},[1931,1935],[1802,8019,8021],{"className":8020},[1940],[1802,8022,8024,8050],{"className":8023},[1944,1945],[1802,8025,8027,8047],{"className":8026},[1949],[1802,8028,8030],{"className":8029,"style":7541},[1953],[1802,8031,8032,8035],{"style":5688},[1802,8033],{"className":8034,"style":1962},[1961],[1802,8036,8038],{"className":8037},[1966,1967,1968,1969],[1802,8039,8041,8044],{"className":8040},[1931,1969],[1802,8042,5297],{"className":8043,"style":5649},[1931,1935,1969],[1802,8045,6590],{"className":8046,"style":6649},[1931,1935,1969],[1802,8048,1994],{"className":8049},[1993],[1802,8051,8053],{"className":8052},[1949],[1802,8054,8056],{"className":8055,"style":2063},[1953],[1802,8057],{}," 的简化情形下，可以形式化地写出 IR：",[1802,8060,8062],{"className":8061},[1805],[1802,8063,8065,8107],{"className":8064},[1809],[1802,8066,8068],{"className":8067},[1813],[1815,8069,8070],{"xmlns":1817,"display":1818},[1820,8071,8072,8104],{},[1823,8073,8074,8076,8078,8080,8102],{},[1829,8075,5297],{},[1829,8077,4454],{},[1838,8079,1854],{},[3286,8081,8082,8092],{},[1826,8083,8084,8086],{},[1829,8085,4837],{},[1823,8087,8088,8090],{},[1829,8089,5297],{},[1829,8091,6590],{},[1826,8093,8094,8096],{},[1829,8095,4840],{},[1823,8097,8098,8100],{},[1829,8099,5297],{},[1829,8101,6590],{},[1838,8103,1841],{"separator":1840},[1911,8105,8106],{"encoding":1913},"IR = \\frac{\\mu_{IC}}{\\sigma_{IC}},",[1802,8108,8110,8131],{"className":8109,"ariaHidden":1840},[1918],[1802,8111,8113,8116,8119,8122,8125,8128],{"className":8112},[1922],[1802,8114],{"className":8115,"style":3307},[1926],[1802,8117,5297],{"className":8118,"style":5649},[1931,1935],[1802,8120,4454],{"className":8121,"style":4512},[1931,1935],[1802,8123],{"className":8124,"style":2008},[2007],[1802,8126,1854],{"className":8127},[2012],[1802,8129],{"className":8130,"style":2008},[2007],[1802,8132,8134,8138,8287],{"className":8133},[1922],[1802,8135],{"className":8136,"style":8137},[1926],"height:1.9436em;vertical-align:-0.836em;",[1802,8139,8141,8144,8284],{"className":8140},[1931],[1802,8142],{"className":8143},[3338,3339],[1802,8145,8147],{"className":8146},[3286],[1802,8148,8150,8276],{"className":8149},[1944,1945],[1802,8151,8153,8273],{"className":8152},[1949],[1802,8154,8157,8211,8219],{"className":8155,"style":8156},[1953],"height:1.1076em;",[1802,8158,8159,8162],{"style":3355},[1802,8160],{"className":8161,"style":3359},[1961],[1802,8163,8165],{"className":8164},[1931],[1802,8166,8168,8171],{"className":8167},[1931],[1802,8169,4840],{"className":8170,"style":4941},[1931,1935],[1802,8172,8174],{"className":8173},[1940],[1802,8175,8177,8203],{"className":8176},[1944,1945],[1802,8178,8180,8200],{"className":8179},[1949],[1802,8181,8183],{"className":8182,"style":7541},[1953],[1802,8184,8185,8188],{"style":5688},[1802,8186],{"className":8187,"style":1962},[1961],[1802,8189,8191],{"className":8190},[1966,1967,1968,1969],[1802,8192,8194,8197],{"className":8193},[1931,1969],[1802,8195,5297],{"className":8196,"style":5649},[1931,1935,1969],[1802,8198,6590],{"className":8199,"style":6649},[1931,1935,1969],[1802,8201,1994],{"className":8202},[1993],[1802,8204,8206],{"className":8205},[1949],[1802,8207,8209],{"className":8208,"style":2063},[1953],[1802,8210],{},[1802,8212,8213,8216],{"style":3378},[1802,8214],{"className":8215,"style":3359},[1961],[1802,8217],{"className":8218,"style":3386},[3385],[1802,8220,8221,8224],{"style":3389},[1802,8222],{"className":8223,"style":3359},[1961],[1802,8225,8227],{"className":8226},[1931],[1802,8228,8230,8233],{"className":8229},[1931],[1802,8231,4837],{"className":8232},[1931,1935],[1802,8234,8236],{"className":8235},[1940],[1802,8237,8239,8265],{"className":8238},[1944,1945],[1802,8240,8242,8262],{"className":8241},[1949],[1802,8243,8245],{"className":8244,"style":7541},[1953],[1802,8246,8247,8250],{"style":2227},[1802,8248],{"className":8249,"style":1962},[1961],[1802,8251,8253],{"className":8252},[1966,1967,1968,1969],[1802,8254,8256,8259],{"className":8255},[1931,1969],[1802,8257,5297],{"className":8258,"style":5649},[1931,1935,1969],[1802,8260,6590],{"className":8261,"style":6649},[1931,1935,1969],[1802,8263,1994],{"className":8264},[1993],[1802,8266,8268],{"className":8267},[1949],[1802,8269,8271],{"className":8270,"style":2063},[1953],[1802,8272],{},[1802,8274,1994],{"className":8275},[1993],[1802,8277,8279],{"className":8278},[1949],[1802,8280,8282],{"className":8281,"style":7807},[1953],[1802,8283],{},[1802,8285],{"className":8286},[3417,3339],[1802,8288,1841],{"className":8289},[1979],[1792,8291,8292],{},"当我们将因子信号线性地转化为组合权重、并在较长时间内稳定交易时，策略的理论信息比率可以近似写成：",[1802,8294,8296],{"className":8295},[1805],[1802,8297,8299,8357],{"className":8298},[1809],[1802,8300,8302],{"className":8301},[1813],[1815,8303,8304],{"xmlns":1817,"display":1818},[1820,8305,8306,8354],{},[1823,8307,8308,8310,8333,8336,8338,8340,8343,8352],{},[1829,8309,5297],{},[1826,8311,8312,8314],{},[1829,8313,4454],{},[1823,8315,8316,8318,8320,8322,8324,8326,8329,8331],{},[1829,8317,5309],{},[1829,8319,1844],{},[1829,8321,1831],{},[1829,8323,6833],{},[1829,8325,1844],{},[1829,8327,8328],{},"e",[1829,8330,6226],{},[1829,8332,5318],{},[1838,8334,8335],{},"≈",[1829,8337,5297],{},[1829,8339,6590],{},[1838,8341,8342],{},"×",[8344,8345,8346],"msqrt",{},[1823,8347,8348,8350],{},[1829,8349,3440],{},[1829,8351,4454],{},[1838,8353,1841],{"separator":1840},[1911,8355,8356],{"encoding":1913},"IR_{strategy} \\approx IC \\times \\sqrt{BR},",[1802,8358,8360,8444,8466],{"className":8359,"ariaHidden":1840},[1918],[1802,8361,8363,8367,8370,8435,8438,8441],{"className":8362},[1922],[1802,8364],{"className":8365,"style":8366},[1926],"height:0.9694em;vertical-align:-0.2861em;",[1802,8368,5297],{"className":8369,"style":5649},[1931,1935],[1802,8371,8373,8376],{"className":8372},[1931],[1802,8374,4454],{"className":8375,"style":4512},[1931,1935],[1802,8377,8379],{"className":8378},[1940],[1802,8380,8382,8427],{"className":8381},[1944,1945],[1802,8383,8385,8424],{"className":8384},[1949],[1802,8386,8388],{"className":8387,"style":3866},[1953],[1802,8389,8391,8394],{"style":8390},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[1802,8392],{"className":8393,"style":1962},[1961],[1802,8395,8397],{"className":8396},[1966,1967,1968,1969],[1802,8398,8400,8403,8406,8409,8412,8415,8418,8421],{"className":8399},[1931,1969],[1802,8401,5309],{"className":8402},[1931,1935,1969],[1802,8404,1844],{"className":8405},[1931,1935,1969],[1802,8407,1831],{"className":8408,"style":1936},[1931,1935,1969],[1802,8410,6833],{"className":8411},[1931,1935,1969],[1802,8413,1844],{"className":8414},[1931,1935,1969],[1802,8416,8328],{"className":8417},[1931,1935,1969],[1802,8419,6226],{"className":8420,"style":4941},[1931,1935,1969],[1802,8422,5318],{"className":8423,"style":4941},[1931,1935,1969],[1802,8425,1994],{"className":8426},[1993],[1802,8428,8430],{"className":8429},[1949],[1802,8431,8433],{"className":8432,"style":2001},[1953],[1802,8434],{},[1802,8436],{"className":8437,"style":2008},[2007],[1802,8439,8335],{"className":8440},[2012],[1802,8442],{"className":8443,"style":2008},[2007],[1802,8445,8447,8451,8454,8457,8460,8463],{"className":8446},[1922],[1802,8448],{"className":8449,"style":8450},[1926],"height:0.7667em;vertical-align:-0.0833em;",[1802,8452,5297],{"className":8453,"style":5649},[1931,1935],[1802,8455,6590],{"className":8456,"style":6649},[1931,1935],[1802,8458],{"className":8459,"style":2069},[2007],[1802,8461,8342],{"className":8462},[1986],[1802,8464],{"className":8465,"style":2069},[2007],[1802,8467,8469,8473,8540],{"className":8468},[1922],[1802,8470],{"className":8471,"style":8472},[1926],"height:1.17em;vertical-align:-0.1944em;",[1802,8474,8477],{"className":8475},[1931,8476],"sqrt",[1802,8478,8480,8531],{"className":8479},[1944,1945],[1802,8481,8483,8528],{"className":8482},[1949],[1802,8484,8487,8505],{"className":8485,"style":8486},[1953],"height:0.9755em;",[1802,8488,8492,8495],{"className":8489,"style":8491},[8490],"svg-align","top:-3em;",[1802,8493],{"className":8494,"style":3359},[1961],[1802,8496,8499,8502],{"className":8497,"style":8498},[1931],"padding-left:0.833em;",[1802,8500,3440],{"className":8501,"style":3468},[1931,1935],[1802,8503,4454],{"className":8504,"style":4512},[1931,1935],[1802,8506,8508,8511],{"style":8507},"top:-2.9355em;",[1802,8509],{"className":8510,"style":3359},[1961],[1802,8512,8516],{"className":8513,"style":8515},[8514],"hide-tail","min-width:0.853em;height:1.08em;",[8517,8518,8524],"svg",{"xmlns":8519,"width":8520,"height":8521,"viewBox":8522,"preserveAspectRatio":8523},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[8525,8526],"path",{"d":8527},"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",[1802,8529,1994],{"className":8530},[1993],[1802,8532,8534],{"className":8533},[1949],[1802,8535,8538],{"className":8536,"style":8537},[1953],"height:0.0645em;",[1802,8539],{},[1802,8541,1841],{"className":8542},[1979],[1792,8544,8545,8546,8580],{},"其中 ",[1802,8547,8549,8565],{"className":8548},[1809],[1802,8550,8552],{"className":8551},[1813],[1815,8553,8554],{"xmlns":1817},[1820,8555,8556,8562],{},[1823,8557,8558,8560],{},[1829,8559,3440],{},[1829,8561,4454],{},[1911,8563,8564],{"encoding":1913},"BR",[1802,8566,8568],{"className":8567,"ariaHidden":1840},[1918],[1802,8569,8571,8574,8577],{"className":8570},[1922],[1802,8572],{"className":8573,"style":3307},[1926],[1802,8575,3440],{"className":8576,"style":3468},[1931,1935],[1802,8578,4454],{"className":8579,"style":4512},[1931,1935]," 是“独立投注次数”（breadth），这一关系在 Grinold 的“基本定理（Fundamental Law of Active Management）”中有详细推导：",[1802,8582,8584],{"className":8583},[1805],[1802,8585,8587,8622],{"className":8586},[1809],[1802,8588,8590],{"className":8589},[1813],[1815,8591,8592],{"xmlns":1817,"display":1818},[1820,8593,8594,8619],{},[1823,8595,8596,8598,8600,8602,8604,8606,8608,8616],{},[1829,8597,5297],{},[1829,8599,4454],{},[1838,8601,1854],{},[1829,8603,5297],{},[1829,8605,6590],{},[1838,8607,8342],{},[8344,8609,8610],{},[1823,8611,8612,8614],{},[1829,8613,3440],{},[1829,8615,4454],{},[1829,8617,8618],{"mathvariant":1874},".",[1911,8620,8621],{"encoding":1913},"IR = IC \\times \\sqrt{BR}.",[1802,8623,8625,8646,8667],{"className":8624,"ariaHidden":1840},[1918],[1802,8626,8628,8631,8634,8637,8640,8643],{"className":8627},[1922],[1802,8629],{"className":8630,"style":3307},[1926],[1802,8632,5297],{"className":8633,"style":5649},[1931,1935],[1802,8635,4454],{"className":8636,"style":4512},[1931,1935],[1802,8638],{"className":8639,"style":2008},[2007],[1802,8641,1854],{"className":8642},[2012],[1802,8644],{"className":8645,"style":2008},[2007],[1802,8647,8649,8652,8655,8658,8661,8664],{"className":8648},[1922],[1802,8650],{"className":8651,"style":8450},[1926],[1802,8653,5297],{"className":8654,"style":5649},[1931,1935],[1802,8656,6590],{"className":8657,"style":6649},[1931,1935],[1802,8659],{"className":8660,"style":2069},[2007],[1802,8662,8342],{"className":8663},[1986],[1802,8665],{"className":8666,"style":2069},[2007],[1802,8668,8670,8674,8724],{"className":8669},[1922],[1802,8671],{"className":8672,"style":8673},[1926],"height:1.04em;vertical-align:-0.0645em;",[1802,8675,8677],{"className":8676},[1931,8476],[1802,8678,8680,8716],{"className":8679},[1944,1945],[1802,8681,8683,8713],{"className":8682},[1949],[1802,8684,8686,8701],{"className":8685,"style":8486},[1953],[1802,8687,8689,8692],{"className":8688,"style":8491},[8490],[1802,8690],{"className":8691,"style":3359},[1961],[1802,8693,8695,8698],{"className":8694,"style":8498},[1931],[1802,8696,3440],{"className":8697,"style":3468},[1931,1935],[1802,8699,4454],{"className":8700,"style":4512},[1931,1935],[1802,8702,8703,8706],{"style":8507},[1802,8704],{"className":8705,"style":3359},[1961],[1802,8707,8709],{"className":8708,"style":8515},[8514],[8517,8710,8711],{"xmlns":8519,"width":8520,"height":8521,"viewBox":8522,"preserveAspectRatio":8523},[8525,8712],{"d":8527},[1802,8714,1994],{"className":8715},[1993],[1802,8717,8719],{"className":8718},[1949],[1802,8720,8722],{"className":8721,"style":8537},[1953],[1802,8723],{},[1802,8725,8618],{"className":8726},[1931],[1792,8728,8729],{},"尽管在现实世界中“独立投注次数”的定义远比理论中复杂，这一公式仍然为我们提供了一个直观的启示：",[2270,8731,8732,8735],{},[2273,8733,8734],{},"在保持因子质量（IC）不变的情况下，增加频率、扩展标的池可以提升策略的 IR；",[2273,8736,8737],{},"反之，再强的因子，如果可交易机会很少，其最终 IR 也可能有限。",[3205,8739,8741],{"id":8740},"_6-信号合成与多因子模型","6. 信号合成与多因子模型",[1792,8743,8744],{},"实际策略中很少只依赖单一因子，更多是多个因子共同决定一个资产的“打分”或“目标权重”。",[3250,8746,8748],{"id":8747},"_61-线性打分模型","6.1 线性打分模型",[1792,8750,8751],{},"最简单的形式是线性组合：",[1802,8753,8755],{"className":8754},[1805],[1802,8756,8758,8846],{"className":8757},[1809],[1802,8759,8761],{"className":8760},[1813],[1815,8762,8763],{"xmlns":1817,"display":1818},[1820,8764,8765,8843],{},[1823,8766,8767,8770,8772,8774,8776,8782,8784,8791,8801,8803,8809,8819,8821,8824,8826,8833],{},[1829,8768,8769],{},"S",[1829,8771,6597],{},[1829,8773,6221],{},[1829,8775,1831],{},[1826,8777,8778,8780],{},[1829,8779,8328],{},[1829,8781,1836],{},[1838,8783,1854],{},[1826,8785,8786,8789],{},[1829,8787,8788],{},"w",[1849,8790,1851],{},[1826,8792,8793,8795],{},[1829,8794,1880],{},[1823,8796,8797,8799],{},[1849,8798,1851],{},[1829,8800,1836],{},[1838,8802,1847],{},[1826,8804,8805,8807],{},[1829,8806,8788],{},[1849,8808,4139],{},[1826,8810,8811,8813],{},[1829,8812,1880],{},[1823,8814,8815,8817],{},[1849,8816,4139],{},[1829,8818,1836],{},[1838,8820,1847],{},[1838,8822,8823],{},"⋯",[1838,8825,1847],{},[1826,8827,8828,8830],{},[1829,8829,8788],{},[1829,8831,8832],{},"K",[1826,8834,8835,8837],{},[1829,8836,1880],{},[1823,8838,8839,8841],{},[1829,8840,8832],{},[1829,8842,1836],{},[1911,8844,8845],{"encoding":1913}," Score_i = w_1 f_{1i} + w_2 f_{2i} + \\dots + w_K f_{Ki}",[1802,8847,8849,8910,9013,9114,9133],{"className":8848,"ariaHidden":1840},[1918],[1802,8850,8852,8855,8858,8861,8901,8904,8907],{"className":8851},[1922],[1802,8853],{"className":8854,"style":3840},[1926],[1802,8856,8769],{"className":8857,"style":3315},[1931,1935],[1802,8859,6703],{"className":8860,"style":1936},[1931,1935],[1802,8862,8864,8867],{"className":8863},[1931],[1802,8865,8328],{"className":8866},[1931,1935],[1802,8868,8870],{"className":8869},[1940],[1802,8871,8873,8893],{"className":8872},[1944,1945],[1802,8874,8876,8890],{"className":8875},[1949],[1802,8877,8879],{"className":8878,"style":1954},[1953],[1802,8880,8881,8884],{"style":2227},[1802,8882],{"className":8883,"style":1962},[1961],[1802,8885,8887],{"className":8886},[1966,1967,1968,1969],[1802,8888,1836],{"className":8889},[1931,1935,1969],[1802,8891,1994],{"className":8892},[1993],[1802,8894,8896],{"className":8895},[1949],[1802,8897,8899],{"className":8898,"style":2063},[1953],[1802,8900],{},[1802,8902],{"className":8903,"style":2008},[2007],[1802,8905,1854],{"className":8906},[2012],[1802,8908],{"className":8909,"style":2008},[2007],[1802,8911,8913,8916,8958,9004,9007,9010],{"className":8912},[1922],[1802,8914],{"className":8915,"style":2606},[1926],[1802,8917,8919,8923],{"className":8918},[1931],[1802,8920,8788],{"className":8921,"style":8922},[1931,1935],"margin-right:0.0269em;",[1802,8924,8926],{"className":8925},[1940],[1802,8927,8929,8950],{"className":8928},[1944,1945],[1802,8930,8932,8947],{"className":8931},[1949],[1802,8933,8935],{"className":8934,"style":2158},[1953],[1802,8936,8938,8941],{"style":8937},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1802,8939],{"className":8940,"style":1962},[1961],[1802,8942,8944],{"className":8943},[1966,1967,1968,1969],[1802,8945,1851],{"className":8946},[1931,1969],[1802,8948,1994],{"className":8949},[1993],[1802,8951,8953],{"className":8952},[1949],[1802,8954,8956],{"className":8955,"style":2063},[1953],[1802,8957],{},[1802,8959,8961,8964],{"className":8960},[1931],[1802,8962,1880],{"className":8963,"style":2145},[1931,1935],[1802,8965,8967],{"className":8966},[1940],[1802,8968,8970,8996],{"className":8969},[1944,1945],[1802,8971,8973,8993],{"className":8972},[1949],[1802,8974,8976],{"className":8975,"style":1954},[1953],[1802,8977,8978,8981],{"style":2161},[1802,8979],{"className":8980,"style":1962},[1961],[1802,8982,8984],{"className":8983},[1966,1967,1968,1969],[1802,8985,8987,8990],{"className":8986},[1931,1969],[1802,8988,1851],{"className":8989},[1931,1969],[1802,8991,1836],{"className":8992},[1931,1935,1969],[1802,8994,1994],{"className":8995},[1993],[1802,8997,8999],{"className":8998},[1949],[1802,9000,9002],{"className":9001,"style":2063},[1953],[1802,9003],{},[1802,9005],{"className":9006,"style":2069},[2007],[1802,9008,1847],{"className":9009},[1986],[1802,9011],{"className":9012,"style":2069},[2007],[1802,9014,9016,9019,9059,9105,9108,9111],{"className":9015},[1922],[1802,9017],{"className":9018,"style":2606},[1926],[1802,9020,9022,9025],{"className":9021},[1931],[1802,9023,8788],{"className":9024,"style":8922},[1931,1935],[1802,9026,9028],{"className":9027},[1940],[1802,9029,9031,9051],{"className":9030},[1944,1945],[1802,9032,9034,9048],{"className":9033},[1949],[1802,9035,9037],{"className":9036,"style":2158},[1953],[1802,9038,9039,9042],{"style":8937},[1802,9040],{"className":9041,"style":1962},[1961],[1802,9043,9045],{"className":9044},[1966,1967,1968,1969],[1802,9046,4139],{"className":9047},[1931,1969],[1802,9049,1994],{"className":9050},[1993],[1802,9052,9054],{"className":9053},[1949],[1802,9055,9057],{"className":9056,"style":2063},[1953],[1802,9058],{},[1802,9060,9062,9065],{"className":9061},[1931],[1802,9063,1880],{"className":9064,"style":2145},[1931,1935],[1802,9066,9068],{"className":9067},[1940],[1802,9069,9071,9097],{"className":9070},[1944,1945],[1802,9072,9074,9094],{"className":9073},[1949],[1802,9075,9077],{"className":9076,"style":1954},[1953],[1802,9078,9079,9082],{"style":2161},[1802,9080],{"className":9081,"style":1962},[1961],[1802,9083,9085],{"className":9084},[1966,1967,1968,1969],[1802,9086,9088,9091],{"className":9087},[1931,1969],[1802,9089,4139],{"className":9090},[1931,1969],[1802,9092,1836],{"className":9093},[1931,1935,1969],[1802,9095,1994],{"className":9096},[1993],[1802,9098,9100],{"className":9099},[1949],[1802,9101,9103],{"className":9102,"style":2063},[1953],[1802,9104],{},[1802,9106],{"className":9107,"style":2069},[2007],[1802,9109,1847],{"className":9110},[1986],[1802,9112],{"className":9113,"style":2069},[2007],[1802,9115,9117,9120,9124,9127,9130],{"className":9116},[1922],[1802,9118],{"className":9119,"style":5403},[1926],[1802,9121,8823],{"className":9122},[9123],"minner",[1802,9125],{"className":9126,"style":2069},[2007],[1802,9128,1847],{"className":9129},[1986],[1802,9131],{"className":9132,"style":2069},[2007],[1802,9134,9136,9139,9179],{"className":9135},[1922],[1802,9137],{"className":9138,"style":2606},[1926],[1802,9140,9142,9145],{"className":9141},[1931],[1802,9143,8788],{"className":9144,"style":8922},[1931,1935],[1802,9146,9148],{"className":9147},[1940],[1802,9149,9151,9171],{"className":9150},[1944,1945],[1802,9152,9154,9168],{"className":9153},[1949],[1802,9155,9157],{"className":9156,"style":7541},[1953],[1802,9158,9159,9162],{"style":8937},[1802,9160],{"className":9161,"style":1962},[1961],[1802,9163,9165],{"className":9164},[1966,1967,1968,1969],[1802,9166,8832],{"className":9167,"style":6649},[1931,1935,1969],[1802,9169,1994],{"className":9170},[1993],[1802,9172,9174],{"className":9173},[1949],[1802,9175,9177],{"className":9176,"style":2063},[1953],[1802,9178],{},[1802,9180,9182,9185],{"className":9181},[1931],[1802,9183,1880],{"className":9184,"style":2145},[1931,1935],[1802,9186,9188],{"className":9187},[1940],[1802,9189,9191,9217],{"className":9190},[1944,1945],[1802,9192,9194,9214],{"className":9193},[1949],[1802,9195,9197],{"className":9196,"style":7541},[1953],[1802,9198,9199,9202],{"style":2161},[1802,9200],{"className":9201,"style":1962},[1961],[1802,9203,9205],{"className":9204},[1966,1967,1968,1969],[1802,9206,9208,9211],{"className":9207},[1931,1969],[1802,9209,8832],{"className":9210,"style":6649},[1931,1935,1969],[1802,9212,1836],{"className":9213},[1931,1935,1969],[1802,9215,1994],{"className":9216},[1993],[1802,9218,9220],{"className":9219},[1949],[1802,9221,9223],{"className":9222,"style":2063},[1953],[1802,9224],{},[1792,9226,2268],{},[2270,9228,9229,9371],{},[2273,9230,9231,9311,9312,9341,9342,9370],{},[1802,9232,9234,9256],{"className":9233},[1809],[1802,9235,9237],{"className":9236},[1813],[1815,9238,9239],{"xmlns":1817},[1820,9240,9241,9253],{},[1823,9242,9243],{},[1826,9244,9245,9247],{},[1829,9246,1880],{},[1823,9248,9249,9251],{},[1829,9250,5285],{},[1829,9252,1836],{},[1911,9254,9255],{"encoding":1913},"f_{ki}",[1802,9257,9259],{"className":9258,"ariaHidden":1840},[1918],[1802,9260,9262,9265],{"className":9261},[1922],[1802,9263],{"className":9264,"style":2606},[1926],[1802,9266,9268,9271],{"className":9267},[1931],[1802,9269,1880],{"className":9270,"style":2145},[1931,1935],[1802,9272,9274],{"className":9273},[1940],[1802,9275,9277,9303],{"className":9276},[1944,1945],[1802,9278,9280,9300],{"className":9279},[1949],[1802,9281,9283],{"className":9282,"style":5607},[1953],[1802,9284,9285,9288],{"style":2161},[1802,9286],{"className":9287,"style":1962},[1961],[1802,9289,9291],{"className":9290},[1966,1967,1968,1969],[1802,9292,9294,9297],{"className":9293},[1931,1969],[1802,9295,5285],{"className":9296,"style":5561},[1931,1935,1969],[1802,9298,1836],{"className":9299},[1931,1935,1969],[1802,9301,1994],{"className":9302},[1993],[1802,9304,9306],{"className":9305},[1949],[1802,9307,9309],{"className":9308,"style":2063},[1953],[1802,9310],{}," 是第 ",[1802,9313,9315,9328],{"className":9314},[1809],[1802,9316,9318],{"className":9317},[1813],[1815,9319,9320],{"xmlns":1817},[1820,9321,9322,9326],{},[1823,9323,9324],{},[1829,9325,5285],{},[1911,9327,5285],{"encoding":1913},[1802,9329,9331],{"className":9330,"ariaHidden":1840},[1918],[1802,9332,9334,9338],{"className":9333},[1922],[1802,9335],{"className":9336,"style":9337},[1926],"height:0.6944em;",[1802,9339,5285],{"className":9340,"style":5561},[1931,1935]," 个因子在资产 ",[1802,9343,9345,9358],{"className":9344},[1809],[1802,9346,9348],{"className":9347},[1813],[1815,9349,9350],{"xmlns":1817},[1820,9351,9352,9356],{},[1823,9353,9354],{},[1829,9355,1836],{},[1911,9357,1836],{"encoding":1913},[1802,9359,9361],{"className":9360,"ariaHidden":1840},[1918],[1802,9362,9364,9367],{"className":9363},[1922],[1802,9365],{"className":9366,"style":2396},[1926],[1802,9368,1836],{"className":9369},[1931,1935]," 上的值（通常已标准化）；",[2273,9372,9373,9443,9444],{},[1802,9374,9376,9394],{"className":9375},[1809],[1802,9377,9379],{"className":9378},[1813],[1815,9380,9381],{"xmlns":1817},[1820,9382,9383,9391],{},[1823,9384,9385],{},[1826,9386,9387,9389],{},[1829,9388,8788],{},[1829,9390,5285],{},[1911,9392,9393],{"encoding":1913},"w_k",[1802,9395,9397],{"className":9396,"ariaHidden":1840},[1918],[1802,9398,9400,9403],{"className":9399},[1922],[1802,9401],{"className":9402,"style":2709},[1926],[1802,9404,9406,9409],{"className":9405},[1931],[1802,9407,8788],{"className":9408,"style":8922},[1931,1935],[1802,9410,9412],{"className":9411},[1940],[1802,9413,9415,9435],{"className":9414},[1944,1945],[1802,9416,9418,9432],{"className":9417},[1949],[1802,9419,9421],{"className":9420,"style":5607},[1953],[1802,9422,9423,9426],{"style":8937},[1802,9424],{"className":9425,"style":1962},[1961],[1802,9427,9429],{"className":9428},[1966,1967,1968,1969],[1802,9430,5285],{"className":9431,"style":5561},[1931,1935,1969],[1802,9433,1994],{"className":9434},[1993],[1802,9436,9438],{"className":9437},[1949],[1802,9439,9441],{"className":9440,"style":2063},[1953],[1802,9442],{}," 是该因子的权重，可以：\n",[2270,9445,9446,9449],{},[2273,9447,9448],{},"手工设定（如等权、经验权重）；",[2273,9450,9451],{},"通过回归或优化估计。",[1792,9453,9454],{},"打分越高，代表越应该“多持有”该资产，打分越低则反之。后续可将打分转换为：",[2270,9456,9457,9460],{},[2273,9458,9459],{},"排名选股（例如选出前 20% 构建多头组合）；",[2273,9461,9462],{},"或者通过线性变换直接得到目标持仓权重。",[1792,9464,9465,9466,9550,9551,9579,9580,9762],{},"在资产定价的语境下，",[1802,9467,9469,9495],{"className":9468},[1809],[1802,9470,9472],{"className":9471},[1813],[1815,9473,9474],{"xmlns":1817},[1820,9475,9476,9492],{},[1823,9477,9478,9480,9482,9484,9486],{},[1829,9479,8769],{},[1829,9481,6597],{},[1829,9483,6221],{},[1829,9485,1831],{},[1826,9487,9488,9490],{},[1829,9489,8328],{},[1829,9491,1836],{},[1911,9493,9494],{"encoding":1913},"Score_i",[1802,9496,9498],{"className":9497,"ariaHidden":1840},[1918],[1802,9499,9501,9504,9507,9510],{"className":9500},[1922],[1802,9502],{"className":9503,"style":3840},[1926],[1802,9505,8769],{"className":9506,"style":3315},[1931,1935],[1802,9508,6703],{"className":9509,"style":1936},[1931,1935],[1802,9511,9513,9516],{"className":9512},[1931],[1802,9514,8328],{"className":9515},[1931,1935],[1802,9517,9519],{"className":9518},[1940],[1802,9520,9522,9542],{"className":9521},[1944,1945],[1802,9523,9525,9539],{"className":9524},[1949],[1802,9526,9528],{"className":9527,"style":1954},[1953],[1802,9529,9530,9533],{"style":2227},[1802,9531],{"className":9532,"style":1962},[1961],[1802,9534,9536],{"className":9535},[1966,1967,1968,1969],[1802,9537,1836],{"className":9538},[1931,1935,1969],[1802,9540,1994],{"className":9541},[1993],[1802,9543,9545],{"className":9544},[1949],[1802,9546,9548],{"className":9547,"style":2063},[1953],[1802,9549],{}," 可以被视为对资产 ",[1802,9552,9554,9567],{"className":9553},[1809],[1802,9555,9557],{"className":9556},[1813],[1815,9558,9559],{"xmlns":1817},[1820,9560,9561,9565],{},[1823,9562,9563],{},[1829,9564,1836],{},[1911,9566,1836],{"encoding":1913},[1802,9568,9570],{"className":9569,"ariaHidden":1840},[1918],[1802,9571,9573,9576],{"className":9572},[1922],[1802,9574],{"className":9575,"style":2396},[1926],[1802,9577,1836],{"className":9578},[1931,1935]," 未来超额收益 ",[1802,9581,9583,9629],{"className":9582},[1809],[1802,9584,9586],{"className":9585},[1813],[1815,9587,9588],{"xmlns":1817},[1820,9589,9590,9626],{},[1823,9591,9592,9595,9597,9613,9616,9624],{},[1829,9593,3282],{"mathvariant":9594},"double-struck",[1838,9596,7409],{"stretchy":4144},[1826,9598,9599,9601],{},[1829,9600,1831],{},[1823,9602,9603,9605,9607,9609,9611],{},[1829,9604,1836],{},[1838,9606,1841],{"separator":1840},[1829,9608,1844],{},[1838,9610,1847],{},[1849,9612,1851],{},[1838,9614,9615],{},"∣",[1826,9617,9618,9622],{},[1829,9619,9621],{"mathvariant":9620},"script","F",[1829,9623,1844],{},[1838,9625,7420],{"stretchy":4144},[1911,9627,9628],{"encoding":1913},"\\mathbb{E}[r_{i,t+1}\\mid\\mathcal{F}_t]",[1802,9630,9632,9710],{"className":9631,"ariaHidden":1840},[1918],[1802,9633,9635,9639,9643,9646,9701,9704,9707],{"className":9634},[1922],[1802,9636],{"className":9637,"style":9638},[1926],"height:1.0361em;vertical-align:-0.2861em;",[1802,9640,3282],{"className":9641},[1931,9642],"mathbb",[1802,9644,7409],{"className":9645},[3338],[1802,9647,9649,9652],{"className":9648},[1931],[1802,9650,1831],{"className":9651,"style":1936},[1931,1935],[1802,9653,9655],{"className":9654},[1940],[1802,9656,9658,9693],{"className":9657},[1944,1945],[1802,9659,9661,9690],{"className":9660},[1949],[1802,9662,9664],{"className":9663,"style":1954},[1953],[1802,9665,9666,9669],{"style":1957},[1802,9667],{"className":9668,"style":1962},[1961],[1802,9670,9672],{"className":9671},[1966,1967,1968,1969],[1802,9673,9675,9678,9681,9684,9687],{"className":9674},[1931,1969],[1802,9676,1836],{"className":9677},[1931,1935,1969],[1802,9679,1841],{"className":9680},[1979,1969],[1802,9682,1844],{"className":9683},[1931,1935,1969],[1802,9685,1847],{"className":9686},[1986,1969],[1802,9688,1851],{"className":9689},[1931,1969],[1802,9691,1994],{"className":9692},[1993],[1802,9694,9696],{"className":9695},[1949],[1802,9697,9699],{"className":9698,"style":2001},[1953],[1802,9700],{},[1802,9702],{"className":9703,"style":2008},[2007],[1802,9705,9615],{"className":9706},[2012],[1802,9708],{"className":9709,"style":2008},[2007],[1802,9711,9713,9716,9759],{"className":9712},[1922],[1802,9714],{"className":9715,"style":4357},[1926],[1802,9717,9719,9724],{"className":9718},[1931],[1802,9720,9621],{"className":9721,"style":9723},[1931,9722],"mathcal","margin-right:0.0993em;",[1802,9725,9727],{"className":9726},[1940],[1802,9728,9730,9751],{"className":9729},[1944,1945],[1802,9731,9733,9748],{"className":9732},[1949],[1802,9734,9736],{"className":9735,"style":3866},[1953],[1802,9737,9739,9742],{"style":9738},"top:-2.55em;margin-left:-0.0993em;margin-right:0.05em;",[1802,9740],{"className":9741,"style":1962},[1961],[1802,9743,9745],{"className":9744},[1966,1967,1968,1969],[1802,9746,1844],{"className":9747},[1931,1935,1969],[1802,9749,1994],{"className":9750},[1993],[1802,9752,9754],{"className":9753},[1949],[1802,9755,9757],{"className":9756,"style":2063},[1953],[1802,9758],{},[1802,9760,7420],{"className":9761},[3417]," 的一个线性估计器；在 Grinold–Kahn 框架中，若我们假设",[1802,9764,9766],{"className":9765},[1805],[1802,9767,9769,9834],{"className":9768},[1809],[1802,9770,9772],{"className":9771},[1813],[1815,9773,9774],{"xmlns":1817,"display":1818},[1820,9775,9776,9831],{},[1823,9777,9778,9780,9782,9798,9800,9806,9808,9810,9813,9815,9817,9819,9821,9823,9829],{},[1829,9779,3282],{"mathvariant":9594},[1838,9781,7409],{"stretchy":4144},[1826,9783,9784,9786],{},[1829,9785,1831],{},[1823,9787,9788,9790,9792,9794,9796],{},[1829,9789,1836],{},[1838,9791,1841],{"separator":1840},[1829,9793,1844],{},[1838,9795,1847],{},[1849,9797,1851],{},[1838,9799,9615],{},[1826,9801,9802,9804],{},[1829,9803,9621],{"mathvariant":9620},[1829,9805,1844],{},[1838,9807,7420],{"stretchy":4144},[1838,9809,1854],{},[1829,9811,9812],{},"θ",[1838,9814,5266],{},[1829,9816,8769],{},[1829,9818,6597],{},[1829,9820,6221],{},[1829,9822,1831],{},[1826,9824,9825,9827],{},[1829,9826,8328],{},[1829,9828,1836],{},[1838,9830,1841],{"separator":1840},[1911,9832,9833],{"encoding":1913},"\\mathbb{E}[r_{i,t+1}\\mid\\mathcal{F}_t] = \\theta \\cdot Score_i,",[1802,9835,9837,9913,9971,9989],{"className":9836,"ariaHidden":1840},[1918],[1802,9838,9840,9843,9846,9849,9904,9907,9910],{"className":9839},[1922],[1802,9841],{"className":9842,"style":9638},[1926],[1802,9844,3282],{"className":9845},[1931,9642],[1802,9847,7409],{"className":9848},[3338],[1802,9850,9852,9855],{"className":9851},[1931],[1802,9853,1831],{"className":9854,"style":1936},[1931,1935],[1802,9856,9858],{"className":9857},[1940],[1802,9859,9861,9896],{"className":9860},[1944,1945],[1802,9862,9864,9893],{"className":9863},[1949],[1802,9865,9867],{"className":9866,"style":1954},[1953],[1802,9868,9869,9872],{"style":1957},[1802,9870],{"className":9871,"style":1962},[1961],[1802,9873,9875],{"className":9874},[1966,1967,1968,1969],[1802,9876,9878,9881,9884,9887,9890],{"className":9877},[1931,1969],[1802,9879,1836],{"className":9880},[1931,1935,1969],[1802,9882,1841],{"className":9883},[1979,1969],[1802,9885,1844],{"className":9886},[1931,1935,1969],[1802,9888,1847],{"className":9889},[1986,1969],[1802,9891,1851],{"className":9892},[1931,1969],[1802,9894,1994],{"className":9895},[1993],[1802,9897,9899],{"className":9898},[1949],[1802,9900,9902],{"className":9901,"style":2001},[1953],[1802,9903],{},[1802,9905],{"className":9906,"style":2008},[2007],[1802,9908,9615],{"className":9909},[2012],[1802,9911],{"className":9912,"style":2008},[2007],[1802,9914,9916,9919,9959,9962,9965,9968],{"className":9915},[1922],[1802,9917],{"className":9918,"style":4357},[1926],[1802,9920,9922,9925],{"className":9921},[1931],[1802,9923,9621],{"className":9924,"style":9723},[1931,9722],[1802,9926,9928],{"className":9927},[1940],[1802,9929,9931,9951],{"className":9930},[1944,1945],[1802,9932,9934,9948],{"className":9933},[1949],[1802,9935,9937],{"className":9936,"style":3866},[1953],[1802,9938,9939,9942],{"style":9738},[1802,9940],{"className":9941,"style":1962},[1961],[1802,9943,9945],{"className":9944},[1966,1967,1968,1969],[1802,9946,1844],{"className":9947},[1931,1935,1969],[1802,9949,1994],{"className":9950},[1993],[1802,9952,9954],{"className":9953},[1949],[1802,9955,9957],{"className":9956,"style":2063},[1953],[1802,9958],{},[1802,9960,7420],{"className":9961},[3417],[1802,9963],{"className":9964,"style":2008},[2007],[1802,9966,1854],{"className":9967},[2012],[1802,9969],{"className":9970,"style":2008},[2007],[1802,9972,9974,9977,9980,9983,9986],{"className":9973},[1922],[1802,9975],{"className":9976,"style":9337},[1926],[1802,9978,9812],{"className":9979,"style":1936},[1931,1935],[1802,9981],{"className":9982,"style":2069},[2007],[1802,9984,5266],{"className":9985},[1986],[1802,9987],{"className":9988,"style":2069},[2007],[1802,9990,9992,9996,9999,10002,10042],{"className":9991},[1922],[1802,9993],{"className":9994,"style":9995},[1926],"height:0.8778em;vertical-align:-0.1944em;",[1802,9997,8769],{"className":9998,"style":3315},[1931,1935],[1802,10000,6703],{"className":10001,"style":1936},[1931,1935],[1802,10003,10005,10008],{"className":10004},[1931],[1802,10006,8328],{"className":10007},[1931,1935],[1802,10009,10011],{"className":10010},[1940],[1802,10012,10014,10034],{"className":10013},[1944,1945],[1802,10015,10017,10031],{"className":10016},[1949],[1802,10018,10020],{"className":10019,"style":1954},[1953],[1802,10021,10022,10025],{"style":2227},[1802,10023],{"className":10024,"style":1962},[1961],[1802,10026,10028],{"className":10027},[1966,1967,1968,1969],[1802,10029,1836],{"className":10030},[1931,1935,1969],[1802,10032,1994],{"className":10033},[1993],[1802,10035,10037],{"className":10036},[1949],[1802,10038,10040],{"className":10039,"style":2063},[1953],[1802,10041],{},[1802,10043,1841],{"className":10044},[1979],[1792,10046,10047,10048,10117],{},"则上式中的 ",[1802,10049,10051,10068],{"className":10050},[1809],[1802,10052,10054],{"className":10053},[1813],[1815,10055,10056],{"xmlns":1817},[1820,10057,10058,10066],{},[1823,10059,10060],{},[1826,10061,10062,10064],{},[1829,10063,8788],{},[1829,10065,5285],{},[1911,10067,9393],{"encoding":1913},[1802,10069,10071],{"className":10070,"ariaHidden":1840},[1918],[1802,10072,10074,10077],{"className":10073},[1922],[1802,10075],{"className":10076,"style":2709},[1926],[1802,10078,10080,10083],{"className":10079},[1931],[1802,10081,8788],{"className":10082,"style":8922},[1931,1935],[1802,10084,10086],{"className":10085},[1940],[1802,10087,10089,10109],{"className":10088},[1944,1945],[1802,10090,10092,10106],{"className":10091},[1949],[1802,10093,10095],{"className":10094,"style":5607},[1953],[1802,10096,10097,10100],{"style":8937},[1802,10098],{"className":10099,"style":1962},[1961],[1802,10101,10103],{"className":10102},[1966,1967,1968,1969],[1802,10104,5285],{"className":10105,"style":5561},[1931,1935,1969],[1802,10107,1994],{"className":10108},[1993],[1802,10110,10112],{"className":10111},[1949],[1802,10113,10115],{"className":10114,"style":2063},[1953],[1802,10116],{}," 实际上反映了各因子对预期超额收益贡献的大小。进一步结合协方差矩阵，就可以在均值–方差框架下得到最优组合权重（见第 04 章）。",[3250,10119,10121],{"id":10120},"_62-基于机器学习的信号模型概览","6.2 基于机器学习的信号模型（概览）",[1792,10123,10124],{},"在更复杂的场景中，可以使用机器学习模型从因子中学习非线性关系，例如：",[2270,10126,10127,10130,10133],{},[2273,10128,10129],{},"树模型：随机森林、梯度提升树等；",[2273,10131,10132],{},"线性\u002F逻辑回归：预测超额收益或上涨概率；",[2273,10134,10135],{},"简单神经网络等。",[1792,10137,10138],{},"注意事项：",[2270,10140,10141,10144,10147],{},[2273,10142,10143],{},"机器学习模型更易发生过拟合；",[2273,10145,10146],{},"需要更严格的样本划分、交叉验证和稳定性检验；",[2273,10148,10149],{},"在生产环境中还要考虑模型可解释性、计算成本和延迟。",[1792,10151,10152],{},"近年来有大量研究尝试将机器学习用于因子挖掘与资产定价（例如 Gu, Kelly & Xiu, 2020），结果表明在控制好过拟合和交易成本的前提下，复杂模型可以在横截面预测中获得一定增益。不过，模型复杂度与解释性之间的权衡在实务中非常重要。",[1792,10154,10155],{},"从计量经济学的视角看，这类模型本质上是在拟合一个高维非线性条件期望：",[1802,10157,10159],{"className":10158},[1805],[1802,10160,10162,10233],{"className":10161},[1809],[1802,10163,10165],{"className":10164},[1813],[1815,10166,10167],{"xmlns":1817,"display":1818},[1820,10168,10169,10230],{},[1823,10170,10171,10173,10175,10191,10193,10206,10208,10210,10212,10214,10226,10228],{},[1829,10172,3282],{"mathvariant":9594},[1838,10174,7409],{"stretchy":4144},[1826,10176,10177,10179],{},[1829,10178,1831],{},[1823,10180,10181,10183,10185,10187,10189],{},[1829,10182,1836],{},[1838,10184,1841],{"separator":1840},[1829,10186,1844],{},[1838,10188,1847],{},[1849,10190,1851],{},[1838,10192,9615],{},[1826,10194,10195,10198],{},[1829,10196,10197],{},"X",[1823,10199,10200,10202,10204],{},[1829,10201,1836],{},[1838,10203,1841],{"separator":1840},[1829,10205,1844],{},[1838,10207,7420],{"stretchy":4144},[1838,10209,1854],{},[1829,10211,3823],{},[1838,10213,4145],{"stretchy":4144},[1826,10215,10216,10218],{},[1829,10217,10197],{},[1823,10219,10220,10222,10224],{},[1829,10221,1836],{},[1838,10223,1841],{"separator":1840},[1829,10225,1844],{},[1838,10227,4158],{"stretchy":4144},[1838,10229,1841],{"separator":1840},[1911,10231,10232],{"encoding":1913},"\\mathbb{E}[r_{i,t+1} \\mid X_{i,t}] = m(X_{i,t}),",[1802,10234,10236,10312,10380],{"className":10235,"ariaHidden":1840},[1918],[1802,10237,10239,10242,10245,10248,10303,10306,10309],{"className":10238},[1922],[1802,10240],{"className":10241,"style":9638},[1926],[1802,10243,3282],{"className":10244},[1931,9642],[1802,10246,7409],{"className":10247},[3338],[1802,10249,10251,10254],{"className":10250},[1931],[1802,10252,1831],{"className":10253,"style":1936},[1931,1935],[1802,10255,10257],{"className":10256},[1940],[1802,10258,10260,10295],{"className":10259},[1944,1945],[1802,10261,10263,10292],{"className":10262},[1949],[1802,10264,10266],{"className":10265,"style":1954},[1953],[1802,10267,10268,10271],{"style":1957},[1802,10269],{"className":10270,"style":1962},[1961],[1802,10272,10274],{"className":10273},[1966,1967,1968,1969],[1802,10275,10277,10280,10283,10286,10289],{"className":10276},[1931,1969],[1802,10278,1836],{"className":10279},[1931,1935,1969],[1802,10281,1841],{"className":10282},[1979,1969],[1802,10284,1844],{"className":10285},[1931,1935,1969],[1802,10287,1847],{"className":10288},[1986,1969],[1802,10290,1851],{"className":10291},[1931,1969],[1802,10293,1994],{"className":10294},[1993],[1802,10296,10298],{"className":10297},[1949],[1802,10299,10301],{"className":10300,"style":2001},[1953],[1802,10302],{},[1802,10304],{"className":10305,"style":2008},[2007],[1802,10307,9615],{"className":10308},[2012],[1802,10310],{"className":10311,"style":2008},[2007],[1802,10313,10315,10318,10368,10371,10374,10377],{"className":10314},[1922],[1802,10316],{"className":10317,"style":9638},[1926],[1802,10319,10321,10324],{"className":10320},[1931],[1802,10322,10197],{"className":10323,"style":5649},[1931,1935],[1802,10325,10327],{"className":10326},[1940],[1802,10328,10330,10360],{"className":10329},[1944,1945],[1802,10331,10333,10357],{"className":10332},[1949],[1802,10334,10336],{"className":10335,"style":1954},[1953],[1802,10337,10339,10342],{"style":10338},"top:-2.55em;margin-left:-0.0785em;margin-right:0.05em;",[1802,10340],{"className":10341,"style":1962},[1961],[1802,10343,10345],{"className":10344},[1966,1967,1968,1969],[1802,10346,10348,10351,10354],{"className":10347},[1931,1969],[1802,10349,1836],{"className":10350},[1931,1935,1969],[1802,10352,1841],{"className":10353},[1979,1969],[1802,10355,1844],{"className":10356},[1931,1935,1969],[1802,10358,1994],{"className":10359},[1993],[1802,10361,10363],{"className":10362},[1949],[1802,10364,10366],{"className":10365,"style":2001},[1953],[1802,10367],{},[1802,10369,7420],{"className":10370},[3417],[1802,10372],{"className":10373,"style":2008},[2007],[1802,10375,1854],{"className":10376},[2012],[1802,10378],{"className":10379,"style":2008},[2007],[1802,10381,10383,10386,10389,10392,10441,10444],{"className":10382},[1922],[1802,10384],{"className":10385,"style":9638},[1926],[1802,10387,3823],{"className":10388},[1931,1935],[1802,10390,4145],{"className":10391},[3338],[1802,10393,10395,10398],{"className":10394},[1931],[1802,10396,10197],{"className":10397,"style":5649},[1931,1935],[1802,10399,10401],{"className":10400},[1940],[1802,10402,10404,10433],{"className":10403},[1944,1945],[1802,10405,10407,10430],{"className":10406},[1949],[1802,10408,10410],{"className":10409,"style":1954},[1953],[1802,10411,10412,10415],{"style":10338},[1802,10413],{"className":10414,"style":1962},[1961],[1802,10416,10418],{"className":10417},[1966,1967,1968,1969],[1802,10419,10421,10424,10427],{"className":10420},[1931,1969],[1802,10422,1836],{"className":10423},[1931,1935,1969],[1802,10425,1841],{"className":10426},[1979,1969],[1802,10428,1844],{"className":10429},[1931,1935,1969],[1802,10431,1994],{"className":10432},[1993],[1802,10434,10436],{"className":10435},[1949],[1802,10437,10439],{"className":10438,"style":2001},[1953],[1802,10440],{},[1802,10442,4158],{"className":10443},[3417],[1802,10445,1841],{"className":10446},[1979],[1792,10448,8545,10449,10534,10535,10579],{},[1802,10450,10452,10476],{"className":10451},[1809],[1802,10453,10455],{"className":10454},[1813],[1815,10456,10457],{"xmlns":1817},[1820,10458,10459,10473],{},[1823,10460,10461],{},[1826,10462,10463,10465],{},[1829,10464,10197],{},[1823,10466,10467,10469,10471],{},[1829,10468,1836],{},[1838,10470,1841],{"separator":1840},[1829,10472,1844],{},[1911,10474,10475],{"encoding":1913},"X_{i,t}",[1802,10477,10479],{"className":10478,"ariaHidden":1840},[1918],[1802,10480,10482,10485],{"className":10481},[1922],[1802,10483],{"className":10484,"style":8366},[1926],[1802,10486,10488,10491],{"className":10487},[1931],[1802,10489,10197],{"className":10490,"style":5649},[1931,1935],[1802,10492,10494],{"className":10493},[1940],[1802,10495,10497,10526],{"className":10496},[1944,1945],[1802,10498,10500,10523],{"className":10499},[1949],[1802,10501,10503],{"className":10502,"style":1954},[1953],[1802,10504,10505,10508],{"style":10338},[1802,10506],{"className":10507,"style":1962},[1961],[1802,10509,10511],{"className":10510},[1966,1967,1968,1969],[1802,10512,10514,10517,10520],{"className":10513},[1931,1969],[1802,10515,1836],{"className":10516},[1931,1935,1969],[1802,10518,1841],{"className":10519},[1979,1969],[1802,10521,1844],{"className":10522},[1931,1935,1969],[1802,10524,1994],{"className":10525},[1993],[1802,10527,10529],{"className":10528},[1949],[1802,10530,10532],{"className":10531,"style":2001},[1953],[1802,10533],{}," 是一个高维特征向量，",[1802,10536,10538,10558],{"className":10537},[1809],[1802,10539,10541],{"className":10540},[1813],[1815,10542,10543],{"xmlns":1817},[1820,10544,10545,10555],{},[1823,10546,10547,10549,10551,10553],{},[1829,10548,3823],{},[1838,10550,4145],{"stretchy":4144},[1838,10552,5266],{},[1838,10554,4158],{"stretchy":4144},[1911,10556,10557],{"encoding":1913},"m(\\cdot)",[1802,10559,10561],{"className":10560,"ariaHidden":1840},[1918],[1802,10562,10564,10567,10570,10573,10576],{"className":10563},[1922],[1802,10565],{"className":10566,"style":4357},[1926],[1802,10568,3823],{"className":10569},[1931,1935],[1802,10571,4145],{"className":10572},[3338],[1802,10574,5266],{"className":10575},[1931],[1802,10577,4158],{"className":10578},[3417]," 可以由树模型、神经网络等逼近。Gu, Kelly & Xiu (2020) 将这一框架与 Fama–MacBeth 回归结合，提出了“机器学习版”的资产定价横截面检验思路，为后续大量工作奠定了基础。",[3205,10581,10583],{"id":10582},"_7-因子筛选从候选到可投因子","7. 因子筛选：从候选到“可投因子”",[1792,10585,10586,10587,10590,10591,10594],{},"前面的章节更多关注因子",[3214,10588,10589],{},"构建","和",[3214,10592,10593],{},"单因子检验","，在实务中，从“数十到数百个候选因子”走到“真正在组合里拿资金”的过程，往往会经历一套相对标准化的因子筛选流程。下面给出一个常见的“实战标准版”工作流，可视为对前文内容的系统组织。",[3250,10596,10598],{"id":10597},"_71-阶段-1因子构建factor-construction","7.1 阶段 1：因子构建（Factor Construction）",[1792,10600,10601],{},"目标：生成一篮子候选因子，数量可以从几十到几百不等。",[1792,10603,10604],{},"典型步骤：",[3228,10606,10607,10624],{},[2273,10608,10609,10612,10613],{},[3214,10610,10611],{},"数据预处理","（对应第 01 章）：\n",[2270,10614,10615,10618,10621],{},[2273,10616,10617],{},"去极值：MAD、分位数剪裁（quantile clipping）；",[2273,10619,10620],{},"标准化：z-score 或秩标准化（rank-based）；",[2273,10622,10623],{},"（可选）行业\u002F市值中性化：剔除行业和大小盘效应，得到“纯风格”因子。",[2273,10625,10626,3764,10629],{},[3214,10627,10628],{},"因子生成方式",[2270,10630,10631,10634,10637,10640,10643],{},[2273,10632,10633],{},"经典财务因子：Value\u002FQuality\u002FGrowth 等；",[2273,10635,10636],{},"技术因子：动量、波动率、成交量\u002F换手率相关因子；",[2273,10638,10639],{},"量价微结构因子：订单簿深度、买卖盘不平衡、成交簇等（高频数据）；",[2273,10641,10642],{},"特征工程：滑动窗口统计量（均值、标准差、偏度、峰度）、极值计数等；",[2273,10644,10645],{},"机器学习特征：embeddings、autoencoder 提取的低维表示等。",[1792,10647,10648],{},"阶段 1 的产出是一个包含大量候选因子的“因子库草稿”。",[3250,10650,10652],{"id":10651},"_72-阶段-2单因子横截面检验cross-sectional-predictive-test","7.2 阶段 2：单因子横截面检验（Cross-sectional Predictive Test）",[1792,10654,10655],{},"目标：通过截面预测能力初步筛掉明显无效的因子。",[1792,10657,10658],{},"主要工具：本章第 5 节中已经介绍的 IC\u002FRank IC 与分组回测。",[1792,10660,10661],{},"关键指标：",[2270,10663,10664,10667,10670,10673],{},[2273,10665,10666],{},"截面 IC \u002F Rank IC 时间序列；",[2273,10668,10669],{},"IC 的 t 统计和信息比率（IR）；",[2273,10671,10672],{},"IC 稳定性：正 IC 的比例、IC decay（例如从 t+1 到 t+5 的 IC 衰减曲线）；",[2273,10674,10675],{},"分组收益：long top quantile \u002F short bottom quantile 的多空组合收益和 t 统计。",[1792,10677,10678],{},"常用评估逻辑：",[2270,10680,10681,10684,10687,10690],{},[2273,10682,10683],{},"截面预测能力弱且不稳定 → 直接剔除；",[2273,10685,10686],{},"只有在极短期（如 t+1 日）有效且对成本非常敏感 → 谨慎处理，多放在短期策略池中；",[2273,10688,10689],{},"只有同时通过时间外推、横截面支持、分组单调性和成本敏感性检查，才进入下一阶段；",[2273,10691,10692],{},"进入下一阶段表示“值得继续检验”，不表示已经可配置资金。",[1792,10694,10695],{},"阶段 2 的产出是“通过单因子检验的因子集合”。",[3250,10697,10699],{"id":10698},"_73-阶段-3时序稳定性与鲁棒性验证robustness-tests","7.3 阶段 3：时序稳定性与鲁棒性验证（Robustness Tests）",[1792,10701,10702],{},"目标：避免因子只在特定时间段或少数行业里有效。",[1792,10704,10705],{},"检查内容：",[2270,10707,10708,10716,10724,10732,10740],{},[2273,10709,10710,10711],{},"不同时间段可重复性：\n",[2270,10712,10713],{},[2273,10714,10715],{},"将样本划分为多个子期（如牛市、熊市、震荡市）分别检验 IC 与分组收益；",[2273,10717,10718,10719],{},"不同行业的泛化能力：\n",[2270,10720,10721],{},[2273,10722,10723],{},"计算行业内 IC（industry IC）、比较因子在各行业的表现；",[2273,10725,10726,10727],{},"样本内 vs 样本外表现：\n",[2270,10728,10729],{},[2273,10730,10731],{},"使用滚动窗口或时间切分（train\u002Fvalidation\u002Ftest）检查是否过拟合；",[2273,10733,10734,10735],{},"再采样\u002F交叉验证（Rolling CV）：\n",[2270,10736,10737],{},[2273,10738,10739],{},"在滚动子样本上重复因子检验，观察结果一致性；",[2273,10741,10742,10743],{},"极端行情敏感度：\n",[2270,10744,10745],{},[2273,10746,10747],{},"针对疫情、流动性危机等极端时期，检查因子表现是否异常恶化。",[1792,10749,10750],{},"判定标准（示意）：",[2270,10752,10753,10756],{},[2273,10754,10755],{},"若因子在任何一个关键阶段出现结构性退化（例如长期为正的 IC 在某段时间持续为负且显著）→ 降权或剔除；",[2273,10757,10758],{},"若因子只在某个细分行业或风格上有效 → 可以考虑将其作为“行业特定因子”，而非广义横截面因子。",[1792,10760,10761],{},"阶段 3 的产出是“跨周期、跨行业具有一定稳健性的因子集合”。",[3250,10763,10765],{"id":10764},"_74-阶段-4风险暴露与冗余检测risk-redundancy-tests","7.4 阶段 4：风险暴露与冗余检测（Risk \u002F Redundancy Tests）",[1792,10767,10768],{},"目标：确保因子的收益不是简单的已知风险溢价，也不是对团队现有因子的重复。",[3228,10770,10771,11617],{},[2273,10772,10773,4738,10776],{},[3214,10774,10775],{},"与传统风险因子的正交检测",[2270,10777,10778,10851],{},[2273,10779,10780,10781],{},"与 Beta、Size、Value、Momentum、Volatility 等标准因子做相关性检验：",[2270,10782,10783],{},[2273,10784,10785,10786,10850],{},"若相关系数 ",[1802,10787,10789,10814],{"className":10788},[1809],[1802,10790,10792],{"className":10791},[1813],[1815,10793,10794],{"xmlns":1817},[1820,10795,10796,10811],{},[1823,10797,10798,10800,10803,10805,10808],{},[1829,10799,9615],{"mathvariant":1874},[1829,10801,10802],{},"ρ",[1829,10804,9615],{"mathvariant":1874},[1838,10806,10807],{},">",[1849,10809,10810],{},"0.7",[1911,10812,10813],{"encoding":1913},"|\\rho| > 0.7",[1802,10815,10817,10841],{"className":10816,"ariaHidden":1840},[1918],[1802,10818,10820,10823,10826,10829,10832,10835,10838],{"className":10819},[1922],[1802,10821],{"className":10822,"style":4357},[1926],[1802,10824,9615],{"className":10825},[1931],[1802,10827,10802],{"className":10828},[1931,1935],[1802,10830,9615],{"className":10831},[1931],[1802,10833],{"className":10834,"style":2008},[2007],[1802,10836,10807],{"className":10837},[2012],[1802,10839],{"className":10840,"style":2008},[2007],[1802,10842,10844,10847],{"className":10843},[1922],[1802,10845],{"className":10846,"style":2480},[1926],[1802,10848,10810],{"className":10849},[1931],"，则新因子很可能只是旧因子的线性变换；",[2273,10852,10853,10854,11371,8545,11374,11459,11460,11545,11546,11616],{},"使用截面回归检验边际贡献：",[1802,10855,10857],{"className":10856},[1805],[1802,10858,10860,10958],{"className":10859},[1809],[1802,10861,10863],{"className":10862},[1813],[1815,10864,10865],{"xmlns":1817,"display":1818},[1820,10866,10867,10955],{},[1823,10868,10869,10885,10887,10893,10895,10903,10915,10917,10923,10935,10937,10953],{},[1826,10870,10871,10873],{},[1829,10872,1831],{},[1823,10874,10875,10877,10879,10881,10883],{},[1829,10876,1836],{},[1838,10878,1841],{"separator":1840},[1829,10880,1844],{},[1838,10882,1847],{},[1849,10884,1851],{},[1838,10886,1854],{},[1826,10888,10889,10891],{},[1829,10890,1859],{},[1829,10892,1844],{},[1838,10894,1847],{},[1865,10896,10897,10899,10901],{},[1829,10898,1869],{},[1829,10900,1844],{},[1829,10902,1875],{"mathvariant":1874},[1826,10904,10905,10907],{},[1829,10906,9621],{},[1823,10908,10909,10911,10913],{},[1829,10910,1836],{},[1838,10912,1841],{"separator":1840},[1829,10914,1844],{},[1838,10916,1847],{},[1826,10918,10919,10921],{},[1829,10920,5290],{},[1829,10922,1844],{},[1826,10924,10925,10927],{},[1829,10926,6226],{},[1823,10928,10929,10931,10933],{},[1829,10930,1836],{},[1838,10932,1841],{"separator":1840},[1829,10934,1844],{},[1838,10936,1847],{},[1826,10938,10939,10941],{},[1829,10940,1895],{},[1823,10942,10943,10945,10947,10949,10951],{},[1829,10944,1836],{},[1838,10946,1841],{"separator":1840},[1829,10948,1844],{},[1838,10950,1847],{},[1849,10952,1851],{},[1838,10954,1841],{"separator":1840},[1911,10956,10957],{"encoding":1913},"r_{i,t+1} = \\alpha_t + \\beta_t^\\top F_{i,t} + \\gamma_t g_{i,t} + \\epsilon_{i,t+1},",[1802,10959,10961,11031,11086,11202,11307],{"className":10960,"ariaHidden":1840},[1918],[1802,10962,10964,10967,11022,11025,11028],{"className":10963},[1922],[1802,10965],{"className":10966,"style":1927},[1926],[1802,10968,10970,10973],{"className":10969},[1931],[1802,10971,1831],{"className":10972,"style":1936},[1931,1935],[1802,10974,10976],{"className":10975},[1940],[1802,10977,10979,11014],{"className":10978},[1944,1945],[1802,10980,10982,11011],{"className":10981},[1949],[1802,10983,10985],{"className":10984,"style":1954},[1953],[1802,10986,10987,10990],{"style":1957},[1802,10988],{"className":10989,"style":1962},[1961],[1802,10991,10993],{"className":10992},[1966,1967,1968,1969],[1802,10994,10996,10999,11002,11005,11008],{"className":10995},[1931,1969],[1802,10997,1836],{"className":10998},[1931,1935,1969],[1802,11000,1841],{"className":11001},[1979,1969],[1802,11003,1844],{"className":11004},[1931,1935,1969],[1802,11006,1847],{"className":11007},[1986,1969],[1802,11009,1851],{"className":11010},[1931,1969],[1802,11012,1994],{"className":11013},[1993],[1802,11015,11017],{"className":11016},[1949],[1802,11018,11020],{"className":11019,"style":2001},[1953],[1802,11021],{},[1802,11023],{"className":11024,"style":2008},[2007],[1802,11026,1854],{"className":11027},[2012],[1802,11029],{"className":11030,"style":2008},[2007],[1802,11032,11034,11037,11077,11080,11083],{"className":11033},[1922],[1802,11035],{"className":11036,"style":2022},[1926],[1802,11038,11040,11043],{"className":11039},[1931],[1802,11041,1859],{"className":11042,"style":2029},[1931,1935],[1802,11044,11046],{"className":11045},[1940],[1802,11047,11049,11069],{"className":11048},[1944,1945],[1802,11050,11052,11066],{"className":11051},[1949],[1802,11053,11055],{"className":11054,"style":3866},[1953],[1802,11056,11057,11060],{"style":2044},[1802,11058],{"className":11059,"style":1962},[1961],[1802,11061,11063],{"className":11062},[1966,1967,1968,1969],[1802,11064,1844],{"className":11065},[1931,1935,1969],[1802,11067,1994],{"className":11068},[1993],[1802,11070,11072],{"className":11071},[1949],[1802,11073,11075],{"className":11074,"style":2063},[1953],[1802,11076],{},[1802,11078],{"className":11079,"style":2069},[2007],[1802,11081,1847],{"className":11082},[1986],[1802,11084],{"className":11085,"style":2069},[2007],[1802,11087,11089,11093,11144,11193,11196,11199],{"className":11088},[1922],[1802,11090],{"className":11091,"style":11092},[1926],"height:1.1852em;vertical-align:-0.2861em;",[1802,11094,11096,11099],{"className":11095},[1931],[1802,11097,1869],{"className":11098,"style":2089},[1931,1935],[1802,11100,11102],{"className":11101},[1940],[1802,11103,11105,11136],{"className":11104},[1944,1945],[1802,11106,11108,11133],{"className":11107},[1949],[1802,11109,11111,11122],{"className":11110,"style":2102},[1953],[1802,11112,11113,11116],{"style":2105},[1802,11114],{"className":11115,"style":1962},[1961],[1802,11117,11119],{"className":11118},[1966,1967,1968,1969],[1802,11120,1844],{"className":11121},[1931,1935,1969],[1802,11123,11124,11127],{"style":2117},[1802,11125],{"className":11126,"style":1962},[1961],[1802,11128,11130],{"className":11129},[1966,1967,1968,1969],[1802,11131,1875],{"className":11132},[1931,1969],[1802,11134,1994],{"className":11135},[1993],[1802,11137,11139],{"className":11138},[1949],[1802,11140,11142],{"className":11141,"style":2136},[1953],[1802,11143],{},[1802,11145,11147,11150],{"className":11146},[1931],[1802,11148,9621],{"className":11149,"style":3311},[1931,1935],[1802,11151,11153],{"className":11152},[1940],[1802,11154,11156,11185],{"className":11155},[1944,1945],[1802,11157,11159,11182],{"className":11158},[1949],[1802,11160,11162],{"className":11161,"style":1954},[1953],[1802,11163,11164,11167],{"style":3955},[1802,11165],{"className":11166,"style":1962},[1961],[1802,11168,11170],{"className":11169},[1966,1967,1968,1969],[1802,11171,11173,11176,11179],{"className":11172},[1931,1969],[1802,11174,1836],{"className":11175},[1931,1935,1969],[1802,11177,1841],{"className":11178},[1979,1969],[1802,11180,1844],{"className":11181},[1931,1935,1969],[1802,11183,1994],{"className":11184},[1993],[1802,11186,11188],{"className":11187},[1949],[1802,11189,11191],{"className":11190,"style":2001},[1953],[1802,11192],{},[1802,11194],{"className":11195,"style":2069},[2007],[1802,11197,1847],{"className":11198},[1986],[1802,11200],{"className":11201,"style":2069},[2007],[1802,11203,11205,11209,11249,11298,11301,11304],{"className":11204},[1922],[1802,11206],{"className":11207,"style":11208},[1926],"height:0.8694em;vertical-align:-0.2861em;",[1802,11210,11212,11215],{"className":11211},[1931],[1802,11213,5290],{"className":11214,"style":5594},[1931,1935],[1802,11216,11218],{"className":11217},[1940],[1802,11219,11221,11241],{"className":11220},[1944,1945],[1802,11222,11224,11238],{"className":11223},[1949],[1802,11225,11227],{"className":11226,"style":3866},[1953],[1802,11228,11229,11232],{"style":5610},[1802,11230],{"className":11231,"style":1962},[1961],[1802,11233,11235],{"className":11234},[1966,1967,1968,1969],[1802,11236,1844],{"className":11237},[1931,1935,1969],[1802,11239,1994],{"className":11240},[1993],[1802,11242,11244],{"className":11243},[1949],[1802,11245,11247],{"className":11246,"style":2063},[1953],[1802,11248],{},[1802,11250,11252,11255],{"className":11251},[1931],[1802,11253,6226],{"className":11254,"style":4941},[1931,1935],[1802,11256,11258],{"className":11257},[1940],[1802,11259,11261,11290],{"className":11260},[1944,1945],[1802,11262,11264,11287],{"className":11263},[1949],[1802,11265,11267],{"className":11266,"style":1954},[1953],[1802,11268,11269,11272],{"style":5688},[1802,11270],{"className":11271,"style":1962},[1961],[1802,11273,11275],{"className":11274},[1966,1967,1968,1969],[1802,11276,11278,11281,11284],{"className":11277},[1931,1969],[1802,11279,1836],{"className":11280},[1931,1935,1969],[1802,11282,1841],{"className":11283},[1979,1969],[1802,11285,1844],{"className":11286},[1931,1935,1969],[1802,11288,1994],{"className":11289},[1993],[1802,11291,11293],{"className":11292},[1949],[1802,11294,11296],{"className":11295,"style":2001},[1953],[1802,11297],{},[1802,11299],{"className":11300,"style":2069},[2007],[1802,11302,1847],{"className":11303},[1986],[1802,11305],{"className":11306,"style":2069},[2007],[1802,11308,11310,11313,11368],{"className":11309},[1922],[1802,11311],{"className":11312,"style":1927},[1926],[1802,11314,11316,11319],{"className":11315},[1931],[1802,11317,1895],{"className":11318},[1931,1935],[1802,11320,11322],{"className":11321},[1940],[1802,11323,11325,11360],{"className":11324},[1944,1945],[1802,11326,11328,11357],{"className":11327},[1949],[1802,11329,11331],{"className":11330,"style":1954},[1953],[1802,11332,11333,11336],{"style":2227},[1802,11334],{"className":11335,"style":1962},[1961],[1802,11337,11339],{"className":11338},[1966,1967,1968,1969],[1802,11340,11342,11345,11348,11351,11354],{"className":11341},[1931,1969],[1802,11343,1836],{"className":11344},[1931,1935,1969],[1802,11346,1841],{"className":11347},[1979,1969],[1802,11349,1844],{"className":11350},[1931,1935,1969],[1802,11352,1847],{"className":11353},[1986,1969],[1802,11355,1851],{"className":11356},[1931,1969],[1802,11358,1994],{"className":11359},[1993],[1802,11361,11363],{"className":11362},[1949],[1802,11364,11366],{"className":11365,"style":2001},[1953],[1802,11367],{},[1802,11369,1841],{"className":11370},[1979],[11372,11373],"br",{},[1802,11375,11377,11401],{"className":11376},[1809],[1802,11378,11380],{"className":11379},[1813],[1815,11381,11382],{"xmlns":1817},[1820,11383,11384,11398],{},[1823,11385,11386],{},[1826,11387,11388,11390],{},[1829,11389,9621],{},[1823,11391,11392,11394,11396],{},[1829,11393,1836],{},[1838,11395,1841],{"separator":1840},[1829,11397,1844],{},[1911,11399,11400],{"encoding":1913},"F_{i,t}",[1802,11402,11404],{"className":11403,"ariaHidden":1840},[1918],[1802,11405,11407,11410],{"className":11406},[1922],[1802,11408],{"className":11409,"style":8366},[1926],[1802,11411,11413,11416],{"className":11412},[1931],[1802,11414,9621],{"className":11415,"style":3311},[1931,1935],[1802,11417,11419],{"className":11418},[1940],[1802,11420,11422,11451],{"className":11421},[1944,1945],[1802,11423,11425,11448],{"className":11424},[1949],[1802,11426,11428],{"className":11427,"style":1954},[1953],[1802,11429,11430,11433],{"style":3955},[1802,11431],{"className":11432,"style":1962},[1961],[1802,11434,11436],{"className":11435},[1966,1967,1968,1969],[1802,11437,11439,11442,11445],{"className":11438},[1931,1969],[1802,11440,1836],{"className":11441},[1931,1935,1969],[1802,11443,1841],{"className":11444},[1979,1969],[1802,11446,1844],{"className":11447},[1931,1935,1969],[1802,11449,1994],{"className":11450},[1993],[1802,11452,11454],{"className":11453},[1949],[1802,11455,11457],{"className":11456,"style":2001},[1953],[1802,11458],{}," 是已有风格因子暴露，新因子为 ",[1802,11461,11463,11487],{"className":11462},[1809],[1802,11464,11466],{"className":11465},[1813],[1815,11467,11468],{"xmlns":1817},[1820,11469,11470,11484],{},[1823,11471,11472],{},[1826,11473,11474,11476],{},[1829,11475,6226],{},[1823,11477,11478,11480,11482],{},[1829,11479,1836],{},[1838,11481,1841],{"separator":1840},[1829,11483,1844],{},[1911,11485,11486],{"encoding":1913},"g_{i,t}",[1802,11488,11490],{"className":11489,"ariaHidden":1840},[1918],[1802,11491,11493,11496],{"className":11492},[1922],[1802,11494],{"className":11495,"style":1927},[1926],[1802,11497,11499,11502],{"className":11498},[1931],[1802,11500,6226],{"className":11501,"style":4941},[1931,1935],[1802,11503,11505],{"className":11504},[1940],[1802,11506,11508,11537],{"className":11507},[1944,1945],[1802,11509,11511,11534],{"className":11510},[1949],[1802,11512,11514],{"className":11513,"style":1954},[1953],[1802,11515,11516,11519],{"style":5688},[1802,11517],{"className":11518,"style":1962},[1961],[1802,11520,11522],{"className":11521},[1966,1967,1968,1969],[1802,11523,11525,11528,11531],{"className":11524},[1931,1969],[1802,11526,1836],{"className":11527},[1931,1935,1969],[1802,11529,1841],{"className":11530},[1979,1969],[1802,11532,1844],{"className":11533},[1931,1935,1969],[1802,11535,1994],{"className":11536},[1993],[1802,11538,11540],{"className":11539},[1949],[1802,11541,11543],{"className":11542,"style":2001},[1953],[1802,11544],{},"；如果 ",[1802,11547,11549,11567],{"className":11548},[1809],[1802,11550,11552],{"className":11551},[1813],[1815,11553,11554],{"xmlns":1817},[1820,11555,11556,11564],{},[1823,11557,11558],{},[1826,11559,11560,11562],{},[1829,11561,5290],{},[1829,11563,1844],{},[1911,11565,11566],{"encoding":1913},"\\gamma_t",[1802,11568,11570],{"className":11569,"ariaHidden":1840},[1918],[1802,11571,11573,11576],{"className":11572},[1922],[1802,11574],{"className":11575,"style":5158},[1926],[1802,11577,11579,11582],{"className":11578},[1931],[1802,11580,5290],{"className":11581,"style":5594},[1931,1935],[1802,11583,11585],{"className":11584},[1940],[1802,11586,11588,11608],{"className":11587},[1944,1945],[1802,11589,11591,11605],{"className":11590},[1949],[1802,11592,11594],{"className":11593,"style":3866},[1953],[1802,11595,11596,11599],{"style":5610},[1802,11597],{"className":11598,"style":1962},[1961],[1802,11600,11602],{"className":11601},[1966,1967,1968,1969],[1802,11603,1844],{"className":11604},[1931,1935,1969],[1802,11606,1994],{"className":11607},[1993],[1802,11609,11611],{"className":11610},[1949],[1802,11612,11614],{"className":11613,"style":2063},[1953],[1802,11615],{}," 的平均值不显著，则说明新因子在控制已有因子后没有额外解释力。",[2273,11618,11619,4738,11622],{},[3214,11620,11621],{},"与内部因子库的相关性",[2270,11623,11624,11627,11630],{},[2273,11625,11626],{},"将新因子与已有因子库中的所有因子计算相关矩阵；",[2273,11628,11629],{},"若新因子与某些已有因子高度相关且构造逻辑相近 → 视为冗余，除非其在组合层面的边际贡献显著更好；",[2273,11631,11632],{},"也可以在组合优化中加入“因子多样性”目标，限制因子间相关性过高。",[1792,11634,11635],{},"阶段 4 的产出是“在风险空间和因子库空间中具有边际独立性的因子集合”。",[3250,11637,11639],{"id":11638},"_75-阶段-5可投资性评估tradability-capacity-test","7.5 阶段 5：可投资性评估（Tradability & Capacity Test）",[1792,11641,11642],{},"目标：判断因子是否可以在真实市场中以合理成本实现其理论收益。",[1792,11644,11645],{},"主要考察：",[3228,11647,11648,11661,11674],{},[2273,11649,11650,4738,11653],{},[3214,11651,11652],{},"交易成本与冲击",[2270,11654,11655,11658],{},[2273,11656,11657],{},"在加入合理的成本模型（见第 05 章）后，因子多空组合的收益是否仍为正且显著；",[2273,11659,11660],{},"对不同参与率\u002F规模下的表现做敏感性分析。",[2273,11662,11663,4738,11666],{},[3214,11664,11665],{},"板块与市值偏差",[2270,11667,11668,11671],{},[2273,11669,11670],{},"检查因子多空组合的持仓分布，是否过度偏向小盘股或流动性较差板块；",[2273,11672,11673],{},"对小盘或冷门板块的暴露进行约束，避免滑点和冲击成本过大。",[2273,11675,11676,4738,11679],{},[3214,11677,11678],{},"容量评估（Capacity）",[2270,11680,11681,11684],{},[2273,11682,11683],{},"在不同资金规模（如 100M \u002F 1B \u002F 10B）下模拟执行，估算可承载的资产规模；",[2273,11685,11686],{},"若因子策略在较小资金下表现良好但在放大规模时收益完全被成本吞噬，则其仅适合小资金或自营账户使用。",[1792,11688,11689],{},"阶段 5 的产出是“可真实部署且容量可接受的因子”。",[3250,11691,11693],{"id":11692},"_76-阶段-6因子组合贡献评估portfolio-ir-contribution","7.6 阶段 6：因子组合贡献评估（Portfolio \u002F IR Contribution）",[1792,11695,11696,11697,11700],{},"目标：判断某个因子在加入现有多因子组合后，是否在",[3214,11698,11699],{},"组合层面","带来实质性的改进。",[1792,11702,11703],{},"评价标准：",[2270,11705,11706,11709,11712,11715],{},[2273,11707,11708],{},"信息比率提升（组合 IR 的增量）；",[2273,11710,11711],{},"边际夏普增量（Marginal Sharpe）：加入因子后的组合夏普 vs 原组合夏普；",[2273,11713,11714],{},"与现有组合的低相关度（因子层面和组合收益层面）；",[2273,11716,11717],{},"对组合回撤分布的影响（尾部风险是否改善）。",[1792,11719,11720],{},"常见的组合测试方式：",[2270,11722,11723,11726,11729],{},[2273,11724,11725],{},"等权组合：简单检验加入新因子后的整体表现变化；",[2273,11727,11728],{},"风险平价组合：按风险贡献平衡因子，观察新因子的风险–收益比；",[2273,11730,11731],{},"基于 IC 或预期收益的最优权重组合（例如 IC weighting、均值–方差框架、Black–Litterman 等）。",[1792,11733,11734],{},"只有当新因子在上述各阶段测试中表现良好，并在组合层面带来正向的边际贡献时，才会被纳入最终的“可投因子库”。",[11736,11737],"hr",{},[1792,11739,11740,4738],{},[3214,11741,11742],{},"参考文献（节选）",[2270,11744,11745,11752,11757,11763,11770],{},[2273,11746,11747,11748],{},"Fama, E. F., & French, K. R. (1993). \"Common risk factors in the returns on stocks and bonds.\" ",[11749,11750,11751],"em",{},"Journal of Financial Economics.",[2273,11753,11754,11755],{},"Fama, E. F., & French, K. R. (2015). \"A five-factor asset pricing model.\" ",[11749,11756,11751],{},[2273,11758,11759,11760],{},"Jegadeesh, N., & Titman, S. (1993). \"Returns to buying winners and selling losers: Implications for stock market efficiency.\" ",[11749,11761,11762],{},"The Journal of Finance.",[2273,11764,11765,11766,11769],{},"Grinold, R. C., & Kahn, R. N. (2000). ",[11749,11767,11768],{},"Active Portfolio Management."," McGraw-Hill.",[2273,11771,11772,11773],{},"Gu, S., Kelly, B., & Xiu, D. (2020). \"Empirical asset pricing via machine learning.\" ",[11749,11774,11775],{},"The Review of Financial Studies.",[3205,11777,11779],{"id":11778},"_8-从因子到交易信号","8. 从因子到交易信号",[1792,11781,11782,11783,11786],{},"因子价值本身并不直接产生收益，需要转换为",[3214,11784,11785],{},"实际操作指令","。常见转化步骤：",[3228,11788,11789,12001,12011],{},[2273,11790,11791,4738,11794],{},[3214,11792,11793],{},"确定持仓方向与强度",[2270,11795,11796,11998],{},[2273,11797,11798,11799],{},"根据因子得分改变目标权重，如：\n",[1802,11800,11802],{"className":11801},[1805],[1802,11803,11805,11854],{"className":11804},[1809],[1802,11806,11808],{"className":11807},[1813],[1815,11809,11810],{"xmlns":1817,"display":1818},[1820,11811,11812,11851],{},[1823,11813,11814,11834,11837,11839,11841,11843,11845],{},[1865,11815,11816,11818,11820],{},[1829,11817,8788],{},[1829,11819,1836],{},[1823,11821,11822,11824,11826,11828,11830,11832],{},[1829,11823,1844],{},[1829,11825,6833],{},[1829,11827,1831],{},[1829,11829,6226],{},[1829,11831,8328],{},[1829,11833,1844],{},[1838,11835,11836],{},"∝",[1829,11838,8769],{},[1829,11840,6597],{},[1829,11842,6221],{},[1829,11844,1831],{},[1826,11846,11847,11849],{},[1829,11848,8328],{},[1829,11850,1836],{},[1911,11852,11853],{"encoding":1913},"w_i^{target} \\propto Score_i",[1802,11855,11857,11946],{"className":11856,"ariaHidden":1840},[1918],[1802,11858,11860,11864,11937,11940,11943],{"className":11859},[1922],[1802,11861],{"className":11862,"style":11863},[1926],"height:1.1883em;vertical-align:-0.2769em;",[1802,11865,11867,11870],{"className":11866},[1931],[1802,11868,8788],{"className":11869,"style":8922},[1931,1935],[1802,11871,11873],{"className":11872},[1940],[1802,11874,11876,11928],{"className":11875},[1944,1945],[1802,11877,11879,11925],{"className":11878},[1949],[1802,11880,11883,11895],{"className":11881,"style":11882},[1953],"height:0.9115em;",[1802,11884,11886,11889],{"style":11885},"top:-2.4231em;margin-left:-0.0269em;margin-right:0.05em;",[1802,11887],{"className":11888,"style":1962},[1961],[1802,11890,11892],{"className":11891},[1966,1967,1968,1969],[1802,11893,1836],{"className":11894},[1931,1935,1969],[1802,11896,11898,11901],{"style":11897},"top:-3.1809em;margin-right:0.05em;",[1802,11899],{"className":11900,"style":1962},[1961],[1802,11902,11904],{"className":11903},[1966,1967,1968,1969],[1802,11905,11907,11910,11913,11916,11919,11922],{"className":11906},[1931,1969],[1802,11908,1844],{"className":11909},[1931,1935,1969],[1802,11911,6833],{"className":11912},[1931,1935,1969],[1802,11914,1831],{"className":11915,"style":1936},[1931,1935,1969],[1802,11917,6226],{"className":11918,"style":4941},[1931,1935,1969],[1802,11920,8328],{"className":11921},[1931,1935,1969],[1802,11923,1844],{"className":11924},[1931,1935,1969],[1802,11926,1994],{"className":11927},[1993],[1802,11929,11931],{"className":11930},[1949],[1802,11932,11935],{"className":11933,"style":11934},[1953],"height:0.2769em;",[1802,11936],{},[1802,11938],{"className":11939,"style":2008},[2007],[1802,11941,11836],{"className":11942},[2012],[1802,11944],{"className":11945,"style":2008},[2007],[1802,11947,11949,11952,11955,11958],{"className":11948},[1922],[1802,11950],{"className":11951,"style":3840},[1926],[1802,11953,8769],{"className":11954,"style":3315},[1931,1935],[1802,11956,6703],{"className":11957,"style":1936},[1931,1935],[1802,11959,11961,11964],{"className":11960},[1931],[1802,11962,8328],{"className":11963},[1931,1935],[1802,11965,11967],{"className":11966},[1940],[1802,11968,11970,11990],{"className":11969},[1944,1945],[1802,11971,11973,11987],{"className":11972},[1949],[1802,11974,11976],{"className":11975,"style":1954},[1953],[1802,11977,11978,11981],{"style":2227},[1802,11979],{"className":11980,"style":1962},[1961],[1802,11982,11984],{"className":11983},[1966,1967,1968,1969],[1802,11985,1836],{"className":11986},[1931,1935,1969],[1802,11988,1994],{"className":11989},[1993],[1802,11991,11993],{"className":11992},[1949],[1802,11994,11996],{"className":11995,"style":2063},[1953],[1802,11997],{},[2273,11999,12000],{},"或者采用分组方法：Q1 组权重最低，Q5 组最高。",[2273,12002,12003,4738,12006],{},[3214,12004,12005],{},"加上风险和约束条件",[2270,12007,12008],{},[2273,12009,12010],{},"控制总杠杆、行业权重、市值暴露等（将在组合与风险管理章节详细展开）。",[2273,12012,12013,4738,12016],{},[3214,12014,12015],{},"生成订单",[2270,12017,12018,12021],{},[2273,12019,12020],{},"计算当前持仓与目标持仓的差异，生成买卖指令；",[2273,12022,12023],{},"将指令提交给执行模块。",[11736,12025],{},[3205,12027,12029],{"id":12028},"_9-自学手册从候选因子到可投信号","9. 自学手册：从候选因子到可投信号",[3250,12031,12033],{"id":12032},"_91-学习目标","9.1 学习目标",[1792,12035,12036],{},"学完本章后，你应当能够：",[3228,12038,12039,12042,12045,12048,12051],{},[2273,12040,12041],{},"区分“因子值”“alpha 预测”和“交易信号”三件事；",[2273,12043,12044],{},"为一个候选因子写出经济假设、计算公式、频率和数据口径；",[2273,12046,12047],{},"使用标准化、中性化、分组回测和 IC\u002FRank IC 做初步检验；",[2273,12049,12050],{},"判断一个因子是否只是行业、市值或旧因子的变形；",[2273,12052,12053],{},"说明为什么通过单因子检验的因子仍然未必适合真实组合。",[3250,12055,12057],{"id":12056},"_92-研究场景","9.2 研究场景",[1792,12059,12060],{},"假设你发现“过去 12 个月盈利预测上调幅度较大的股票，下个月表现更好”。团队要求你把它做成候选因子。你不能只交一条公式，而需要交一份研究包：",[2270,12062,12063,12066,12069,12072,12075],{},[2273,12064,12065],{},"因子的经济解释是什么？",[2273,12067,12068],{},"预测目标是未来 1 日、1 周还是 1 月收益？",[2273,12070,12071],{},"是否做行业、市值中性化？",[2273,12073,12074],{},"Rank IC 是否稳定？IC decay 是否合理？",[2273,12076,12077],{},"加入交易成本和容量约束后是否还可投？",[1792,12079,12080],{},"本章的手册化目标，就是把“一个想法”推进到“可进入组合评审的信号”。",[3250,12082,12084],{"id":12083},"_93-定义与工作流逻辑","9.3 定义与工作流逻辑",[12086,12087,12088,12104],"table",{},[12089,12090,12091],"thead",{},[12092,12093,12094,12098,12101],"tr",{},[12095,12096,12097],"th",{},"层级",[12095,12099,12100],{},"问题",[12095,12102,12103],{},"输出",[12105,12106,12107,12119,12215,12226,12322,12471],"tbody",{},[12092,12108,12109,12113,12116],{},[12110,12111,12112],"td",{},"原始指标",[12110,12114,12115],{},"数据字段如何计算？",[12110,12117,12118],{},"如盈利预测上调比例、过去收益、换手率",[12092,12120,12121,12124,12127],{},[12110,12122,12123],{},"因子",[12110,12125,12126],{},"指标是否有稳定经济含义？",[12110,12128,12129],{},[1802,12130,12132,12156],{"className":12131},[1809],[1802,12133,12135],{"className":12134},[1813],[1815,12136,12137],{"xmlns":1817},[1820,12138,12139,12153],{},[1823,12140,12141],{},[1826,12142,12143,12145],{},[1829,12144,1880],{},[1823,12146,12147,12149,12151],{},[1829,12148,1836],{},[1838,12150,1841],{"separator":1840},[1829,12152,1844],{},[1911,12154,12155],{"encoding":1913},"f_{i,t}",[1802,12157,12159],{"className":12158,"ariaHidden":1840},[1918],[1802,12160,12162,12166],{"className":12161},[1922],[1802,12163],{"className":12164,"style":12165},[1926],"height:0.9805em;vertical-align:-0.2861em;",[1802,12167,12169,12172],{"className":12168},[1931],[1802,12170,1880],{"className":12171,"style":2145},[1931,1935],[1802,12173,12175],{"className":12174},[1940],[1802,12176,12178,12207],{"className":12177},[1944,1945],[1802,12179,12181,12204],{"className":12180},[1949],[1802,12182,12184],{"className":12183,"style":1954},[1953],[1802,12185,12186,12189],{"style":2161},[1802,12187],{"className":12188,"style":1962},[1961],[1802,12190,12192],{"className":12191},[1966,1967,1968,1969],[1802,12193,12195,12198,12201],{"className":12194},[1931,1969],[1802,12196,1836],{"className":12197},[1931,1935,1969],[1802,12199,1841],{"className":12200},[1979,1969],[1802,12202,1844],{"className":12203},[1931,1935,1969],[1802,12205,1994],{"className":12206},[1993],[1802,12208,12210],{"className":12209},[1949],[1802,12211,12213],{"className":12212,"style":2001},[1953],[1802,12214],{},[12092,12216,12217,12220,12223],{},[12110,12218,12219],{},"标准化因子",[12110,12221,12222],{},"不同资产之间是否可比较？",[12110,12224,12225],{},"z-score 或 rank score",[12092,12227,12228,12231,12234],{},[12110,12229,12230],{},"中性化因子",[12110,12232,12233],{},"是否剔除行业、市值等已知暴露？",[12110,12235,12236,12237],{},"回归残差 ",[1802,12238,12240,12264],{"className":12239},[1809],[1802,12241,12243],{"className":12242},[1813],[1815,12244,12245],{"xmlns":1817},[1820,12246,12247,12261],{},[1823,12248,12249],{},[1826,12250,12251,12253],{},[1829,12252,1895],{},[1823,12254,12255,12257,12259],{},[1829,12256,1836],{},[1838,12258,1841],{"separator":1840},[1829,12260,1844],{},[1911,12262,12263],{"encoding":1913},"\\epsilon_{i,t}",[1802,12265,12267],{"className":12266,"ariaHidden":1840},[1918],[1802,12268,12270,12273],{"className":12269},[1922],[1802,12271],{"className":12272,"style":1927},[1926],[1802,12274,12276,12279],{"className":12275},[1931],[1802,12277,1895],{"className":12278},[1931,1935],[1802,12280,12282],{"className":12281},[1940],[1802,12283,12285,12314],{"className":12284},[1944,1945],[1802,12286,12288,12311],{"className":12287},[1949],[1802,12289,12291],{"className":12290,"style":1954},[1953],[1802,12292,12293,12296],{"style":2227},[1802,12294],{"className":12295,"style":1962},[1961],[1802,12297,12299],{"className":12298},[1966,1967,1968,1969],[1802,12300,12302,12305,12308],{"className":12301},[1931,1969],[1802,12303,1836],{"className":12304},[1931,1935,1969],[1802,12306,1841],{"className":12307},[1979,1969],[1802,12309,1844],{"className":12310},[1931,1935,1969],[1802,12312,1994],{"className":12313},[1993],[1802,12315,12317],{"className":12316},[1949],[1802,12318,12320],{"className":12319,"style":2001},[1953],[1802,12321],{},[12092,12323,12324,12327,12330],{},[12110,12325,12326],{},"alpha 预测",[12110,12328,12329],{},"因子如何映射到预期收益？",[12110,12331,12332,12466,12467],{},[1802,12333,12335,12365],{"className":12334},[1809],[1802,12336,12338],{"className":12337},[1813],[1815,12339,12340],{"xmlns":1817},[1820,12341,12342,12362],{},[1823,12343,12344],{},[1826,12345,12346,12354],{},[12347,12348,12349,12351],"mover",{"accent":1840},[1829,12350,4837],{},[1838,12352,12353],{},"^",[1823,12355,12356,12358,12360],{},[1829,12357,1836],{},[1838,12359,1841],{"separator":1840},[1829,12361,1844],{},[1911,12363,12364],{"encoding":1913},"\\hat{\\mu}_{i,t}",[1802,12366,12368],{"className":12367,"ariaHidden":1840},[1918],[1802,12369,12371,12374],{"className":12370},[1922],[1802,12372],{"className":12373,"style":12165},[1926],[1802,12375,12377,12423],{"className":12376},[1931],[1802,12378,12381],{"className":12379},[1931,12380],"accent",[1802,12382,12384,12414],{"className":12383},[1944,1945],[1802,12385,12387,12411],{"className":12386},[1949],[1802,12388,12390,12398],{"className":12389,"style":9337},[1953],[1802,12391,12392,12395],{"style":8491},[1802,12393],{"className":12394,"style":3359},[1961],[1802,12396,4837],{"className":12397},[1931,1935],[1802,12399,12400,12403],{"style":8491},[1802,12401],{"className":12402,"style":3359},[1961],[1802,12404,12408],{"className":12405,"style":12407},[12406],"accent-body","left:-0.2222em;",[1802,12409,12353],{"className":12410},[1931],[1802,12412,1994],{"className":12413},[1993],[1802,12415,12417],{"className":12416},[1949],[1802,12418,12421],{"className":12419,"style":12420},[1953],"height:0.1944em;",[1802,12422],{},[1802,12424,12426],{"className":12425},[1940],[1802,12427,12429,12458],{"className":12428},[1944,1945],[1802,12430,12432,12455],{"className":12431},[1949],[1802,12433,12435],{"className":12434,"style":1954},[1953],[1802,12436,12437,12440],{"style":2227},[1802,12438],{"className":12439,"style":1962},[1961],[1802,12441,12443],{"className":12442},[1966,1967,1968,1969],[1802,12444,12446,12449,12452],{"className":12445},[1931,1969],[1802,12447,1836],{"className":12448},[1931,1935,1969],[1802,12450,1841],{"className":12451},[1979,1969],[1802,12453,1844],{"className":12454},[1931,1935,1969],[1802,12456,1994],{"className":12457},[1993],[1802,12459,12461],{"className":12460},[1949],[1802,12462,12464],{"className":12463,"style":2001},[1953],[1802,12465],{}," 或 ",[12468,12469,12470],"code",{},"Score",[12092,12472,12473,12476,12479],{},[12110,12474,12475],{},"交易信号",[12110,12477,12478],{},"如何转成目标权重或订单？",[12110,12480,12481,12611,12612],{},[1802,12482,12484,12522],{"className":12483},[1809],[1802,12485,12487],{"className":12486},[1813],[1815,12488,12489],{"xmlns":1817},[1820,12490,12491,12519],{},[1823,12492,12493],{},[1865,12494,12495,12497,12505],{},[1829,12496,8788],{},[1823,12498,12499,12501,12503],{},[1829,12500,1836],{},[1838,12502,1841],{"separator":1840},[1829,12504,1844],{},[1823,12506,12507,12509,12511,12513,12515,12517],{},[1829,12508,1844],{},[1829,12510,6833],{},[1829,12512,1831],{},[1829,12514,6226],{},[1829,12516,8328],{},[1829,12518,1844],{},[1911,12520,12521],{"encoding":1913},"w_{i,t}^{target}",[1802,12523,12525],{"className":12524,"ariaHidden":1840},[1918],[1802,12526,12528,12532],{"className":12527},[1922],[1802,12529],{"className":12530,"style":12531},[1926],"height:1.3244em;vertical-align:-0.413em;",[1802,12533,12535,12538],{"className":12534},[1931],[1802,12536,8788],{"className":12537,"style":8922},[1931,1935],[1802,12539,12541],{"className":12540},[1940],[1802,12542,12544,12602],{"className":12543},[1944,1945],[1802,12545,12547,12599],{"className":12546},[1949],[1802,12548,12550,12570],{"className":12549,"style":11882},[1953],[1802,12551,12552,12555],{"style":11885},[1802,12553],{"className":12554,"style":1962},[1961],[1802,12556,12558],{"className":12557},[1966,1967,1968,1969],[1802,12559,12561,12564,12567],{"className":12560},[1931,1969],[1802,12562,1836],{"className":12563},[1931,1935,1969],[1802,12565,1841],{"className":12566},[1979,1969],[1802,12568,1844],{"className":12569},[1931,1935,1969],[1802,12571,12572,12575],{"style":11897},[1802,12573],{"className":12574,"style":1962},[1961],[1802,12576,12578],{"className":12577},[1966,1967,1968,1969],[1802,12579,12581,12584,12587,12590,12593,12596],{"className":12580},[1931,1969],[1802,12582,1844],{"className":12583},[1931,1935,1969],[1802,12585,6833],{"className":12586},[1931,1935,1969],[1802,12588,1831],{"className":12589,"style":1936},[1931,1935,1969],[1802,12591,6226],{"className":12592,"style":4941},[1931,1935,1969],[1802,12594,8328],{"className":12595},[1931,1935,1969],[1802,12597,1844],{"className":12598},[1931,1935,1969],[1802,12600,1994],{"className":12601},[1993],[1802,12603,12605],{"className":12604},[1949],[1802,12606,12609],{"className":12607,"style":12608},[1953],"height:0.413em;",[1802,12610],{}," \u002F ",[12468,12613,12614],{},"orders",[1792,12616,12617],{},"工作流顺序通常是：",[12619,12620],"mermaid-diagram",{"code64":12621,"locale":7},"Zmxvd2NoYXJ0IExSCiAgQVsi57uP5rWO5YGH6K6+Il0gLS0+IEJbIuWboOWtkOWFrOW8jyJdCiAgQiAtLT4gQ1si5riF5rSX5LiO5qCH5YeG5YyWIl0KICBDIC0tPiBEWyLkuK3mgKfljJYiXQogIEQgLS0+IEVbIklDIC8g5YiG57uE5qOA6aqMIl0KICBFIC0tPiBGWyLnqLPlgaXmgKfkuI7lhpfkvZnmo4DmtYsiXQogIEYgLS0+IEdbIuaIkOacrOS4juWuuemHj+a1i+ivlSJdCiAgRyAtLT4gSFsi57uE5ZCI6LSh54yu6K+E5LywIl0=",[3250,12623,12625],{"id":12624},"_94-迷你案例12-2-动量因子评审清单","9.4 迷你案例：12-2 动量因子评审清单",[1792,12627,12628],{},"以 12-2 月动量为例，研究报告至少应回答：",[2270,12630,12631,12637,12643,12649,12655,12661,12667,12673,12679],{},[2273,12632,12633,12636],{},[3214,12634,12635],{},"公式","：过去 12 个月到过去 2 个月的累计收益，跳过最近 1 个月以降低短期反转干扰。",[2273,12638,12639,12642],{},[3214,12640,12641],{},"频率","：月度调仓，使用月末可见价格。",[2273,12644,12645,12648],{},[3214,12646,12647],{},"清洗","：剔除上市不足 12 个月、长期停牌和流动性过低的股票。",[2273,12650,12651,12654],{},[3214,12652,12653],{},"标准化","：每月横截面 winsorize 后做 z-score。",[2273,12656,12657,12660],{},[3214,12658,12659],{},"中性化","：回归剔除行业和市值暴露。",[2273,12662,12663,12666],{},[3214,12664,12665],{},"检验","：计算月度 Rank IC、五分组收益、Q5-Q1 多空组合收益。",[2273,12668,12669,12672],{},[3214,12670,12671],{},"稳健性","：分牛市、熊市、震荡市检查；按行业分别计算 IC。",[2273,12674,12675,12678],{},[3214,12676,12677],{},"可投资性","：加入半价差、佣金和冲击成本；检查换手率与小盘暴露。",[2273,12680,12681,12684],{},[3214,12682,12683],{},"组合贡献","：与现有 Value、Quality、Low Vol 因子的相关性不能过高，并能提升组合 IR。",[3250,12686,12688],{"id":12687},"_95-常见错误与研究陷阱","9.5 常见错误与研究陷阱",[2270,12690,12691,12697,12703,12709,12715,12721],{},[2273,12692,12693,12696],{},[3214,12694,12695],{},"把相关性当因果","：因子和未来收益相关，不代表有稳定经济机制；先要求合理解释，再谈部署。",[2273,12698,12699,12702],{},[3214,12700,12701],{},"只看平均 IC","：平均值为正但波动极大，可能意味着因子只在少数月份赚钱。",[2273,12704,12705,12708],{},[3214,12706,12707],{},"中性化目标不清","：过度中性化会删掉真实 alpha，不中性化又可能留下无意暴露；要与策略目标一致。",[2273,12710,12711,12714],{},[3214,12712,12713],{},"忽略 IC decay","：如果信号只在下一日有效，却设计成月度调仓，收益会在执行前衰减。",[2273,12716,12717,12720],{},[3214,12718,12719],{},"候选因子互相重复","：多个高相关因子叠加不会自动提高信息量，反而会放大同一风险源。",[2273,12722,12723,12726],{},[3214,12724,12725],{},"先看结果再改公式","：反复调公式直到回测漂亮，会产生严重数据挖掘偏差。",[3250,12728,12730],{"id":12729},"_96-自测题与答案提示","9.6 自测题与答案提示",[3228,12732,12733,12736,12739,12742],{},[2273,12734,12735],{},"为什么因子通过分组检验后，还要看 Rank IC？\n答案提示：分组检验关注组合收益和单调性，Rank IC 关注全截面排序一致性；二者互补。",[2273,12737,12738],{},"一个因子与市值因子相关系数为 0.8，应如何处理？\n答案提示：先判断经济含义是否本来就包含市值；若目标是独立 alpha，应做市值中性化或边际贡献检验。",[2273,12740,12741],{},"为什么“因子收益显著”不等于“策略可投”？\n答案提示：真实策略还受换手、成本、容量、约束、组合冗余和执行风险影响。",[2273,12743,12744],{},"线性多因子打分中，因子权重可以如何设定？\n答案提示：可用等权、基于 IC\u002FIR 的权重、横截面回归系数或组合优化结果；关键是避免样本内过拟合。",[3250,12746,12748],{"id":12747},"_97-小结与过渡","9.7 小结与过渡",[1792,12750,12751],{},"本章把因子研究拆成了从经济假设到可投信号的完整链条。一个合格因子不仅要有统计表现，还要有清晰口径、可复现数据、稳健检验、低冗余和可执行性。下一章会把这些信号放入回测框架，检验它们在真实约束和交易成本下能否形成稳定策略收益。",[11736,12753],{},[1792,12755,12756,12757,12760],{},"本章从概念上介绍了因子与信号，并给出了构建和检验的基本框架。下一章将基于这些因子，介绍如何搭建",[3214,12758,12759],{},"策略回测框架","，评估策略表现并避免常见回测陷阱。",{"title":10,"searchDepth":12762,"depth":12762,"links":12763},2,[12764,12765,12773,12774,12778,12782,12786,12794,12795],{"id":3207,"depth":12762,"text":3208},{"id":3244,"depth":12762,"text":3245,"children":12766},[12767,12769,12770,12771,12772],{"id":3252,"depth":12768,"text":3253},3,{"id":3698,"depth":12768,"text":3699},{"id":3726,"depth":12768,"text":3727},{"id":3752,"depth":12768,"text":3753},{"id":4704,"depth":12768,"text":4705},{"id":4726,"depth":12762,"text":4727},{"id":4789,"depth":12762,"text":4790,"children":12775},[12776,12777],{"id":4793,"depth":12768,"text":4794},{"id":5212,"depth":12768,"text":5213},{"id":6126,"depth":12762,"text":6127,"children":12779},[12780,12781],{"id":6141,"depth":12768,"text":6142},{"id":6556,"depth":12768,"text":6557},{"id":8740,"depth":12762,"text":8741,"children":12783},[12784,12785],{"id":8747,"depth":12768,"text":8748},{"id":10120,"depth":12768,"text":10121},{"id":10582,"depth":12762,"text":10583,"children":12787},[12788,12789,12790,12791,12792,12793],{"id":10597,"depth":12768,"text":10598},{"id":10651,"depth":12768,"text":10652},{"id":10698,"depth":12768,"text":10699},{"id":10764,"depth":12768,"text":10765},{"id":11638,"depth":12768,"text":11639},{"id":11692,"depth":12768,"text":11693},{"id":11778,"depth":12762,"text":11779},{"id":12028,"depth":12762,"text":12029,"children":12796},[12797,12798,12799,12800,12801,12802,12803],{"id":12032,"depth":12768,"text":12033},{"id":12056,"depth":12768,"text":12057},{"id":12083,"depth":12768,"text":12084},{"id":12624,"depth":12768,"text":12625},{"id":12687,"depth":12768,"text":12688},{"id":12729,"depth":12768,"text":12730},{"id":12747,"depth":12768,"text":12748},"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。","md",{"sidebar":12807},{"order":12762},true,{"title":1747,"description":12804},"0QhcnbSGyx4MZd-MZKfwJjGPlzSYwsJVQFU3OsD848U",[12812,12814],{"title":1743,"path":1744,"stem":1745,"description":12813,"children":-1},"构造 point-in-time 研究面板，审计价格、财务、另类数据的可用时点、版本和偏差。",{"title":1751,"path":1752,"stem":1753,"description":12815,"children":-1},"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。",1785754758857]