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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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",[1827,2123,2125,2138],{"className":2124},[1830],[1827,2126,2128],{"className":2127},[1834],[1836,2129,2130],{"xmlns":1838},[1840,2131,2132,2136],{},[1843,2133,2134],{},[1846,2135,1903],{},[1850,2137,1903],{"encoding":1852},[1827,2139,2141],{"className":2140,"ariaHidden":1857},[1856],[1827,2142,2144,2147],{"className":2143},[1861],[1827,2145],{"className":2146,"style":1866},[1865],[1827,2148,1903],{"className":2149},[1870]," 收到随机收益向量 ",[1827,2152,2154,2197],{"className":2153},[1830],[1827,2155,2157],{"className":2156},[1834],[1836,2158,2159],{"xmlns":1838},[1840,2160,2161,2194],{},[1843,2162,2163,2166,2168,2170,2176,2178,2180,2182,2188],{},[1885,2164,2165],{},"r",[1889,2167,1891],{},[1889,2169,1895],{"stretchy":1894},[1897,2171,2172,2174],{},[1885,2173,2165],{},[1846,2175,1903],{},[1889,2177,1906],{"separator":1857},[1889,2179,1909],{},[1889,2181,1906],{"separator":1857},[1897,2183,2184,2186],{},[1885,2185,2165],{},[1885,2187,1918],{},[1920,2189,2190,2192],{},[1889,2191,1924],{"stretchy":1894},[1885,2193,1928],{"mathvariant":1927},[1850,2195,2196],{"encoding":1852},"r = (r_1, \\dots, 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r_p = w^\\top r.",[1827,2397,2399,2457],{"className":2398,"ariaHidden":1857},[1856],[1827,2400,2402,2406,2448,2451,2454],{"className":2401},[1861],[1827,2403],{"className":2404,"style":2405},[1865],"height:0.7167em;vertical-align:-0.2861em;",[1827,2407,2409,2412],{"className":2408},[1870],[1827,2410,2165],{"className":2411,"style":2209},[1870,1945],[1827,2413,2415],{"className":2414},[1979],[1827,2416,2418,2439],{"className":2417},[1983,1984],[1827,2419,2421,2436],{"className":2420},[1988],[1827,2422,2425],{"className":2423,"style":2424},[1992],"height:0.1514em;",[1827,2426,2427,2430],{"style":2248},[1827,2428],{"className":2429,"style":2001},[2000],[1827,2431,2433],{"className":2432},[2005,2006,2007,2008],[1827,2434,1793],{"className":2435},[1870,1945,2008],[1827,2437,2016],{"className":2438},[2015],[1827,2440,2442],{"className":2441},[1988],[1827,2443,2446],{"className":2444,"style":2445},[1992],"height:0.2861em;",[1827,2447],{},[1827,2449],{"className":2450,"style":1951},[1950],[1827,2452,1891],{"className":2453},[1955],[1827,2455],{"className":2456,"style":1951},[1950],[1827,2458,2460,2464,2494,2497],{"className":2459},[1861],[1827,2461],{"className":2462,"style":2463},[1865],"height:0.8991em;",[1827,2465,2467,2470],{"className":2466},[1870],[1827,2468,1887],{"className":2469,"style":1946},[1870,1945],[1827,2471,2473],{"className":2472},[1979],[1827,2474,2476],{"className":2475},[1983],[1827,2477,2479],{"className":2478},[1988],[1827,2480,2482],{"className":2481,"style":2463},[1992],[1827,2483,2485,2488],{"style":2484},"top:-3.113em;margin-right:0.05em;",[1827,2486],{"className":2487,"style":2001},[2000],[1827,2489,2491],{"className":2490},[2005,2006,2007,2008],[1827,2492,1928],{"className":2493},[1870,2008],[1827,2495,2165],{"className":2496,"style":2209},[1870,1945],[1827,2498,2392],{"className":2499},[1870],[1793,2501,2502],{},"我们记：",[2504,2505,2506,2584],"ul",{},[2507,2508,2509,2583],"li",{},[1827,2510,2512,2541],{"className":2511},[1830],[1827,2513,2515],{"className":2514},[1834],[1836,2516,2517],{"xmlns":1838},[1840,2518,2519,2538],{},[1843,2520,2521,2524,2526,2530,2533,2535],{},[1885,2522,2523],{},"μ",[1889,2525,1891],{},[1885,2527,2529],{"mathvariant":2528},"double-struck","E",[1889,2531,2532],{"stretchy":1894},"[",[1885,2534,2165],{},[1889,2536,2537],{"stretchy":1894},"]",[1850,2539,2540],{"encoding":1852},"\\mu = \\mathbb{E}[r]",[1827,2542,2544,2563],{"className":2543,"ariaHidden":1857},[1856],[1827,2545,2547,2551,2554,2557,2560],{"className":2546},[1861],[1827,2548],{"className":2549,"style":2550},[1865],"height:0.625em;vertical-align:-0.1944em;",[1827,2552,2523],{"className":2553},[1870,1945],[1827,2555],{"className":2556,"style":1951},[1950],[1827,2558,1891],{"className":2559},[1955],[1827,2561],{"className":2562,"style":1951},[1950],[1827,2564,2566,2570,2574,2577,2580],{"className":2565},[1861],[1827,2567],{"className":2568,"style":2569},[1865],"height:1em;vertical-align:-0.25em;",[1827,2571,2529],{"className":2572},[1870,2573],"mathbb",[1827,2575,2532],{"className":2576},[1969],[1827,2578,2165],{"className":2579,"style":2209},[1870,1945],[1827,2581,2537],{"className":2582},[2092]," 为资产预期收益向量；",[2507,2585,2586,2664],{},[1827,2587,2589,2618],{"className":2588},[1830],[1827,2590,2592],{"className":2591},[1834],[1836,2593,2594],{"xmlns":1838},[1840,2595,2596,2615],{},[1843,2597,2598,2601,2603,2606,2609,2611,2613],{},[1885,2599,2600],{"mathvariant":1927},"Σ",[1889,2602,1891],{},[1885,2604,2605],{"mathvariant":1927},"Cov",[1889,2607,2608],{},"⁡",[1889,2610,1895],{"stretchy":1894},[1885,2612,2165],{},[1889,2614,1924],{"stretchy":1894},[1850,2616,2617],{"encoding":1852},"\\Sigma = \\operatorname{Cov}(r)",[1827,2619,2621,2640],{"className":2620,"ariaHidden":1857},[1856],[1827,2622,2624,2628,2631,2634,2637],{"className":2623},[1861],[1827,2625],{"className":2626,"style":2627},[1865],"height:0.6833em;",[1827,2629,2600],{"className":2630},[1870],[1827,2632],{"className":2633,"style":1951},[1950],[1827,2635,1891],{"className":2636},[1955],[1827,2638],{"className":2639,"style":1951},[1950],[1827,2641,2643,2646,2655,2658,2661],{"className":2642},[1861],[1827,2644],{"className":2645,"style":2569},[1865],[1827,2647,2650],{"className":2648},[2649],"mop",[1827,2651,2605],{"className":2652,"style":2654},[1870,2653],"mathrm","margin-right:0.0139em;",[1827,2656,1895],{"className":2657},[1969],[1827,2659,2165],{"className":2660,"style":2209},[1870,1945],[1827,2662,1924],{"className":2663},[2092]," 为收益协方差矩阵。",[1793,2666,2667,2668,2738,2739,2883,2884,3037],{},"在均值–方差框架中，投资者只关心 ",[1827,2669,2671,2689],{"className":2670},[1830],[1827,2672,2674],{"className":2673},[1834],[1836,2675,2676],{"xmlns":1838},[1840,2677,2678,2686],{},[1843,2679,2680],{},[1897,2681,2682,2684],{},[1885,2683,2165],{},[1885,2685,1793],{},[1850,2687,2688],{"encoding":1852},"r_p",[1827,2690,2692],{"className":2691,"ariaHidden":1857},[1856],[1827,2693,2695,2698],{"className":2694},[1861],[1827,2696],{"className":2697,"style":2405},[1865],[1827,2699,2701,2704],{"className":2700},[1870],[1827,2702,2165],{"className":2703,"style":2209},[1870,1945],[1827,2705,2707],{"className":2706},[1979],[1827,2708,2710,2730],{"className":2709},[1983,1984],[1827,2711,2713,2727],{"className":2712},[1988],[1827,2714,2716],{"className":2715,"style":2424},[1992],[1827,2717,2718,2721],{"style":2248},[1827,2719],{"className":2720,"style":2001},[2000],[1827,2722,2724],{"className":2723},[2005,2006,2007,2008],[1827,2725,1793],{"className":2726},[1870,1945,2008],[1827,2728,2016],{"className":2729},[2015],[1827,2731,2733],{"className":2732},[1988],[1827,2734,2736],{"className":2735,"style":2445},[1992],[1827,2737],{}," 的均值 ",[1827,2740,2742,2776],{"className":2741},[1830],[1827,2743,2745],{"className":2744},[1834],[1836,2746,2747],{"xmlns":1838},[1840,2748,2749,2773],{},[1843,2750,2751,2753,2755,2761,2763,2765,2771],{},[1885,2752,2529],{"mathvariant":2528},[1889,2754,2532],{"stretchy":1894},[1897,2756,2757,2759],{},[1885,2758,2165],{},[1885,2760,1793],{},[1889,2762,2537],{"stretchy":1894},[1889,2764,1891],{},[1920,2766,2767,2769],{},[1885,2768,1887],{},[1885,2770,1928],{"mathvariant":1927},[1885,2772,2523],{},[1850,2774,2775],{"encoding":1852},"\\mathbb{E}[r_p] = w^\\top \\mu",[1827,2777,2779,2844],{"className":2778,"ariaHidden":1857},[1856],[1827,2780,2782,2786,2789,2792,2832,2835,2838,2841],{"className":2781},[1861],[1827,2783],{"className":2784,"style":2785},[1865],"height:1.0361em;vertical-align:-0.2861em;",[1827,2787,2529],{"className":2788},[1870,2573],[1827,2790,2532],{"className":2791},[1969],[1827,2793,2795,2798],{"className":2794},[1870],[1827,2796,2165],{"className":2797,"style":2209},[1870,1945],[1827,2799,2801],{"className":2800},[1979],[1827,2802,2804,2824],{"className":2803},[1983,1984],[1827,2805,2807,2821],{"className":2806},[1988],[1827,2808,2810],{"className":2809,"style":2424},[1992],[1827,2811,2812,2815],{"style":2248},[1827,2813],{"className":2814,"style":2001},[2000],[1827,2816,2818],{"className":2817},[2005,2006,2007,2008],[1827,2819,1793],{"className":2820},[1870,1945,2008],[1827,2822,2016],{"className":2823},[2015],[1827,2825,2827],{"className":2826},[1988],[1827,2828,2830],{"className":2829,"style":2445},[1992],[1827,2831],{},[1827,2833,2537],{"className":2834},[2092],[1827,2836],{"className":2837,"style":1951},[1950],[1827,2839,1891],{"className":2840},[1955],[1827,2842],{"className":2843,"style":1951},[1950],[1827,2845,2847,2851,2880],{"className":2846},[1861],[1827,2848],{"className":2849,"style":2850},[1865],"height:1.0435em;vertical-align:-0.1944em;",[1827,2852,2854,2857],{"className":2853},[1870],[1827,2855,1887],{"className":2856,"style":1946},[1870,1945],[1827,2858,2860],{"className":2859},[1979],[1827,2861,2863],{"className":2862},[1983],[1827,2864,2866],{"className":2865},[1988],[1827,2867,2869],{"className":2868,"style":2108},[1992],[1827,2870,2871,2874],{"style":2111},[1827,2872],{"className":2873,"style":2001},[2000],[1827,2875,2877],{"className":2876},[2005,2006,2007,2008],[1827,2878,1928],{"className":2879},[1870,2008],[1827,2881,2523],{"className":2882},[1870,1945]," 和方差 ",[1827,2885,2887,2926],{"className":2886},[1830],[1827,2888,2890],{"className":2889},[1834],[1836,2891,2892],{"xmlns":1838},[1840,2893,2894,2923],{},[1843,2895,2896,2899,2901,2903,2909,2911,2913,2919,2921],{},[1885,2897,2898],{"mathvariant":1927},"Var",[1889,2900,2608],{},[1889,2902,1895],{"stretchy":1894},[1897,2904,2905,2907],{},[1885,2906,2165],{},[1885,2908,1793],{},[1889,2910,1924],{"stretchy":1894},[1889,2912,1891],{},[1920,2914,2915,2917],{},[1885,2916,1887],{},[1885,2918,1928],{"mathvariant":1927},[1885,2920,2600],{"mathvariant":1927},[1885,2922,1887],{},[1850,2924,2925],{"encoding":1852},"\\operatorname{Var}(r_p) = w^\\top \\Sigma w",[1827,2927,2929,2996],{"className":2928,"ariaHidden":1857},[1856],[1827,2930,2932,2935,2941,2944,2984,2987,2990,2993],{"className":2931},[1861],[1827,2933],{"className":2934,"style":2785},[1865],[1827,2936,2938],{"className":2937},[2649],[1827,2939,2898],{"className":2940},[1870,2653],[1827,2942,1895],{"className":2943},[1969],[1827,2945,2947,2950],{"className":2946},[1870],[1827,2948,2165],{"className":2949,"style":2209},[1870,1945],[1827,2951,2953],{"className":2952},[1979],[1827,2954,2956,2976],{"className":2955},[1983,1984],[1827,2957,2959,2973],{"className":2958},[1988],[1827,2960,2962],{"className":2961,"style":2424},[1992],[1827,2963,2964,2967],{"style":2248},[1827,2965],{"className":2966,"style":2001},[2000],[1827,2968,2970],{"className":2969},[2005,2006,2007,2008],[1827,2971,1793],{"className":2972},[1870,1945,2008],[1827,2974,2016],{"className":2975},[2015],[1827,2977,2979],{"className":2978},[1988],[1827,2980,2982],{"className":2981,"style":2445},[1992],[1827,2983],{},[1827,2985,1924],{"className":2986},[2092],[1827,2988],{"className":2989,"style":1951},[1950],[1827,2991,1891],{"className":2992},[1955],[1827,2994],{"className":2995,"style":1951},[1950],[1827,2997,2999,3002,3031,3034],{"className":2998},[1861],[1827,3000],{"className":3001,"style":2108},[1865],[1827,3003,3005,3008],{"className":3004},[1870],[1827,3006,1887],{"className":3007,"style":1946},[1870,1945],[1827,3009,3011],{"className":3010},[1979],[1827,3012,3014],{"className":3013},[1983],[1827,3015,3017],{"className":3016},[1988],[1827,3018,3020],{"className":3019,"style":2108},[1992],[1827,3021,3022,3025],{"style":2111},[1827,3023],{"className":3024,"style":2001},[2000],[1827,3026,3028],{"className":3027},[2005,2006,2007,2008],[1827,3029,1928],{"className":3030},[1870,2008],[1827,3032,2600],{"className":3033},[1870],[1827,3035,1887],{"className":3036,"style":1946},[1870,1945],"，通常考虑如下优化问题之一：",[2504,3039,3040,3046],{},[2507,3041,3042,3045],{},[1797,3043,3044],{},"给定目标收益最大化方差的对偶问题","；",[2507,3047,3048,3049,3084,3085],{},"或",[1797,3050,3051,3052,3083],{},"在给定风险厌恶系数 ",[1827,3053,3055,3070],{"className":3054},[1830],[1827,3056,3058],{"className":3057},[1834],[1836,3059,3060],{"xmlns":1838},[1840,3061,3062,3067],{},[1843,3063,3064],{},[1885,3065,3066],{},"λ",[1850,3068,3069],{"encoding":1852},"\\lambda",[1827,3071,3073],{"className":3072,"ariaHidden":1857},[1856],[1827,3074,3076,3080],{"className":3075},[1861],[1827,3077],{"className":3078,"style":3079},[1865],"height:0.6944em;",[1827,3081,3066],{"className":3082},[1870,1945]," 时最大化均值–方差效用","：",[1827,3086,3088],{"className":3087},[2360],[1827,3089,3091,3150],{"className":3090},[1830],[1827,3092,3094],{"className":3093},[1834],[1836,3095,3096],{"xmlns":1838,"display":2369},[1840,3097,3098,3147],{},[1843,3099,3100,3112,3116,3122,3124,3127,3135,3141,3143,3145],{},[3101,3102,3103,3110],"munder",{},[1843,3104,3105,3108],{},[1885,3106,3107],{},"max",[1889,3109,2608],{},[1885,3111,1887],{},[3113,3114,3115],"mtext",{}," ",[1920,3117,3118,3120],{},[1885,3119,1887],{},[1885,3121,1928],{"mathvariant":1927},[1885,3123,2523],{},[1889,3125,3126],{},"−",[3128,3129,3130,3132],"mfrac",{},[1885,3131,3066],{},[1846,3133,3134],{},"2",[1920,3136,3137,3139],{},[1885,3138,1887],{},[1885,3140,1928],{"mathvariant":1927},[1885,3142,2600],{"mathvariant":1927},[1885,3144,1887],{},[1885,3146,2392],{"mathvariant":1927},[1850,3148,3149],{"encoding":1852},"\\max_w \\ w^\\top \\mu - \\frac{\\lambda}{2} w^\\top \\Sigma w.",[1827,3151,3153,3258],{"className":3152,"ariaHidden":1857},[1856],[1827,3154,3156,3160,3209,3212,3215,3244,3247,3251,3255],{"className":3155},[1861],[1827,3157],{"className":3158,"style":3159},[1865],"height:1.5991em;vertical-align:-0.7em;",[1827,3161,3164],{"className":3162},[2649,3163],"op-limits",[1827,3165,3167,3200],{"className":3166},[1983,1984],[1827,3168,3170,3197],{"className":3169},[1988],[1827,3171,3173,3186],{"className":3172,"style":1941},[1992],[1827,3174,3176,3180],{"style":3175},"top:-2.4em;margin-left:0em;",[1827,3177],{"className":3178,"style":3179},[2000],"height:3em;",[1827,3181,3183],{"className":3182},[2005,2006,2007,2008],[1827,3184,1887],{"className":3185,"style":1946},[1870,1945,2008],[1827,3187,3189,3192],{"style":3188},"top:-3em;",[1827,3190],{"className":3191,"style":3179},[2000],[1827,3193,3194],{},[1827,3195,3107],{"className":3196},[2649],[1827,3198,2016],{"className":3199},[2015],[1827,3201,3203],{"className":3202},[1988],[1827,3204,3207],{"className":3205,"style":3206},[1992],"height:0.7em;",[1827,3208],{},[1827,3210,3115],{"className":3211},[1950],[1827,3213],{"className":3214,"style":2033},[1950],[1827,3216,3218,3221],{"className":3217},[1870],[1827,3219,1887],{"className":3220,"style":1946},[1870,1945],[1827,3222,3224],{"className":3223},[1979],[1827,3225,3227],{"className":3226},[1983],[1827,3228,3230],{"className":3229},[1988],[1827,3231,3233],{"className":3232,"style":2463},[1992],[1827,3234,3235,3238],{"style":2484},[1827,3236],{"className":3237,"style":2001},[2000],[1827,3239,3241],{"className":3240},[2005,2006,2007,2008],[1827,3242,1928],{"className":3243},[1870,2008],[1827,3245,2523],{"className":3246},[1870,1945],[1827,3248],{"className":3249,"style":3250},[1950],"margin-right:0.2222em;",[1827,3252,3126],{"className":3253},[3254],"mbin",[1827,3256],{"className":3257,"style":3250},[1950],[1827,3259,3261,3265,3335,3364,3367,3370],{"className":3260},[1861],[1827,3262],{"className":3263,"style":3264},[1865],"height:2.0574em;vertical-align:-0.686em;",[1827,3266,3268,3272,3332],{"className":3267},[1870],[1827,3269],{"className":3270},[1969,3271],"nulldelimiter",[1827,3273,3275],{"className":3274},[3128],[1827,3276,3278,3323],{"className":3277},[1983,1984],[1827,3279,3281,3320],{"className":3280},[1988],[1827,3282,3285,3297,3308],{"className":3283,"style":3284},[1992],"height:1.3714em;",[1827,3286,3288,3291],{"style":3287},"top:-2.314em;",[1827,3289],{"className":3290,"style":3179},[2000],[1827,3292,3294],{"className":3293},[1870],[1827,3295,3134],{"className":3296},[1870],[1827,3298,3300,3303],{"style":3299},"top:-3.23em;",[1827,3301],{"className":3302,"style":3179},[2000],[1827,3304],{"className":3305,"style":3307},[3306],"frac-line","border-bottom-width:0.04em;",[1827,3309,3311,3314],{"style":3310},"top:-3.677em;",[1827,3312],{"className":3313,"style":3179},[2000],[1827,3315,3317],{"className":3316},[1870],[1827,3318,3066],{"className":3319},[1870,1945],[1827,3321,2016],{"className":3322},[2015],[1827,3324,3326],{"className":3325},[1988],[1827,3327,3330],{"className":3328,"style":3329},[1992],"height:0.686em;",[1827,3331],{},[1827,3333],{"className":3334},[2092,3271],[1827,3336,3338,3341],{"className":3337},[1870],[1827,3339,1887],{"className":3340,"style":1946},[1870,1945],[1827,3342,3344],{"className":3343},[1979],[1827,3345,3347],{"className":3346},[1983],[1827,3348,3350],{"className":3349},[1988],[1827,3351,3353],{"className":3352,"style":2463},[1992],[1827,3354,3355,3358],{"style":2484},[1827,3356],{"className":3357,"style":2001},[2000],[1827,3359,3361],{"className":3360},[2005,2006,2007,2008],[1827,3362,1928],{"className":3363},[1870,2008],[1827,3365,2600],{"className":3366},[1870],[1827,3368,1887],{"className":3369,"style":1946},[1870,1945],[1827,3371,2392],{"className":3372},[1870],[1793,3374,3375],{},"在无约束（除资金约束）情况下，该问题是一个凸二次规划，其一阶条件为：",[1827,3377,3379],{"className":3378},[2360],[1827,3380,3382,3445],{"className":3381},[1830],[1827,3383,3385],{"className":3384},[1834],[1836,3386,3387],{"xmlns":1838,"display":2369},[1840,3388,3389,3442],{},[1843,3390,3391,3393,3395,3397,3399,3401,3403,3405,3408,3411,3413,3420,3422,3428,3438,3440],{},[1885,3392,2523],{},[1889,3394,3126],{},[1885,3396,3066],{},[1885,3398,2600],{"mathvariant":1927},[1885,3400,1887],{},[1889,3402,1891],{},[1846,3404,1848],{},[3113,3406,3407],{},"  ",[1889,3409,3410],{},"⇒",[3113,3412,3407],{},[1920,3414,3415,3417],{},[1885,3416,1887],{},[1889,3418,3419],{},"∗",[1889,3421,1891],{},[3128,3423,3424,3426],{},[1846,3425,1903],{},[1885,3427,3066],{},[1920,3429,3430,3432],{},[1885,3431,2600],{"mathvariant":1927},[1843,3433,3434,3436],{},[1889,3435,3126],{},[1846,3437,1903],{},[1885,3439,2523],{},[1885,3441,2392],{"mathvariant":1927},[1850,3443,3444],{"encoding":1852}," \\mu - \\lambda \\Sigma w = 0 \\;\\Rightarrow\\; w^* = \\frac{1}{\\lambda} \\Sigma^{-1} \\mu.",[1827,3446,3448,3467,3491,3515,3560],{"className":3447,"ariaHidden":1857},[1856],[1827,3449,3451,3455,3458,3461,3464],{"className":3450},[1861],[1827,3452],{"className":3453,"style":3454},[1865],"height:0.7778em;vertical-align:-0.1944em;",[1827,3456,2523],{"className":3457},[1870,1945],[1827,3459],{"className":3460,"style":3250},[1950],[1827,3462,3126],{"className":3463},[3254],[1827,3465],{"className":3466,"style":3250},[1950],[1827,3468,3470,3473,3476,3479,3482,3485,3488],{"className":3469},[1861],[1827,3471],{"className":3472,"style":3079},[1865],[1827,3474,3066],{"className":3475},[1870,1945],[1827,3477,2600],{"className":3478},[1870],[1827,3480,1887],{"className":3481,"style":1946},[1870,1945],[1827,3483],{"className":3484,"style":1951},[1950],[1827,3486,1891],{"className":3487},[1955],[1827,3489],{"className":3490,"style":1951},[1950],[1827,3492,3494,3497,3500,3503,3506,3509,3512],{"className":3493},[1861],[1827,3495],{"className":3496,"style":1866},[1865],[1827,3498,1848],{"className":3499},[1870],[1827,3501],{"className":3502,"style":1951},[1950],[1827,3504],{"className":3505,"style":1951},[1950],[1827,3507,3410],{"className":3508},[1955],[1827,3510],{"className":3511,"style":1951},[1950],[1827,3513],{"className":3514,"style":1951},[1950],[1827,3516,3518,3522,3551,3554,3557],{"className":3517},[1861],[1827,3519],{"className":3520,"style":3521},[1865],"height:0.7387em;",[1827,3523,3525,3528],{"className":3524},[1870],[1827,3526,1887],{"className":3527,"style":1946},[1870,1945],[1827,3529,3531],{"className":3530},[1979],[1827,3532,3534],{"className":3533},[1983],[1827,3535,3537],{"className":3536},[1988],[1827,3538,3540],{"className":3539,"style":3521},[1992],[1827,3541,3542,3545],{"style":2484},[1827,3543],{"className":3544,"style":2001},[2000],[1827,3546,3548],{"className":3547},[2005,2006,2007,2008],[1827,3549,3419],{"className":3550},[3254,2008],[1827,3552],{"className":3553,"style":1951},[1950],[1827,3555,1891],{"className":3556},[1955],[1827,3558],{"className":3559,"style":1951},[1950],[1827,3561,3563,3567,3630,3666,3669],{"className":3562},[1861],[1827,3564],{"className":3565,"style":3566},[1865],"height:2.0074em;vertical-align:-0.686em;",[1827,3568,3570,3573,3627],{"className":3569},[1870],[1827,3571],{"className":3572},[1969,3271],[1827,3574,3576],{"className":3575},[3128],[1827,3577,3579,3619],{"className":3578},[1983,1984],[1827,3580,3582,3616],{"className":3581},[1988],[1827,3583,3586,3597,3605],{"className":3584,"style":3585},[1992],"height:1.3214em;",[1827,3587,3588,3591],{"style":3287},[1827,3589],{"className":3590,"style":3179},[2000],[1827,3592,3594],{"className":3593},[1870],[1827,3595,3066],{"className":3596},[1870,1945],[1827,3598,3599,3602],{"style":3299},[1827,3600],{"className":3601,"style":3179},[2000],[1827,3603],{"className":3604,"style":3307},[3306],[1827,3606,3607,3610],{"style":3310},[1827,3608],{"className":3609,"style":3179},[2000],[1827,3611,3613],{"className":3612},[1870],[1827,3614,1903],{"className":3615},[1870],[1827,3617,2016],{"className":3618},[2015],[1827,3620,3622],{"className":3621},[1988],[1827,3623,3625],{"className":3624,"style":3329},[1992],[1827,3626],{},[1827,3628],{"className":3629},[2092,3271],[1827,3631,3633,3636],{"className":3632},[1870],[1827,3634,2600],{"className":3635},[1870],[1827,3637,3639],{"className":3638},[1979],[1827,3640,3642],{"className":3641},[1983],[1827,3643,3645],{"className":3644},[1988],[1827,3646,3649],{"className":3647,"style":3648},[1992],"height:0.8641em;",[1827,3650,3651,3654],{"style":2484},[1827,3652],{"className":3653,"style":2001},[2000],[1827,3655,3657],{"className":3656},[2005,2006,2007,2008],[1827,3658,3660,3663],{"className":3659},[1870,2008],[1827,3661,3126],{"className":3662},[1870,2008],[1827,3664,1903],{"className":3665},[1870,2008],[1827,3667,2523],{"className":3668},[1870,1945],[1827,3670,2392],{"className":3671},[1870],[1793,3673,3674,3675,3735,3736,3739,3740,3743],{},"这里 ",[1827,3676,3678,3696],{"className":3677},[1830],[1827,3679,3681],{"className":3680},[1834],[1836,3682,3683],{"xmlns":1838},[1840,3684,3685,3693],{},[1843,3686,3687],{},[1920,3688,3689,3691],{},[1885,3690,1887],{},[1889,3692,3419],{},[1850,3694,3695],{"encoding":1852},"w^*",[1827,3697,3699],{"className":3698,"ariaHidden":1857},[1856],[1827,3700,3702,3706],{"className":3701},[1861],[1827,3703],{"className":3704,"style":3705},[1865],"height:0.6887em;",[1827,3707,3709,3712],{"className":3708},[1870],[1827,3710,1887],{"className":3711,"style":1946},[1870,1945],[1827,3713,3715],{"className":3714},[1979],[1827,3716,3718],{"className":3717},[1983],[1827,3719,3721],{"className":3720},[1988],[1827,3722,3724],{"className":3723,"style":3705},[1992],[1827,3725,3726,3729],{"style":2111},[1827,3727],{"className":3728,"style":2001},[2000],[1827,3730,3732],{"className":3731},[2005,2006,2007,2008],[1827,3733,3419],{"className":3734},[3254,2008]," 是所谓“切点组合”（tangency portfolio）的方向，其具体规模取决于投资者的风险厌恶程度和是否允许杠杆。在后续我们会将这一形式推广到",[1797,3737,3738],{},"多因子风险模型","和",[1797,3741,3742],{},"带约束的组合优化","。",[1819,3745,3747],{"id":3746},"_12-有无风险资产与有效前沿","1.2 有无风险资产与有效前沿",[1793,3749,3750,3751,3824,3825,3894,3895,3084],{},"引入无风险资产（收益率 ",[1827,3752,3754,3773],{"className":3753},[1830],[1827,3755,3757],{"className":3756},[1834],[1836,3758,3759],{"xmlns":1838},[1840,3760,3761,3770],{},[1843,3762,3763],{},[1897,3764,3765,3767],{},[1885,3766,2165],{},[1885,3768,3769],{},"f",[1850,3771,3772],{"encoding":1852},"r_f",[1827,3774,3776],{"className":3775,"ariaHidden":1857},[1856],[1827,3777,3779,3782],{"className":3778},[1861],[1827,3780],{"className":3781,"style":2405},[1865],[1827,3783,3785,3788],{"className":3784},[1870],[1827,3786,2165],{"className":3787,"style":2209},[1870,1945],[1827,3789,3791],{"className":3790},[1979],[1827,3792,3794,3816],{"className":3793},[1983,1984],[1827,3795,3797,3813],{"className":3796},[1988],[1827,3798,3801],{"className":3799,"style":3800},[1992],"height:0.3361em;",[1827,3802,3803,3806],{"style":2248},[1827,3804],{"className":3805,"style":2001},[2000],[1827,3807,3809],{"className":3808},[2005,2006,2007,2008],[1827,3810,3769],{"className":3811,"style":3812},[1870,1945,2008],"margin-right:0.1076em;",[1827,3814,2016],{"className":3815},[2015],[1827,3817,3819],{"className":3818},[1988],[1827,3820,3822],{"className":3821,"style":2445},[1992],[1827,3823],{},"）后，把所有收益换成相对于 ",[1827,3826,3828,3845],{"className":3827},[1830],[1827,3829,3831],{"className":3830},[1834],[1836,3832,3833],{"xmlns":1838},[1840,3834,3835,3843],{},[1843,3836,3837],{},[1897,3838,3839,3841],{},[1885,3840,2165],{},[1885,3842,3769],{},[1850,3844,3772],{"encoding":1852},[1827,3846,3848],{"className":3847,"ariaHidden":1857},[1856],[1827,3849,3851,3854],{"className":3850},[1861],[1827,3852],{"className":3853,"style":2405},[1865],[1827,3855,3857,3860],{"className":3856},[1870],[1827,3858,2165],{"className":3859,"style":2209},[1870,1945],[1827,3861,3863],{"className":3862},[1979],[1827,3864,3866,3886],{"className":3865},[1983,1984],[1827,3867,3869,3883],{"className":3868},[1988],[1827,3870,3872],{"className":3871,"style":3800},[1992],[1827,3873,3874,3877],{"style":2248},[1827,3875],{"className":3876,"style":2001},[2000],[1827,3878,3880],{"className":3879},[2005,2006,2007,2008],[1827,3881,3769],{"className":3882,"style":3812},[1870,1945,2008],[1827,3884,2016],{"className":3885},[2015],[1827,3887,3889],{"className":3888},[1988],[1827,3890,3892],{"className":3891,"style":2445},[1992],[1827,3893],{}," 的",[1797,3896,3897],{},"超额收益",[1827,3899,3901],{"className":3900},[2360],[1827,3902,3904,3945],{"className":3903},[1830],[1827,3905,3907],{"className":3906},[1834],[1836,3908,3909],{"xmlns":1838,"display":2369},[1840,3910,3911,3942],{},[1843,3912,3913,3924,3926,3932,3934,3940],{},[3914,3915,3916,3918,3921],"msubsup",{},[1885,3917,2165],{},[1885,3919,3920],{},"i",[1885,3922,3923],{},"e",[1889,3925,1891],{},[1897,3927,3928,3930],{},[1885,3929,2165],{},[1885,3931,3920],{},[1889,3933,3126],{},[1897,3935,3936,3938],{},[1885,3937,2165],{},[1885,3939,3769],{},[1885,3941,2392],{"mathvariant":1927},[1850,3943,3944],{"encoding":1852}," r_i^{e} = r_i - r_f.",[1827,3946,3948,4021,4078],{"className":3947,"ariaHidden":1857},[1856],[1827,3949,3951,3955,4012,4015,4018],{"className":3950},[1861],[1827,3952],{"className":3953,"style":3954},[1865],"height:0.9614em;vertical-align:-0.247em;",[1827,3956,3958,3961],{"className":3957},[1870],[1827,3959,2165],{"className":3960,"style":2209},[1870,1945],[1827,3962,3964],{"className":3963},[1979],[1827,3965,3967,4003],{"className":3966},[1983,1984],[1827,3968,3970,4000],{"className":3969},[1988],[1827,3971,3974,3986],{"className":3972,"style":3973},[1992],"height:0.7144em;",[1827,3975,3977,3980],{"style":3976},"top:-2.453em;margin-left:-0.0278em;margin-right:0.05em;",[1827,3978],{"className":3979,"style":2001},[2000],[1827,3981,3983],{"className":3982},[2005,2006,2007,2008],[1827,3984,3920],{"className":3985},[1870,1945,2008],[1827,3987,3988,3991],{"style":2484},[1827,3989],{"className":3990,"style":2001},[2000],[1827,3992,3994],{"className":3993},[2005,2006,2007,2008],[1827,3995,3997],{"className":3996},[1870,2008],[1827,3998,3923],{"className":3999},[1870,1945,2008],[1827,4001,2016],{"className":4002},[2015],[1827,4004,4006],{"className":4005},[1988],[1827,4007,4010],{"className":4008,"style":4009},[1992],"height:0.247em;",[1827,4011],{},[1827,4013],{"className":4014,"style":1951},[1950],[1827,4016,1891],{"className":4017},[1955],[1827,4019],{"className":4020,"style":1951},[1950],[1827,4022,4024,4028,4069,4072,4075],{"className":4023},[1861],[1827,4025],{"className":4026,"style":4027},[1865],"height:0.7333em;vertical-align:-0.15em;",[1827,4029,4031,4034],{"className":4030},[1870],[1827,4032,2165],{"className":4033,"style":2209},[1870,1945],[1827,4035,4037],{"className":4036},[1979],[1827,4038,4040,4061],{"className":4039},[1983,1984],[1827,4041,4043,4058],{"className":4042},[1988],[1827,4044,4047],{"className":4045,"style":4046},[1992],"height:0.3117em;",[1827,4048,4049,4052],{"style":2248},[1827,4050],{"className":4051,"style":2001},[2000],[1827,4053,4055],{"className":4054},[2005,2006,2007,2008],[1827,4056,3920],{"className":4057},[1870,1945,2008],[1827,4059,2016],{"className":4060},[2015],[1827,4062,4064],{"className":4063},[1988],[1827,4065,4067],{"className":4066,"style":2023},[1992],[1827,4068],{},[1827,4070],{"className":4071,"style":3250},[1950],[1827,4073,3126],{"className":4074},[3254],[1827,4076],{"className":4077,"style":3250},[1950],[1827,4079,4081,4084,4124],{"className":4080},[1861],[1827,4082],{"className":4083,"style":2405},[1865],[1827,4085,4087,4090],{"className":4086},[1870],[1827,4088,2165],{"className":4089,"style":2209},[1870,1945],[1827,4091,4093],{"className":4092},[1979],[1827,4094,4096,4116],{"className":4095},[1983,1984],[1827,4097,4099,4113],{"className":4098},[1988],[1827,4100,4102],{"className":4101,"style":3800},[1992],[1827,4103,4104,4107],{"style":2248},[1827,4105],{"className":4106,"style":2001},[2000],[1827,4108,4110],{"className":4109},[2005,2006,2007,2008],[1827,4111,3769],{"className":4112,"style":3812},[1870,1945,2008],[1827,4114,2016],{"className":4115},[2015],[1827,4117,4119],{"className":4118},[1988],[1827,4120,4122],{"className":4121,"style":2445},[1992],[1827,4123],{},[1827,4125,2392],{"className":4126},[1870],[1793,4128,4129],{},"此时，若允许借贷并且无风险资产与风险资产之间可以自由组合，则有效组合都可以表示为：",[2504,4131,4132,4135],{},[2507,4133,4134],{},"在风险资产空间中选择一个“市场组合”（切点组合）；",[2507,4136,4137],{},"再与无风险资产按不同比例线性组合。",[1793,4139,4140],{},"这是 CAPM 中“所有投资者都持有相同的市场组合”的核心假设之一，在实证多因子模型中会被放松（允许存在多个“定价因子”）。",[1814,4142,4144],{"id":4143},"_2-多因子风险模型","2. 多因子风险模型",[1819,4146,4148],{"id":4147},"_21-截面资产定价与因子结构","2.1 截面资产定价与因子结构",[1793,4150,4151],{},"我们在前一章已经写出线性因子模型：",[1827,4153,4155],{"className":4154},[2360],[1827,4156,4158,4241],{"className":4157},[1830],[1827,4159,4161],{"className":4160},[1834],[1836,4162,4163],{"xmlns":1838,"display":2369},[1840,4164,4165,4238],{},[1843,4166,4167,4185,4187,4194,4196,4205,4217,4219,4236],{},[1897,4168,4169,4171],{},[1885,4170,2165],{},[1843,4172,4173,4175,4177,4180,4183],{},[1885,4174,3920],{},[1889,4176,1906],{"separator":1857},[1885,4178,4179],{},"t",[1889,4181,4182],{},"+",[1846,4184,1903],{},[1889,4186,1891],{},[1897,4188,4189,4192],{},[1885,4190,4191],{},"α",[1885,4193,3920],{},[1889,4195,4182],{},[3914,4197,4198,4201,4203],{},[1885,4199,4200],{},"β",[1885,4202,3920],{},[1885,4204,1928],{"mathvariant":1927},[1897,4206,4207,4209],{},[1885,4208,3769],{},[1843,4210,4211,4213,4215],{},[1885,4212,4179],{},[1889,4214,4182],{},[1846,4216,1903],{},[1889,4218,4182],{},[1897,4220,4221,4224],{},[1885,4222,4223],{},"ϵ",[1843,4225,4226,4228,4230,4232,4234],{},[1885,4227,3920],{},[1889,4229,1906],{"separator":1857},[1885,4231,4179],{},[1889,4233,4182],{},[1846,4235,1903],{},[1889,4237,1906],{"separator":1857},[1850,4239,4240],{"encoding":1852}," r_{i,t+1} = \\alpha_i + \\beta_i^\\top f_{t+1} + \\epsilon_{i,t+1},",[1827,4242,4244,4314,4371,4491],{"className":4243,"ariaHidden":1857},[1856],[1827,4245,4247,4250,4305,4308,4311],{"className":4246},[1861],[1827,4248],{"className":4249,"style":2405},[1865],[1827,4251,4253,4256],{"className":4252},[1870],[1827,4254,2165],{"className":4255,"style":2209},[1870,1945],[1827,4257,4259],{"className":4258},[1979],[1827,4260,4262,4297],{"className":4261},[1983,1984],[1827,4263,4265,4294],{"className":4264},[1988],[1827,4266,4268],{"className":4267,"style":4046},[1992],[1827,4269,4270,4273],{"style":2248},[1827,4271],{"className":4272,"style":2001},[2000],[1827,4274,4276],{"className":4275},[2005,2006,2007,2008],[1827,4277,4279,4282,4285,4288,4291],{"className":4278},[1870,2008],[1827,4280,3920],{"className":4281},[1870,1945,2008],[1827,4283,1906],{"className":4284},[2029,2008],[1827,4286,4179],{"className":4287},[1870,1945,2008],[1827,4289,4182],{"className":4290},[3254,2008],[1827,4292,1903],{"className":4293},[1870,2008],[1827,4295,2016],{"className":4296},[2015],[1827,4298,4300],{"className":4299},[1988],[1827,4301,4303],{"className":4302,"style":2445},[1992],[1827,4304],{},[1827,4306],{"className":4307,"style":1951},[1950],[1827,4309,1891],{"className":4310},[1955],[1827,4312],{"className":4313,"style":1951},[1950],[1827,4315,4317,4320,4362,4365,4368],{"className":4316},[1861],[1827,4318],{"className":4319,"style":4027},[1865],[1827,4321,4323,4327],{"className":4322},[1870],[1827,4324,4191],{"className":4325,"style":4326},[1870,1945],"margin-right:0.0037em;",[1827,4328,4330],{"className":4329},[1979],[1827,4331,4333,4354],{"className":4332},[1983,1984],[1827,4334,4336,4351],{"className":4335},[1988],[1827,4337,4339],{"className":4338,"style":4046},[1992],[1827,4340,4342,4345],{"style":4341},"top:-2.55em;margin-left:-0.0037em;margin-right:0.05em;",[1827,4343],{"className":4344,"style":2001},[2000],[1827,4346,4348],{"className":4347},[2005,2006,2007,2008],[1827,4349,3920],{"className":4350},[1870,1945,2008],[1827,4352,2016],{"className":4353},[2015],[1827,4355,4357],{"className":4356},[1988],[1827,4358,4360],{"className":4359,"style":2023},[1992],[1827,4361],{},[1827,4363],{"className":4364,"style":3250},[1950],[1827,4366,4182],{"className":4367},[3254],[1827,4369],{"className":4370,"style":3250},[1950],[1827,4372,4374,4378,4431,4482,4485,4488],{"className":4373},[1861],[1827,4375],{"className":4376,"style":4377},[1865],"height:1.1461em;vertical-align:-0.247em;",[1827,4379,4381,4385],{"className":4380},[1870],[1827,4382,4200],{"className":4383,"style":4384},[1870,1945],"margin-right:0.0528em;",[1827,4386,4388],{"className":4387},[1979],[1827,4389,4391,4423],{"className":4390},[1983,1984],[1827,4392,4394,4420],{"className":4393},[1988],[1827,4395,4397,4409],{"className":4396,"style":2463},[1992],[1827,4398,4400,4403],{"style":4399},"top:-2.453em;margin-left:-0.0528em;margin-right:0.05em;",[1827,4401],{"className":4402,"style":2001},[2000],[1827,4404,4406],{"className":4405},[2005,2006,2007,2008],[1827,4407,3920],{"className":4408},[1870,1945,2008],[1827,4410,4411,4414],{"style":2484},[1827,4412],{"className":4413,"style":2001},[2000],[1827,4415,4417],{"className":4416},[2005,2006,2007,2008],[1827,4418,1928],{"className":4419},[1870,2008],[1827,4421,2016],{"className":4422},[2015],[1827,4424,4426],{"className":4425},[1988],[1827,4427,4429],{"className":4428,"style":4009},[1992],[1827,4430],{},[1827,4432,4434,4437],{"className":4433},[1870],[1827,4435,3769],{"className":4436,"style":3812},[1870,1945],[1827,4438,4440],{"className":4439},[1979],[1827,4441,4443,4473],{"className":4442},[1983,1984],[1827,4444,4446,4470],{"className":4445},[1988],[1827,4447,4449],{"className":4448,"style":1993},[1992],[1827,4450,4452,4455],{"style":4451},"top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;",[1827,4453],{"className":4454,"style":2001},[2000],[1827,4456,4458],{"className":4457},[2005,2006,2007,2008],[1827,4459,4461,4464,4467],{"className":4460},[1870,2008],[1827,4462,4179],{"className":4463},[1870,1945,2008],[1827,4465,4182],{"className":4466},[3254,2008],[1827,4468,1903],{"className":4469},[1870,2008],[1827,4471,2016],{"className":4472},[2015],[1827,4474,4476],{"className":4475},[1988],[1827,4477,4480],{"className":4478,"style":4479},[1992],"height:0.2083em;",[1827,4481],{},[1827,4483],{"className":4484,"style":3250},[1950],[1827,4486,4182],{"className":4487},[3254],[1827,4489],{"className":4490,"style":3250},[1950],[1827,4492,4494,4497,4553],{"className":4493},[1861],[1827,4495],{"className":4496,"style":2405},[1865],[1827,4498,4500,4503],{"className":4499},[1870],[1827,4501,4223],{"className":4502},[1870,1945],[1827,4504,4506],{"className":4505},[1979],[1827,4507,4509,4545],{"className":4508},[1983,1984],[1827,4510,4512,4542],{"className":4511},[1988],[1827,4513,4515],{"className":4514,"style":4046},[1992],[1827,4516,4518,4521],{"style":4517},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[1827,4519],{"className":4520,"style":2001},[2000],[1827,4522,4524],{"className":4523},[2005,2006,2007,2008],[1827,4525,4527,4530,4533,4536,4539],{"className":4526},[1870,2008],[1827,4528,3920],{"className":4529},[1870,1945,2008],[1827,4531,1906],{"className":4532},[2029,2008],[1827,4534,4179],{"className":4535},[1870,1945,2008],[1827,4537,4182],{"className":4538},[3254,2008],[1827,4540,1903],{"className":4541},[1870,2008],[1827,4543,2016],{"className":4544},[2015],[1827,4546,4548],{"className":4547},[1988],[1827,4549,4551],{"className":4550,"style":2445},[1992],[1827,4552],{},[1827,4554,1906],{"className":4555},[2029],[1793,4557,4558,4559,4645,4646,4676,4677,4749,4750,4779,4780,4783],{},"其中 ",[1827,4560,4562,4586],{"className":4561},[1830],[1827,4563,4565],{"className":4564},[1834],[1836,4566,4567],{"xmlns":1838},[1840,4568,4569,4583],{},[1843,4570,4571],{},[1897,4572,4573,4575],{},[1885,4574,3769],{},[1843,4576,4577,4579,4581],{},[1885,4578,4179],{},[1889,4580,4182],{},[1846,4582,1903],{},[1850,4584,4585],{"encoding":1852},"f_{t+1}",[1827,4587,4589],{"className":4588,"ariaHidden":1857},[1856],[1827,4590,4592,4596],{"className":4591},[1861],[1827,4593],{"className":4594,"style":4595},[1865],"height:0.9028em;vertical-align:-0.2083em;",[1827,4597,4599,4602],{"className":4598},[1870],[1827,4600,3769],{"className":4601,"style":3812},[1870,1945],[1827,4603,4605],{"className":4604},[1979],[1827,4606,4608,4637],{"className":4607},[1983,1984],[1827,4609,4611,4634],{"className":4610},[1988],[1827,4612,4614],{"className":4613,"style":1993},[1992],[1827,4615,4616,4619],{"style":4451},[1827,4617],{"className":4618,"style":2001},[2000],[1827,4620,4622],{"className":4621},[2005,2006,2007,2008],[1827,4623,4625,4628,4631],{"className":4624},[1870,2008],[1827,4626,4179],{"className":4627},[1870,1945,2008],[1827,4629,4182],{"className":4630},[3254,2008],[1827,4632,1903],{"className":4633},[1870,2008],[1827,4635,2016],{"className":4636},[2015],[1827,4638,4640],{"className":4639},[1988],[1827,4641,4643],{"className":4642,"style":4479},[1992],[1827,4644],{}," 为 ",[1827,4647,4649,4663],{"className":4648},[1830],[1827,4650,4652],{"className":4651},[1834],[1836,4653,4654],{"xmlns":1838},[1840,4655,4656,4661],{},[1843,4657,4658],{},[1885,4659,4660],{},"K",[1850,4662,4660],{"encoding":1852},[1827,4664,4666],{"className":4665,"ariaHidden":1857},[1856],[1827,4667,4669,4672],{"className":4668},[1861],[1827,4670],{"className":4671,"style":2627},[1865],[1827,4673,4660],{"className":4674,"style":4675},[1870,1945],"margin-right:0.0715em;"," 维因子收益，",[1827,4678,4680,4698],{"className":4679},[1830],[1827,4681,4683],{"className":4682},[1834],[1836,4684,4685],{"xmlns":1838},[1840,4686,4687,4695],{},[1843,4688,4689],{},[1897,4690,4691,4693],{},[1885,4692,4200],{},[1885,4694,3920],{},[1850,4696,4697],{"encoding":1852},"\\beta_i",[1827,4699,4701],{"className":4700,"ariaHidden":1857},[1856],[1827,4702,4704,4708],{"className":4703},[1861],[1827,4705],{"className":4706,"style":4707},[1865],"height:0.8889em;vertical-align:-0.1944em;",[1827,4709,4711,4714],{"className":4710},[1870],[1827,4712,4200],{"className":4713,"style":4384},[1870,1945],[1827,4715,4717],{"className":4716},[1979],[1827,4718,4720,4741],{"className":4719},[1983,1984],[1827,4721,4723,4738],{"className":4722},[1988],[1827,4724,4726],{"className":4725,"style":4046},[1992],[1827,4727,4729,4732],{"style":4728},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[1827,4730],{"className":4731,"style":2001},[2000],[1827,4733,4735],{"className":4734},[2005,2006,2007,2008],[1827,4736,3920],{"className":4737},[1870,1945,2008],[1827,4739,2016],{"className":4740},[2015],[1827,4742,4744],{"className":4743},[1988],[1827,4745,4747],{"className":4746,"style":2023},[1992],[1827,4748],{}," 为资产 ",[1827,4751,4753,4766],{"className":4752},[1830],[1827,4754,4756],{"className":4755},[1834],[1836,4757,4758],{"xmlns":1838},[1840,4759,4760,4764],{},[1843,4761,4762],{},[1885,4763,3920],{},[1850,4765,3920],{"encoding":1852},[1827,4767,4769],{"className":4768,"ariaHidden":1857},[1856],[1827,4770,4772,4776],{"className":4771},[1861],[1827,4773],{"className":4774,"style":4775},[1865],"height:0.6595em;",[1827,4777,3920],{"className":4778},[1870,1945]," 的因子暴露。若我们关注的是",[1797,4781,4782],{},"协方差结构","而非预期收益，可以将其写成：",[1827,4785,4787],{"className":4786},[2360],[1827,4788,4790,4905],{"className":4789},[1830],[1827,4791,4793],{"className":4792},[1834],[1836,4794,4795],{"xmlns":1838,"display":2369},[1840,4796,4797,4902],{},[1843,4798,4799,4815,4817,4825,4837,4839,4855,4857,4860,4862,4864,4880,4883,4895,4897,4899],{},[1897,4800,4801,4803],{},[1885,4802,2165],{},[1843,4804,4805,4807,4809,4811,4813],{},[1885,4806,3920],{},[1889,4808,1906],{"separator":1857},[1885,4810,4179],{},[1889,4812,4182],{},[1846,4814,1903],{},[1889,4816,1891],{},[3914,4818,4819,4821,4823],{},[1885,4820,4200],{},[1885,4822,3920],{},[1885,4824,1928],{"mathvariant":1927},[1897,4826,4827,4829],{},[1885,4828,3769],{},[1843,4830,4831,4833,4835],{},[1885,4832,4179],{},[1889,4834,4182],{},[1846,4836,1903],{},[1889,4838,4182],{},[1897,4840,4841,4843],{},[1885,4842,4223],{},[1843,4844,4845,4847,4849,4851,4853],{},[1885,4846,3920],{},[1889,4848,1906],{"separator":1857},[1885,4850,4179],{},[1889,4852,4182],{},[1846,4854,1903],{},[1889,4856,1906],{"separator":1857},[1950,4858],{"width":4859},"1em",[1885,4861,2529],{"mathvariant":2528},[1889,4863,2532],{"stretchy":1894},[1897,4865,4866,4868],{},[1885,4867,4223],{},[1843,4869,4870,4872,4874,4876,4878],{},[1885,4871,3920],{},[1889,4873,1906],{"separator":1857},[1885,4875,4179],{},[1889,4877,4182],{},[1846,4879,1903],{},[1885,4881,4882],{"mathvariant":1927},"∣",[1897,4884,4885,4887],{},[1885,4886,3769],{},[1843,4888,4889,4891,4893],{},[1885,4890,4179],{},[1889,4892,4182],{},[1846,4894,1903],{},[1889,4896,2537],{"stretchy":1894},[1889,4898,1891],{},[1846,4900,4901],{},"0.",[1850,4903,4904],{"encoding":1852}," r_{i,t+1} = \\beta_i^\\top f_{t+1} + \\epsilon_{i,t+1}, \\quad \\mathbb{E}[\\epsilon_{i,t+1} | f_{t+1}] = 0.",[1827,4906,4908,4978,5093,5289],{"className":4907,"ariaHidden":1857},[1856],[1827,4909,4911,4914,4969,4972,4975],{"className":4910},[1861],[1827,4912],{"className":4913,"style":2405},[1865],[1827,4915,4917,4920],{"className":4916},[1870],[1827,4918,2165],{"className":4919,"style":2209},[1870,1945],[1827,4921,4923],{"className":4922},[1979],[1827,4924,4926,4961],{"className":4925},[1983,1984],[1827,4927,4929,4958],{"className":4928},[1988],[1827,4930,4932],{"className":4931,"style":4046},[1992],[1827,4933,4934,4937],{"style":2248},[1827,4935],{"className":4936,"style":2001},[2000],[1827,4938,4940],{"className":4939},[2005,2006,2007,2008],[1827,4941,4943,4946,4949,4952,4955],{"className":4942},[1870,2008],[1827,4944,3920],{"className":4945},[1870,1945,2008],[1827,4947,1906],{"className":4948},[2029,2008],[1827,4950,4179],{"className":4951},[1870,1945,2008],[1827,4953,4182],{"className":4954},[3254,2008],[1827,4956,1903],{"className":4957},[1870,2008],[1827,4959,2016],{"className":4960},[2015],[1827,4962,4964],{"className":4963},[1988],[1827,4965,4967],{"className":4966,"style":2445},[1992],[1827,4968],{},[1827,4970],{"className":4971,"style":1951},[1950],[1827,4973,1891],{"className":4974},[1955],[1827,4976],{"className":4977,"style":1951},[1950],[1827,4979,4981,4984,5035,5084,5087,5090],{"className":4980},[1861],[1827,4982],{"className":4983,"style":4377},[1865],[1827,4985,4987,4990],{"className":4986},[1870],[1827,4988,4200],{"className":4989,"style":4384},[1870,1945],[1827,4991,4993],{"className":4992},[1979],[1827,4994,4996,5027],{"className":4995},[1983,1984],[1827,4997,4999,5024],{"className":4998},[1988],[1827,5000,5002,5013],{"className":5001,"style":2463},[1992],[1827,5003,5004,5007],{"style":4399},[1827,5005],{"className":5006,"style":2001},[2000],[1827,5008,5010],{"className":5009},[2005,2006,2007,2008],[1827,5011,3920],{"className":5012},[1870,1945,2008],[1827,5014,5015,5018],{"style":2484},[1827,5016],{"className":5017,"style":2001},[2000],[1827,5019,5021],{"className":5020},[2005,2006,2007,2008],[1827,5022,1928],{"className":5023},[1870,2008],[1827,5025,2016],{"className":5026},[2015],[1827,5028,5030],{"className":5029},[1988],[1827,5031,5033],{"className":5032,"style":4009},[1992],[1827,5034],{},[1827,5036,5038,5041],{"className":5037},[1870],[1827,5039,3769],{"className":5040,"style":3812},[1870,1945],[1827,5042,5044],{"className":5043},[1979],[1827,5045,5047,5076],{"className":5046},[1983,1984],[1827,5048,5050,5073],{"className":5049},[1988],[1827,5051,5053],{"className":5052,"style":1993},[1992],[1827,5054,5055,5058],{"style":4451},[1827,5056],{"className":5057,"style":2001},[2000],[1827,5059,5061],{"className":5060},[2005,2006,2007,2008],[1827,5062,5064,5067,5070],{"className":5063},[1870,2008],[1827,5065,4179],{"className":5066},[1870,1945,2008],[1827,5068,4182],{"className":5069},[3254,2008],[1827,5071,1903],{"className":5072},[1870,2008],[1827,5074,2016],{"className":5075},[2015],[1827,5077,5079],{"className":5078},[1988],[1827,5080,5082],{"className":5081,"style":4479},[1992],[1827,5083],{},[1827,5085],{"className":5086,"style":3250},[1950],[1827,5088,4182],{"className":5089},[3254],[1827,5091],{"className":5092,"style":3250},[1950],[1827,5094,5096,5099,5154,5157,5161,5164,5167,5170,5225,5228,5277,5280,5283,5286],{"className":5095},[1861],[1827,5097],{"className":5098,"style":2785},[1865],[1827,5100,5102,5105],{"className":5101},[1870],[1827,5103,4223],{"className":5104},[1870,1945],[1827,5106,5108],{"className":5107},[1979],[1827,5109,5111,5146],{"className":5110},[1983,1984],[1827,5112,5114,5143],{"className":5113},[1988],[1827,5115,5117],{"className":5116,"style":4046},[1992],[1827,5118,5119,5122],{"style":4517},[1827,5120],{"className":5121,"style":2001},[2000],[1827,5123,5125],{"className":5124},[2005,2006,2007,2008],[1827,5126,5128,5131,5134,5137,5140],{"className":5127},[1870,2008],[1827,5129,3920],{"className":5130},[1870,1945,2008],[1827,5132,1906],{"className":5133},[2029,2008],[1827,5135,4179],{"className":5136},[1870,1945,2008],[1827,5138,4182],{"className":5139},[3254,2008],[1827,5141,1903],{"className":5142},[1870,2008],[1827,5144,2016],{"className":5145},[2015],[1827,5147,5149],{"className":5148},[1988],[1827,5150,5152],{"className":5151,"style":2445},[1992],[1827,5153],{},[1827,5155,1906],{"className":5156},[2029],[1827,5158],{"className":5159,"style":5160},[1950],"margin-right:1em;",[1827,5162],{"className":5163,"style":2033},[1950],[1827,5165,2529],{"className":5166},[1870,2573],[1827,5168,2532],{"className":5169},[1969],[1827,5171,5173,5176],{"className":5172},[1870],[1827,5174,4223],{"className":5175},[1870,1945],[1827,5177,5179],{"className":5178},[1979],[1827,5180,5182,5217],{"className":5181},[1983,1984],[1827,5183,5185,5214],{"className":5184},[1988],[1827,5186,5188],{"className":5187,"style":4046},[1992],[1827,5189,5190,5193],{"style":4517},[1827,5191],{"className":5192,"style":2001},[2000],[1827,5194,5196],{"className":5195},[2005,2006,2007,2008],[1827,5197,5199,5202,5205,5208,5211],{"className":5198},[1870,2008],[1827,5200,3920],{"className":5201},[1870,1945,2008],[1827,5203,1906],{"className":5204},[2029,2008],[1827,5206,4179],{"className":5207},[1870,1945,2008],[1827,5209,4182],{"className":5210},[3254,2008],[1827,5212,1903],{"className":5213},[1870,2008],[1827,5215,2016],{"className":5216},[2015],[1827,5218,5220],{"className":5219},[1988],[1827,5221,5223],{"className":5222,"style":2445},[1992],[1827,5224],{},[1827,5226,4882],{"className":5227},[1870],[1827,5229,5231,5234],{"className":5230},[1870],[1827,5232,3769],{"className":5233,"style":3812},[1870,1945],[1827,5235,5237],{"className":5236},[1979],[1827,5238,5240,5269],{"className":5239},[1983,1984],[1827,5241,5243,5266],{"className":5242},[1988],[1827,5244,5246],{"className":5245,"style":1993},[1992],[1827,5247,5248,5251],{"style":4451},[1827,5249],{"className":5250,"style":2001},[2000],[1827,5252,5254],{"className":5253},[2005,2006,2007,2008],[1827,5255,5257,5260,5263],{"className":5256},[1870,2008],[1827,5258,4179],{"className":5259},[1870,1945,2008],[1827,5261,4182],{"className":5262},[3254,2008],[1827,5264,1903],{"className":5265},[1870,2008],[1827,5267,2016],{"className":5268},[2015],[1827,5270,5272],{"className":5271},[1988],[1827,5273,5275],{"className":5274,"style":4479},[1992],[1827,5276],{},[1827,5278,2537],{"className":5279},[2092],[1827,5281],{"className":5282,"style":1951},[1950],[1827,5284,1891],{"className":5285},[1955],[1827,5287],{"className":5288,"style":1951},[1950],[1827,5290,5292,5295],{"className":5291},[1861],[1827,5293],{"className":5294,"style":1866},[1865],[1827,5296,4901],{"className":5297},[1870],[1793,5299,5300],{},"对所有资产叠加，用矩阵形式写作：",[1827,5302,5304],{"className":5303},[2360],[1827,5305,5307,5364],{"className":5306},[1830],[1827,5308,5310],{"className":5309},[1834],[1836,5311,5312],{"xmlns":1838,"display":2369},[1840,5313,5314,5361],{},[1843,5315,5316,5328,5330,5333,5345,5347,5359],{},[1897,5317,5318,5320],{},[1885,5319,2165],{},[1843,5321,5322,5324,5326],{},[1885,5323,4179],{},[1889,5325,4182],{},[1846,5327,1903],{},[1889,5329,1891],{},[1885,5331,5332],{},"B",[1897,5334,5335,5337],{},[1885,5336,3769],{},[1843,5338,5339,5341,5343],{},[1885,5340,4179],{},[1889,5342,4182],{},[1846,5344,1903],{},[1889,5346,4182],{},[1897,5348,5349,5351],{},[1885,5350,4223],{},[1843,5352,5353,5355,5357],{},[1885,5354,4179],{},[1889,5356,4182],{},[1846,5358,1903],{},[1889,5360,1906],{"separator":1857},[1850,5362,5363],{"encoding":1852}," r_{t+1} = B f_{t+1} + \\epsilon_{t+1},",[1827,5365,5367,5432,5500],{"className":5366,"ariaHidden":1857},[1856],[1827,5368,5370,5374,5423,5426,5429],{"className":5369},[1861],[1827,5371],{"className":5372,"style":5373},[1865],"height:0.6389em;vertical-align:-0.2083em;",[1827,5375,5377,5380],{"className":5376},[1870],[1827,5378,2165],{"className":5379,"style":2209},[1870,1945],[1827,5381,5383],{"className":5382},[1979],[1827,5384,5386,5415],{"className":5385},[1983,1984],[1827,5387,5389,5412],{"className":5388},[1988],[1827,5390,5392],{"className":5391,"style":1993},[1992],[1827,5393,5394,5397],{"style":2248},[1827,5395],{"className":5396,"style":2001},[2000],[1827,5398,5400],{"className":5399},[2005,2006,2007,2008],[1827,5401,5403,5406,5409],{"className":5402},[1870,2008],[1827,5404,4179],{"className":5405},[1870,1945,2008],[1827,5407,4182],{"className":5408},[3254,2008],[1827,5410,1903],{"className":5411},[1870,2008],[1827,5413,2016],{"className":5414},[2015],[1827,5416,5418],{"className":5417},[1988],[1827,5419,5421],{"className":5420,"style":4479},[1992],[1827,5422],{},[1827,5424],{"className":5425,"style":1951},[1950],[1827,5427,1891],{"className":5428},[1955],[1827,5430],{"className":5431,"style":1951},[1950],[1827,5433,5435,5438,5442,5491,5494,5497],{"className":5434},[1861],[1827,5436],{"className":5437,"style":4595},[1865],[1827,5439,5332],{"className":5440,"style":5441},[1870,1945],"margin-right:0.0502em;",[1827,5443,5445,5448],{"className":5444},[1870],[1827,5446,3769],{"className":5447,"style":3812},[1870,1945],[1827,5449,5451],{"className":5450},[1979],[1827,5452,5454,5483],{"className":5453},[1983,1984],[1827,5455,5457,5480],{"className":5456},[1988],[1827,5458,5460],{"className":5459,"style":1993},[1992],[1827,5461,5462,5465],{"style":4451},[1827,5463],{"className":5464,"style":2001},[2000],[1827,5466,5468],{"className":5467},[2005,2006,2007,2008],[1827,5469,5471,5474,5477],{"className":5470},[1870,2008],[1827,5472,4179],{"className":5473},[1870,1945,2008],[1827,5475,4182],{"className":5476},[3254,2008],[1827,5478,1903],{"className":5479},[1870,2008],[1827,5481,2016],{"className":5482},[2015],[1827,5484,5486],{"className":5485},[1988],[1827,5487,5489],{"className":5488,"style":4479},[1992],[1827,5490],{},[1827,5492],{"className":5493,"style":3250},[1950],[1827,5495,4182],{"className":5496},[3254],[1827,5498],{"className":5499,"style":3250},[1950],[1827,5501,5503,5506,5555],{"className":5502},[1861],[1827,5504],{"className":5505,"style":5373},[1865],[1827,5507,5509,5512],{"className":5508},[1870],[1827,5510,4223],{"className":5511},[1870,1945],[1827,5513,5515],{"className":5514},[1979],[1827,5516,5518,5547],{"className":5517},[1983,1984],[1827,5519,5521,5544],{"className":5520},[1988],[1827,5522,5524],{"className":5523,"style":1993},[1992],[1827,5525,5526,5529],{"style":4517},[1827,5527],{"className":5528,"style":2001},[2000],[1827,5530,5532],{"className":5531},[2005,2006,2007,2008],[1827,5533,5535,5538,5541],{"className":5534},[1870,2008],[1827,5536,4179],{"className":5537},[1870,1945,2008],[1827,5539,4182],{"className":5540},[3254,2008],[1827,5542,1903],{"className":5543},[1870,2008],[1827,5545,2016],{"className":5546},[2015],[1827,5548,5550],{"className":5549},[1988],[1827,5551,5553],{"className":5552,"style":4479},[1992],[1827,5554],{},[1827,5556,1906],{"className":5557},[2029],[1793,5559,5560],{},"其中：",[2504,5562,5563,5647],{},[2507,5564,5565,4645,5593,5646],{},[1827,5566,5568,5581],{"className":5567},[1830],[1827,5569,5571],{"className":5570},[1834],[1836,5572,5573],{"xmlns":1838},[1840,5574,5575,5579],{},[1843,5576,5577],{},[1885,5578,5332],{},[1850,5580,5332],{"encoding":1852},[1827,5582,5584],{"className":5583,"ariaHidden":1857},[1856],[1827,5585,5587,5590],{"className":5586},[1861],[1827,5588],{"className":5589,"style":2627},[1865],[1827,5591,5332],{"className":5592,"style":5441},[1870,1945],[1827,5594,5596,5615],{"className":5595},[1830],[1827,5597,5599],{"className":5598},[1834],[1836,5600,5601],{"xmlns":1838},[1840,5602,5603,5612],{},[1843,5604,5605,5607,5610],{},[1885,5606,1918],{},[1889,5608,5609],{},"×",[1885,5611,4660],{},[1850,5613,5614],{"encoding":1852},"N \\times K",[1827,5616,5618,5637],{"className":5617,"ariaHidden":1857},[1856],[1827,5619,5621,5625,5628,5631,5634],{"className":5620},[1861],[1827,5622],{"className":5623,"style":5624},[1865],"height:0.7667em;vertical-align:-0.0833em;",[1827,5626,1918],{"className":5627,"style":2077},[1870,1945],[1827,5629],{"className":5630,"style":3250},[1950],[1827,5632,5609],{"className":5633},[3254],[1827,5635],{"className":5636,"style":3250},[1950],[1827,5638,5640,5643],{"className":5639},[1861],[1827,5641],{"className":5642,"style":2627},[1865],[1827,5644,4660],{"className":5645,"style":4675},[1870,1945]," 的因子暴露矩阵；",[2507,5648,5649,5734,5735,5863],{},[1827,5650,5652,5676],{"className":5651},[1830],[1827,5653,5655],{"className":5654},[1834],[1836,5656,5657],{"xmlns":1838},[1840,5658,5659,5673],{},[1843,5660,5661],{},[1897,5662,5663,5665],{},[1885,5664,4223],{},[1843,5666,5667,5669,5671],{},[1885,5668,4179],{},[1889,5670,4182],{},[1846,5672,1903],{},[1850,5674,5675],{"encoding":1852},"\\epsilon_{t+1}",[1827,5677,5679],{"className":5678,"ariaHidden":1857},[1856],[1827,5680,5682,5685],{"className":5681},[1861],[1827,5683],{"className":5684,"style":5373},[1865],[1827,5686,5688,5691],{"className":5687},[1870],[1827,5689,4223],{"className":5690},[1870,1945],[1827,5692,5694],{"className":5693},[1979],[1827,5695,5697,5726],{"className":5696},[1983,1984],[1827,5698,5700,5723],{"className":5699},[1988],[1827,5701,5703],{"className":5702,"style":1993},[1992],[1827,5704,5705,5708],{"style":4517},[1827,5706],{"className":5707,"style":2001},[2000],[1827,5709,5711],{"className":5710},[2005,2006,2007,2008],[1827,5712,5714,5717,5720],{"className":5713},[1870,2008],[1827,5715,4179],{"className":5716},[1870,1945,2008],[1827,5718,4182],{"className":5719},[3254,2008],[1827,5721,1903],{"className":5722},[1870,2008],[1827,5724,2016],{"className":5725},[2015],[1827,5727,5729],{"className":5728},[1988],[1827,5730,5732],{"className":5731,"style":4479},[1992],[1827,5733],{}," 为特异收益向量（常假设 ",[1827,5736,5738,5775],{"className":5737},[1830],[1827,5739,5741],{"className":5740},[1834],[1836,5742,5743],{"xmlns":1838},[1840,5744,5745,5772],{},[1843,5746,5747,5749,5751,5753,5765,5767,5769],{},[1885,5748,2605],{"mathvariant":1927},[1889,5750,2608],{},[1889,5752,1895],{"stretchy":1894},[1897,5754,5755,5757],{},[1885,5756,4223],{},[1843,5758,5759,5761,5763],{},[1885,5760,4179],{},[1889,5762,4182],{},[1846,5764,1903],{},[1889,5766,1924],{"stretchy":1894},[1889,5768,1891],{},[1885,5770,5771],{"mathvariant":1927},"Δ",[1850,5773,5774],{"encoding":1852},"\\operatorname{Cov}(\\epsilon_{t+1}) = \\Delta",[1827,5776,5778,5854],{"className":5777,"ariaHidden":1857},[1856],[1827,5779,5781,5784,5790,5793,5842,5845,5848,5851],{"className":5780},[1861],[1827,5782],{"className":5783,"style":2569},[1865],[1827,5785,5787],{"className":5786},[2649],[1827,5788,2605],{"className":5789,"style":2654},[1870,2653],[1827,5791,1895],{"className":5792},[1969],[1827,5794,5796,5799],{"className":5795},[1870],[1827,5797,4223],{"className":5798},[1870,1945],[1827,5800,5802],{"className":5801},[1979],[1827,5803,5805,5834],{"className":5804},[1983,1984],[1827,5806,5808,5831],{"className":5807},[1988],[1827,5809,5811],{"className":5810,"style":1993},[1992],[1827,5812,5813,5816],{"style":4517},[1827,5814],{"className":5815,"style":2001},[2000],[1827,5817,5819],{"className":5818},[2005,2006,2007,2008],[1827,5820,5822,5825,5828],{"className":5821},[1870,2008],[1827,5823,4179],{"className":5824},[1870,1945,2008],[1827,5826,4182],{"className":5827},[3254,2008],[1827,5829,1903],{"className":5830},[1870,2008],[1827,5832,2016],{"className":5833},[2015],[1827,5835,5837],{"className":5836},[1988],[1827,5838,5840],{"className":5839,"style":4479},[1992],[1827,5841],{},[1827,5843,1924],{"className":5844},[2092],[1827,5846],{"className":5847,"style":1951},[1950],[1827,5849,1891],{"className":5850},[1955],[1827,5852],{"className":5853,"style":1951},[1950],[1827,5855,5857,5860],{"className":5856},[1861],[1827,5858],{"className":5859,"style":2627},[1865],[1827,5861,5771],{"className":5862},[1870]," 为对角矩阵）。",[1793,5865,5866],{},"则组合收益协方差矩阵可以写成：",[1827,5868,5870],{"className":5869},[2360],[1827,5871,5873,5928],{"className":5872},[1830],[1827,5874,5876],{"className":5875},[1834],[1836,5877,5878],{"xmlns":1838,"display":2369},[1840,5879,5880,5925],{},[1843,5881,5882,5884,5886,5888,5890,5892,5904,5906,5908,5910,5913,5919,5921,5923],{},[1885,5883,2600],{"mathvariant":1927},[1889,5885,1891],{},[1885,5887,2605],{"mathvariant":1927},[1889,5889,2608],{},[1889,5891,1895],{"stretchy":1894},[1897,5893,5894,5896],{},[1885,5895,2165],{},[1843,5897,5898,5900,5902],{},[1885,5899,4179],{},[1889,5901,4182],{},[1846,5903,1903],{},[1889,5905,1924],{"stretchy":1894},[1889,5907,1891],{},[1885,5909,5332],{},[1885,5911,5912],{},"F",[1920,5914,5915,5917],{},[1885,5916,5332],{},[1885,5918,1928],{"mathvariant":1927},[1889,5920,4182],{},[1885,5922,5771],{"mathvariant":1927},[1889,5924,1906],{"separator":1857},[1850,5926,5927],{"encoding":1852}," \\Sigma = \\operatorname{Cov}(r_{t+1}) = B F B^\\top + \\Delta,",[1827,5929,5931,5949,6025,6077],{"className":5930,"ariaHidden":1857},[1856],[1827,5932,5934,5937,5940,5943,5946],{"className":5933},[1861],[1827,5935],{"className":5936,"style":2627},[1865],[1827,5938,2600],{"className":5939},[1870],[1827,5941],{"className":5942,"style":1951},[1950],[1827,5944,1891],{"className":5945},[1955],[1827,5947],{"className":5948,"style":1951},[1950],[1827,5950,5952,5955,5961,5964,6013,6016,6019,6022],{"className":5951},[1861],[1827,5953],{"className":5954,"style":2569},[1865],[1827,5956,5958],{"className":5957},[2649],[1827,5959,2605],{"className":5960,"style":2654},[1870,2653],[1827,5962,1895],{"className":5963},[1969],[1827,5965,5967,5970],{"className":5966},[1870],[1827,5968,2165],{"className":5969,"style":2209},[1870,1945],[1827,5971,5973],{"className":5972},[1979],[1827,5974,5976,6005],{"className":5975},[1983,1984],[1827,5977,5979,6002],{"className":5978},[1988],[1827,5980,5982],{"className":5981,"style":1993},[1992],[1827,5983,5984,5987],{"style":2248},[1827,5985],{"className":5986,"style":2001},[2000],[1827,5988,5990],{"className":5989},[2005,2006,2007,2008],[1827,5991,5993,5996,5999],{"className":5992},[1870,2008],[1827,5994,4179],{"className":5995},[1870,1945,2008],[1827,5997,4182],{"className":5998},[3254,2008],[1827,6000,1903],{"className":6001},[1870,2008],[1827,6003,2016],{"className":6004},[2015],[1827,6006,6008],{"className":6007},[1988],[1827,6009,6011],{"className":6010,"style":4479},[1992],[1827,6012],{},[1827,6014,1924],{"className":6015},[2092],[1827,6017],{"className":6018,"style":1951},[1950],[1827,6020,1891],{"className":6021},[1955],[1827,6023],{"className":6024,"style":1951},[1950],[1827,6026,6028,6032,6035,6039,6068,6071,6074],{"className":6027},[1861],[1827,6029],{"className":6030,"style":6031},[1865],"height:0.9824em;vertical-align:-0.0833em;",[1827,6033,5332],{"className":6034,"style":5441},[1870,1945],[1827,6036,5912],{"className":6037,"style":6038},[1870,1945],"margin-right:0.1389em;",[1827,6040,6042,6045],{"className":6041},[1870],[1827,6043,5332],{"className":6044,"style":5441},[1870,1945],[1827,6046,6048],{"className":6047},[1979],[1827,6049,6051],{"className":6050},[1983],[1827,6052,6054],{"className":6053},[1988],[1827,6055,6057],{"className":6056,"style":2463},[1992],[1827,6058,6059,6062],{"style":2484},[1827,6060],{"className":6061,"style":2001},[2000],[1827,6063,6065],{"className":6064},[2005,2006,2007,2008],[1827,6066,1928],{"className":6067},[1870,2008],[1827,6069],{"className":6070,"style":3250},[1950],[1827,6072,4182],{"className":6073},[3254],[1827,6075],{"className":6076,"style":3250},[1950],[1827,6078,6080,6084,6087],{"className":6079},[1861],[1827,6081],{"className":6082,"style":6083},[1865],"height:0.8778em;vertical-align:-0.1944em;",[1827,6085,5771],{"className":6086},[1870],[1827,6088,1906],{"className":6089},[2029],[1793,6091,4558,6092,6219,6220,6222],{},[1827,6093,6095,6131],{"className":6094},[1830],[1827,6096,6098],{"className":6097},[1834],[1836,6099,6100],{"xmlns":1838},[1840,6101,6102,6128],{},[1843,6103,6104,6106,6108,6110,6112,6114,6126],{},[1885,6105,5912],{},[1889,6107,1891],{},[1885,6109,2605],{"mathvariant":1927},[1889,6111,2608],{},[1889,6113,1895],{"stretchy":1894},[1897,6115,6116,6118],{},[1885,6117,3769],{},[1843,6119,6120,6122,6124],{},[1885,6121,4179],{},[1889,6123,4182],{},[1846,6125,1903],{},[1889,6127,1924],{"stretchy":1894},[1850,6129,6130],{"encoding":1852},"F = \\operatorname{Cov}(f_{t+1})",[1827,6132,6134,6152],{"className":6133,"ariaHidden":1857},[1856],[1827,6135,6137,6140,6143,6146,6149],{"className":6136},[1861],[1827,6138],{"className":6139,"style":2627},[1865],[1827,6141,5912],{"className":6142,"style":6038},[1870,1945],[1827,6144],{"className":6145,"style":1951},[1950],[1827,6147,1891],{"className":6148},[1955],[1827,6150],{"className":6151,"style":1951},[1950],[1827,6153,6155,6158,6164,6167,6216],{"className":6154},[1861],[1827,6156],{"className":6157,"style":2569},[1865],[1827,6159,6161],{"className":6160},[2649],[1827,6162,2605],{"className":6163,"style":2654},[1870,2653],[1827,6165,1895],{"className":6166},[1969],[1827,6168,6170,6173],{"className":6169},[1870],[1827,6171,3769],{"className":6172,"style":3812},[1870,1945],[1827,6174,6176],{"className":6175},[1979],[1827,6177,6179,6208],{"className":6178},[1983,1984],[1827,6180,6182,6205],{"className":6181},[1988],[1827,6183,6185],{"className":6184,"style":1993},[1992],[1827,6186,6187,6190],{"style":4451},[1827,6188],{"className":6189,"style":2001},[2000],[1827,6191,6193],{"className":6192},[2005,2006,2007,2008],[1827,6194,6196,6199,6202],{"className":6195},[1870,2008],[1827,6197,4179],{"className":6198},[1870,1945,2008],[1827,6200,4182],{"className":6201},[3254,2008],[1827,6203,1903],{"className":6204},[1870,2008],[1827,6206,2016],{"className":6207},[2015],[1827,6209,6211],{"className":6210},[1988],[1827,6212,6214],{"className":6213,"style":4479},[1992],[1827,6215],{},[1827,6217,1924],{"className":6218},[2092]," 是因子协方差矩阵。上述结构即为",[1797,6221,3738],{},"（Barra 风格模型的原型）。",[1793,6224,6225,6226,6279,6280,6331,6332,1808,6360,6388],{},"这一表示的好处是：当 ",[1827,6227,6229,6248],{"className":6228},[1830],[1827,6230,6232],{"className":6231},[1834],[1836,6233,6234],{"xmlns":1838},[1840,6235,6236,6245],{},[1843,6237,6238,6240,6243],{},[1885,6239,4660],{},[1889,6241,6242],{},"≪",[1885,6244,1918],{},[1850,6246,6247],{"encoding":1852},"K \\ll N",[1827,6249,6251,6270],{"className":6250,"ariaHidden":1857},[1856],[1827,6252,6254,6258,6261,6264,6267],{"className":6253},[1861],[1827,6255],{"className":6256,"style":6257},[1865],"height:0.7224em;vertical-align:-0.0391em;",[1827,6259,4660],{"className":6260,"style":4675},[1870,1945],[1827,6262],{"className":6263,"style":1951},[1950],[1827,6265,6242],{"className":6266},[1955],[1827,6268],{"className":6269,"style":1951},[1950],[1827,6271,6273,6276],{"className":6272},[1861],[1827,6274],{"className":6275,"style":2627},[1865],[1827,6277,1918],{"className":6278,"style":2077},[1870,1945]," 时，我们不用直接估计一个 ",[1827,6281,6283,6301],{"className":6282},[1830],[1827,6284,6286],{"className":6285},[1834],[1836,6287,6288],{"xmlns":1838},[1840,6289,6290,6298],{},[1843,6291,6292,6294,6296],{},[1885,6293,1918],{},[1889,6295,5609],{},[1885,6297,1918],{},[1850,6299,6300],{"encoding":1852},"N\\times N",[1827,6302,6304,6322],{"className":6303,"ariaHidden":1857},[1856],[1827,6305,6307,6310,6313,6316,6319],{"className":6306},[1861],[1827,6308],{"className":6309,"style":5624},[1865],[1827,6311,1918],{"className":6312,"style":2077},[1870,1945],[1827,6314],{"className":6315,"style":3250},[1950],[1827,6317,5609],{"className":6318},[3254],[1827,6320],{"className":6321,"style":3250},[1950],[1827,6323,6325,6328],{"className":6324},[1861],[1827,6326],{"className":6327,"style":2627},[1865],[1827,6329,1918],{"className":6330,"style":2077},[1870,1945]," 的协方差矩阵，而是在较低维度的因子空间中估计 ",[1827,6333,6335,6348],{"className":6334},[1830],[1827,6336,6338],{"className":6337},[1834],[1836,6339,6340],{"xmlns":1838},[1840,6341,6342,6346],{},[1843,6343,6344],{},[1885,6345,5912],{},[1850,6347,5912],{"encoding":1852},[1827,6349,6351],{"className":6350,"ariaHidden":1857},[1856],[1827,6352,6354,6357],{"className":6353},[1861],[1827,6355],{"className":6356,"style":2627},[1865],[1827,6358,5912],{"className":6359,"style":6038},[1870,1945],[1827,6361,6363,6376],{"className":6362},[1830],[1827,6364,6366],{"className":6365},[1834],[1836,6367,6368],{"xmlns":1838},[1840,6369,6370,6374],{},[1843,6371,6372],{},[1885,6373,5332],{},[1850,6375,5332],{"encoding":1852},[1827,6377,6379],{"className":6378,"ariaHidden":1857},[1856],[1827,6380,6382,6385],{"className":6381},[1861],[1827,6383],{"className":6384,"style":2627},[1865],[1827,6386,5332],{"className":6387,"style":5441},[1870,1945],"，提高稳健性和可解释性（参见 Ross, 1976; Connor & Korajczyk, 1988）。",[1819,6390,6392],{"id":6391},"_22-因子风险贡献","2.2 因子风险贡献",[1793,6394,6395],{},"在多因子模型下，组合方差可以写为：",[1827,6397,6399],{"className":6398},[2360],[1827,6400,6402,6470],{"className":6401},[1830],[1827,6403,6405],{"className":6404},[1834],[1836,6406,6407],{"xmlns":1838,"display":2369},[1840,6408,6409,6467],{},[1843,6410,6411,6413,6415,6417,6423,6425,6427,6433,6435,6437,6439,6445,6447,6449,6451,6457,6459,6461,6463,6465],{},[1885,6412,2898],{"mathvariant":1927},[1889,6414,2608],{},[1889,6416,1895],{"stretchy":1894},[1897,6418,6419,6421],{},[1885,6420,2165],{},[1885,6422,1793],{},[1889,6424,1924],{"stretchy":1894},[1889,6426,1891],{},[1920,6428,6429,6431],{},[1885,6430,1887],{},[1885,6432,1928],{"mathvariant":1927},[1885,6434,2600],{"mathvariant":1927},[1885,6436,1887],{},[1889,6438,1891],{},[1920,6440,6441,6443],{},[1885,6442,1887],{},[1885,6444,1928],{"mathvariant":1927},[1889,6446,1895],{"stretchy":1894},[1885,6448,5332],{},[1885,6450,5912],{},[1920,6452,6453,6455],{},[1885,6454,5332],{},[1885,6456,1928],{"mathvariant":1927},[1889,6458,4182],{},[1885,6460,5771],{"mathvariant":1927},[1889,6462,1924],{"stretchy":1894},[1885,6464,1887],{},[1885,6466,2392],{"mathvariant":1927},[1850,6468,6469],{"encoding":1852}," \\operatorname{Var}(r_p) = w^\\top \\Sigma w = w^\\top (B F B^\\top + \\Delta) w.",[1827,6471,6473,6540,6590,6673],{"className":6472,"ariaHidden":1857},[1856],[1827,6474,6476,6479,6485,6488,6528,6531,6534,6537],{"className":6475},[1861],[1827,6477],{"className":6478,"style":2785},[1865],[1827,6480,6482],{"className":6481},[2649],[1827,6483,2898],{"className":6484},[1870,2653],[1827,6486,1895],{"className":6487},[1969],[1827,6489,6491,6494],{"className":6490},[1870],[1827,6492,2165],{"className":6493,"style":2209},[1870,1945],[1827,6495,6497],{"className":6496},[1979],[1827,6498,6500,6520],{"className":6499},[1983,1984],[1827,6501,6503,6517],{"className":6502},[1988],[1827,6504,6506],{"className":6505,"style":2424},[1992],[1827,6507,6508,6511],{"style":2248},[1827,6509],{"className":6510,"style":2001},[2000],[1827,6512,6514],{"className":6513},[2005,2006,2007,2008],[1827,6515,1793],{"className":6516},[1870,1945,2008],[1827,6518,2016],{"className":6519},[2015],[1827,6521,6523],{"className":6522},[1988],[1827,6524,6526],{"className":6525,"style":2445},[1992],[1827,6527],{},[1827,6529,1924],{"className":6530},[2092],[1827,6532],{"className":6533,"style":1951},[1950],[1827,6535,1891],{"className":6536},[1955],[1827,6538],{"className":6539,"style":1951},[1950],[1827,6541,6543,6546,6575,6578,6581,6584,6587],{"className":6542},[1861],[1827,6544],{"className":6545,"style":2463},[1865],[1827,6547,6549,6552],{"className":6548},[1870],[1827,6550,1887],{"className":6551,"style":1946},[1870,1945],[1827,6553,6555],{"className":6554},[1979],[1827,6556,6558],{"className":6557},[1983],[1827,6559,6561],{"className":6560},[1988],[1827,6562,6564],{"className":6563,"style":2463},[1992],[1827,6565,6566,6569],{"style":2484},[1827,6567],{"className":6568,"style":2001},[2000],[1827,6570,6572],{"className":6571},[2005,2006,2007,2008],[1827,6573,1928],{"className":6574},[1870,2008],[1827,6576,2600],{"className":6577},[1870],[1827,6579,1887],{"className":6580,"style":1946},[1870,1945],[1827,6582],{"className":6583,"style":1951},[1950],[1827,6585,1891],{"className":6586},[1955],[1827,6588],{"className":6589,"style":1951},[1950],[1827,6591,6593,6597,6626,6629,6632,6635,6664,6667,6670],{"className":6592},[1861],[1827,6594],{"className":6595,"style":6596},[1865],"height:1.1491em;vertical-align:-0.25em;",[1827,6598,6600,6603],{"className":6599},[1870],[1827,6601,1887],{"className":6602,"style":1946},[1870,1945],[1827,6604,6606],{"className":6605},[1979],[1827,6607,6609],{"className":6608},[1983],[1827,6610,6612],{"className":6611},[1988],[1827,6613,6615],{"className":6614,"style":2463},[1992],[1827,6616,6617,6620],{"style":2484},[1827,6618],{"className":6619,"style":2001},[2000],[1827,6621,6623],{"className":6622},[2005,2006,2007,2008],[1827,6624,1928],{"className":6625},[1870,2008],[1827,6627,1895],{"className":6628},[1969],[1827,6630,5332],{"className":6631,"style":5441},[1870,1945],[1827,6633,5912],{"className":6634,"style":6038},[1870,1945],[1827,6636,6638,6641],{"className":6637},[1870],[1827,6639,5332],{"className":6640,"style":5441},[1870,1945],[1827,6642,6644],{"className":6643},[1979],[1827,6645,6647],{"className":6646},[1983],[1827,6648,6650],{"className":6649},[1988],[1827,6651,6653],{"className":6652,"style":2463},[1992],[1827,6654,6655,6658],{"style":2484},[1827,6656],{"className":6657,"style":2001},[2000],[1827,6659,6661],{"className":6660},[2005,2006,2007,2008],[1827,6662,1928],{"className":6663},[1870,2008],[1827,6665],{"className":6666,"style":3250},[1950],[1827,6668,4182],{"className":6669},[3254],[1827,6671],{"className":6672,"style":3250},[1950],[1827,6674,6676,6679,6682,6685,6688],{"className":6675},[1861],[1827,6677],{"className":6678,"style":2569},[1865],[1827,6680,5771],{"className":6681},[1870],[1827,6683,1924],{"className":6684},[2092],[1827,6686,1887],{"className":6687,"style":1946},[1870,1945],[1827,6689,2392],{"className":6690},[1870],[1793,6692,6693],{},"记组合的因子暴露向量为：",[1827,6695,6697],{"className":6696},[2360],[1827,6698,6700,6736],{"className":6699},[1830],[1827,6701,6703],{"className":6702},[1834],[1836,6704,6705],{"xmlns":1838,"display":2369},[1840,6706,6707,6733],{},[1843,6708,6709,6716,6718,6724,6726,6728,6730],{},[1897,6710,6711,6714],{},[1885,6712,6713],{},"b",[1885,6715,1793],{},[1889,6717,1891],{},[1920,6719,6720,6722],{},[1885,6721,5332],{},[1885,6723,1928],{"mathvariant":1927},[1885,6725,1887],{},[1889,6727,1906],{"separator":1857},[1950,6729],{"width":4859},[3113,6731,6732],{},"(K 维)",[1850,6734,6735],{"encoding":1852}," b_p = B^\\top w, \\quad \\text{(K 维)}",[1827,6737,6739,6795],{"className":6738,"ariaHidden":1857},[1856],[1827,6740,6742,6746,6786,6789,6792],{"className":6741},[1861],[1827,6743],{"className":6744,"style":6745},[1865],"height:0.9805em;vertical-align:-0.2861em;",[1827,6747,6749,6752],{"className":6748},[1870],[1827,6750,6713],{"className":6751},[1870,1945],[1827,6753,6755],{"className":6754},[1979],[1827,6756,6758,6778],{"className":6757},[1983,1984],[1827,6759,6761,6775],{"className":6760},[1988],[1827,6762,6764],{"className":6763,"style":2424},[1992],[1827,6765,6766,6769],{"style":4517},[1827,6767],{"className":6768,"style":2001},[2000],[1827,6770,6772],{"className":6771},[2005,2006,2007,2008],[1827,6773,1793],{"className":6774},[1870,1945,2008],[1827,6776,2016],{"className":6777},[2015],[1827,6779,6781],{"className":6780},[1988],[1827,6782,6784],{"className":6783,"style":2445},[1992],[1827,6785],{},[1827,6787],{"className":6788,"style":1951},[1950],[1827,6790,1891],{"className":6791},[1955],[1827,6793],{"className":6794,"style":1951},[1950],[1827,6796,6798,6801,6830,6833,6836,6839,6842],{"className":6797},[1861],[1827,6799],{"className":6800,"style":6596},[1865],[1827,6802,6804,6807],{"className":6803},[1870],[1827,6805,5332],{"className":6806,"style":5441},[1870,1945],[1827,6808,6810],{"className":6809},[1979],[1827,6811,6813],{"className":6812},[1983],[1827,6814,6816],{"className":6815},[1988],[1827,6817,6819],{"className":6818,"style":2463},[1992],[1827,6820,6821,6824],{"style":2484},[1827,6822],{"className":6823,"style":2001},[2000],[1827,6825,6827],{"className":6826},[2005,2006,2007,2008],[1827,6828,1928],{"className":6829},[1870,2008],[1827,6831,1887],{"className":6832,"style":1946},[1870,1945],[1827,6834,1906],{"className":6835},[2029],[1827,6837],{"className":6838,"style":5160},[1950],[1827,6840],{"className":6841,"style":2033},[1950],[1827,6843,6846,6850,6855],{"className":6844},[1870,6845],"text",[1827,6847,6849],{"className":6848},[1870],"(K ",[1827,6851,6854],{"className":6852},[1870,6853],"cjk_fallback","维",[1827,6856,1924],{"className":6857},[1870],[1793,6859,6860],{},"则因子部分的方差贡献为：",[1827,6862,6864],{"className":6863},[2360],[1827,6865,6867,6909],{"className":6866},[1830],[1827,6868,6870],{"className":6869},[1834],[1836,6871,6872],{"xmlns":1838,"display":2369},[1840,6873,6874,6906],{},[1843,6875,6876,6886,6888,6896,6898,6904],{},[3914,6877,6878,6881,6884],{},[1885,6879,6880],{},"σ",[3113,6882,6883],{},"factor",[1846,6885,3134],{},[1889,6887,1891],{},[3914,6889,6890,6892,6894],{},[1885,6891,6713],{},[1885,6893,1793],{},[1885,6895,1928],{"mathvariant":1927},[1885,6897,5912],{},[1897,6899,6900,6902],{},[1885,6901,6713],{},[1885,6903,1793],{},[1885,6905,2392],{"mathvariant":1927},[1850,6907,6908],{"encoding":1852}," \\sigma_{\\text{factor}}^2 = b_p^\\top F b_p.",[1827,6910,6912,6987],{"className":6911,"ariaHidden":1857},[1856],[1827,6913,6915,6919,6978,6981,6984],{"className":6914},[1861],[1827,6916],{"className":6917,"style":6918},[1865],"height:1.1111em;vertical-align:-0.247em;",[1827,6920,6922,6926],{"className":6921},[1870],[1827,6923,6880],{"className":6924,"style":6925},[1870,1945],"margin-right:0.0359em;",[1827,6927,6929],{"className":6928},[1979],[1827,6930,6932,6970],{"className":6931},[1983,1984],[1827,6933,6935,6967],{"className":6934},[1988],[1827,6936,6938,6956],{"className":6937,"style":3648},[1992],[1827,6939,6941,6944],{"style":6940},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1827,6942],{"className":6943,"style":2001},[2000],[1827,6945,6947],{"className":6946},[2005,2006,2007,2008],[1827,6948,6950],{"className":6949},[1870,2008],[1827,6951,6953],{"className":6952},[1870,6845,2008],[1827,6954,6883],{"className":6955},[1870,2008],[1827,6957,6958,6961],{"style":2484},[1827,6959],{"className":6960,"style":2001},[2000],[1827,6962,6964],{"className":6963},[2005,2006,2007,2008],[1827,6965,3134],{"className":6966},[1870,2008],[1827,6968,2016],{"className":6969},[2015],[1827,6971,6973],{"className":6972},[1988],[1827,6974,6976],{"className":6975,"style":4009},[1992],[1827,6977],{},[1827,6979],{"className":6980,"style":1951},[1950],[1827,6982,1891],{"className":6983},[1955],[1827,6985],{"className":6986,"style":1951},[1950],[1827,6988,6990,6994,7047,7050,7090],{"className":6989},[1861],[1827,6991],{"className":6992,"style":6993},[1865],"height:1.2822em;vertical-align:-0.3831em;",[1827,6995,6997,7000],{"className":6996},[1870],[1827,6998,6713],{"className":6999},[1870,1945],[1827,7001,7003],{"className":7002},[1979],[1827,7004,7006,7038],{"className":7005},[1983,1984],[1827,7007,7009,7035],{"className":7008},[1988],[1827,7010,7012,7024],{"className":7011,"style":2463},[1992],[1827,7013,7015,7018],{"style":7014},"top:-2.453em;margin-left:0em;margin-right:0.05em;",[1827,7016],{"className":7017,"style":2001},[2000],[1827,7019,7021],{"className":7020},[2005,2006,2007,2008],[1827,7022,1793],{"className":7023},[1870,1945,2008],[1827,7025,7026,7029],{"style":2484},[1827,7027],{"className":7028,"style":2001},[2000],[1827,7030,7032],{"className":7031},[2005,2006,2007,2008],[1827,7033,1928],{"className":7034},[1870,2008],[1827,7036,2016],{"className":7037},[2015],[1827,7039,7041],{"className":7040},[1988],[1827,7042,7045],{"className":7043,"style":7044},[1992],"height:0.3831em;",[1827,7046],{},[1827,7048,5912],{"className":7049,"style":6038},[1870,1945],[1827,7051,7053,7056],{"className":7052},[1870],[1827,7054,6713],{"className":7055},[1870,1945],[1827,7057,7059],{"className":7058},[1979],[1827,7060,7062,7082],{"className":7061},[1983,1984],[1827,7063,7065,7079],{"className":7064},[1988],[1827,7066,7068],{"className":7067,"style":2424},[1992],[1827,7069,7070,7073],{"style":4517},[1827,7071],{"className":7072,"style":2001},[2000],[1827,7074,7076],{"className":7075},[2005,2006,2007,2008],[1827,7077,1793],{"className":7078},[1870,1945,2008],[1827,7080,2016],{"className":7081},[2015],[1827,7083,7085],{"className":7084},[1988],[1827,7086,7088],{"className":7087,"style":2445},[1992],[1827,7089],{},[1827,7091,2392],{"className":7092},[1870],[1793,7094,7095],{},"特异风险贡献为：",[1827,7097,7099],{"className":7098},[2360],[1827,7100,7102,7137],{"className":7101},[1830],[1827,7103,7105],{"className":7104},[1834],[1836,7106,7107],{"xmlns":1838,"display":2369},[1840,7108,7109,7134],{},[1843,7110,7111,7120,7122,7128,7130,7132],{},[3914,7112,7113,7115,7118],{},[1885,7114,6880],{},[3113,7116,7117],{},"specific",[1846,7119,3134],{},[1889,7121,1891],{},[1920,7123,7124,7126],{},[1885,7125,1887],{},[1885,7127,1928],{"mathvariant":1927},[1885,7129,5771],{"mathvariant":1927},[1885,7131,1887],{},[1885,7133,2392],{"mathvariant":1927},[1850,7135,7136],{"encoding":1852}," \\sigma_{\\text{specific}}^2 = w^\\top \\Delta w.",[1827,7138,7140,7213],{"className":7139,"ariaHidden":1857},[1856],[1827,7141,7143,7147,7204,7207,7210],{"className":7142},[1861],[1827,7144],{"className":7145,"style":7146},[1865],"height:1.2472em;vertical-align:-0.3831em;",[1827,7148,7150,7153],{"className":7149},[1870],[1827,7151,6880],{"className":7152,"style":6925},[1870,1945],[1827,7154,7156],{"className":7155},[1979],[1827,7157,7159,7196],{"className":7158},[1983,1984],[1827,7160,7162,7193],{"className":7161},[1988],[1827,7163,7165,7182],{"className":7164,"style":3648},[1992],[1827,7166,7167,7170],{"style":6940},[1827,7168],{"className":7169,"style":2001},[2000],[1827,7171,7173],{"className":7172},[2005,2006,2007,2008],[1827,7174,7176],{"className":7175},[1870,2008],[1827,7177,7179],{"className":7178},[1870,6845,2008],[1827,7180,7117],{"className":7181},[1870,2008],[1827,7183,7184,7187],{"style":2484},[1827,7185],{"className":7186,"style":2001},[2000],[1827,7188,7190],{"className":7189},[2005,2006,2007,2008],[1827,7191,3134],{"className":7192},[1870,2008],[1827,7194,2016],{"className":7195},[2015],[1827,7197,7199],{"className":7198},[1988],[1827,7200,7202],{"className":7201,"style":7044},[1992],[1827,7203],{},[1827,7205],{"className":7206,"style":1951},[1950],[1827,7208,1891],{"className":7209},[1955],[1827,7211],{"className":7212,"style":1951},[1950],[1827,7214,7216,7219,7248,7251,7254],{"className":7215},[1861],[1827,7217],{"className":7218,"style":2463},[1865],[1827,7220,7222,7225],{"className":7221},[1870],[1827,7223,1887],{"className":7224,"style":1946},[1870,1945],[1827,7226,7228],{"className":7227},[1979],[1827,7229,7231],{"className":7230},[1983],[1827,7232,7234],{"className":7233},[1988],[1827,7235,7237],{"className":7236,"style":2463},[1992],[1827,7238,7239,7242],{"style":2484},[1827,7240],{"className":7241,"style":2001},[2000],[1827,7243,7245],{"className":7244},[2005,2006,2007,2008],[1827,7246,1928],{"className":7247},[1870,2008],[1827,7249,5771],{"className":7250},[1870],[1827,7252,1887],{"className":7253,"style":1946},[1870,1945],[1827,7255,2392],{"className":7256},[1870],[1793,7258,7259],{},"总风险可拆解为两部分之和：",[1827,7261,7263],{"className":7262},[2360],[1827,7264,7266,7308],{"className":7265},[1830],[1827,7267,7269],{"className":7268},[1834],[1836,7270,7271],{"xmlns":1838,"display":2369},[1840,7272,7273,7305],{},[1843,7274,7275,7283,7285,7293,7295,7303],{},[3914,7276,7277,7279,7281],{},[1885,7278,6880],{},[1885,7280,1793],{},[1846,7282,3134],{},[1889,7284,1891],{},[3914,7286,7287,7289,7291],{},[1885,7288,6880],{},[3113,7290,6883],{},[1846,7292,3134],{},[1889,7294,4182],{},[3914,7296,7297,7299,7301],{},[1885,7298,6880],{},[3113,7300,7117],{},[1846,7302,3134],{},[1885,7304,2392],{"mathvariant":1927},[1850,7306,7307],{"encoding":1852}," \\sigma_p^2 = \\sigma_{\\text{factor}}^2 + \\sigma_{\\text{specific}}^2.",[1827,7309,7311,7377,7449],{"className":7310,"ariaHidden":1857},[1856],[1827,7312,7314,7317,7368,7371,7374],{"className":7313},[1861],[1827,7315],{"className":7316,"style":7146},[1865],[1827,7318,7320,7323],{"className":7319},[1870],[1827,7321,6880],{"className":7322,"style":6925},[1870,1945],[1827,7324,7326],{"className":7325},[1979],[1827,7327,7329,7360],{"className":7328},[1983,1984],[1827,7330,7332,7357],{"className":7331},[1988],[1827,7333,7335,7346],{"className":7334,"style":3648},[1992],[1827,7336,7337,7340],{"style":6940},[1827,7338],{"className":7339,"style":2001},[2000],[1827,7341,7343],{"className":7342},[2005,2006,2007,2008],[1827,7344,1793],{"className":7345},[1870,1945,2008],[1827,7347,7348,7351],{"style":2484},[1827,7349],{"className":7350,"style":2001},[2000],[1827,7352,7354],{"className":7353},[2005,2006,2007,2008],[1827,7355,3134],{"className":7356},[1870,2008],[1827,7358,2016],{"className":7359},[2015],[1827,7361,7363],{"className":7362},[1988],[1827,7364,7366],{"className":7365,"style":7044},[1992],[1827,7367],{},[1827,7369],{"className":7370,"style":1951},[1950],[1827,7372,1891],{"className":7373},[1955],[1827,7375],{"className":7376,"style":1951},[1950],[1827,7378,7380,7383,7440,7443,7446],{"className":7379},[1861],[1827,7381],{"className":7382,"style":6918},[1865],[1827,7384,7386,7389],{"className":7385},[1870],[1827,7387,6880],{"className":7388,"style":6925},[1870,1945],[1827,7390,7392],{"className":7391},[1979],[1827,7393,7395,7432],{"className":7394},[1983,1984],[1827,7396,7398,7429],{"className":7397},[1988],[1827,7399,7401,7418],{"className":7400,"style":3648},[1992],[1827,7402,7403,7406],{"style":6940},[1827,7404],{"className":7405,"style":2001},[2000],[1827,7407,7409],{"className":7408},[2005,2006,2007,2008],[1827,7410,7412],{"className":7411},[1870,2008],[1827,7413,7415],{"className":7414},[1870,6845,2008],[1827,7416,6883],{"className":7417},[1870,2008],[1827,7419,7420,7423],{"style":2484},[1827,7421],{"className":7422,"style":2001},[2000],[1827,7424,7426],{"className":7425},[2005,2006,2007,2008],[1827,7427,3134],{"className":7428},[1870,2008],[1827,7430,2016],{"className":7431},[2015],[1827,7433,7435],{"className":7434},[1988],[1827,7436,7438],{"className":7437,"style":4009},[1992],[1827,7439],{},[1827,7441],{"className":7442,"style":3250},[1950],[1827,7444,4182],{"className":7445},[3254],[1827,7447],{"className":7448,"style":3250},[1950],[1827,7450,7452,7455,7512],{"className":7451},[1861],[1827,7453],{"className":7454,"style":7146},[1865],[1827,7456,7458,7461],{"className":7457},[1870],[1827,7459,6880],{"className":7460,"style":6925},[1870,1945],[1827,7462,7464],{"className":7463},[1979],[1827,7465,7467,7504],{"className":7466},[1983,1984],[1827,7468,7470,7501],{"className":7469},[1988],[1827,7471,7473,7490],{"className":7472,"style":3648},[1992],[1827,7474,7475,7478],{"style":6940},[1827,7476],{"className":7477,"style":2001},[2000],[1827,7479,7481],{"className":7480},[2005,2006,2007,2008],[1827,7482,7484],{"className":7483},[1870,2008],[1827,7485,7487],{"className":7486},[1870,6845,2008],[1827,7488,7117],{"className":7489},[1870,2008],[1827,7491,7492,7495],{"style":2484},[1827,7493],{"className":7494,"style":2001},[2000],[1827,7496,7498],{"className":7497},[2005,2006,2007,2008],[1827,7499,3134],{"className":7500},[1870,2008],[1827,7502,2016],{"className":7503},[2015],[1827,7505,7507],{"className":7506},[1988],[1827,7508,7510],{"className":7509,"style":7044},[1992],[1827,7511],{},[1827,7513,2392],{"className":7514},[1870],[1793,7516,7517],{},"在实务中，这种拆分用于回答诸如：“组合总风险里有多少来自风格因子（价值、动量、规模）、多少来自个股特异风险”等问题。",[1819,7519,7521],{"id":7520},"_23-边际风险贡献与风险预算","2.3 边际风险贡献与风险预算",[1793,7523,7524,7525,7528,7529,7575,7576,7604],{},"风险分解的一个重要工具是",[1797,7526,7527],{},"边际风险贡献（Marginal Contribution to Risk, MCR）","。对于任意可微风险度量 ",[1827,7530,7532,7553],{"className":7531},[1830],[1827,7533,7535],{"className":7534},[1834],[1836,7536,7537],{"xmlns":1838},[1840,7538,7539,7550],{},[1843,7540,7541,7544,7546,7548],{},[1885,7542,7543],{},"R",[1889,7545,1895],{"stretchy":1894},[1885,7547,1887],{},[1889,7549,1924],{"stretchy":1894},[1850,7551,7552],{"encoding":1852},"R(w)",[1827,7554,7556],{"className":7555,"ariaHidden":1857},[1856],[1827,7557,7559,7562,7566,7569,7572],{"className":7558},[1861],[1827,7560],{"className":7561,"style":2569},[1865],[1827,7563,7543],{"className":7564,"style":7565},[1870,1945],"margin-right:0.0077em;",[1827,7567,1895],{"className":7568},[1969],[1827,7570,1887],{"className":7571,"style":1946},[1870,1945],[1827,7573,1924],{"className":7574},[2092],"，资产 ",[1827,7577,7579,7592],{"className":7578},[1830],[1827,7580,7582],{"className":7581},[1834],[1836,7583,7584],{"xmlns":1838},[1840,7585,7586,7590],{},[1843,7587,7588],{},[1885,7589,3920],{},[1850,7591,3920],{"encoding":1852},[1827,7593,7595],{"className":7594,"ariaHidden":1857},[1856],[1827,7596,7598,7601],{"className":7597},[1861],[1827,7599],{"className":7600,"style":4775},[1865],[1827,7602,3920],{"className":7603},[1870,1945]," 的边际风险贡献定义为：",[1827,7606,7608],{"className":7607},[2360],[1827,7609,7611,7659],{"className":7610},[1830],[1827,7612,7614],{"className":7613},[1834],[1836,7615,7616],{"xmlns":1838,"display":2369},[1840,7617,7618,7656],{},[1843,7619,7620,7627,7629,7654],{},[1897,7621,7622,7625],{},[3113,7623,7624],{},"MCR",[1885,7626,3920],{},[1889,7628,1891],{},[3128,7630,7631,7644],{},[1843,7632,7633,7636,7638,7640,7642],{},[1885,7634,7635],{"mathvariant":1927},"∂",[1885,7637,7543],{},[1889,7639,1895],{"stretchy":1894},[1885,7641,1887],{},[1889,7643,1924],{"stretchy":1894},[1843,7645,7646,7648],{},[1885,7647,7635],{"mathvariant":1927},[1897,7649,7650,7652],{},[1885,7651,1887],{},[1885,7653,3920],{},[1885,7655,2392],{"mathvariant":1927},[1850,7657,7658],{"encoding":1852}," \\text{MCR}_i = \\frac{\\partial R(w)}{\\partial w_i}.",[1827,7660,7662,7722],{"className":7661,"ariaHidden":1857},[1856],[1827,7663,7665,7669,7713,7716,7719],{"className":7664},[1861],[1827,7666],{"className":7667,"style":7668},[1865],"height:0.8333em;vertical-align:-0.15em;",[1827,7670,7672,7678],{"className":7671},[1870],[1827,7673,7675],{"className":7674},[1870,6845],[1827,7676,7624],{"className":7677},[1870],[1827,7679,7681],{"className":7680},[1979],[1827,7682,7684,7705],{"className":7683},[1983,1984],[1827,7685,7687,7702],{"className":7686},[1988],[1827,7688,7690],{"className":7689,"style":4046},[1992],[1827,7691,7693,7696],{"style":7692},"top:-2.55em;margin-right:0.05em;",[1827,7694],{"className":7695,"style":2001},[2000],[1827,7697,7699],{"className":7698},[2005,2006,2007,2008],[1827,7700,3920],{"className":7701},[1870,1945,2008],[1827,7703,2016],{"className":7704},[2015],[1827,7706,7708],{"className":7707},[1988],[1827,7709,7711],{"className":7710,"style":2023},[1992],[1827,7712],{},[1827,7714],{"className":7715,"style":1951},[1950],[1827,7717,1891],{"className":7718},[1955],[1827,7720],{"className":7721,"style":1951},[1950],[1827,7723,7725,7729,7846],{"className":7724},[1861],[1827,7726],{"className":7727,"style":7728},[1865],"height:2.263em;vertical-align:-0.836em;",[1827,7730,7732,7735,7843],{"className":7731},[1870],[1827,7733],{"className":7734},[1969,3271],[1827,7736,7738],{"className":7737},[3128],[1827,7739,7741,7834],{"className":7740},[1983,1984],[1827,7742,7744,7831],{"className":7743},[1988],[1827,7745,7748,7800,7808],{"className":7746,"style":7747},[1992],"height:1.427em;",[1827,7749,7750,7753],{"style":3287},[1827,7751],{"className":7752,"style":3179},[2000],[1827,7754,7756,7760],{"className":7755},[1870],[1827,7757,7635],{"className":7758,"style":7759},[1870],"margin-right:0.0556em;",[1827,7761,7763,7766],{"className":7762},[1870],[1827,7764,1887],{"className":7765,"style":1946},[1870,1945],[1827,7767,7769],{"className":7768},[1979],[1827,7770,7772,7792],{"className":7771},[1983,1984],[1827,7773,7775,7789],{"className":7774},[1988],[1827,7776,7778],{"className":7777,"style":4046},[1992],[1827,7779,7780,7783],{"style":1996},[1827,7781],{"className":7782,"style":2001},[2000],[1827,7784,7786],{"className":7785},[2005,2006,2007,2008],[1827,7787,3920],{"className":7788},[1870,1945,2008],[1827,7790,2016],{"className":7791},[2015],[1827,7793,7795],{"className":7794},[1988],[1827,7796,7798],{"className":7797,"style":2023},[1992],[1827,7799],{},[1827,7801,7802,7805],{"style":3299},[1827,7803],{"className":7804,"style":3179},[2000],[1827,7806],{"className":7807,"style":3307},[3306],[1827,7809,7810,7813],{"style":3310},[1827,7811],{"className":7812,"style":3179},[2000],[1827,7814,7816,7819,7822,7825,7828],{"className":7815},[1870],[1827,7817,7635],{"className":7818,"style":7759},[1870],[1827,7820,7543],{"className":7821,"style":7565},[1870,1945],[1827,7823,1895],{"className":7824},[1969],[1827,7826,1887],{"className":7827,"style":1946},[1870,1945],[1827,7829,1924],{"className":7830},[2092],[1827,7832,2016],{"className":7833},[2015],[1827,7835,7837],{"className":7836},[1988],[1827,7838,7841],{"className":7839,"style":7840},[1992],"height:0.836em;",[1827,7842],{},[1827,7844],{"className":7845},[2092,3271],[1827,7847,2392],{"className":7848},[1870],[1793,7850,7851,7852,8090],{},"在线性–二次的方差度量下，取 ",[1827,7853,7855,7900],{"className":7854},[1830],[1827,7856,7858],{"className":7857},[1834],[1836,7859,7860],{"xmlns":1838},[1840,7861,7862,7897],{},[1843,7863,7864,7866,7868,7870,7872,7874,7880,7882],{},[1885,7865,7543],{},[1889,7867,1895],{"stretchy":1894},[1885,7869,1887],{},[1889,7871,1924],{"stretchy":1894},[1889,7873,1891],{},[1897,7875,7876,7878],{},[1885,7877,6880],{},[1885,7879,1793],{},[1889,7881,1891],{},[7883,7884,7885],"msqrt",{},[1843,7886,7887,7893,7895],{},[1920,7888,7889,7891],{},[1885,7890,1887],{},[1885,7892,1928],{"mathvariant":1927},[1885,7894,2600],{"mathvariant":1927},[1885,7896,1887],{},[1850,7898,7899],{"encoding":1852},"R(w) = \\sigma_p = \\sqrt{w^\\top \\Sigma w}",[1827,7901,7903,7930,7986],{"className":7902,"ariaHidden":1857},[1856],[1827,7904,7906,7909,7912,7915,7918,7921,7924,7927],{"className":7905},[1861],[1827,7907],{"className":7908,"style":2569},[1865],[1827,7910,7543],{"className":7911,"style":7565},[1870,1945],[1827,7913,1895],{"className":7914},[1969],[1827,7916,1887],{"className":7917,"style":1946},[1870,1945],[1827,7919,1924],{"className":7920},[2092],[1827,7922],{"className":7923,"style":1951},[1950],[1827,7925,1891],{"className":7926},[1955],[1827,7928],{"className":7929,"style":1951},[1950],[1827,7931,7933,7936,7977,7980,7983],{"className":7932},[1861],[1827,7934],{"className":7935,"style":2405},[1865],[1827,7937,7939,7942],{"className":7938},[1870],[1827,7940,6880],{"className":7941,"style":6925},[1870,1945],[1827,7943,7945],{"className":7944},[1979],[1827,7946,7948,7969],{"className":7947},[1983,1984],[1827,7949,7951,7966],{"className":7950},[1988],[1827,7952,7954],{"className":7953,"style":2424},[1992],[1827,7955,7957,7960],{"style":7956},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1827,7958],{"className":7959,"style":2001},[2000],[1827,7961,7963],{"className":7962},[2005,2006,2007,2008],[1827,7964,1793],{"className":7965},[1870,1945,2008],[1827,7967,2016],{"className":7968},[2015],[1827,7970,7972],{"className":7971},[1988],[1827,7973,7975],{"className":7974,"style":2445},[1992],[1827,7976],{},[1827,7978],{"className":7979,"style":1951},[1950],[1827,7981,1891],{"className":7982},[1955],[1827,7984],{"className":7985,"style":1951},[1950],[1827,7987,7989,7993],{"className":7988},[1861],[1827,7990],{"className":7991,"style":7992},[1865],"height:1.04em;vertical-align:-0.0674em;",[1827,7994,7997],{"className":7995},[1870,7996],"sqrt",[1827,7998,8000,8081],{"className":7999},[1983,1984],[1827,8001,8003,8078],{"className":8002},[1988],[1827,8004,8007,8055],{"className":8005,"style":8006},[1992],"height:0.9726em;",[1827,8008,8011,8014],{"className":8009,"style":3188},[8010],"svg-align",[1827,8012],{"className":8013,"style":3179},[2000],[1827,8015,8018,8049,8052],{"className":8016,"style":8017},[1870],"padding-left:0.833em;",[1827,8019,8021,8024],{"className":8020},[1870],[1827,8022,1887],{"className":8023,"style":1946},[1870,1945],[1827,8025,8027],{"className":8026},[1979],[1827,8028,8030],{"className":8029},[1983],[1827,8031,8033],{"className":8032},[1988],[1827,8034,8037],{"className":8035,"style":8036},[1992],"height:0.7751em;",[1827,8038,8040,8043],{"style":8039},"top:-2.989em;margin-right:0.05em;",[1827,8041],{"className":8042,"style":2001},[2000],[1827,8044,8046],{"className":8045},[2005,2006,2007,2008],[1827,8047,1928],{"className":8048},[1870,2008],[1827,8050,2600],{"className":8051},[1870],[1827,8053,1887],{"className":8054,"style":1946},[1870,1945],[1827,8056,8058,8061],{"style":8057},"top:-2.9326em;",[1827,8059],{"className":8060,"style":3179},[2000],[1827,8062,8066],{"className":8063,"style":8065},[8064],"hide-tail","min-width:0.853em;height:1.08em;",[8067,8068,8074],"svg",{"xmlns":8069,"width":8070,"height":8071,"viewBox":8072,"preserveAspectRatio":8073},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[8075,8076],"path",{"d":8077},"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",[1827,8079,2016],{"className":8080},[2015],[1827,8082,8084],{"className":8083},[1988],[1827,8085,8088],{"className":8086,"style":8087},[1992],"height:0.0674em;",[1827,8089],{},"，可得：",[1827,8092,8094],{"className":8093},[2360],[1827,8095,8097,8141],{"className":8096},[1830],[1827,8098,8100],{"className":8099},[1834],[1836,8101,8102],{"xmlns":1838,"display":2369},[1840,8103,8104,8138],{},[1843,8105,8106,8112,8114,8136],{},[1897,8107,8108,8110],{},[3113,8109,7624],{},[1885,8111,3920],{},[1889,8113,1891],{},[3128,8115,8116,8130],{},[1843,8117,8118,8120,8122,8124],{},[1889,8119,1895],{"stretchy":1894},[1885,8121,2600],{"mathvariant":1927},[1885,8123,1887],{},[1897,8125,8126,8128],{},[1889,8127,1924],{"stretchy":1894},[1885,8129,3920],{},[1897,8131,8132,8134],{},[1885,8133,6880],{},[1885,8135,1793],{},[1885,8137,2392],{"mathvariant":1927},[1850,8139,8140],{"encoding":1852}," \\text{MCR}_i = \\frac{(\\Sigma w)_i}{\\sigma_p}.",[1827,8142,8144,8202],{"className":8143,"ariaHidden":1857},[1856],[1827,8145,8147,8150,8193,8196,8199],{"className":8146},[1861],[1827,8148],{"className":8149,"style":7668},[1865],[1827,8151,8153,8159],{"className":8152},[1870],[1827,8154,8156],{"className":8155},[1870,6845],[1827,8157,7624],{"className":8158},[1870],[1827,8160,8162],{"className":8161},[1979],[1827,8163,8165,8185],{"className":8164},[1983,1984],[1827,8166,8168,8182],{"className":8167},[1988],[1827,8169,8171],{"className":8170,"style":4046},[1992],[1827,8172,8173,8176],{"style":7692},[1827,8174],{"className":8175,"style":2001},[2000],[1827,8177,8179],{"className":8178},[2005,2006,2007,2008],[1827,8180,3920],{"className":8181},[1870,1945,2008],[1827,8183,2016],{"className":8184},[2015],[1827,8186,8188],{"className":8187},[1988],[1827,8189,8191],{"className":8190,"style":2023},[1992],[1827,8192],{},[1827,8194],{"className":8195,"style":1951},[1950],[1827,8197,1891],{"className":8198},[1955],[1827,8200],{"className":8201,"style":1951},[1950],[1827,8203,8205,8209,8355],{"className":8204},[1861],[1827,8206],{"className":8207,"style":8208},[1865],"height:2.3991em;vertical-align:-0.9721em;",[1827,8210,8212,8215,8352],{"className":8211},[1870],[1827,8213],{"className":8214},[1969,3271],[1827,8216,8218],{"className":8217},[3128],[1827,8219,8221,8343],{"className":8220},[1983,1984],[1827,8222,8224,8340],{"className":8223},[1988],[1827,8225,8227,8275,8283],{"className":8226,"style":7747},[1992],[1827,8228,8229,8232],{"style":3287},[1827,8230],{"className":8231,"style":3179},[2000],[1827,8233,8235],{"className":8234},[1870],[1827,8236,8238,8241],{"className":8237},[1870],[1827,8239,6880],{"className":8240,"style":6925},[1870,1945],[1827,8242,8244],{"className":8243},[1979],[1827,8245,8247,8267],{"className":8246},[1983,1984],[1827,8248,8250,8264],{"className":8249},[1988],[1827,8251,8253],{"className":8252,"style":2424},[1992],[1827,8254,8255,8258],{"style":7956},[1827,8256],{"className":8257,"style":2001},[2000],[1827,8259,8261],{"className":8260},[2005,2006,2007,2008],[1827,8262,1793],{"className":8263},[1870,1945,2008],[1827,8265,2016],{"className":8266},[2015],[1827,8268,8270],{"className":8269},[1988],[1827,8271,8273],{"className":8272,"style":2445},[1992],[1827,8274],{},[1827,8276,8277,8280],{"style":3299},[1827,8278],{"className":8279,"style":3179},[2000],[1827,8281],{"className":8282,"style":3307},[3306],[1827,8284,8285,8288],{"style":3310},[1827,8286],{"className":8287,"style":3179},[2000],[1827,8289,8291,8294,8297,8300],{"className":8290},[1870],[1827,8292,1895],{"className":8293},[1969],[1827,8295,2600],{"className":8296},[1870],[1827,8298,1887],{"className":8299,"style":1946},[1870,1945],[1827,8301,8303,8306],{"className":8302},[2092],[1827,8304,1924],{"className":8305},[2092],[1827,8307,8309],{"className":8308},[1979],[1827,8310,8312,8332],{"className":8311},[1983,1984],[1827,8313,8315,8329],{"className":8314},[1988],[1827,8316,8318],{"className":8317,"style":4046},[1992],[1827,8319,8320,8323],{"style":4517},[1827,8321],{"className":8322,"style":2001},[2000],[1827,8324,8326],{"className":8325},[2005,2006,2007,2008],[1827,8327,3920],{"className":8328},[1870,1945,2008],[1827,8330,2016],{"className":8331},[2015],[1827,8333,8335],{"className":8334},[1988],[1827,8336,8338],{"className":8337,"style":2023},[1992],[1827,8339],{},[1827,8341,2016],{"className":8342},[2015],[1827,8344,8346],{"className":8345},[1988],[1827,8347,8350],{"className":8348,"style":8349},[1992],"height:0.9721em;",[1827,8351],{},[1827,8353],{"className":8354},[2092,3271],[1827,8356,2392],{"className":8357},[1870],[1793,8359,8360,8361,3084],{},"进一步可定义",[1797,8362,8363],{},"成分风险贡献（Component Contribution to Risk, CCR）",[1827,8365,8367],{"className":8366},[2360],[1827,8368,8370,8440],{"className":8369},[1830],[1827,8371,8373],{"className":8372},[1834],[1836,8374,8375],{"xmlns":1838,"display":2369},[1840,8376,8377,8437],{},[1843,8378,8379,8386,8388,8394,8397,8403,8405,8411,8413,8435],{},[1897,8380,8381,8384],{},[3113,8382,8383],{},"CCR",[1885,8385,3920],{},[1889,8387,1891],{},[1897,8389,8390,8392],{},[1885,8391,1887],{},[1885,8393,3920],{},[1889,8395,8396],{},"⋅",[1897,8398,8399,8401],{},[3113,8400,7624],{},[1885,8402,3920],{},[1889,8404,1891],{},[1897,8406,8407,8409],{},[1885,8408,1887],{},[1885,8410,3920],{},[1889,8412,8396],{},[3128,8414,8415,8429],{},[1843,8416,8417,8419,8421,8423],{},[1889,8418,1895],{"stretchy":1894},[1885,8420,2600],{"mathvariant":1927},[1885,8422,1887],{},[1897,8424,8425,8427],{},[1889,8426,1924],{"stretchy":1894},[1885,8428,3920],{},[1897,8430,8431,8433],{},[1885,8432,6880],{},[1885,8434,1793],{},[1885,8436,2392],{"mathvariant":1927},[1850,8438,8439],{"encoding":1852}," \\text{CCR}_i = w_i \\cdot \\text{MCR}_i = w_i \\cdot \\frac{(\\Sigma w)_i}{\\sigma_p}.",[1827,8441,8443,8501,8557,8615,8670],{"className":8442,"ariaHidden":1857},[1856],[1827,8444,8446,8449,8492,8495,8498],{"className":8445},[1861],[1827,8447],{"className":8448,"style":7668},[1865],[1827,8450,8452,8458],{"className":8451},[1870],[1827,8453,8455],{"className":8454},[1870,6845],[1827,8456,8383],{"className":8457},[1870],[1827,8459,8461],{"className":8460},[1979],[1827,8462,8464,8484],{"className":8463},[1983,1984],[1827,8465,8467,8481],{"className":8466},[1988],[1827,8468,8470],{"className":8469,"style":4046},[1992],[1827,8471,8472,8475],{"style":7692},[1827,8473],{"className":8474,"style":2001},[2000],[1827,8476,8478],{"className":8477},[2005,2006,2007,2008],[1827,8479,3920],{"className":8480},[1870,1945,2008],[1827,8482,2016],{"className":8483},[2015],[1827,8485,8487],{"className":8486},[1988],[1827,8488,8490],{"className":8489,"style":2023},[1992],[1827,8491],{},[1827,8493],{"className":8494,"style":1951},[1950],[1827,8496,1891],{"className":8497},[1955],[1827,8499],{"className":8500,"style":1951},[1950],[1827,8502,8504,8508,8548,8551,8554],{"className":8503},[1861],[1827,8505],{"className":8506,"style":8507},[1865],"height:0.5945em;vertical-align:-0.15em;",[1827,8509,8511,8514],{"className":8510},[1870],[1827,8512,1887],{"className":8513,"style":1946},[1870,1945],[1827,8515,8517],{"className":8516},[1979],[1827,8518,8520,8540],{"className":8519},[1983,1984],[1827,8521,8523,8537],{"className":8522},[1988],[1827,8524,8526],{"className":8525,"style":4046},[1992],[1827,8527,8528,8531],{"style":1996},[1827,8529],{"className":8530,"style":2001},[2000],[1827,8532,8534],{"className":8533},[2005,2006,2007,2008],[1827,8535,3920],{"className":8536},[1870,1945,2008],[1827,8538,2016],{"className":8539},[2015],[1827,8541,8543],{"className":8542},[1988],[1827,8544,8546],{"className":8545,"style":2023},[1992],[1827,8547],{},[1827,8549],{"className":8550,"style":3250},[1950],[1827,8552,8396],{"className":8553},[3254],[1827,8555],{"className":8556,"style":3250},[1950],[1827,8558,8560,8563,8606,8609,8612],{"className":8559},[1861],[1827,8561],{"className":8562,"style":7668},[1865],[1827,8564,8566,8572],{"className":8565},[1870],[1827,8567,8569],{"className":8568},[1870,6845],[1827,8570,7624],{"className":8571},[1870],[1827,8573,8575],{"className":8574},[1979],[1827,8576,8578,8598],{"className":8577},[1983,1984],[1827,8579,8581,8595],{"className":8580},[1988],[1827,8582,8584],{"className":8583,"style":4046},[1992],[1827,8585,8586,8589],{"style":7692},[1827,8587],{"className":8588,"style":2001},[2000],[1827,8590,8592],{"className":8591},[2005,2006,2007,2008],[1827,8593,3920],{"className":8594},[1870,1945,2008],[1827,8596,2016],{"className":8597},[2015],[1827,8599,8601],{"className":8600},[1988],[1827,8602,8604],{"className":8603,"style":2023},[1992],[1827,8605],{},[1827,8607],{"className":8608,"style":1951},[1950],[1827,8610,1891],{"className":8611},[1955],[1827,8613],{"className":8614,"style":1951},[1950],[1827,8616,8618,8621,8661,8664,8667],{"className":8617},[1861],[1827,8619],{"className":8620,"style":8507},[1865],[1827,8622,8624,8627],{"className":8623},[1870],[1827,8625,1887],{"className":8626,"style":1946},[1870,1945],[1827,8628,8630],{"className":8629},[1979],[1827,8631,8633,8653],{"className":8632},[1983,1984],[1827,8634,8636,8650],{"className":8635},[1988],[1827,8637,8639],{"className":8638,"style":4046},[1992],[1827,8640,8641,8644],{"style":1996},[1827,8642],{"className":8643,"style":2001},[2000],[1827,8645,8647],{"className":8646},[2005,2006,2007,2008],[1827,8648,3920],{"className":8649},[1870,1945,2008],[1827,8651,2016],{"className":8652},[2015],[1827,8654,8656],{"className":8655},[1988],[1827,8657,8659],{"className":8658,"style":2023},[1992],[1827,8660],{},[1827,8662],{"className":8663,"style":3250},[1950],[1827,8665,8396],{"className":8666},[3254],[1827,8668],{"className":8669,"style":3250},[1950],[1827,8671,8673,8676,8821],{"className":8672},[1861],[1827,8674],{"className":8675,"style":8208},[1865],[1827,8677,8679,8682,8818],{"className":8678},[1870],[1827,8680],{"className":8681},[1969,3271],[1827,8683,8685],{"className":8684},[3128],[1827,8686,8688,8810],{"className":8687},[1983,1984],[1827,8689,8691,8807],{"className":8690},[1988],[1827,8692,8694,8742,8750],{"className":8693,"style":7747},[1992],[1827,8695,8696,8699],{"style":3287},[1827,8697],{"className":8698,"style":3179},[2000],[1827,8700,8702],{"className":8701},[1870],[1827,8703,8705,8708],{"className":8704},[1870],[1827,8706,6880],{"className":8707,"style":6925},[1870,1945],[1827,8709,8711],{"className":8710},[1979],[1827,8712,8714,8734],{"className":8713},[1983,1984],[1827,8715,8717,8731],{"className":8716},[1988],[1827,8718,8720],{"className":8719,"style":2424},[1992],[1827,8721,8722,8725],{"style":7956},[1827,8723],{"className":8724,"style":2001},[2000],[1827,8726,8728],{"className":8727},[2005,2006,2007,2008],[1827,8729,1793],{"className":8730},[1870,1945,2008],[1827,8732,2016],{"className":8733},[2015],[1827,8735,8737],{"className":8736},[1988],[1827,8738,8740],{"className":8739,"style":2445},[1992],[1827,8741],{},[1827,8743,8744,8747],{"style":3299},[1827,8745],{"className":8746,"style":3179},[2000],[1827,8748],{"className":8749,"style":3307},[3306],[1827,8751,8752,8755],{"style":3310},[1827,8753],{"className":8754,"style":3179},[2000],[1827,8756,8758,8761,8764,8767],{"className":8757},[1870],[1827,8759,1895],{"className":8760},[1969],[1827,8762,2600],{"className":8763},[1870],[1827,8765,1887],{"className":8766,"style":1946},[1870,1945],[1827,8768,8770,8773],{"className":8769},[2092],[1827,8771,1924],{"className":8772},[2092],[1827,8774,8776],{"className":8775},[1979],[1827,8777,8779,8799],{"className":8778},[1983,1984],[1827,8780,8782,8796],{"className":8781},[1988],[1827,8783,8785],{"className":8784,"style":4046},[1992],[1827,8786,8787,8790],{"style":4517},[1827,8788],{"className":8789,"style":2001},[2000],[1827,8791,8793],{"className":8792},[2005,2006,2007,2008],[1827,8794,3920],{"className":8795},[1870,1945,2008],[1827,8797,2016],{"className":8798},[2015],[1827,8800,8802],{"className":8801},[1988],[1827,8803,8805],{"className":8804,"style":2023},[1992],[1827,8806],{},[1827,8808,2016],{"className":8809},[2015],[1827,8811,8813],{"className":8812},[1988],[1827,8814,8816],{"className":8815,"style":8349},[1992],[1827,8817],{},[1827,8819],{"className":8820},[2092,3271],[1827,8822,2392],{"className":8823},[1870],[1793,8825,8826],{},"所有资产的 CCR 之和等于总波动率：",[1827,8828,8830],{"className":8829},[2360],[1827,8831,8833,8877],{"className":8832},[1830],[1827,8834,8836],{"className":8835},[1834],[1836,8837,8838],{"xmlns":1838,"display":2369},[1840,8839,8840,8874],{},[1843,8841,8842,8858,8864,8866,8872],{},[8843,8844,8845,8848,8856],"munderover",{},[1889,8846,8847],{},"∑",[1843,8849,8850,8852,8854],{},[1885,8851,3920],{},[1889,8853,1891],{},[1846,8855,1903],{},[1885,8857,1918],{},[1897,8859,8860,8862],{},[3113,8861,8383],{},[1885,8863,3920],{},[1889,8865,1891],{},[1897,8867,8868,8870],{},[1885,8869,6880],{},[1885,8871,1793],{},[1885,8873,2392],{"mathvariant":1927},[1850,8875,8876],{"encoding":1852}," \\sum_{i=1}^N \\text{CCR}_i = \\sigma_p.",[1827,8878,8880,9014],{"className":8879,"ariaHidden":1857},[1856],[1827,8881,8883,8887,8959,8962,9005,9008,9011],{"className":8882},[1861],[1827,8884],{"className":8885,"style":8886},[1865],"height:3.106em;vertical-align:-1.2777em;",[1827,8888,8890],{"className":8889},[2649,3163],[1827,8891,8893,8950],{"className":8892},[1983,1984],[1827,8894,8896,8947],{"className":8895},[1988],[1827,8897,8900,8922,8935],{"className":8898,"style":8899},[1992],"height:1.8283em;",[1827,8901,8903,8907],{"style":8902},"top:-1.8723em;margin-left:0em;",[1827,8904],{"className":8905,"style":8906},[2000],"height:3.05em;",[1827,8908,8910],{"className":8909},[2005,2006,2007,2008],[1827,8911,8913,8916,8919],{"className":8912},[1870,2008],[1827,8914,3920],{"className":8915},[1870,1945,2008],[1827,8917,1891],{"className":8918},[1955,2008],[1827,8920,1903],{"className":8921},[1870,2008],[1827,8923,8925,8928],{"style":8924},"top:-3.05em;",[1827,8926],{"className":8927,"style":8906},[2000],[1827,8929,8930],{},[1827,8931,8847],{"className":8932},[2649,8933,8934],"op-symbol","large-op",[1827,8936,8938,8941],{"style":8937},"top:-4.3em;margin-left:0em;",[1827,8939],{"className":8940,"style":8906},[2000],[1827,8942,8944],{"className":8943},[2005,2006,2007,2008],[1827,8945,1918],{"className":8946,"style":2077},[1870,1945,2008],[1827,8948,2016],{"className":8949},[2015],[1827,8951,8953],{"className":8952},[1988],[1827,8954,8957],{"className":8955,"style":8956},[1992],"height:1.2777em;",[1827,8958],{},[1827,8960],{"className":8961,"style":2033},[1950],[1827,8963,8965,8971],{"className":8964},[1870],[1827,8966,8968],{"className":8967},[1870,6845],[1827,8969,8383],{"className":8970},[1870],[1827,8972,8974],{"className":8973},[1979],[1827,8975,8977,8997],{"className":8976},[1983,1984],[1827,8978,8980,8994],{"className":8979},[1988],[1827,8981,8983],{"className":8982,"style":4046},[1992],[1827,8984,8985,8988],{"style":7692},[1827,8986],{"className":8987,"style":2001},[2000],[1827,8989,8991],{"className":8990},[2005,2006,2007,2008],[1827,8992,3920],{"className":8993},[1870,1945,2008],[1827,8995,2016],{"className":8996},[2015],[1827,8998,9000],{"className":8999},[1988],[1827,9001,9003],{"className":9002,"style":2023},[1992],[1827,9004],{},[1827,9006],{"className":9007,"style":1951},[1950],[1827,9009,1891],{"className":9010},[1955],[1827,9012],{"className":9013,"style":1951},[1950],[1827,9015,9017,9020,9060],{"className":9016},[1861],[1827,9018],{"className":9019,"style":2405},[1865],[1827,9021,9023,9026],{"className":9022},[1870],[1827,9024,6880],{"className":9025,"style":6925},[1870,1945],[1827,9027,9029],{"className":9028},[1979],[1827,9030,9032,9052],{"className":9031},[1983,1984],[1827,9033,9035,9049],{"className":9034},[1988],[1827,9036,9038],{"className":9037,"style":2424},[1992],[1827,9039,9040,9043],{"style":7956},[1827,9041],{"className":9042,"style":2001},[2000],[1827,9044,9046],{"className":9045},[2005,2006,2007,2008],[1827,9047,1793],{"className":9048},[1870,1945,2008],[1827,9050,2016],{"className":9051},[2015],[1827,9053,9055],{"className":9054},[1988],[1827,9056,9058],{"className":9057,"style":2445},[1992],[1827,9059],{},[1827,9061,2392],{"className":9062},[1870],[1793,9064,9065,9066,3084],{},"基于此，可以构建所谓",[1797,9067,9068],{},"风险平价组合（Risk Parity）",[2504,9070,9071,9074],{},[2507,9072,9073],{},"要求每个资产或每类因子的风险贡献相等；",[2507,9075,9076],{},"或者按给定比例分配不同资产\u002F因子的风险预算。",[1793,9078,9079],{},"这类思路在学术和实务中都有广泛讨论（例如 Qian, 2005; Maillard, Roncalli & Teiletche, 2010）。",[1814,9081,9083],{"id":9082},"_3-带约束的组合优化","3. 带约束的组合优化",[1793,9085,9086],{},"真实世界中的组合构建几乎总是带有复杂约束：",[2504,9088,9089,9355,9358,9574],{},[2507,9090,9091,9092,3045],{},"单资产权重上下限：",[1827,9093,9095,9139],{"className":9094},[1830],[1827,9096,9098],{"className":9097},[1834],[1836,9099,9100],{"xmlns":1838},[1840,9101,9102,9136],{},[1843,9103,9104,9115,9118,9124,9126],{},[3914,9105,9106,9108,9110,9113],{},[1885,9107,1887],{},[1885,9109,3920],{},[1885,9111,9112],{},"min",[1889,9114,2608],{},[1889,9116,9117],{},"≤",[1897,9119,9120,9122],{},[1885,9121,1887],{},[1885,9123,3920],{},[1889,9125,9117],{},[3914,9127,9128,9130,9132,9134],{},[1885,9129,1887],{},[1885,9131,3920],{},[1885,9133,3107],{},[1889,9135,2608],{},[1850,9137,9138],{"encoding":1852},"w_i^{\\min} \\le w_i \\le w_i^{\\max}",[1827,9140,9142,9226,9282],{"className":9141,"ariaHidden":1857},[1856],[1827,9143,9145,9149,9217,9220,9223],{"className":9144},[1861],[1827,9146],{"className":9147,"style":9148},[1865],"height:1.0892em;vertical-align:-0.2587em;",[1827,9150,9152,9155],{"className":9151},[1870],[1827,9153,1887],{"className":9154,"style":1946},[1870,1945],[1827,9156,9158],{"className":9157},[1979],[1827,9159,9161,9208],{"className":9160},[1983,1984],[1827,9162,9164,9205],{"className":9163},[1988],[1827,9165,9168,9180],{"className":9166,"style":9167},[1992],"height:0.8305em;",[1827,9169,9171,9174],{"style":9170},"top:-2.4413em;margin-left:-0.0269em;margin-right:0.05em;",[1827,9172],{"className":9173,"style":2001},[2000],[1827,9175,9177],{"className":9176},[2005,2006,2007,2008],[1827,9178,3920],{"className":9179},[1870,1945,2008],[1827,9181,9182,9185],{"style":2111},[1827,9183],{"className":9184,"style":2001},[2000],[1827,9186,9188],{"className":9187},[2005,2006,2007,2008],[1827,9189,9191],{"className":9190},[1870,2008],[1827,9192,9194,9198,9201],{"className":9193},[2649,2008],[1827,9195,9197],{"className":9196},[2008],"m",[1827,9199,3920],{"className":9200},[2008],[1827,9202,9204],{"className":9203},[2008],"n",[1827,9206,2016],{"className":9207},[2015],[1827,9209,9211],{"className":9210},[1988],[1827,9212,9215],{"className":9213,"style":9214},[1992],"height:0.2587em;",[1827,9216],{},[1827,9218],{"className":9219,"style":1951},[1950],[1827,9221,9117],{"className":9222},[1955],[1827,9224],{"className":9225,"style":1951},[1950],[1827,9227,9229,9233,9273,9276,9279],{"className":9228},[1861],[1827,9230],{"className":9231,"style":9232},[1865],"height:0.786em;vertical-align:-0.15em;",[1827,9234,9236,9239],{"className":9235},[1870],[1827,9237,1887],{"className":9238,"style":1946},[1870,1945],[1827,9240,9242],{"className":9241},[1979],[1827,9243,9245,9265],{"className":9244},[1983,1984],[1827,9246,9248,9262],{"className":9247},[1988],[1827,9249,9251],{"className":9250,"style":4046},[1992],[1827,9252,9253,9256],{"style":1996},[1827,9254],{"className":9255,"style":2001},[2000],[1827,9257,9259],{"className":9258},[2005,2006,2007,2008],[1827,9260,3920],{"className":9261},[1870,1945,2008],[1827,9263,2016],{"className":9264},[2015],[1827,9266,9268],{"className":9267},[1988],[1827,9269,9271],{"className":9270,"style":2023},[1992],[1827,9272],{},[1827,9274],{"className":9275,"style":1951},[1950],[1827,9277,9117],{"className":9278},[1955],[1827,9280],{"className":9281,"style":1951},[1950],[1827,9283,9285,9289],{"className":9284},[1861],[1827,9286],{"className":9287,"style":9288},[1865],"height:0.9231em;vertical-align:-0.2587em;",[1827,9290,9292,9295],{"className":9291},[1870],[1827,9293,1887],{"className":9294,"style":1946},[1870,1945],[1827,9296,9298],{"className":9297},[1979],[1827,9299,9301,9347],{"className":9300},[1983,1984],[1827,9302,9304,9344],{"className":9303},[1988],[1827,9305,9308,9319],{"className":9306,"style":9307},[1992],"height:0.6644em;",[1827,9309,9310,9313],{"style":9170},[1827,9311],{"className":9312,"style":2001},[2000],[1827,9314,9316],{"className":9315},[2005,2006,2007,2008],[1827,9317,3920],{"className":9318},[1870,1945,2008],[1827,9320,9321,9324],{"style":2111},[1827,9322],{"className":9323,"style":2001},[2000],[1827,9325,9327],{"className":9326},[2005,2006,2007,2008],[1827,9328,9330],{"className":9329},[1870,2008],[1827,9331,9333,9336,9340],{"className":9332},[2649,2008],[1827,9334,9197],{"className":9335},[2008],[1827,9337,9339],{"className":9338},[2008],"a",[1827,9341,9343],{"className":9342},[2008],"x",[1827,9345,2016],{"className":9346},[2015],[1827,9348,9350],{"className":9349},[1988],[1827,9351,9353],{"className":9352,"style":9214},[1992],[1827,9354],{},[2507,9356,9357],{},"行业\u002F风格\u002F国家敞口约束；",[2507,9359,9360,9361,3045],{},"总杠杆和融资约束：",[1827,9362,9364,9403],{"className":9363},[1830],[1827,9365,9367],{"className":9366},[1834],[1836,9368,9369],{"xmlns":1838},[1840,9370,9371,9400],{},[1843,9372,9373,9379,9381,9387,9389,9391],{},[1897,9374,9375,9377],{},[1889,9376,8847],{},[1885,9378,3920],{},[1885,9380,4882],{"mathvariant":1927},[1897,9382,9383,9385],{},[1885,9384,1887],{},[1885,9386,3920],{},[1885,9388,4882],{"mathvariant":1927},[1889,9390,9117],{},[1897,9392,9393,9396,9398],{},[1885,9394,9395],{},"L",[1885,9397,3107],{},[1889,9399,2608],{},[1850,9401,9402],{"encoding":1852},"\\sum_i |w_i| \\le L_{\\max}",[1827,9404,9406,9516],{"className":9405,"ariaHidden":1857},[1856],[1827,9407,9409,9413,9458,9461,9464,9504,9507,9510,9513],{"className":9408},[1861],[1827,9410],{"className":9411,"style":9412},[1865],"height:1.0497em;vertical-align:-0.2997em;",[1827,9414,9416,9421],{"className":9415},[2649],[1827,9417,8847],{"className":9418,"style":9420},[2649,8933,9419],"small-op","position:relative;top:0em;",[1827,9422,9424],{"className":9423},[1979],[1827,9425,9427,9449],{"className":9426},[1983,1984],[1827,9428,9430,9446],{"className":9429},[1988],[1827,9431,9434],{"className":9432,"style":9433},[1992],"height:0.162em;",[1827,9435,9437,9440],{"style":9436},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[1827,9438],{"className":9439,"style":2001},[2000],[1827,9441,9443],{"className":9442},[2005,2006,2007,2008],[1827,9444,3920],{"className":9445},[1870,1945,2008],[1827,9447,2016],{"className":9448},[2015],[1827,9450,9452],{"className":9451},[1988],[1827,9453,9456],{"className":9454,"style":9455},[1992],"height:0.2997em;",[1827,9457],{},[1827,9459],{"className":9460,"style":2033},[1950],[1827,9462,4882],{"className":9463},[1870],[1827,9465,9467,9470],{"className":9466},[1870],[1827,9468,1887],{"className":9469,"style":1946},[1870,1945],[1827,9471,9473],{"className":9472},[1979],[1827,9474,9476,9496],{"className":9475},[1983,1984],[1827,9477,9479,9493],{"className":9478},[1988],[1827,9480,9482],{"className":9481,"style":4046},[1992],[1827,9483,9484,9487],{"style":1996},[1827,9485],{"className":9486,"style":2001},[2000],[1827,9488,9490],{"className":9489},[2005,2006,2007,2008],[1827,9491,3920],{"className":9492},[1870,1945,2008],[1827,9494,2016],{"className":9495},[2015],[1827,9497,9499],{"className":9498},[1988],[1827,9500,9502],{"className":9501,"style":2023},[1992],[1827,9503],{},[1827,9505,4882],{"className":9506},[1870],[1827,9508],{"className":9509,"style":1951},[1950],[1827,9511,9117],{"className":9512},[1955],[1827,9514],{"className":9515,"style":1951},[1950],[1827,9517,9519,9522],{"className":9518},[1861],[1827,9520],{"className":9521,"style":7668},[1865],[1827,9523,9525,9528],{"className":9524},[1870],[1827,9526,9395],{"className":9527},[1870,1945],[1827,9529,9531],{"className":9530},[1979],[1827,9532,9534,9566],{"className":9533},[1983,1984],[1827,9535,9537,9563],{"className":9536},[1988],[1827,9538,9540],{"className":9539,"style":2424},[1992],[1827,9541,9542,9545],{"style":4517},[1827,9543],{"className":9544,"style":2001},[2000],[1827,9546,9548],{"className":9547},[2005,2006,2007,2008],[1827,9549,9551],{"className":9550},[1870,2008],[1827,9552,9554,9557,9560],{"className":9553},[2649,2008],[1827,9555,9197],{"className":9556},[2008],[1827,9558,9339],{"className":9559},[2008],[1827,9561,9343],{"className":9562},[2008],[1827,9564,2016],{"className":9565},[2015],[1827,9567,9569],{"className":9568},[1988],[1827,9570,9572],{"className":9571,"style":2023},[1992],[1827,9573],{},[2507,9575,9576,9577,9836],{},"成交量和流动性约束：",[1827,9578,9580,9627],{"className":9579},[1830],[1827,9581,9583],{"className":9582},[1834],[1836,9584,9585],{"xmlns":1838},[1840,9586,9587,9624],{},[1843,9588,9589,9591,9597,9599,9608,9610,9612,9615,9617],{},[1885,9590,4882],{"mathvariant":1927},[1897,9592,9593,9595],{},[1885,9594,1887],{},[1885,9596,3920],{},[1889,9598,3126],{},[3914,9600,9601,9603,9605],{},[1885,9602,1887],{},[1885,9604,3920],{},[3113,9606,9607],{},"prev",[1885,9609,4882],{"mathvariant":1927},[1889,9611,9117],{},[1885,9613,9614],{},"c",[1889,9616,8396],{},[1897,9618,9619,9622],{},[3113,9620,9621],{},"ADV",[1885,9623,3920],{},[1850,9625,9626],{"encoding":1852},"|w_i - w_i^{\\text{prev}}| \\le c \\cdot \\text{ADV}_i",[1827,9628,9630,9688,9768,9787],{"className":9629,"ariaHidden":1857},[1856],[1827,9631,9633,9636,9639,9679,9682,9685],{"className":9632},[1861],[1827,9634],{"className":9635,"style":2569},[1865],[1827,9637,4882],{"className":9638},[1870],[1827,9640,9642,9645],{"className":9641},[1870],[1827,9643,1887],{"className":9644,"style":1946},[1870,1945],[1827,9646,9648],{"className":9647},[1979],[1827,9649,9651,9671],{"className":9650},[1983,1984],[1827,9652,9654,9668],{"className":9653},[1988],[1827,9655,9657],{"className":9656,"style":4046},[1992],[1827,9658,9659,9662],{"style":1996},[1827,9660],{"className":9661,"style":2001},[2000],[1827,9663,9665],{"className":9664},[2005,2006,2007,2008],[1827,9666,3920],{"className":9667},[1870,1945,2008],[1827,9669,2016],{"className":9670},[2015],[1827,9672,9674],{"className":9673},[1988],[1827,9675,9677],{"className":9676,"style":2023},[1992],[1827,9678],{},[1827,9680],{"className":9681,"style":3250},[1950],[1827,9683,3126],{"className":9684},[3254],[1827,9686],{"className":9687,"style":3250},[1950],[1827,9689,9691,9695,9756,9759,9762,9765],{"className":9690},[1861],[1827,9692],{"className":9693,"style":9694},[1865],"height:1.0592em;vertical-align:-0.2769em;",[1827,9696,9698,9701],{"className":9697},[1870],[1827,9699,1887],{"className":9700,"style":1946},[1870,1945],[1827,9702,9704],{"className":9703},[1979],[1827,9705,9707,9747],{"className":9706},[1983,1984],[1827,9708,9710,9744],{"className":9709},[1988],[1827,9711,9714,9726],{"className":9712,"style":9713},[1992],"height:0.7823em;",[1827,9715,9717,9720],{"style":9716},"top:-2.4231em;margin-left:-0.0269em;margin-right:0.05em;",[1827,9718],{"className":9719,"style":2001},[2000],[1827,9721,9723],{"className":9722},[2005,2006,2007,2008],[1827,9724,3920],{"className":9725},[1870,1945,2008],[1827,9727,9729,9732],{"style":9728},"top:-3.1809em;margin-right:0.05em;",[1827,9730],{"className":9731,"style":2001},[2000],[1827,9733,9735],{"className":9734},[2005,2006,2007,2008],[1827,9736,9738],{"className":9737},[1870,2008],[1827,9739,9741],{"className":9740},[1870,6845,2008],[1827,9742,9607],{"className":9743},[1870,2008],[1827,9745,2016],{"className":9746},[2015],[1827,9748,9750],{"className":9749},[1988],[1827,9751,9754],{"className":9752,"style":9753},[1992],"height:0.2769em;",[1827,9755],{},[1827,9757,4882],{"className":9758},[1870],[1827,9760],{"className":9761,"style":1951},[1950],[1827,9763,9117],{"className":9764},[1955],[1827,9766],{"className":9767,"style":1951},[1950],[1827,9769,9771,9775,9778,9781,9784],{"className":9770},[1861],[1827,9772],{"className":9773,"style":9774},[1865],"height:0.4445em;",[1827,9776,9614],{"className":9777},[1870,1945],[1827,9779],{"className":9780,"style":3250},[1950],[1827,9782,8396],{"className":9783},[3254],[1827,9785],{"className":9786,"style":3250},[1950],[1827,9788,9790,9793],{"className":9789},[1861],[1827,9791],{"className":9792,"style":7668},[1865],[1827,9794,9796,9802],{"className":9795},[1870],[1827,9797,9799],{"className":9798},[1870,6845],[1827,9800,9621],{"className":9801},[1870],[1827,9803,9805],{"className":9804},[1979],[1827,9806,9808,9828],{"className":9807},[1983,1984],[1827,9809,9811,9825],{"className":9810},[1988],[1827,9812,9814],{"className":9813,"style":4046},[1992],[1827,9815,9816,9819],{"style":7692},[1827,9817],{"className":9818,"style":2001},[2000],[1827,9820,9822],{"className":9821},[2005,2006,2007,2008],[1827,9823,3920],{"className":9824},[1870,1945,2008],[1827,9826,2016],{"className":9827},[2015],[1827,9829,9831],{"className":9830},[1988],[1827,9832,9834],{"className":9833,"style":2023},[1992],[1827,9835],{}," 等。",[1793,9838,9839],{},"在资产定价风格的组合优化中，常见目标之一是：",[9841,9842,9843],"blockquote",{},[1793,9844,9845,9846,9875,9876,9936],{},"在给定风险模型 ",[1827,9847,9849,9863],{"className":9848},[1830],[1827,9850,9852],{"className":9851},[1834],[1836,9853,9854],{"xmlns":1838},[1840,9855,9856,9860],{},[1843,9857,9858],{},[1885,9859,2600],{"mathvariant":1927},[1850,9861,9862],{"encoding":1852},"\\Sigma",[1827,9864,9866],{"className":9865,"ariaHidden":1857},[1856],[1827,9867,9869,9872],{"className":9868},[1861],[1827,9870],{"className":9871,"style":2627},[1865],[1827,9873,2600],{"className":9874},[1870]," 和预期超额收益向量 ",[1827,9877,9879,9897],{"className":9878},[1830],[1827,9880,9882],{"className":9881},[1834],[1836,9883,9884],{"xmlns":1838},[1840,9885,9886,9894],{},[1843,9887,9888],{},[1920,9889,9890,9892],{},[1885,9891,2523],{},[1885,9893,3923],{},[1850,9895,9896],{"encoding":1852},"\\mu^e",[1827,9898,9900],{"className":9899,"ariaHidden":1857},[1856],[1827,9901,9903,9907],{"className":9902},[1861],[1827,9904],{"className":9905,"style":9906},[1865],"height:0.8588em;vertical-align:-0.1944em;",[1827,9908,9910,9913],{"className":9909},[1870],[1827,9911,2523],{"className":9912},[1870,1945],[1827,9914,9916],{"className":9915},[1979],[1827,9917,9919],{"className":9918},[1983],[1827,9920,9922],{"className":9921},[1988],[1827,9923,9925],{"className":9924,"style":9307},[1992],[1827,9926,9927,9930],{"style":2111},[1827,9928],{"className":9929,"style":2001},[2000],[1827,9931,9933],{"className":9932},[2005,2006,2007,2008],[1827,9934,3923],{"className":9935},[1870,1945,2008]," 的条件下，求解带约束的均值–方差优化。",[1793,9938,9939],{},"形式上可写为：",[1827,9941,9943],{"className":9942},[2360],[1827,9944,9946,10019],{"className":9945},[1830],[1827,9947,9949],{"className":9948},[1834],[1836,9950,9951],{"xmlns":1838,"display":2369},[1840,9952,9953,10016],{},[1843,9954,9955,9965,9967,9973,9979,9981,9987,9993,9995,9997,9999,10002,10006,10008,10010,10012,10014],{},[3101,9956,9957,9963],{},[1843,9958,9959,9961],{},[1885,9960,3107],{},[1889,9962,2608],{},[1885,9964,1887],{},[3113,9966,3115],{},[1920,9968,9969,9971],{},[1885,9970,1887],{},[1885,9972,1928],{"mathvariant":1927},[1920,9974,9975,9977],{},[1885,9976,2523],{},[1885,9978,3923],{},[1889,9980,3126],{},[3128,9982,9983,9985],{},[1885,9984,3066],{},[1846,9986,3134],{},[1920,9988,9989,9991],{},[1885,9990,1887],{},[1885,9992,1928],{"mathvariant":1927},[1885,9994,2600],{"mathvariant":1927},[1885,9996,1887],{},[1950,9998],{"width":4859},[3113,10000,10001],{},"s.t. 约束集合 ",[1885,10003,10005],{"mathvariant":10004},"script","C",[1889,10007,1895],{"stretchy":1894},[1885,10009,1887],{},[1889,10011,1924],{"stretchy":1894},[1889,10013,9117],{},[1846,10015,4901],{},[1850,10017,10018],{"encoding":1852}," \\max_w \\ w^\\top \\mu^e - \\frac{\\lambda}{2} w^\\top \\Sigma w \\quad \\text{s.t. 约束集合 } \\mathcal{C}(w) \\le 0.",[1827,10020,10022,10145,10288],{"className":10021,"ariaHidden":1857},[1856],[1827,10023,10025,10028,10072,10075,10078,10107,10136,10139,10142],{"className":10024},[1861],[1827,10026],{"className":10027,"style":3159},[1865],[1827,10029,10031],{"className":10030},[2649,3163],[1827,10032,10034,10064],{"className":10033},[1983,1984],[1827,10035,10037,10061],{"className":10036},[1988],[1827,10038,10040,10051],{"className":10039,"style":1941},[1992],[1827,10041,10042,10045],{"style":3175},[1827,10043],{"className":10044,"style":3179},[2000],[1827,10046,10048],{"className":10047},[2005,2006,2007,2008],[1827,10049,1887],{"className":10050,"style":1946},[1870,1945,2008],[1827,10052,10053,10056],{"style":3188},[1827,10054],{"className":10055,"style":3179},[2000],[1827,10057,10058],{},[1827,10059,3107],{"className":10060},[2649],[1827,10062,2016],{"className":10063},[2015],[1827,10065,10067],{"className":10066},[1988],[1827,10068,10070],{"className":10069,"style":3206},[1992],[1827,10071],{},[1827,10073,3115],{"className":10074},[1950],[1827,10076],{"className":10077,"style":2033},[1950],[1827,10079,10081,10084],{"className":10080},[1870],[1827,10082,1887],{"className":10083,"style":1946},[1870,1945],[1827,10085,10087],{"className":10086},[1979],[1827,10088,10090],{"className":10089},[1983],[1827,10091,10093],{"className":10092},[1988],[1827,10094,10096],{"className":10095,"style":2463},[1992],[1827,10097,10098,10101],{"style":2484},[1827,10099],{"className":10100,"style":2001},[2000],[1827,10102,10104],{"className":10103},[2005,2006,2007,2008],[1827,10105,1928],{"className":10106},[1870,2008],[1827,10108,10110,10113],{"className":10109},[1870],[1827,10111,2523],{"className":10112},[1870,1945],[1827,10114,10116],{"className":10115},[1979],[1827,10117,10119],{"className":10118},[1983],[1827,10120,10122],{"className":10121},[1988],[1827,10123,10125],{"className":10124,"style":3973},[1992],[1827,10126,10127,10130],{"style":2484},[1827,10128],{"className":10129,"style":2001},[2000],[1827,10131,10133],{"className":10132},[2005,2006,2007,2008],[1827,10134,3923],{"className":10135},[1870,1945,2008],[1827,10137],{"className":10138,"style":3250},[1950],[1827,10140,3126],{"className":10141},[3254],[1827,10143],{"className":10144,"style":3250},[1950],[1827,10146,10148,10151,10213,10242,10245,10248,10251,10265,10270,10273,10276,10279,10282,10285],{"className":10147},[1861],[1827,10149],{"className":10150,"style":3264},[1865],[1827,10152,10154,10157,10210],{"className":10153},[1870],[1827,10155],{"className":10156},[1969,3271],[1827,10158,10160],{"className":10159},[3128],[1827,10161,10163,10202],{"className":10162},[1983,1984],[1827,10164,10166,10199],{"className":10165},[1988],[1827,10167,10169,10180,10188],{"className":10168,"style":3284},[1992],[1827,10170,10171,10174],{"style":3287},[1827,10172],{"className":10173,"style":3179},[2000],[1827,10175,10177],{"className":10176},[1870],[1827,10178,3134],{"className":10179},[1870],[1827,10181,10182,10185],{"style":3299},[1827,10183],{"className":10184,"style":3179},[2000],[1827,10186],{"className":10187,"style":3307},[3306],[1827,10189,10190,10193],{"style":3310},[1827,10191],{"className":10192,"style":3179},[2000],[1827,10194,10196],{"className":10195},[1870],[1827,10197,3066],{"className":10198},[1870,1945],[1827,10200,2016],{"className":10201},[2015],[1827,10203,10205],{"className":10204},[1988],[1827,10206,10208],{"className":10207,"style":3329},[1992],[1827,10209],{},[1827,10211],{"className":10212},[2092,3271],[1827,10214,10216,10219],{"className":10215},[1870],[1827,10217,1887],{"className":10218,"style":1946},[1870,1945],[1827,10220,10222],{"className":10221},[1979],[1827,10223,10225],{"className":10224},[1983],[1827,10226,10228],{"className":10227},[1988],[1827,10229,10231],{"className":10230,"style":2463},[1992],[1827,10232,10233,10236],{"style":2484},[1827,10234],{"className":10235,"style":2001},[2000],[1827,10237,10239],{"className":10238},[2005,2006,2007,2008],[1827,10240,1928],{"className":10241},[1870,2008],[1827,10243,2600],{"className":10244},[1870],[1827,10246,1887],{"className":10247,"style":1946},[1870,1945],[1827,10249],{"className":10250,"style":5160},[1950],[1827,10252,10254,10258,10262],{"className":10253},[1870,6845],[1827,10255,10257],{"className":10256},[1870],"s.t. ",[1827,10259,10261],{"className":10260},[1870,6853],"约束集合",[1827,10263,3115],{"className":10264},[1870],[1827,10266,10005],{"className":10267,"style":10269},[1870,10268],"mathcal","margin-right:0.0583em;",[1827,10271,1895],{"className":10272},[1969],[1827,10274,1887],{"className":10275,"style":1946},[1870,1945],[1827,10277,1924],{"className":10278},[2092],[1827,10280],{"className":10281,"style":1951},[1950],[1827,10283,9117],{"className":10284},[1955],[1827,10286],{"className":10287,"style":1951},[1950],[1827,10289,10291,10294],{"className":10290},[1861],[1827,10292],{"className":10293,"style":1866},[1865],[1827,10295,4901],{"className":10296},[1870],[1793,10298,10299],{},"这是一个带线性\u002F二次约束的凸优化问题，可以用二次规划（Quadratic Programming, QP）求解。在研究层面，很多论文会讨论：",[2504,10301,10302,10412],{},[2507,10303,10304,10305,10411],{},"当约束较少时，解析解与无约束解 ",[1827,10306,10308,10336],{"className":10307},[1830],[1827,10309,10311],{"className":10310},[1834],[1836,10312,10313],{"xmlns":1838},[1840,10314,10315,10333],{},[1843,10316,10317,10327],{},[1920,10318,10319,10321],{},[1885,10320,2600],{"mathvariant":1927},[1843,10322,10323,10325],{},[1889,10324,3126],{},[1846,10326,1903],{},[1920,10328,10329,10331],{},[1885,10330,2523],{},[1885,10332,3923],{},[1850,10334,10335],{"encoding":1852},"\\Sigma^{-1} \\mu^e",[1827,10337,10339],{"className":10338,"ariaHidden":1857},[1856],[1827,10340,10342,10346,10382],{"className":10341},[1861],[1827,10343],{"className":10344,"style":10345},[1865],"height:1.0085em;vertical-align:-0.1944em;",[1827,10347,10349,10352],{"className":10348},[1870],[1827,10350,2600],{"className":10351},[1870],[1827,10353,10355],{"className":10354},[1979],[1827,10356,10358],{"className":10357},[1983],[1827,10359,10361],{"className":10360},[1988],[1827,10362,10365],{"className":10363,"style":10364},[1992],"height:0.8141em;",[1827,10366,10367,10370],{"style":2111},[1827,10368],{"className":10369,"style":2001},[2000],[1827,10371,10373],{"className":10372},[2005,2006,2007,2008],[1827,10374,10376,10379],{"className":10375},[1870,2008],[1827,10377,3126],{"className":10378},[1870,2008],[1827,10380,1903],{"className":10381},[1870,2008],[1827,10383,10385,10388],{"className":10384},[1870],[1827,10386,2523],{"className":10387},[1870,1945],[1827,10389,10391],{"className":10390},[1979],[1827,10392,10394],{"className":10393},[1983],[1827,10395,10397],{"className":10396},[1988],[1827,10398,10400],{"className":10399,"style":9307},[1992],[1827,10401,10402,10405],{"style":2111},[1827,10403],{"className":10404,"style":2001},[2000],[1827,10406,10408],{"className":10407},[2005,2006,2007,2008],[1827,10409,3923],{"className":10410},[1870,1945,2008]," 的关系；",[2507,10413,10414],{},"当约束较多时，如何在数值上保持稳健（例如正则化协方差矩阵、限制权重集中度）。",[1793,10416,10417],{},"在最简单的“仅有资金约束”情形下，可以写出拉格朗日函数：",[1827,10419,10421],{"className":10420},[2360],[1827,10422,10424,10506],{"className":10423},[1830],[1827,10425,10427],{"className":10426},[1834],[1836,10428,10429],{"xmlns":1838,"display":2369},[1840,10430,10431,10503],{},[1843,10432,10433,10435,10437,10439,10441,10444,10446,10448,10454,10460,10462,10468,10474,10476,10478,10480,10482,10485,10487,10493,10495,10497,10499,10501],{},[1885,10434,9395],{"mathvariant":10004},[1889,10436,1895],{"stretchy":1894},[1885,10438,1887],{},[1889,10440,1906],{"separator":1857},[1885,10442,10443],{},"ν",[1889,10445,1924],{"stretchy":1894},[1889,10447,1891],{},[1920,10449,10450,10452],{},[1885,10451,1887],{},[1885,10453,1928],{"mathvariant":1927},[1920,10455,10456,10458],{},[1885,10457,2523],{},[1885,10459,3923],{},[1889,10461,3126],{},[3128,10463,10464,10466],{},[1885,10465,3066],{},[1846,10467,3134],{},[1920,10469,10470,10472],{},[1885,10471,1887],{},[1885,10473,1928],{"mathvariant":1927},[1885,10475,2600],{"mathvariant":1927},[1885,10477,1887],{},[1889,10479,4182],{},[1885,10481,10443],{},[3113,10483,10484],{}," ",[1889,10486,1895],{"stretchy":1894},[1920,10488,10489,10491],{},[1846,10490,1903],{},[1885,10492,1928],{"mathvariant":1927},[1885,10494,1887],{},[1889,10496,3126],{},[1846,10498,1903],{},[1889,10500,1924],{"stretchy":1894},[1889,10502,1906],{"separator":1857},[1850,10504,10505],{"encoding":1852},"\\mathcal{L}(w,\\nu) = w^\\top \\mu^e - \\frac{\\lambda}{2} w^\\top \\Sigma w + \\nu\\,(1^\\top w - 1),",[1827,10507,10509,10546,10620,10732,10788],{"className":10508,"ariaHidden":1857},[1856],[1827,10510,10512,10515,10518,10521,10524,10527,10530,10534,10537,10540,10543],{"className":10511},[1861],[1827,10513],{"className":10514,"style":2569},[1865],[1827,10516,9395],{"className":10517},[1870,10268],[1827,10519,1895],{"className":10520},[1969],[1827,10522,1887],{"className":10523,"style":1946},[1870,1945],[1827,10525,1906],{"className":10526},[2029],[1827,10528],{"className":10529,"style":2033},[1950],[1827,10531,10443],{"className":10532,"style":10533},[1870,1945],"margin-right:0.0637em;",[1827,10535,1924],{"className":10536},[2092],[1827,10538],{"className":10539,"style":1951},[1950],[1827,10541,1891],{"className":10542},[1955],[1827,10544],{"className":10545,"style":1951},[1950],[1827,10547,10549,10553,10582,10611,10614,10617],{"className":10548},[1861],[1827,10550],{"className":10551,"style":10552},[1865],"height:1.0935em;vertical-align:-0.1944em;",[1827,10554,10556,10559],{"className":10555},[1870],[1827,10557,1887],{"className":10558,"style":1946},[1870,1945],[1827,10560,10562],{"className":10561},[1979],[1827,10563,10565],{"className":10564},[1983],[1827,10566,10568],{"className":10567},[1988],[1827,10569,10571],{"className":10570,"style":2463},[1992],[1827,10572,10573,10576],{"style":2484},[1827,10574],{"className":10575,"style":2001},[2000],[1827,10577,10579],{"className":10578},[2005,2006,2007,2008],[1827,10580,1928],{"className":10581},[1870,2008],[1827,10583,10585,10588],{"className":10584},[1870],[1827,10586,2523],{"className":10587},[1870,1945],[1827,10589,10591],{"className":10590},[1979],[1827,10592,10594],{"className":10593},[1983],[1827,10595,10597],{"className":10596},[1988],[1827,10598,10600],{"className":10599,"style":3973},[1992],[1827,10601,10602,10605],{"style":2484},[1827,10603],{"className":10604,"style":2001},[2000],[1827,10606,10608],{"className":10607},[2005,2006,2007,2008],[1827,10609,3923],{"className":10610},[1870,1945,2008],[1827,10612],{"className":10613,"style":3250},[1950],[1827,10615,3126],{"className":10616},[3254],[1827,10618],{"className":10619,"style":3250},[1950],[1827,10621,10623,10626,10688,10717,10720,10723,10726,10729],{"className":10622},[1861],[1827,10624],{"className":10625,"style":3264},[1865],[1827,10627,10629,10632,10685],{"className":10628},[1870],[1827,10630],{"className":10631},[1969,3271],[1827,10633,10635],{"className":10634},[3128],[1827,10636,10638,10677],{"className":10637},[1983,1984],[1827,10639,10641,10674],{"className":10640},[1988],[1827,10642,10644,10655,10663],{"className":10643,"style":3284},[1992],[1827,10645,10646,10649],{"style":3287},[1827,10647],{"className":10648,"style":3179},[2000],[1827,10650,10652],{"className":10651},[1870],[1827,10653,3134],{"className":10654},[1870],[1827,10656,10657,10660],{"style":3299},[1827,10658],{"className":10659,"style":3179},[2000],[1827,10661],{"className":10662,"style":3307},[3306],[1827,10664,10665,10668],{"style":3310},[1827,10666],{"className":10667,"style":3179},[2000],[1827,10669,10671],{"className":10670},[1870],[1827,10672,3066],{"className":10673},[1870,1945],[1827,10675,2016],{"className":10676},[2015],[1827,10678,10680],{"className":10679},[1988],[1827,10681,10683],{"className":10682,"style":3329},[1992],[1827,10684],{},[1827,10686],{"className":10687},[2092,3271],[1827,10689,10691,10694],{"className":10690},[1870],[1827,10692,1887],{"className":10693,"style":1946},[1870,1945],[1827,10695,10697],{"className":10696},[1979],[1827,10698,10700],{"className":10699},[1983],[1827,10701,10703],{"className":10702},[1988],[1827,10704,10706],{"className":10705,"style":2463},[1992],[1827,10707,10708,10711],{"style":2484},[1827,10709],{"className":10710,"style":2001},[2000],[1827,10712,10714],{"className":10713},[2005,2006,2007,2008],[1827,10715,1928],{"className":10716},[1870,2008],[1827,10718,2600],{"className":10719},[1870],[1827,10721,1887],{"className":10722,"style":1946},[1870,1945],[1827,10724],{"className":10725,"style":3250},[1950],[1827,10727,4182],{"className":10728},[3254],[1827,10730],{"className":10731,"style":3250},[1950],[1827,10733,10735,10738,10741,10744,10747,10776,10779,10782,10785],{"className":10734},[1861],[1827,10736],{"className":10737,"style":6596},[1865],[1827,10739,10443],{"className":10740,"style":10533},[1870,1945],[1827,10742],{"className":10743,"style":2033},[1950],[1827,10745,1895],{"className":10746},[1969],[1827,10748,10750,10753],{"className":10749},[1870],[1827,10751,1903],{"className":10752},[1870],[1827,10754,10756],{"className":10755},[1979],[1827,10757,10759],{"className":10758},[1983],[1827,10760,10762],{"className":10761},[1988],[1827,10763,10765],{"className":10764,"style":2463},[1992],[1827,10766,10767,10770],{"style":2484},[1827,10768],{"className":10769,"style":2001},[2000],[1827,10771,10773],{"className":10772},[2005,2006,2007,2008],[1827,10774,1928],{"className":10775},[1870,2008],[1827,10777,1887],{"className":10778,"style":1946},[1870,1945],[1827,10780],{"className":10781,"style":3250},[1950],[1827,10783,3126],{"className":10784},[3254],[1827,10786],{"className":10787,"style":3250},[1950],[1827,10789,10791,10794,10797,10800],{"className":10790},[1861],[1827,10792],{"className":10793,"style":2569},[1865],[1827,10795,1903],{"className":10796},[1870],[1827,10798,1924],{"className":10799},[2092],[1827,10801,1906],{"className":10802},[2029],[1793,10804,10805,10806,10834],{},"对 ",[1827,10807,10809,10822],{"className":10808},[1830],[1827,10810,10812],{"className":10811},[1834],[1836,10813,10814],{"xmlns":1838},[1840,10815,10816,10820],{},[1843,10817,10818],{},[1885,10819,1887],{},[1850,10821,1887],{"encoding":1852},[1827,10823,10825],{"className":10824,"ariaHidden":1857},[1856],[1827,10826,10828,10831],{"className":10827},[1861],[1827,10829],{"className":10830,"style":1941},[1865],[1827,10832,1887],{"className":10833,"style":1946},[1870,1945]," 求一阶条件得到：",[1827,10836,10838],{"className":10837},[2360],[1827,10839,10841,10894],{"className":10840},[1830],[1827,10842,10844],{"className":10843},[1834],[1836,10845,10846],{"xmlns":1838,"display":2369},[1840,10847,10848,10891],{},[1843,10849,10850,10856,10858,10860,10862,10864,10866,10868,10870,10872,10874,10876,10878,10884,10886,10888],{},[1920,10851,10852,10854],{},[1885,10853,2523],{},[1885,10855,3923],{},[1889,10857,3126],{},[1885,10859,3066],{},[1885,10861,2600],{"mathvariant":1927},[1885,10863,1887],{},[1889,10865,4182],{},[1885,10867,10443],{},[1846,10869,1903],{},[1889,10871,1891],{},[1846,10873,1848],{},[1889,10875,1906],{"separator":1857},[1950,10877],{"width":4859},[1920,10879,10880,10882],{},[1846,10881,1903],{},[1885,10883,1928],{"mathvariant":1927},[1885,10885,1887],{},[1889,10887,1891],{},[1846,10889,10890],{},"1.",[1850,10892,10893],{"encoding":1852},"\\mu^e - \\lambda \\Sigma w + \\nu 1 = 0, \\quad 1^\\top w = 1.",[1827,10895,10897,10942,10967,10988,11047],{"className":10896,"ariaHidden":1857},[1856],[1827,10898,10900,10904,10933,10936,10939],{"className":10899},[1861],[1827,10901],{"className":10902,"style":10903},[1865],"height:0.9088em;vertical-align:-0.1944em;",[1827,10905,10907,10910],{"className":10906},[1870],[1827,10908,2523],{"className":10909},[1870,1945],[1827,10911,10913],{"className":10912},[1979],[1827,10914,10916],{"className":10915},[1983],[1827,10917,10919],{"className":10918},[1988],[1827,10920,10922],{"className":10921,"style":3973},[1992],[1827,10923,10924,10927],{"style":2484},[1827,10925],{"className":10926,"style":2001},[2000],[1827,10928,10930],{"className":10929},[2005,2006,2007,2008],[1827,10931,3923],{"className":10932},[1870,1945,2008],[1827,10934],{"className":10935,"style":3250},[1950],[1827,10937,3126],{"className":10938},[3254],[1827,10940],{"className":10941,"style":3250},[1950],[1827,10943,10945,10949,10952,10955,10958,10961,10964],{"className":10944},[1861],[1827,10946],{"className":10947,"style":10948},[1865],"height:0.7778em;vertical-align:-0.0833em;",[1827,10950,3066],{"className":10951},[1870,1945],[1827,10953,2600],{"className":10954},[1870],[1827,10956,1887],{"className":10957,"style":1946},[1870,1945],[1827,10959],{"className":10960,"style":3250},[1950],[1827,10962,4182],{"className":10963},[3254],[1827,10965],{"className":10966,"style":3250},[1950],[1827,10968,10970,10973,10976,10979,10982,10985],{"className":10969},[1861],[1827,10971],{"className":10972,"style":1866},[1865],[1827,10974,10443],{"className":10975,"style":10533},[1870,1945],[1827,10977,1903],{"className":10978},[1870],[1827,10980],{"className":10981,"style":1951},[1950],[1827,10983,1891],{"className":10984},[1955],[1827,10986],{"className":10987,"style":1951},[1950],[1827,10989,10991,10994,10997,11000,11003,11006,11035,11038,11041,11044],{"className":10990},[1861],[1827,10992],{"className":10993,"style":10552},[1865],[1827,10995,1848],{"className":10996},[1870],[1827,10998,1906],{"className":10999},[2029],[1827,11001],{"className":11002,"style":5160},[1950],[1827,11004],{"className":11005,"style":2033},[1950],[1827,11007,11009,11012],{"className":11008},[1870],[1827,11010,1903],{"className":11011},[1870],[1827,11013,11015],{"className":11014},[1979],[1827,11016,11018],{"className":11017},[1983],[1827,11019,11021],{"className":11020},[1988],[1827,11022,11024],{"className":11023,"style":2463},[1992],[1827,11025,11026,11029],{"style":2484},[1827,11027],{"className":11028,"style":2001},[2000],[1827,11030,11032],{"className":11031},[2005,2006,2007,2008],[1827,11033,1928],{"className":11034},[1870,2008],[1827,11036,1887],{"className":11037,"style":1946},[1870,1945],[1827,11039],{"className":11040,"style":1951},[1950],[1827,11042,1891],{"className":11043},[1955],[1827,11045],{"className":11046,"style":1951},[1950],[1827,11048,11050,11053],{"className":11049},[1861],[1827,11051],{"className":11052,"style":1866},[1865],[1827,11054,10890],{"className":11055},[1870],[1793,11057,11058,11059,11087,11088,11116,11117,11146,11147,11149],{},"配合 ",[1827,11060,11062,11075],{"className":11061},[1830],[1827,11063,11065],{"className":11064},[1834],[1836,11066,11067],{"xmlns":1838},[1840,11068,11069,11073],{},[1843,11070,11071],{},[1885,11072,2600],{"mathvariant":1927},[1850,11074,9862],{"encoding":1852},[1827,11076,11078],{"className":11077,"ariaHidden":1857},[1856],[1827,11079,11081,11084],{"className":11080},[1861],[1827,11082],{"className":11083,"style":2627},[1865],[1827,11085,2600],{"className":11086},[1870]," 的可逆性，可以显式求解 ",[1827,11089,11091,11104],{"className":11090},[1830],[1827,11092,11094],{"className":11093},[1834],[1836,11095,11096],{"xmlns":1838},[1840,11097,11098,11102],{},[1843,11099,11100],{},[1885,11101,1887],{},[1850,11103,1887],{"encoding":1852},[1827,11105,11107],{"className":11106,"ariaHidden":1857},[1856],[1827,11108,11110,11113],{"className":11109},[1861],[1827,11111],{"className":11112,"style":1941},[1865],[1827,11114,1887],{"className":11115,"style":1946},[1870,1945]," 与 ",[1827,11118,11120,11134],{"className":11119},[1830],[1827,11121,11123],{"className":11122},[1834],[1836,11124,11125],{"xmlns":1838},[1840,11126,11127,11131],{},[1843,11128,11129],{},[1885,11130,10443],{},[1850,11132,11133],{"encoding":1852},"\\nu",[1827,11135,11137],{"className":11136,"ariaHidden":1857},[1856],[1827,11138,11140,11143],{"className":11139},[1861],[1827,11141],{"className":11142,"style":1941},[1865],[1827,11144,10443],{"className":11145,"style":10533},[1870,1945],"。这一推导在 ",[1805,11148,1807],{}," 中已有更完整展开，这里更关心的是：",[2504,11151,11152,11155],{},[2507,11153,11154],{},"一旦引入不等式约束（如多空限制、个股上限等），KKT 条件会变得相对复杂；",[2507,11156,11157,11158,11261],{},"在实务中通常交由数值优化器求解，但理解上述“无约束 + 一个资金约束”的解析解，有助于直观把握优化结果是否合理（例如方向是否接近 ",[1827,11159,11161,11188],{"className":11160},[1830],[1827,11162,11164],{"className":11163},[1834],[1836,11165,11166],{"xmlns":1838},[1840,11167,11168,11186],{},[1843,11169,11170,11180],{},[1920,11171,11172,11174],{},[1885,11173,2600],{"mathvariant":1927},[1843,11175,11176,11178],{},[1889,11177,3126],{},[1846,11179,1903],{},[1920,11181,11182,11184],{},[1885,11183,2523],{},[1885,11185,3923],{},[1850,11187,10335],{"encoding":1852},[1827,11189,11191],{"className":11190,"ariaHidden":1857},[1856],[1827,11192,11194,11197,11232],{"className":11193},[1861],[1827,11195],{"className":11196,"style":10345},[1865],[1827,11198,11200,11203],{"className":11199},[1870],[1827,11201,2600],{"className":11202},[1870],[1827,11204,11206],{"className":11205},[1979],[1827,11207,11209],{"className":11208},[1983],[1827,11210,11212],{"className":11211},[1988],[1827,11213,11215],{"className":11214,"style":10364},[1992],[1827,11216,11217,11220],{"style":2111},[1827,11218],{"className":11219,"style":2001},[2000],[1827,11221,11223],{"className":11222},[2005,2006,2007,2008],[1827,11224,11226,11229],{"className":11225},[1870,2008],[1827,11227,3126],{"className":11228},[1870,2008],[1827,11230,1903],{"className":11231},[1870,2008],[1827,11233,11235,11238],{"className":11234},[1870],[1827,11236,2523],{"className":11237},[1870,1945],[1827,11239,11241],{"className":11240},[1979],[1827,11242,11244],{"className":11243},[1983],[1827,11245,11247],{"className":11246},[1988],[1827,11248,11250],{"className":11249,"style":9307},[1992],[1827,11251,11252,11255],{"style":2111},[1827,11253],{"className":11254,"style":2001},[2000],[1827,11256,11258],{"className":11257},[2005,2006,2007,2008],[1827,11259,3923],{"className":11260},[1870,1945,2008],"）。",[1814,11263,11265],{"id":11264},"_4-从因子定价到因子组合","4. 从因子定价到“因子组合”",[1819,11267,11269],{"id":11268},"_41-因子组合与smart-beta","4.1 因子组合与“smart beta”",[1793,11271,11272],{},"在 Fama–French 框架中，每个因子（如市场、规模、价值、盈利、投资）都对应一个可交易的因子组合，例如：",[2504,11274,11275,11278],{},[2507,11276,11277],{},"SMB（Small Minus Big）：小市值减大市值组合；",[2507,11279,11280],{},"HML（High Minus Low）：高账面市值比减低账面市值比组合。",[1793,11282,11283],{},"这些因子组合本身就是投资组合，其收益可以写作：",[1827,11285,11287],{"className":11286},[2360],[1827,11288,11290,11353],{"className":11289},[1830],[1827,11291,11293],{"className":11292},[1834],[1836,11294,11295],{"xmlns":1838,"display":2369},[1840,11296,11297,11350],{},[1843,11298,11299,11320,11322,11336,11348],{},[1897,11300,11301,11303],{},[1885,11302,2165],{},[1843,11304,11305,11307,11309,11312,11314,11316,11318],{},[3113,11306,6883],{},[1889,11308,1906],{"separator":1857},[1885,11310,11311],{},"k",[1889,11313,1906],{"separator":1857},[1885,11315,4179],{},[1889,11317,4182],{},[1846,11319,1903],{},[1889,11321,1891],{},[3914,11323,11324,11326,11334],{},[1885,11325,1887],{},[1843,11327,11328,11330,11332],{},[1885,11329,11311],{},[1889,11331,1906],{"separator":1857},[1885,11333,4179],{},[1885,11335,1928],{"mathvariant":1927},[1897,11337,11338,11340],{},[1885,11339,2165],{},[1843,11341,11342,11344,11346],{},[1885,11343,4179],{},[1889,11345,4182],{},[1846,11347,1903],{},[1889,11349,1906],{"separator":1857},[1850,11351,11352],{"encoding":1852}," r_{\\text{factor},k,t+1} = w_{k,t}^\\top r_{t+1},",[1827,11354,11356,11436],{"className":11355,"ariaHidden":1857},[1856],[1827,11357,11359,11362,11427,11430,11433],{"className":11358},[1861],[1827,11360],{"className":11361,"style":2405},[1865],[1827,11363,11365,11368],{"className":11364},[1870],[1827,11366,2165],{"className":11367,"style":2209},[1870,1945],[1827,11369,11371],{"className":11370},[1979],[1827,11372,11374,11419],{"className":11373},[1983,1984],[1827,11375,11377,11416],{"className":11376},[1988],[1827,11378,11380],{"className":11379,"style":3800},[1992],[1827,11381,11382,11385],{"style":2248},[1827,11383],{"className":11384,"style":2001},[2000],[1827,11386,11388],{"className":11387},[2005,2006,2007,2008],[1827,11389,11391,11397,11400,11404,11407,11410,11413],{"className":11390},[1870,2008],[1827,11392,11394],{"className":11393},[1870,6845,2008],[1827,11395,6883],{"className":11396},[1870,2008],[1827,11398,1906],{"className":11399},[2029,2008],[1827,11401,11311],{"className":11402,"style":11403},[1870,1945,2008],"margin-right:0.0315em;",[1827,11405,1906],{"className":11406},[2029,2008],[1827,11408,4179],{"className":11409},[1870,1945,2008],[1827,11411,4182],{"className":11412},[3254,2008],[1827,11414,1903],{"className":11415},[1870,2008],[1827,11417,2016],{"className":11418},[2015],[1827,11420,11422],{"className":11421},[1988],[1827,11423,11425],{"className":11424,"style":2445},[1992],[1827,11426],{},[1827,11428],{"className":11429,"style":1951},[1950],[1827,11431,1891],{"className":11432},[1955],[1827,11434],{"className":11435,"style":1951},[1950],[1827,11437,11439,11442,11503,11552],{"className":11438},[1861],[1827,11440],{"className":11441,"style":6993},[1865],[1827,11443,11445,11448],{"className":11444},[1870],[1827,11446,1887],{"className":11447,"style":1946},[1870,1945],[1827,11449,11451],{"className":11450},[1979],[1827,11452,11454,11495],{"className":11453},[1983,1984],[1827,11455,11457,11492],{"className":11456},[1988],[1827,11458,11460,11481],{"className":11459,"style":2463},[1992],[1827,11461,11463,11466],{"style":11462},"top:-2.453em;margin-left:-0.0269em;margin-right:0.05em;",[1827,11464],{"className":11465,"style":2001},[2000],[1827,11467,11469],{"className":11468},[2005,2006,2007,2008],[1827,11470,11472,11475,11478],{"className":11471},[1870,2008],[1827,11473,11311],{"className":11474,"style":11403},[1870,1945,2008],[1827,11476,1906],{"className":11477},[2029,2008],[1827,11479,4179],{"className":11480},[1870,1945,2008],[1827,11482,11483,11486],{"style":2484},[1827,11484],{"className":11485,"style":2001},[2000],[1827,11487,11489],{"className":11488},[2005,2006,2007,2008],[1827,11490,1928],{"className":11491},[1870,2008],[1827,11493,2016],{"className":11494},[2015],[1827,11496,11498],{"className":11497},[1988],[1827,11499,11501],{"className":11500,"style":7044},[1992],[1827,11502],{},[1827,11504,11506,11509],{"className":11505},[1870],[1827,11507,2165],{"className":11508,"style":2209},[1870,1945],[1827,11510,11512],{"className":11511},[1979],[1827,11513,11515,11544],{"className":11514},[1983,1984],[1827,11516,11518,11541],{"className":11517},[1988],[1827,11519,11521],{"className":11520,"style":1993},[1992],[1827,11522,11523,11526],{"style":2248},[1827,11524],{"className":11525,"style":2001},[2000],[1827,11527,11529],{"className":11528},[2005,2006,2007,2008],[1827,11530,11532,11535,11538],{"className":11531},[1870,2008],[1827,11533,4179],{"className":11534},[1870,1945,2008],[1827,11536,4182],{"className":11537},[3254,2008],[1827,11539,1903],{"className":11540},[1870,2008],[1827,11542,2016],{"className":11543},[2015],[1827,11545,11547],{"className":11546},[1988],[1827,11548,11550],{"className":11549,"style":4479},[1992],[1827,11551],{},[1827,11553,1906],{"className":11554},[2029],[1793,11556,4558,11557,11642,11643,11671],{},[1827,11558,11560,11584],{"className":11559},[1830],[1827,11561,11563],{"className":11562},[1834],[1836,11564,11565],{"xmlns":1838},[1840,11566,11567,11581],{},[1843,11568,11569],{},[1897,11570,11571,11573],{},[1885,11572,1887],{},[1843,11574,11575,11577,11579],{},[1885,11576,11311],{},[1889,11578,1906],{"separator":1857},[1885,11580,4179],{},[1850,11582,11583],{"encoding":1852},"w_{k,t}",[1827,11585,11587],{"className":11586,"ariaHidden":1857},[1856],[1827,11588,11590,11593],{"className":11589},[1861],[1827,11591],{"className":11592,"style":2405},[1865],[1827,11594,11596,11599],{"className":11595},[1870],[1827,11597,1887],{"className":11598,"style":1946},[1870,1945],[1827,11600,11602],{"className":11601},[1979],[1827,11603,11605,11634],{"className":11604},[1983,1984],[1827,11606,11608,11631],{"className":11607},[1988],[1827,11609,11611],{"className":11610,"style":3800},[1992],[1827,11612,11613,11616],{"style":1996},[1827,11614],{"className":11615,"style":2001},[2000],[1827,11617,11619],{"className":11618},[2005,2006,2007,2008],[1827,11620,11622,11625,11628],{"className":11621},[1870,2008],[1827,11623,11311],{"className":11624,"style":11403},[1870,1945,2008],[1827,11626,1906],{"className":11627},[2029,2008],[1827,11629,4179],{"className":11630},[1870,1945,2008],[1827,11632,2016],{"className":11633},[2015],[1827,11635,11637],{"className":11636},[1988],[1827,11638,11640],{"className":11639,"style":2445},[1992],[1827,11641],{}," 是构造第 ",[1827,11644,11646,11659],{"className":11645},[1830],[1827,11647,11649],{"className":11648},[1834],[1836,11650,11651],{"xmlns":1838},[1840,11652,11653,11657],{},[1843,11654,11655],{},[1885,11656,11311],{},[1850,11658,11311],{"encoding":1852},[1827,11660,11662],{"className":11661,"ariaHidden":1857},[1856],[1827,11663,11665,11668],{"className":11664},[1861],[1827,11666],{"className":11667,"style":3079},[1865],[1827,11669,11311],{"className":11670,"style":11403},[1870,1945]," 个因子的权重。若我们进一步在这些因子组合上再做一次组合优化，就得到所谓“因子层面的组合”（有时被称为 smart beta 或 style investing）。",[1793,11673,11674],{},"从资产定价角度看：",[2504,11676,11677,11680],{},[2507,11678,11679],{},"因子组合提供了解释横截面资产收益的基底；",[2507,11681,11682],{},"投资者的策略可以被分解为对各个因子组合的暴露叠加。",[1819,11684,11686],{"id":11685},"_42-alpha-叠加与风险控制","4.2 Alpha 叠加与风险控制",[1793,11688,11689],{},"很多机构的实践是：",[11691,11692,11693,11696,11699],"ol",{},[2507,11694,11695],{},"用多因子模型估计“基准风险因子”的暴露和风险；",[2507,11697,11698],{},"将自研 alpha 策略视为在基准之上的“增量组合”；",[2507,11700,11701],{},"在组合优化时，约束整体组合的因子暴露不偏离基准过多，同时最大化自研 alpha 的预期收益。",[1793,11703,11704],{},"形式上，可以表达为：",[2504,11706,11707,11776,11929,12413],{},[2507,11708,11709,11710,3045],{},"给定基准指数权重 ",[1827,11711,11713,11732],{"className":11712},[1830],[1827,11714,11716],{"className":11715},[1834],[1836,11717,11718],{"xmlns":1838},[1840,11719,11720,11729],{},[1843,11721,11722],{},[1920,11723,11724,11726],{},[1885,11725,1887],{},[3113,11727,11728],{},"bench",[1850,11730,11731],{"encoding":1852},"w^{\\text{bench}}",[1827,11733,11735],{"className":11734,"ariaHidden":1857},[1856],[1827,11736,11738,11741],{"className":11737},[1861],[1827,11739],{"className":11740,"style":2108},[1865],[1827,11742,11744,11747],{"className":11743},[1870],[1827,11745,1887],{"className":11746,"style":1946},[1870,1945],[1827,11748,11750],{"className":11749},[1979],[1827,11751,11753],{"className":11752},[1983],[1827,11754,11756],{"className":11755},[1988],[1827,11757,11759],{"className":11758,"style":2108},[1992],[1827,11760,11761,11764],{"style":2111},[1827,11762],{"className":11763,"style":2001},[2000],[1827,11765,11767],{"className":11766},[2005,2006,2007,2008],[1827,11768,11770],{"className":11769},[1870,2008],[1827,11771,11773],{"className":11772},[1870,6845,2008],[1827,11774,11728],{"className":11775},[1870,2008],[2507,11777,11778,11779,11813,11814,3045],{},"寻找主动权重 ",[1827,11780,11782,11798],{"className":11781},[1830],[1827,11783,11785],{"className":11784},[1834],[1836,11786,11787],{"xmlns":1838},[1840,11788,11789,11795],{},[1843,11790,11791,11793],{},[1885,11792,5771],{"mathvariant":1927},[1885,11794,1887],{},[1850,11796,11797],{"encoding":1852},"\\Delta w",[1827,11799,11801],{"className":11800,"ariaHidden":1857},[1856],[1827,11802,11804,11807,11810],{"className":11803},[1861],[1827,11805],{"className":11806,"style":2627},[1865],[1827,11808,5771],{"className":11809},[1870],[1827,11811,1887],{"className":11812,"style":1946},[1870,1945],"，使得 ",[1827,11815,11817,11845],{"className":11816},[1830],[1827,11818,11820],{"className":11819},[1834],[1836,11821,11822],{"xmlns":1838},[1840,11823,11824,11842],{},[1843,11825,11826,11828,11830,11836,11838,11840],{},[1885,11827,1887],{},[1889,11829,1891],{},[1920,11831,11832,11834],{},[1885,11833,1887],{},[3113,11835,11728],{},[1889,11837,4182],{},[1885,11839,5771],{"mathvariant":1927},[1885,11841,1887],{},[1850,11843,11844],{"encoding":1852},"w = w^{\\text{bench}} + \\Delta w",[1827,11846,11848,11866,11917],{"className":11847,"ariaHidden":1857},[1856],[1827,11849,11851,11854,11857,11860,11863],{"className":11850},[1861],[1827,11852],{"className":11853,"style":1941},[1865],[1827,11855,1887],{"className":11856,"style":1946},[1870,1945],[1827,11858],{"className":11859,"style":1951},[1950],[1827,11861,1891],{"className":11862},[1955],[1827,11864],{"className":11865,"style":1951},[1950],[1827,11867,11869,11873,11908,11911,11914],{"className":11868},[1861],[1827,11870],{"className":11871,"style":11872},[1865],"height:0.9324em;vertical-align:-0.0833em;",[1827,11874,11876,11879],{"className":11875},[1870],[1827,11877,1887],{"className":11878,"style":1946},[1870,1945],[1827,11880,11882],{"className":11881},[1979],[1827,11883,11885],{"className":11884},[1983],[1827,11886,11888],{"className":11887},[1988],[1827,11889,11891],{"className":11890,"style":2108},[1992],[1827,11892,11893,11896],{"style":2111},[1827,11894],{"className":11895,"style":2001},[2000],[1827,11897,11899],{"className":11898},[2005,2006,2007,2008],[1827,11900,11902],{"className":11901},[1870,2008],[1827,11903,11905],{"className":11904},[1870,6845,2008],[1827,11906,11728],{"className":11907},[1870,2008],[1827,11909],{"className":11910,"style":3250},[1950],[1827,11912,4182],{"className":11913},[3254],[1827,11915],{"className":11916,"style":3250},[1950],[1827,11918,11920,11923,11926],{"className":11919},[1861],[1827,11921],{"className":11922,"style":2627},[1865],[1827,11924,5771],{"className":11925},[1870],[1827,11927,1887],{"className":11928,"style":1946},[1870,1945],[2507,11930,11931,11932],{},"目标为最大化主动组合的信息比率：",[1827,11933,11935],{"className":11934},[2360],[1827,11936,11938,12016],{"className":11937},[1830],[1827,11939,11941],{"className":11940},[1834],[1836,11942,11943],{"xmlns":1838,"display":2369},[1840,11944,11945,12013],{},[1843,11946,11947,11961,11963],{},[3101,11948,11949,11955],{},[1843,11950,11951,11953],{},[1885,11952,3107],{},[1889,11954,2608],{},[1843,11956,11957,11959],{},[1885,11958,5771],{"mathvariant":1927},[1885,11960,1887],{},[3113,11962,3115],{},[3128,11964,11965,11987],{},[1843,11966,11967,11969,11971,11977,11979,11985],{},[1885,11968,2529],{"mathvariant":2528},[1889,11970,2532],{"stretchy":1894},[1897,11972,11973,11975],{},[1885,11974,2165],{},[1885,11976,1793],{},[1889,11978,3126],{},[1897,11980,11981,11983],{},[1885,11982,2165],{},[3113,11984,11728],{},[1889,11986,2537],{"stretchy":1894},[7883,11988,11989],{},[1843,11990,11991,11993,11995,11997,12003,12005,12011],{},[1885,11992,2898],{"mathvariant":1927},[1889,11994,2608],{},[1889,11996,1895],{"stretchy":1894},[1897,11998,11999,12001],{},[1885,12000,2165],{},[1885,12002,1793],{},[1889,12004,3126],{},[1897,12006,12007,12009],{},[1885,12008,2165],{},[3113,12010,11728],{},[1889,12012,1924],{"stretchy":1894},[1850,12014,12015],{"encoding":1852},"\\max_{\\Delta w} \\ \\frac{\\mathbb{E}[r_{p} - r_{\\text{bench}}]}{\\sqrt{\\operatorname{Var}(r_{p} - r_{\\text{bench}})}}",[1827,12017,12019],{"className":12018,"ariaHidden":1857},[1856],[1827,12020,12022,12026,12078,12081,12084],{"className":12021},[1861],[1827,12023],{"className":12024,"style":12025},[1865],"height:2.557em;vertical-align:-1.13em;",[1827,12027,12029],{"className":12028},[2649,3163],[1827,12030,12032,12069],{"className":12031},[1983,1984],[1827,12033,12035,12066],{"className":12034},[1988],[1827,12036,12038,12056],{"className":12037,"style":1941},[1992],[1827,12039,12041,12044],{"style":12040},"top:-2.3557em;margin-left:0em;",[1827,12042],{"className":12043,"style":3179},[2000],[1827,12045,12047],{"className":12046},[2005,2006,2007,2008],[1827,12048,12050,12053],{"className":12049},[1870,2008],[1827,12051,5771],{"className":12052},[1870,2008],[1827,12054,1887],{"className":12055,"style":1946},[1870,1945,2008],[1827,12057,12058,12061],{"style":3188},[1827,12059],{"className":12060,"style":3179},[2000],[1827,12062,12063],{},[1827,12064,3107],{"className":12065},[2649],[1827,12067,2016],{"className":12068},[2015],[1827,12070,12072],{"className":12071},[1988],[1827,12073,12076],{"className":12074,"style":12075},[1992],"height:0.7443em;",[1827,12077],{},[1827,12079,3115],{"className":12080},[1950],[1827,12082],{"className":12083,"style":2033},[1950],[1827,12085,12087,12090,12410],{"className":12086},[1870],[1827,12088],{"className":12089},[1969,3271],[1827,12091,12093],{"className":12092},[3128],[1827,12094,12096,12401],{"className":12095},[1983,1984],[1827,12097,12099,12398],{"className":12098},[1988],[1827,12100,12102,12275,12283],{"className":12101,"style":7747},[1992],[1827,12103,12105,12108],{"style":12104},"top:-2.1931em;",[1827,12106],{"className":12107,"style":3179},[2000],[1827,12109,12111],{"className":12110},[1870],[1827,12112,12114],{"className":12113},[1870,7996],[1827,12115,12117,12266],{"className":12116},[1983,1984],[1827,12118,12120,12263],{"className":12119},[1988],[1827,12121,12124,12246],{"className":12122,"style":12123},[1992],"height:0.9169em;",[1827,12125,12128,12132],{"className":12126,"style":12127},[8010],"top:-3.2em;",[1827,12129],{"className":12130,"style":12131},[2000],"height:3.2em;",[1827,12133,12136,12142,12145,12188,12191,12194,12197,12243],{"className":12134,"style":12135},[1870],"padding-left:1em;",[1827,12137,12139],{"className":12138},[2649],[1827,12140,2898],{"className":12141},[1870,2653],[1827,12143,1895],{"className":12144},[1969],[1827,12146,12148,12151],{"className":12147},[1870],[1827,12149,2165],{"className":12150,"style":2209},[1870,1945],[1827,12152,12154],{"className":12153},[1979],[1827,12155,12157,12180],{"className":12156},[1983,1984],[1827,12158,12160,12177],{"className":12159},[1988],[1827,12161,12163],{"className":12162,"style":2424},[1992],[1827,12164,12165,12168],{"style":2248},[1827,12166],{"className":12167,"style":2001},[2000],[1827,12169,12171],{"className":12170},[2005,2006,2007,2008],[1827,12172,12174],{"className":12173},[1870,2008],[1827,12175,1793],{"className":12176},[1870,1945,2008],[1827,12178,2016],{"className":12179},[2015],[1827,12181,12183],{"className":12182},[1988],[1827,12184,12186],{"className":12185,"style":2445},[1992],[1827,12187],{},[1827,12189],{"className":12190,"style":3250},[1950],[1827,12192,3126],{"className":12193},[3254],[1827,12195],{"className":12196,"style":3250},[1950],[1827,12198,12200,12203],{"className":12199},[1870],[1827,12201,2165],{"className":12202,"style":2209},[1870,1945],[1827,12204,12206],{"className":12205},[1979],[1827,12207,12209,12235],{"className":12208},[1983,1984],[1827,12210,12212,12232],{"className":12211},[1988],[1827,12213,12215],{"className":12214,"style":3800},[1992],[1827,12216,12217,12220],{"style":2248},[1827,12218],{"className":12219,"style":2001},[2000],[1827,12221,12223],{"className":12222},[2005,2006,2007,2008],[1827,12224,12226],{"className":12225},[1870,2008],[1827,12227,12229],{"className":12228},[1870,6845,2008],[1827,12230,11728],{"className":12231},[1870,2008],[1827,12233,2016],{"className":12234},[2015],[1827,12236,12238],{"className":12237},[1988],[1827,12239,12241],{"className":12240,"style":2023},[1992],[1827,12242],{},[1827,12244,1924],{"className":12245},[2092],[1827,12247,12249,12252],{"style":12248},"top:-2.8769em;",[1827,12250],{"className":12251,"style":12131},[2000],[1827,12253,12256],{"className":12254,"style":12255},[8064],"min-width:1.02em;height:1.28em;",[8067,12257,12260],{"xmlns":8069,"width":8070,"height":12258,"viewBox":12259,"preserveAspectRatio":8073},"1.28em","0 0 400000 1296",[8075,12261],{"d":12262},"M263,681c0.7,0,18,39.7,52,119\nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120\nc340,-704.7,510.7,-1060.3,512,-1067\nl0 -0\nc4.7,-7.3,11,-11,19,-11\nH40000v40H1012.3\ns-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232\nc-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1\ns-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26\nc-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60z\nM1001 80h400000v40h-400000z",[1827,12264,2016],{"className":12265},[2015],[1827,12267,12269],{"className":12268},[1988],[1827,12270,12273],{"className":12271,"style":12272},[1992],"height:0.3231em;",[1827,12274],{},[1827,12276,12277,12280],{"style":3299},[1827,12278],{"className":12279,"style":3179},[2000],[1827,12281],{"className":12282,"style":3307},[3306],[1827,12284,12285,12288],{"style":3310},[1827,12286],{"className":12287,"style":3179},[2000],[1827,12289,12291,12294,12297,12340,12343,12346,12349,12395],{"className":12290},[1870],[1827,12292,2529],{"className":12293},[1870,2573],[1827,12295,2532],{"className":12296},[1969],[1827,12298,12300,12303],{"className":12299},[1870],[1827,12301,2165],{"className":12302,"style":2209},[1870,1945],[1827,12304,12306],{"className":12305},[1979],[1827,12307,12309,12332],{"className":12308},[1983,1984],[1827,12310,12312,12329],{"className":12311},[1988],[1827,12313,12315],{"className":12314,"style":2424},[1992],[1827,12316,12317,12320],{"style":2248},[1827,12318],{"className":12319,"style":2001},[2000],[1827,12321,12323],{"className":12322},[2005,2006,2007,2008],[1827,12324,12326],{"className":12325},[1870,2008],[1827,12327,1793],{"className":12328},[1870,1945,2008],[1827,12330,2016],{"className":12331},[2015],[1827,12333,12335],{"className":12334},[1988],[1827,12336,12338],{"className":12337,"style":2445},[1992],[1827,12339],{},[1827,12341],{"className":12342,"style":3250},[1950],[1827,12344,3126],{"className":12345},[3254],[1827,12347],{"className":12348,"style":3250},[1950],[1827,12350,12352,12355],{"className":12351},[1870],[1827,12353,2165],{"className":12354,"style":2209},[1870,1945],[1827,12356,12358],{"className":12357},[1979],[1827,12359,12361,12387],{"className":12360},[1983,1984],[1827,12362,12364,12384],{"className":12363},[1988],[1827,12365,12367],{"className":12366,"style":3800},[1992],[1827,12368,12369,12372],{"style":2248},[1827,12370],{"className":12371,"style":2001},[2000],[1827,12373,12375],{"className":12374},[2005,2006,2007,2008],[1827,12376,12378],{"className":12377},[1870,2008],[1827,12379,12381],{"className":12380},[1870,6845,2008],[1827,12382,11728],{"className":12383},[1870,2008],[1827,12385,2016],{"className":12386},[2015],[1827,12388,12390],{"className":12389},[1988],[1827,12391,12393],{"className":12392,"style":2023},[1992],[1827,12394],{},[1827,12396,2537],{"className":12397},[2092],[1827,12399,2016],{"className":12400},[2015],[1827,12402,12404],{"className":12403},[1988],[1827,12405,12408],{"className":12406,"style":12407},[1992],"height:1.13em;",[1827,12409],{},[1827,12411],{"className":12412},[2092,3271],[2507,12414,12415,12416,12617,4558,12620,12652],{},"同时控制因子暴露约束：",[1827,12417,12419],{"className":12418},[2360],[1827,12420,12422,12467],{"className":12421},[1830],[1827,12423,12425],{"className":12424},[1834],[1836,12426,12427],{"xmlns":1838,"display":2369},[1840,12428,12429,12464],{},[1843,12430,12431,12433,12439,12441,12443,12449,12455,12457,12459,12462],{},[1885,12432,4882],{"mathvariant":1927},[1920,12434,12435,12437],{},[1885,12436,5332],{},[1885,12438,1928],{"mathvariant":1927},[1885,12440,1887],{},[1889,12442,3126],{},[1920,12444,12445,12447],{},[1885,12446,5332],{},[1885,12448,1928],{"mathvariant":1927},[1920,12450,12451,12453],{},[1885,12452,1887],{},[3113,12454,11728],{},[1885,12456,4882],{"mathvariant":1927},[1889,12458,9117],{},[3113,12460,12461],{},"tol",[1889,12463,1906],{"separator":1857},[1850,12465,12466],{"encoding":1852},"|B^\\top w - B^\\top w^{\\text{bench}}| \\le \\text{tol},",[1827,12468,12470,12520,12602],{"className":12469,"ariaHidden":1857},[1856],[1827,12471,12473,12476,12479,12508,12511,12514,12517],{"className":12472},[1861],[1827,12474],{"className":12475,"style":6596},[1865],[1827,12477,4882],{"className":12478},[1870],[1827,12480,12482,12485],{"className":12481},[1870],[1827,12483,5332],{"className":12484,"style":5441},[1870,1945],[1827,12486,12488],{"className":12487},[1979],[1827,12489,12491],{"className":12490},[1983],[1827,12492,12494],{"className":12493},[1988],[1827,12495,12497],{"className":12496,"style":2463},[1992],[1827,12498,12499,12502],{"style":2484},[1827,12500],{"className":12501,"style":2001},[2000],[1827,12503,12505],{"className":12504},[2005,2006,2007,2008],[1827,12506,1928],{"className":12507},[1870,2008],[1827,12509,1887],{"className":12510,"style":1946},[1870,1945],[1827,12512],{"className":12513,"style":3250},[1950],[1827,12515,3126],{"className":12516},[3254],[1827,12518],{"className":12519,"style":3250},[1950],[1827,12521,12523,12526,12555,12590,12593,12596,12599],{"className":12522},[1861],[1827,12524],{"className":12525,"style":6596},[1865],[1827,12527,12529,12532],{"className":12528},[1870],[1827,12530,5332],{"className":12531,"style":5441},[1870,1945],[1827,12533,12535],{"className":12534},[1979],[1827,12536,12538],{"className":12537},[1983],[1827,12539,12541],{"className":12540},[1988],[1827,12542,12544],{"className":12543,"style":2463},[1992],[1827,12545,12546,12549],{"style":2484},[1827,12547],{"className":12548,"style":2001},[2000],[1827,12550,12552],{"className":12551},[2005,2006,2007,2008],[1827,12553,1928],{"className":12554},[1870,2008],[1827,12556,12558,12561],{"className":12557},[1870],[1827,12559,1887],{"className":12560,"style":1946},[1870,1945],[1827,12562,12564],{"className":12563},[1979],[1827,12565,12567],{"className":12566},[1983],[1827,12568,12570],{"className":12569},[1988],[1827,12571,12573],{"className":12572,"style":2463},[1992],[1827,12574,12575,12578],{"style":2484},[1827,12576],{"className":12577,"style":2001},[2000],[1827,12579,12581],{"className":12580},[2005,2006,2007,2008],[1827,12582,12584],{"className":12583},[1870,2008],[1827,12585,12587],{"className":12586},[1870,6845,2008],[1827,12588,11728],{"className":12589},[1870,2008],[1827,12591,4882],{"className":12592},[1870],[1827,12594],{"className":12595,"style":1951},[1950],[1827,12597,9117],{"className":12598},[1955],[1827,12600],{"className":12601,"style":1951},[1950],[1827,12603,12605,12608,12614],{"className":12604},[1861],[1827,12606],{"className":12607,"style":4707},[1865],[1827,12609,12611],{"className":12610},[1870,6845],[1827,12612,12461],{"className":12613},[1870],[1827,12615,1906],{"className":12616},[2029],[12618,12619],"br",{},[1827,12621,12623,12637],{"className":12622},[1830],[1827,12624,12626],{"className":12625},[1834],[1836,12627,12628],{"xmlns":1838},[1840,12629,12630,12634],{},[1843,12631,12632],{},[3113,12633,12461],{},[1850,12635,12636],{"encoding":1852},"\\text{tol}",[1827,12638,12640],{"className":12639,"ariaHidden":1857},[1856],[1827,12641,12643,12646],{"className":12642},[1861],[1827,12644],{"className":12645,"style":3079},[1865],[1827,12647,12649],{"className":12648},[1870,6845],[1827,12650,12461],{"className":12651},[1870]," 是容忍的因子偏离阈值。",[1814,12654,12656],{"id":12655},"_5-风险度量的扩展视角","5. 风险度量的扩展视角",[1793,12658,12659],{},"虽然均值–方差框架是资产定价与组合理论的基础，但在许多情形下，方差并非最合适的风险度量。例如：",[2504,12661,12662,12665],{},[2507,12663,12664],{},"对尾部风险敏感的策略更关心极端损失；",[2507,12666,12667],{},"对非对称收益分布更关心下行波动。",[1819,12669,12671],{"id":12670},"_51-var-与-cvar概念层面","5.1 VaR 与 CVaR（概念层面）",[1793,12673,12674,12675,12703,12704,12780,12781,3084],{},"设组合在下一期的损失为 ",[1827,12676,12678,12691],{"className":12677},[1830],[1827,12679,12681],{"className":12680},[1834],[1836,12682,12683],{"xmlns":1838},[1840,12684,12685,12689],{},[1843,12686,12687],{},[1885,12688,9395],{},[1850,12690,9395],{"encoding":1852},[1827,12692,12694],{"className":12693,"ariaHidden":1857},[1856],[1827,12695,12697,12700],{"className":12696},[1861],[1827,12698],{"className":12699,"style":2627},[1865],[1827,12701,9395],{"className":12702},[1870,1945],"（损失为正，收益为负）。给定置信水平 ",[1827,12705,12707,12734],{"className":12706},[1830],[1827,12708,12710],{"className":12709},[1834],[1836,12711,12712],{"xmlns":1838},[1840,12713,12714,12731],{},[1843,12715,12716,12718,12721,12723,12725,12727,12729],{},[1885,12717,4191],{},[1889,12719,12720],{},"∈",[1889,12722,1895],{"stretchy":1894},[1846,12724,1848],{},[1889,12726,1906],{"separator":1857},[1846,12728,1903],{},[1889,12730,1924],{"stretchy":1894},[1850,12732,12733],{"encoding":1852},"\\alpha \\in (0,1)",[1827,12735,12737,12756],{"className":12736,"ariaHidden":1857},[1856],[1827,12738,12740,12744,12747,12750,12753],{"className":12739},[1861],[1827,12741],{"className":12742,"style":12743},[1865],"height:0.5782em;vertical-align:-0.0391em;",[1827,12745,4191],{"className":12746,"style":4326},[1870,1945],[1827,12748],{"className":12749,"style":1951},[1950],[1827,12751,12720],{"className":12752},[1955],[1827,12754],{"className":12755,"style":1951},[1950],[1827,12757,12759,12762,12765,12768,12771,12774,12777],{"className":12758},[1861],[1827,12760],{"className":12761,"style":2569},[1865],[1827,12763,1895],{"className":12764},[1969],[1827,12766,1848],{"className":12767},[1870],[1827,12769,1906],{"className":12770},[2029],[1827,12772],{"className":12773,"style":2033},[1950],[1827,12775,1903],{"className":12776},[1870],[1827,12778,1924],{"className":12779},[2092],"，",[1797,12782,12783],{},"在分布已知的理想情况下",[2504,12785,12786,13061],{},[2507,12787,12788,12789,12817,12818,12847,12848],{},"VaR（Value at Risk）定义为 ",[1827,12790,12792,12805],{"className":12791},[1830],[1827,12793,12795],{"className":12794},[1834],[1836,12796,12797],{"xmlns":1838},[1840,12798,12799,12803],{},[1843,12800,12801],{},[1885,12802,9395],{},[1850,12804,9395],{"encoding":1852},[1827,12806,12808],{"className":12807,"ariaHidden":1857},[1856],[1827,12809,12811,12814],{"className":12810},[1861],[1827,12812],{"className":12813,"style":2627},[1865],[1827,12815,9395],{"className":12816},[1870,1945]," 的 ",[1827,12819,12821,12835],{"className":12820},[1830],[1827,12822,12824],{"className":12823},[1834],[1836,12825,12826],{"xmlns":1838},[1840,12827,12828,12832],{},[1843,12829,12830],{},[1885,12831,4191],{},[1850,12833,12834],{"encoding":1852},"\\alpha",[1827,12836,12838],{"className":12837,"ariaHidden":1857},[1856],[1827,12839,12841,12844],{"className":12840},[1861],[1827,12842],{"className":12843,"style":1941},[1865],[1827,12845,4191],{"className":12846,"style":4326},[1870,1945]," 分位数：",[1827,12849,12851],{"className":12850},[2360],[1827,12852,12854,12912],{"className":12853},[1830],[1827,12855,12857],{"className":12856},[1834],[1836,12858,12859],{"xmlns":1838,"display":2369},[1840,12860,12861,12909],{},[1843,12862,12863,12870,12872,12875,12877,12880,12883,12886,12889,12891,12893,12895,12897,12899,12902,12904,12907],{},[1897,12864,12865,12868],{},[3113,12866,12867],{},"VaR",[1885,12869,4191],{},[1889,12871,1891],{},[1885,12873,12874],{},"inf",[1889,12876,2608],{},[1889,12878,12879],{"stretchy":1894},"{",[1885,12881,12882],{"mathvariant":1927},"ℓ",[1889,12884,12885],{},":",[1885,12887,12888],{"mathvariant":2528},"P",[1889,12890,1895],{"stretchy":1894},[1885,12892,9395],{},[1889,12894,9117],{},[1885,12896,12882],{"mathvariant":1927},[1889,12898,1924],{"stretchy":1894},[1889,12900,12901],{},"≥",[1885,12903,4191],{},[1889,12905,12906],{"stretchy":1894},"}",[1885,12908,2392],{"mathvariant":1927},[1850,12910,12911],{"encoding":1852},"\\text{VaR}_\\alpha = \\inf\\{\\ell : \\mathbb{P}(L \\le \\ell) \\ge \\alpha\\}.",[1827,12913,12915,12973,13001,13025,13046],{"className":12914,"ariaHidden":1857},[1856],[1827,12916,12918,12921,12964,12967,12970],{"className":12917},[1861],[1827,12919],{"className":12920,"style":7668},[1865],[1827,12922,12924,12930],{"className":12923},[1870],[1827,12925,12927],{"className":12926},[1870,6845],[1827,12928,12867],{"className":12929},[1870],[1827,12931,12933],{"className":12932},[1979],[1827,12934,12936,12956],{"className":12935},[1983,1984],[1827,12937,12939,12953],{"className":12938},[1988],[1827,12940,12942],{"className":12941,"style":2424},[1992],[1827,12943,12944,12947],{"style":7692},[1827,12945],{"className":12946,"style":2001},[2000],[1827,12948,12950],{"className":12949},[2005,2006,2007,2008],[1827,12951,4191],{"className":12952,"style":4326},[1870,1945,2008],[1827,12954,2016],{"className":12955},[2015],[1827,12957,12959],{"className":12958},[1988],[1827,12960,12962],{"className":12961,"style":2023},[1992],[1827,12963],{},[1827,12965],{"className":12966,"style":1951},[1950],[1827,12968,1891],{"className":12969},[1955],[1827,12971],{"className":12972,"style":1951},[1950],[1827,12974,12976,12979,12986,12989,12992,12995,12998],{"className":12975},[1861],[1827,12977],{"className":12978,"style":2569},[1865],[1827,12980,12982,12983],{"className":12981},[2649],"in",[1827,12984,3769],{"style":12985},"margin-right:0.0778em;",[1827,12987,12879],{"className":12988},[1969],[1827,12990,12882],{"className":12991},[1870],[1827,12993],{"className":12994,"style":1951},[1950],[1827,12996,12885],{"className":12997},[1955],[1827,12999],{"className":13000,"style":1951},[1950],[1827,13002,13004,13007,13010,13013,13016,13019,13022],{"className":13003},[1861],[1827,13005],{"className":13006,"style":2569},[1865],[1827,13008,12888],{"className":13009},[1870,2573],[1827,13011,1895],{"className":13012},[1969],[1827,13014,9395],{"className":13015},[1870,1945],[1827,13017],{"className":13018,"style":1951},[1950],[1827,13020,9117],{"className":13021},[1955],[1827,13023],{"className":13024,"style":1951},[1950],[1827,13026,13028,13031,13034,13037,13040,13043],{"className":13027},[1861],[1827,13029],{"className":13030,"style":2569},[1865],[1827,13032,12882],{"className":13033},[1870],[1827,13035,1924],{"className":13036},[2092],[1827,13038],{"className":13039,"style":1951},[1950],[1827,13041,12901],{"className":13042},[1955],[1827,13044],{"className":13045,"style":1951},[1950],[1827,13047,13049,13052,13055,13058],{"className":13048},[1861],[1827,13050],{"className":13051,"style":2569},[1865],[1827,13053,4191],{"className":13054,"style":4326},[1870,1945],[1827,13056,12906],{"className":13057},[2092],[1827,13059,2392],{"className":13060},[1870],[2507,13062,13063,13064],{},"CVaR（Conditional VaR，或 Expected Shortfall）定义为在超过 VaR 时的条件期望：",[1827,13065,13067],{"className":13066},[2360],[1827,13068,13070,13113],{"className":13069},[1830],[1827,13071,13073],{"className":13072},[1834],[1836,13074,13075],{"xmlns":1838,"display":2369},[1840,13076,13077,13110],{},[1843,13078,13079,13086,13088,13090,13092,13094,13096,13098,13100,13106,13108],{},[1897,13080,13081,13084],{},[3113,13082,13083],{},"CVaR",[1885,13085,4191],{},[1889,13087,1891],{},[1885,13089,2529],{"mathvariant":2528},[1889,13091,2532],{"stretchy":1894},[1885,13093,9395],{},[1889,13095,4882],{},[1885,13097,9395],{},[1889,13099,12901],{},[1897,13101,13102,13104],{},[3113,13103,12867],{},[1885,13105,4191],{},[1889,13107,2537],{"stretchy":1894},[1885,13109,2392],{"mathvariant":1927},[1850,13111,13112],{"encoding":1852},"\\text{CVaR}_\\alpha = \\mathbb{E}[L \\mid L \\ge \\text{VaR}_\\alpha].",[1827,13114,13116,13174,13198,13217],{"className":13115,"ariaHidden":1857},[1856],[1827,13117,13119,13122,13165,13168,13171],{"className":13118},[1861],[1827,13120],{"className":13121,"style":7668},[1865],[1827,13123,13125,13131],{"className":13124},[1870],[1827,13126,13128],{"className":13127},[1870,6845],[1827,13129,13083],{"className":13130},[1870],[1827,13132,13134],{"className":13133},[1979],[1827,13135,13137,13157],{"className":13136},[1983,1984],[1827,13138,13140,13154],{"className":13139},[1988],[1827,13141,13143],{"className":13142,"style":2424},[1992],[1827,13144,13145,13148],{"style":7692},[1827,13146],{"className":13147,"style":2001},[2000],[1827,13149,13151],{"className":13150},[2005,2006,2007,2008],[1827,13152,4191],{"className":13153,"style":4326},[1870,1945,2008],[1827,13155,2016],{"className":13156},[2015],[1827,13158,13160],{"className":13159},[1988],[1827,13161,13163],{"className":13162,"style":2023},[1992],[1827,13164],{},[1827,13166],{"className":13167,"style":1951},[1950],[1827,13169,1891],{"className":13170},[1955],[1827,13172],{"className":13173,"style":1951},[1950],[1827,13175,13177,13180,13183,13186,13189,13192,13195],{"className":13176},[1861],[1827,13178],{"className":13179,"style":2569},[1865],[1827,13181,2529],{"className":13182},[1870,2573],[1827,13184,2532],{"className":13185},[1969],[1827,13187,9395],{"className":13188},[1870,1945],[1827,13190],{"className":13191,"style":1951},[1950],[1827,13193,4882],{"className":13194},[1955],[1827,13196],{"className":13197,"style":1951},[1950],[1827,13199,13201,13205,13208,13211,13214],{"className":13200},[1861],[1827,13202],{"className":13203,"style":13204},[1865],"height:0.8193em;vertical-align:-0.136em;",[1827,13206,9395],{"className":13207},[1870,1945],[1827,13209],{"className":13210,"style":1951},[1950],[1827,13212,12901],{"className":13213},[1955],[1827,13215],{"className":13216,"style":1951},[1950],[1827,13218,13220,13223,13266,13269],{"className":13219},[1861],[1827,13221],{"className":13222,"style":2569},[1865],[1827,13224,13226,13232],{"className":13225},[1870],[1827,13227,13229],{"className":13228},[1870,6845],[1827,13230,12867],{"className":13231},[1870],[1827,13233,13235],{"className":13234},[1979],[1827,13236,13238,13258],{"className":13237},[1983,1984],[1827,13239,13241,13255],{"className":13240},[1988],[1827,13242,13244],{"className":13243,"style":2424},[1992],[1827,13245,13246,13249],{"style":7692},[1827,13247],{"className":13248,"style":2001},[2000],[1827,13250,13252],{"className":13251},[2005,2006,2007,2008],[1827,13253,4191],{"className":13254,"style":4326},[1870,1945,2008],[1827,13256,2016],{"className":13257},[2015],[1827,13259,13261],{"className":13260},[1988],[1827,13262,13264],{"className":13263,"style":2023},[1992],[1827,13265],{},[1827,13267,2537],{"className":13268},[2092],[1827,13270,2392],{"className":13271},[1870],[1793,13273,13274],{},"在实务中，VaR\u002FCVaR 的估计会涉及大量计量方法（历史模拟、参数法、蒙特卡洛等），这些将在未来“计量”和“风险管理”更专门的笔记中展开。",[1819,13276,13278],{"id":13277},"_52-下行风险与半方差","5.2 下行风险与半方差",[1793,13280,13281,13282,3084],{},"另一类风险度量关注“只统计坏的波动”，例如",[1797,13283,13284],{},"半方差",[1827,13286,13288],{"className":13287},[2360],[1827,13289,13291,13338],{"className":13290},[1830],[1827,13292,13294],{"className":13293},[1834],[1836,13295,13296],{"xmlns":1838,"display":2369},[1840,13297,13298,13335],{},[1843,13299,13300,13303,13305,13307,13309,13311,13313,13315,13321,13323,13325,13331,13333],{},[3113,13301,13302],{},"SemiVar",[1889,13304,1891],{},[1885,13306,2529],{"mathvariant":2528},[1889,13308,2532],{"stretchy":1894},[1885,13310,9112],{},[1889,13312,2608],{},[1889,13314,1895],{"stretchy":1894},[1897,13316,13317,13319],{},[1885,13318,2165],{},[1885,13320,1793],{},[1889,13322,1906],{"separator":1857},[1846,13324,1848],{},[1920,13326,13327,13329],{},[1889,13328,1924],{"stretchy":1894},[1846,13330,3134],{},[1889,13332,2537],{"stretchy":1894},[1885,13334,2392],{"mathvariant":1927},[1850,13336,13337],{"encoding":1852}," \\text{SemiVar} = \\mathbb{E}[\\min(r_p, 0)^2].",[1827,13339,13341,13362],{"className":13340,"ariaHidden":1857},[1856],[1827,13342,13344,13347,13353,13356,13359],{"className":13343},[1861],[1827,13345],{"className":13346,"style":2627},[1865],[1827,13348,13350],{"className":13349},[1870,6845],[1827,13351,13302],{"className":13352},[1870],[1827,13354],{"className":13355,"style":1951},[1950],[1827,13357,1891],{"className":13358},[1955],[1827,13360],{"className":13361,"style":1951},[1950],[1827,13363,13365,13369,13372,13375,13378,13381,13421,13424,13427,13430,13459,13462],{"className":13364},[1861],[1827,13366],{"className":13367,"style":13368},[1865],"height:1.1502em;vertical-align:-0.2861em;",[1827,13370,2529],{"className":13371},[1870,2573],[1827,13373,2532],{"className":13374},[1969],[1827,13376,9112],{"className":13377},[2649],[1827,13379,1895],{"className":13380},[1969],[1827,13382,13384,13387],{"className":13383},[1870],[1827,13385,2165],{"className":13386,"style":2209},[1870,1945],[1827,13388,13390],{"className":13389},[1979],[1827,13391,13393,13413],{"className":13392},[1983,1984],[1827,13394,13396,13410],{"className":13395},[1988],[1827,13397,13399],{"className":13398,"style":2424},[1992],[1827,13400,13401,13404],{"style":2248},[1827,13402],{"className":13403,"style":2001},[2000],[1827,13405,13407],{"className":13406},[2005,2006,2007,2008],[1827,13408,1793],{"className":13409},[1870,1945,2008],[1827,13411,2016],{"className":13412},[2015],[1827,13414,13416],{"className":13415},[1988],[1827,13417,13419],{"className":13418,"style":2445},[1992],[1827,13420],{},[1827,13422,1906],{"className":13423},[2029],[1827,13425],{"className":13426,"style":2033},[1950],[1827,13428,1848],{"className":13429},[1870],[1827,13431,13433,13436],{"className":13432},[2092],[1827,13434,1924],{"className":13435},[2092],[1827,13437,13439],{"className":13438},[1979],[1827,13440,13442],{"className":13441},[1983],[1827,13443,13445],{"className":13444},[1988],[1827,13446,13448],{"className":13447,"style":3648},[1992],[1827,13449,13450,13453],{"style":2484},[1827,13451],{"className":13452,"style":2001},[2000],[1827,13454,13456],{"className":13455},[2005,2006,2007,2008],[1827,13457,3134],{"className":13458},[1870,2008],[1827,13460,2537],{"className":13461},[2092],[1827,13463,2392],{"className":13464},[1870],[1793,13466,13467],{},"在一定条件下，可以将下行风险度量纳入类似均值–方差的优化框架，但会导致问题变为非凸或需要近似求解。",[1814,13469,13471],{"id":13470},"_6-小结与资产定价视角的-checklist","6. 小结与资产定价视角的 Checklist",[1793,13473,13474],{},"从资产定价 \u002F 组合理论的视角看，一个“规范”的组合构建和风险建模流程至少应包含：",[11691,13476,13477,13544,13669,13680,13691],{},[2507,13478,13479,13480,13538,13539],{},"明确预期收益向量 ",[1827,13481,13483,13500],{"className":13482},[1830],[1827,13484,13486],{"className":13485},[1834],[1836,13487,13488],{"xmlns":1838},[1840,13489,13490,13498],{},[1843,13491,13492],{},[1920,13493,13494,13496],{},[1885,13495,2523],{},[1885,13497,3923],{},[1850,13499,9896],{"encoding":1852},[1827,13501,13503],{"className":13502,"ariaHidden":1857},[1856],[1827,13504,13506,13509],{"className":13505},[1861],[1827,13507],{"className":13508,"style":9906},[1865],[1827,13510,13512,13515],{"className":13511},[1870],[1827,13513,2523],{"className":13514},[1870,1945],[1827,13516,13518],{"className":13517},[1979],[1827,13519,13521],{"className":13520},[1983],[1827,13522,13524],{"className":13523},[1988],[1827,13525,13527],{"className":13526,"style":9307},[1992],[1827,13528,13529,13532],{"style":2111},[1827,13530],{"className":13531,"style":2001},[2000],[1827,13533,13535],{"className":13534},[2005,2006,2007,2008],[1827,13536,3923],{"className":13537},[1870,1945,2008]," 的来源：\n",[2504,13540,13541],{},[2507,13542,13543],{},"来自历史估计、因子价格估计，还是主观观点（views）？",[2507,13545,13546,13547,13660,13661],{},"使用多因子模型构建协方差矩阵 ",[1827,13548,13550,13580],{"className":13549},[1830],[1827,13551,13553],{"className":13552},[1834],[1836,13554,13555],{"xmlns":1838},[1840,13556,13557,13577],{},[1843,13558,13559,13561,13563,13565,13567,13573,13575],{},[1885,13560,2600],{"mathvariant":1927},[1889,13562,1891],{},[1885,13564,5332],{},[1885,13566,5912],{},[1920,13568,13569,13571],{},[1885,13570,5332],{},[1885,13572,1928],{"mathvariant":1927},[1889,13574,4182],{},[1885,13576,5771],{"mathvariant":1927},[1850,13578,13579],{"encoding":1852},"\\Sigma = B F B^\\top + \\Delta",[1827,13581,13583,13601,13651],{"className":13582,"ariaHidden":1857},[1856],[1827,13584,13586,13589,13592,13595,13598],{"className":13585},[1861],[1827,13587],{"className":13588,"style":2627},[1865],[1827,13590,2600],{"className":13591},[1870],[1827,13593],{"className":13594,"style":1951},[1950],[1827,13596,1891],{"className":13597},[1955],[1827,13599],{"className":13600,"style":1951},[1950],[1827,13602,13604,13607,13610,13613,13642,13645,13648],{"className":13603},[1861],[1827,13605],{"className":13606,"style":11872},[1865],[1827,13608,5332],{"className":13609,"style":5441},[1870,1945],[1827,13611,5912],{"className":13612,"style":6038},[1870,1945],[1827,13614,13616,13619],{"className":13615},[1870],[1827,13617,5332],{"className":13618,"style":5441},[1870,1945],[1827,13620,13622],{"className":13621},[1979],[1827,13623,13625],{"className":13624},[1983],[1827,13626,13628],{"className":13627},[1988],[1827,13629,13631],{"className":13630,"style":2108},[1992],[1827,13632,13633,13636],{"style":2111},[1827,13634],{"className":13635,"style":2001},[2000],[1827,13637,13639],{"className":13638},[2005,2006,2007,2008],[1827,13640,1928],{"className":13641},[1870,2008],[1827,13643],{"className":13644,"style":3250},[1950],[1827,13646,4182],{"className":13647},[3254],[1827,13649],{"className":13650,"style":3250},[1950],[1827,13652,13654,13657],{"className":13653},[1861],[1827,13655],{"className":13656,"style":2627},[1865],[1827,13658,5771],{"className":13659},[1870],"：\n",[2504,13662,13663,13666],{},[2507,13664,13665],{},"确定因子定义与暴露估计方法；",[2507,13667,13668],{},"确定因子协方差和特异风险估计方法（滚动窗口、指数加权等）。",[2507,13670,13671,13672],{},"采用均值–方差或其扩展形式进行组合优化：\n",[2504,13673,13674,13677],{},[2507,13675,13676],{},"明确目标函数（夏普\u002F信息比率\u002F风险平价等）；",[2507,13678,13679],{},"明确约束集合（杠杆、敞口、流动性、交易成本等）。",[2507,13681,13682,13683],{},"对结果进行风险分解与归因：\n",[2504,13684,13685,13688],{},[2507,13686,13687],{},"看清组合风险在因子与特异之间的分布；",[2507,13689,13690],{},"按资产\u002F行业\u002F风格拆解成分风险贡献。",[2507,13692,13693,13694],{},"在回测与实盘监控中，持续评估：\n",[2504,13695,13696,13699,13702],{},[2507,13697,13698],{},"因子暴露是否符合设计；",[2507,13700,13701],{},"组合风险是否在预期范围内；",[2507,13703,13704],{},"资产定价假设（例如线性因子模型）是否出现明显失效迹象。",[13706,13707],"hr",{},[1814,13709,13711],{"id":13710},"_7-自学手册从-alpha-分数到风险可控组合","7. 自学手册：从 alpha 分数到风险可控组合",[1819,13713,13715],{"id":13714},"_71-学习目标","7.1 学习目标",[1793,13717,13718],{},"学完本章后，你应当能够：",[11691,13720,13721,13812,13815,13818,13821],{},[2507,13722,13723,13724,13782,13783,13811],{},"解释 ",[1827,13725,13727,13744],{"className":13726},[1830],[1827,13728,13730],{"className":13729},[1834],[1836,13731,13732],{"xmlns":1838},[1840,13733,13734,13742],{},[1843,13735,13736],{},[1920,13737,13738,13740],{},[1885,13739,2523],{},[1885,13741,3923],{},[1850,13743,9896],{"encoding":1852},[1827,13745,13747],{"className":13746,"ariaHidden":1857},[1856],[1827,13748,13750,13753],{"className":13749},[1861],[1827,13751],{"className":13752,"style":9906},[1865],[1827,13754,13756,13759],{"className":13755},[1870],[1827,13757,2523],{"className":13758},[1870,1945],[1827,13760,13762],{"className":13761},[1979],[1827,13763,13765],{"className":13764},[1983],[1827,13766,13768],{"className":13767},[1988],[1827,13769,13771],{"className":13770,"style":9307},[1992],[1827,13772,13773,13776],{"style":2111},[1827,13774],{"className":13775,"style":2001},[2000],[1827,13777,13779],{"className":13778},[2005,2006,2007,2008],[1827,13780,3923],{"className":13781},[1870,1945,2008],"、",[1827,13784,13786,13799],{"className":13785},[1830],[1827,13787,13789],{"className":13788},[1834],[1836,13790,13791],{"xmlns":1838},[1840,13792,13793,13797],{},[1843,13794,13795],{},[1885,13796,2600],{"mathvariant":1927},[1850,13798,9862],{"encoding":1852},[1827,13800,13802],{"className":13801,"ariaHidden":1857},[1856],[1827,13803,13805,13808],{"className":13804},[1861],[1827,13806],{"className":13807,"style":2627},[1865],[1827,13809,2600],{"className":13810},[1870],"、约束集合和目标函数在组合优化中的角色；",[2507,13813,13814],{},"区分收益预测、风险预测和交易约束三类输入；",[2507,13816,13817],{},"用多因子风险模型拆解组合的因子风险与特异风险；",[2507,13819,13820],{},"判断优化结果是否过度集中、暴露漂移或对估计误差过敏；",[2507,13822,13823],{},"为一个多因子股票策略写出组合构建和风险审查清单。",[1819,13825,13827],{"id":13826},"_72-生产场景","7.2 生产场景",[1793,13829,13830],{},"研究团队给出每只股票的 alpha 分数，风险团队给出行业、市值、波动率等风险模型，交易团队提醒部分小盘股成交困难。你的任务是把分数转成目标权重。一个可上线的组合构建流程要同时回答：",[2504,13832,13833,13895,13927,13930,13933],{},[2507,13834,13835,13836,13894],{},"预期收益向量 ",[1827,13837,13839,13856],{"className":13838},[1830],[1827,13840,13842],{"className":13841},[1834],[1836,13843,13844],{"xmlns":1838},[1840,13845,13846,13854],{},[1843,13847,13848],{},[1920,13849,13850,13852],{},[1885,13851,2523],{},[1885,13853,3923],{},[1850,13855,9896],{"encoding":1852},[1827,13857,13859],{"className":13858,"ariaHidden":1857},[1856],[1827,13860,13862,13865],{"className":13861},[1861],[1827,13863],{"className":13864,"style":9906},[1865],[1827,13866,13868,13871],{"className":13867},[1870],[1827,13869,2523],{"className":13870},[1870,1945],[1827,13872,13874],{"className":13873},[1979],[1827,13875,13877],{"className":13876},[1983],[1827,13878,13880],{"className":13879},[1988],[1827,13881,13883],{"className":13882,"style":9307},[1992],[1827,13884,13885,13888],{"style":2111},[1827,13886],{"className":13887,"style":2001},[2000],[1827,13889,13891],{"className":13890},[2005,2006,2007,2008],[1827,13892,3923],{"className":13893},[1870,1945,2008]," 从哪里来，是否稳定？",[2507,13896,13897,13898,13926],{},"协方差矩阵 ",[1827,13899,13901,13914],{"className":13900},[1830],[1827,13902,13904],{"className":13903},[1834],[1836,13905,13906],{"xmlns":1838},[1840,13907,13908,13912],{},[1843,13909,13910],{},[1885,13911,2600],{"mathvariant":1927},[1850,13913,9862],{"encoding":1852},[1827,13915,13917],{"className":13916,"ariaHidden":1857},[1856],[1827,13918,13920,13923],{"className":13919},[1861],[1827,13921],{"className":13922,"style":2627},[1865],[1827,13924,2600],{"className":13925},[1870]," 是否正定、是否过度依赖短样本？",[2507,13928,13929],{},"行业、市值、杠杆、个股上限和流动性约束是否被满足？",[2507,13931,13932],{},"优化后组合的风险贡献是否集中在少数资产或因子？",[2507,13934,13935],{},"若 alpha 预测误差变大，组合是否仍然稳健？",[1819,13937,13939],{"id":13938},"_73-定义与工作流逻辑","7.3 定义与工作流逻辑",[13941,13942,13943,13959],"table",{},[13944,13945,13946],"thead",{},[13947,13948,13949,13953,13956],"tr",{},[13950,13951,13952],"th",{},"输入\u002F输出",[13950,13954,13955],{},"含义",[13950,13957,13958],{},"审查问题",[13960,13961,13962,14031,14069,14107,14145,14213],"tbody",{},[13947,13963,13964,14025,14028],{},[13965,13966,13967],"td",{},[1827,13968,13970,13987],{"className":13969},[1830],[1827,13971,13973],{"className":13972},[1834],[1836,13974,13975],{"xmlns":1838},[1840,13976,13977,13985],{},[1843,13978,13979],{},[1920,13980,13981,13983],{},[1885,13982,2523],{},[1885,13984,3923],{},[1850,13986,9896],{"encoding":1852},[1827,13988,13990],{"className":13989,"ariaHidden":1857},[1856],[1827,13991,13993,13996],{"className":13992},[1861],[1827,13994],{"className":13995,"style":9906},[1865],[1827,13997,13999,14002],{"className":13998},[1870],[1827,14000,2523],{"className":14001},[1870,1945],[1827,14003,14005],{"className":14004},[1979],[1827,14006,14008],{"className":14007},[1983],[1827,14009,14011],{"className":14010},[1988],[1827,14012,14014],{"className":14013,"style":9307},[1992],[1827,14015,14016,14019],{"style":2111},[1827,14017],{"className":14018,"style":2001},[2000],[1827,14020,14022],{"className":14021},[2005,2006,2007,2008],[1827,14023,3923],{"className":14024},[1870,1945,2008],[13965,14026,14027],{},"预期超额收益或 alpha 分数",[13965,14029,14030],{},"是否经过缩放、去噪和样本外验证",[13947,14032,14033,14063,14066],{},[13965,14034,14035],{},[1827,14036,14038,14051],{"className":14037},[1830],[1827,14039,14041],{"className":14040},[1834],[1836,14042,14043],{"xmlns":1838},[1840,14044,14045,14049],{},[1843,14046,14047],{},[1885,14048,2600],{"mathvariant":1927},[1850,14050,9862],{"encoding":1852},[1827,14052,14054],{"className":14053,"ariaHidden":1857},[1856],[1827,14055,14057,14060],{"className":14056},[1861],[1827,14058],{"className":14059,"style":2627},[1865],[1827,14061,2600],{"className":14062},[1870],[13965,14064,14065],{},"收益协方差或风险模型",[13965,14067,14068],{},"是否稳定、正定、可解释",[13947,14070,14071,14101,14104],{},[13965,14072,14073],{},[1827,14074,14076,14089],{"className":14075},[1830],[1827,14077,14079],{"className":14078},[1834],[1836,14080,14081],{"xmlns":1838},[1840,14082,14083,14087],{},[1843,14084,14085],{},[1885,14086,5332],{},[1850,14088,5332],{"encoding":1852},[1827,14090,14092],{"className":14091,"ariaHidden":1857},[1856],[1827,14093,14095,14098],{"className":14094},[1861],[1827,14096],{"className":14097,"style":2627},[1865],[1827,14099,5332],{"className":14100,"style":5441},[1870,1945],[13965,14102,14103],{},"因子暴露矩阵",[13965,14105,14106],{},"行业、风格、国家暴露是否完整",[13947,14108,14109,14140,14142],{},[13965,14110,14111],{},[1827,14112,14114,14128],{"className":14113},[1830],[1827,14115,14117],{"className":14116},[1834],[1836,14118,14119],{"xmlns":1838},[1840,14120,14121,14125],{},[1843,14122,14123],{},[1885,14124,10005],{"mathvariant":10004},[1850,14126,14127],{"encoding":1852},"\\mathcal{C}",[1827,14129,14131],{"className":14130,"ariaHidden":1857},[1856],[1827,14132,14134,14137],{"className":14133},[1861],[1827,14135],{"className":14136,"style":2627},[1865],[1827,14138,10005],{"className":14139,"style":10269},[1870,10268],[13965,14141,10261],{},[13965,14143,14144],{},"是否反映账户、监管、流动性和交易限制",[13947,14146,14147,14207,14210],{},[13965,14148,14149],{},[1827,14150,14152,14169],{"className":14151},[1830],[1827,14153,14155],{"className":14154},[1834],[1836,14156,14157],{"xmlns":1838},[1840,14158,14159,14167],{},[1843,14160,14161],{},[1920,14162,14163,14165],{},[1885,14164,1887],{},[1889,14166,3419],{},[1850,14168,3695],{"encoding":1852},[1827,14170,14172],{"className":14171,"ariaHidden":1857},[1856],[1827,14173,14175,14178],{"className":14174},[1861],[1827,14176],{"className":14177,"style":3705},[1865],[1827,14179,14181,14184],{"className":14180},[1870],[1827,14182,1887],{"className":14183,"style":1946},[1870,1945],[1827,14185,14187],{"className":14186},[1979],[1827,14188,14190],{"className":14189},[1983],[1827,14191,14193],{"className":14192},[1988],[1827,14194,14196],{"className":14195,"style":3705},[1992],[1827,14197,14198,14201],{"style":2111},[1827,14199],{"className":14200,"style":2001},[2000],[1827,14202,14204],{"className":14203},[2005,2006,2007,2008],[1827,14205,3419],{"className":14206},[3254,2008],[13965,14208,14209],{},"优化后的目标权重",[13965,14211,14212],{},"是否集中、是否可交易、是否符合风险预算",[13947,14214,14215,14218,14221],{},[13965,14216,14217],{},"风险归因",[13965,14219,14220],{},"总风险的来源分解",[13965,14222,14223],{},"alpha 收益是否伴随不可接受暴露",[1793,14225,14226],{},"典型流程是：",[11691,14228,14229,14291,14407,14410,14413,14416,14419],{},[2507,14230,14231,14232,14290],{},"将因子打分映射成 ",[1827,14233,14235,14252],{"className":14234},[1830],[1827,14236,14238],{"className":14237},[1834],[1836,14239,14240],{"xmlns":1838},[1840,14241,14242,14250],{},[1843,14243,14244],{},[1920,14245,14246,14248],{},[1885,14247,2523],{},[1885,14249,3923],{},[1850,14251,9896],{"encoding":1852},[1827,14253,14255],{"className":14254,"ariaHidden":1857},[1856],[1827,14256,14258,14261],{"className":14257},[1861],[1827,14259],{"className":14260,"style":9906},[1865],[1827,14262,14264,14267],{"className":14263},[1870],[1827,14265,2523],{"className":14266},[1870,1945],[1827,14268,14270],{"className":14269},[1979],[1827,14271,14273],{"className":14272},[1983],[1827,14274,14276],{"className":14275},[1988],[1827,14277,14279],{"className":14278,"style":9307},[1992],[1827,14280,14281,14284],{"style":2111},[1827,14282],{"className":14283,"style":2001},[2000],[1827,14285,14287],{"className":14286},[2005,2006,2007,2008],[1827,14288,3923],{"className":14289},[1870,1945,2008],"，并做合理缩放；",[2507,14292,14293,14294,3045],{},"载入风险模型 ",[1827,14295,14297,14327],{"className":14296},[1830],[1827,14298,14300],{"className":14299},[1834],[1836,14301,14302],{"xmlns":1838},[1840,14303,14304,14324],{},[1843,14305,14306,14308,14310,14312,14314,14320,14322],{},[1885,14307,2600],{"mathvariant":1927},[1889,14309,1891],{},[1885,14311,5332],{},[1885,14313,5912],{},[1920,14315,14316,14318],{},[1885,14317,5332],{},[1885,14319,1928],{"mathvariant":1927},[1889,14321,4182],{},[1885,14323,5771],{"mathvariant":1927},[1850,14325,14326],{"encoding":1852},"\\Sigma = BFB^\\top+\\Delta",[1827,14328,14330,14348,14398],{"className":14329,"ariaHidden":1857},[1856],[1827,14331,14333,14336,14339,14342,14345],{"className":14332},[1861],[1827,14334],{"className":14335,"style":2627},[1865],[1827,14337,2600],{"className":14338},[1870],[1827,14340],{"className":14341,"style":1951},[1950],[1827,14343,1891],{"className":14344},[1955],[1827,14346],{"className":14347,"style":1951},[1950],[1827,14349,14351,14354,14357,14360,14389,14392,14395],{"className":14350},[1861],[1827,14352],{"className":14353,"style":11872},[1865],[1827,14355,5332],{"className":14356,"style":5441},[1870,1945],[1827,14358,5912],{"className":14359,"style":6038},[1870,1945],[1827,14361,14363,14366],{"className":14362},[1870],[1827,14364,5332],{"className":14365,"style":5441},[1870,1945],[1827,14367,14369],{"className":14368},[1979],[1827,14370,14372],{"className":14371},[1983],[1827,14373,14375],{"className":14374},[1988],[1827,14376,14378],{"className":14377,"style":2108},[1992],[1827,14379,14380,14383],{"style":2111},[1827,14381],{"className":14382,"style":2001},[2000],[1827,14384,14386],{"className":14385},[2005,2006,2007,2008],[1827,14387,1928],{"className":14388},[1870,2008],[1827,14390],{"className":14391,"style":3250},[1950],[1827,14393,4182],{"className":14394},[3254],[1827,14396],{"className":14397,"style":3250},[1950],[1827,14399,14401,14404],{"className":14400},[1861],[1827,14402],{"className":14403,"style":2627},[1865],[1827,14405,5771],{"className":14406},[1870],[2507,14408,14409],{},"写清目标函数，例如最大化风险调整后 alpha 或主动信息比率；",[2507,14411,14412],{},"加入硬约束（杠杆、个股权重、行业偏离、流动性上限）；",[2507,14414,14415],{},"求解并检查 KKT\u002F数值状态；",[2507,14417,14418],{},"做风险分解、压力测试和换手审查；",[2507,14420,14421],{},"将目标权重传给执行模块。",[1819,14423,14425],{"id":14424},"_74-近期扩展可实现有效前沿","7.4 近期扩展：可实现有效前沿",[1793,14427,14428,14429,14435],{},"教科书有效前沿通常忽略成本，且在无风险资产存在时可沿同一夏普比率直线放大风险。",[9339,14430,14434],{"href":14431,"rel":14432},"https:\u002F\u002Fdoi.org\u002F10.1093\u002Frfs\u002Fhhag022",[14433],"nofollow","Jensen et al. (2026)"," 把策略放到成本后的“可实现有效前沿”上评价：资金规模、换手和市场冲击会使净夏普随风险规模变化，因此不存在一个与账户规模无关的唯一前沿。",[1793,14437,14438],{},"下面的两资产算例不复现论文，只展示交易成本如何把最优权重拉回现有持仓：",[14440,14441],"pyodide",{"code64":14442,"layout":14443,"locale":7,"title":14444},"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\u002FveeVpeaIkOacrCIsIHdpdGhvdXRfY29zdCwgRmFsc2UpLCAoIuiuoeWFpeaIkOacrCIsIHdpdGhfY29zdCwgVHJ1ZSkKXToKICAgIHV0aWxpdHksIG1lYW4sIHZvbCwgdHVybm92ZXIgPSBtZXRyaWNzKHdlaWdodCwgdXNlX2Nvc3QpCiAgICBwcmludChsYWJlbCwgZiJB5p2D6YeNPXt3ZWlnaHQ6LjElfSwg5pyf5pybPXttZWFuOi4yJX0sIOazouWKqD17dm9sOi4yJX0sIOaNouaJiz17dHVybm92ZXI6LjElfSIp","vertical","成本如何改变最优组合",[1793,14446,14447,14448,14451,14452,14455],{},"静态结果：忽略成本时 A 的最优权重为 ",[1797,14449,14450],{},"38.1%","；计入示意成本后降到 ",[1797,14453,14454],{},"22.2%","，更接近原持仓 20%。权重差异来自这个特定目标和成本参数，不是通用配置建议。真实问题还要估计非线性冲击、账户规模、卖空、税费和求解不确定性。",[1819,14457,14459],{"id":14458},"_75-迷你案例等权-alpha-与优化-alpha-的比较","7.5 迷你案例：等权 alpha 与优化 alpha 的比较",[1793,14461,14462],{},"你有 100 只股票的标准化分数。可以先做两个组合对照：",[13941,14464,14465,14478],{},[13944,14466,14467],{},[13947,14468,14469,14472,14475],{},[13950,14470,14471],{},"组合",[13950,14473,14474],{},"构造方式",[13950,14476,14477],{},"你应观察什么",[13960,14479,14480,14491],{},[13947,14481,14482,14485,14488],{},[13965,14483,14484],{},"等权多空",[13965,14486,14487],{},"多头 top 20%，空头 bottom 20%，组内等权",[13965,14489,14490],{},"信号毛收益和换手的基线",[13947,14492,14493,14496,14735],{},[13965,14494,14495],{},"风险约束优化",[13965,14497,14498,14499,14734],{},"最大化 ",[1827,14500,14502,14544],{"className":14501},[1830],[1827,14503,14505],{"className":14504},[1834],[1836,14506,14507],{"xmlns":1838},[1840,14508,14509,14541],{},[1843,14510,14511,14517,14523,14525,14531,14537,14539],{},[1920,14512,14513,14515],{},[1885,14514,1887],{},[1885,14516,1928],{"mathvariant":1927},[1920,14518,14519,14521],{},[1885,14520,2523],{},[1885,14522,3923],{},[1889,14524,3126],{},[3128,14526,14527,14529],{},[1885,14528,3066],{},[1846,14530,3134],{},[1920,14532,14533,14535],{},[1885,14534,1887],{},[1885,14536,1928],{"mathvariant":1927},[1885,14538,2600],{"mathvariant":1927},[1885,14540,1887],{},[1850,14542,14543],{"encoding":1852},"w^\\top\\mu^e-\\frac{\\lambda}{2}w^\\top\\Sigma w",[1827,14545,14547,14620],{"className":14546,"ariaHidden":1857},[1856],[1827,14548,14550,14553,14582,14611,14614,14617],{"className":14549},[1861],[1827,14551],{"className":14552,"style":2850},[1865],[1827,14554,14556,14559],{"className":14555},[1870],[1827,14557,1887],{"className":14558,"style":1946},[1870,1945],[1827,14560,14562],{"className":14561},[1979],[1827,14563,14565],{"className":14564},[1983],[1827,14566,14568],{"className":14567},[1988],[1827,14569,14571],{"className":14570,"style":2108},[1992],[1827,14572,14573,14576],{"style":2111},[1827,14574],{"className":14575,"style":2001},[2000],[1827,14577,14579],{"className":14578},[2005,2006,2007,2008],[1827,14580,1928],{"className":14581},[1870,2008],[1827,14583,14585,14588],{"className":14584},[1870],[1827,14586,2523],{"className":14587},[1870,1945],[1827,14589,14591],{"className":14590},[1979],[1827,14592,14594],{"className":14593},[1983],[1827,14595,14597],{"className":14596},[1988],[1827,14598,14600],{"className":14599,"style":9307},[1992],[1827,14601,14602,14605],{"style":2111},[1827,14603],{"className":14604,"style":2001},[2000],[1827,14606,14608],{"className":14607},[2005,2006,2007,2008],[1827,14609,3923],{"className":14610},[1870,1945,2008],[1827,14612],{"className":14613,"style":3250},[1950],[1827,14615,3126],{"className":14616},[3254],[1827,14618],{"className":14619,"style":3250},[1950],[1827,14621,14623,14627,14699,14728,14731],{"className":14622},[1861],[1827,14624],{"className":14625,"style":14626},[1865],"height:1.2251em;vertical-align:-0.345em;",[1827,14628,14630,14633,14696],{"className":14629},[1870],[1827,14631],{"className":14632},[1969,3271],[1827,14634,14636],{"className":14635},[3128],[1827,14637,14639,14687],{"className":14638},[1983,1984],[1827,14640,14642,14684],{"className":14641},[1988],[1827,14643,14646,14661,14669],{"className":14644,"style":14645},[1992],"height:0.8801em;",[1827,14647,14649,14652],{"style":14648},"top:-2.655em;",[1827,14650],{"className":14651,"style":3179},[2000],[1827,14653,14655],{"className":14654},[2005,2006,2007,2008],[1827,14656,14658],{"className":14657},[1870,2008],[1827,14659,3134],{"className":14660},[1870,2008],[1827,14662,14663,14666],{"style":3299},[1827,14664],{"className":14665,"style":3179},[2000],[1827,14667],{"className":14668,"style":3307},[3306],[1827,14670,14672,14675],{"style":14671},"top:-3.394em;",[1827,14673],{"className":14674,"style":3179},[2000],[1827,14676,14678],{"className":14677},[2005,2006,2007,2008],[1827,14679,14681],{"className":14680},[1870,2008],[1827,14682,3066],{"className":14683},[1870,1945,2008],[1827,14685,2016],{"className":14686},[2015],[1827,14688,14690],{"className":14689},[1988],[1827,14691,14694],{"className":14692,"style":14693},[1992],"height:0.345em;",[1827,14695],{},[1827,14697],{"className":14698},[2092,3271],[1827,14700,14702,14705],{"className":14701},[1870],[1827,14703,1887],{"className":14704,"style":1946},[1870,1945],[1827,14706,14708],{"className":14707},[1979],[1827,14709,14711],{"className":14710},[1983],[1827,14712,14714],{"className":14713},[1988],[1827,14715,14717],{"className":14716,"style":2108},[1992],[1827,14718,14719,14722],{"style":2111},[1827,14720],{"className":14721,"style":2001},[2000],[1827,14723,14725],{"className":14724},[2005,2006,2007,2008],[1827,14726,1928],{"className":14727},[1870,2008],[1827,14729,2600],{"className":14730},[1870],[1827,14732,1887],{"className":14733,"style":1946},[1870,1945],"，加行业\u002F市值\u002F个股约束",[13965,14736,14737],{},"风险暴露是否改善，收益是否被约束过度削弱",[1793,14739,14740],{},"如果优化组合夏普更高但持仓集中在极少数低流动性股票，结论不是“优化有效”，而是需要加入更严格的权重、成交量和冲击成本约束。组合优化的目标不是让历史指标最好看，而是让可执行风险收益更稳健。",[1819,14742,14744],{"id":14743},"_76-常见错误与研究陷阱","7.6 常见错误与研究陷阱",[2504,14746,14747,14812,14893,14899,14905],{},[2507,14748,14749,14752,14753,14811],{},[1797,14750,14751],{},"把 alpha 分数当精确收益预测","：分数通常只有排序意义，直接当 ",[1827,14754,14756,14773],{"className":14755},[1830],[1827,14757,14759],{"className":14758},[1834],[1836,14760,14761],{"xmlns":1838},[1840,14762,14763,14771],{},[1843,14764,14765],{},[1920,14766,14767,14769],{},[1885,14768,2523],{},[1885,14770,3923],{},[1850,14772,9896],{"encoding":1852},[1827,14774,14776],{"className":14775,"ariaHidden":1857},[1856],[1827,14777,14779,14782],{"className":14778},[1861],[1827,14780],{"className":14781,"style":9906},[1865],[1827,14783,14785,14788],{"className":14784},[1870],[1827,14786,2523],{"className":14787},[1870,1945],[1827,14789,14791],{"className":14790},[1979],[1827,14792,14794],{"className":14793},[1983],[1827,14795,14797],{"className":14796},[1988],[1827,14798,14800],{"className":14799,"style":9307},[1992],[1827,14801,14802,14805],{"style":2111},[1827,14803],{"className":14804,"style":2001},[2000],[1827,14806,14808],{"className":14807},[2005,2006,2007,2008],[1827,14809,3923],{"className":14810},[1870,1945,2008]," 会造成极端权重。",[2507,14813,14814,14817,14818,14892],{},[1797,14815,14816],{},"协方差矩阵估计不稳","：短窗口样本下 ",[1827,14819,14821,14845],{"className":14820},[1830],[1827,14822,14824],{"className":14823},[1834],[1836,14825,14826],{"xmlns":1838},[1840,14827,14828,14842],{},[1843,14829,14830,14840],{},[1920,14831,14832,14834],{},[1885,14833,2600],{"mathvariant":1927},[1843,14835,14836,14838],{},[1889,14837,3126],{},[1846,14839,1903],{},[1885,14841,2523],{},[1850,14843,14844],{"encoding":1852},"\\Sigma^{-1}\\mu",[1827,14846,14848],{"className":14847,"ariaHidden":1857},[1856],[1827,14849,14851,14854,14889],{"className":14850},[1861],[1827,14852],{"className":14853,"style":10345},[1865],[1827,14855,14857,14860],{"className":14856},[1870],[1827,14858,2600],{"className":14859},[1870],[1827,14861,14863],{"className":14862},[1979],[1827,14864,14866],{"className":14865},[1983],[1827,14867,14869],{"className":14868},[1988],[1827,14870,14872],{"className":14871,"style":10364},[1992],[1827,14873,14874,14877],{"style":2111},[1827,14875],{"className":14876,"style":2001},[2000],[1827,14878,14880],{"className":14879},[2005,2006,2007,2008],[1827,14881,14883,14886],{"className":14882},[1870,2008],[1827,14884,3126],{"className":14885},[1870,2008],[1827,14887,1903],{"className":14888},[1870,2008],[1827,14890,2523],{"className":14891},[1870,1945]," 对噪声非常敏感，常需要收缩、因子模型或权重上限。",[2507,14894,14895,14898],{},[1797,14896,14897],{},"约束缺失导致隐藏风险","：行业、市值、流动性不约束时，优化器会把资金压到历史上最“划算”的暴露。",[2507,14900,14901,14904],{},[1797,14902,14903],{},"只看总波动不看归因","：总风险正常但单一因子或资产贡献过高，仍然可能在特定行情中崩溃。",[2507,14906,14907,14910],{},[1797,14908,14909],{},"换手没有进入目标函数","：每期重新优化会产生高换手，实际成本可能超过理论 alpha。",[1819,14912,14914],{"id":14913},"_77-自测题与答案提示","7.7 自测题与答案提示",[11691,14916,14917,15106,15144,15147],{},[2507,14918,14919,14920,15047,15048,1808,15077,15105],{},"为什么无约束最优权重 ",[1827,14921,14923,14956],{"className":14922},[1830],[1827,14924,14926],{"className":14925},[1834],[1836,14927,14928],{"xmlns":1838},[1840,14929,14930,14953],{},[1843,14931,14932,14938,14941,14951],{},[1920,14933,14934,14936],{},[1885,14935,1887],{},[1889,14937,3419],{},[1889,14939,14940],{},"∝",[1920,14942,14943,14945],{},[1885,14944,2600],{"mathvariant":1927},[1843,14946,14947,14949],{},[1889,14948,3126],{},[1846,14950,1903],{},[1885,14952,2523],{},[1850,14954,14955],{"encoding":1852},"w^* \\propto \\Sigma^{-1}\\mu",[1827,14957,14959,15003],{"className":14958,"ariaHidden":1857},[1856],[1827,14960,14962,14965,14994,14997,15000],{"className":14961},[1861],[1827,14963],{"className":14964,"style":3705},[1865],[1827,14966,14968,14971],{"className":14967},[1870],[1827,14969,1887],{"className":14970,"style":1946},[1870,1945],[1827,14972,14974],{"className":14973},[1979],[1827,14975,14977],{"className":14976},[1983],[1827,14978,14980],{"className":14979},[1988],[1827,14981,14983],{"className":14982,"style":3705},[1992],[1827,14984,14985,14988],{"style":2111},[1827,14986],{"className":14987,"style":2001},[2000],[1827,14989,14991],{"className":14990},[2005,2006,2007,2008],[1827,14992,3419],{"className":14993},[3254,2008],[1827,14995],{"className":14996,"style":1951},[1950],[1827,14998,14940],{"className":14999},[1955],[1827,15001],{"className":15002,"style":1951},[1950],[1827,15004,15006,15009,15044],{"className":15005},[1861],[1827,15007],{"className":15008,"style":10345},[1865],[1827,15010,15012,15015],{"className":15011},[1870],[1827,15013,2600],{"className":15014},[1870],[1827,15016,15018],{"className":15017},[1979],[1827,15019,15021],{"className":15020},[1983],[1827,15022,15024],{"className":15023},[1988],[1827,15025,15027],{"className":15026,"style":10364},[1992],[1827,15028,15029,15032],{"style":2111},[1827,15030],{"className":15031,"style":2001},[2000],[1827,15033,15035],{"className":15034},[2005,2006,2007,2008],[1827,15036,15038,15041],{"className":15037},[1870,2008],[1827,15039,3126],{"className":15040},[1870,2008],[1827,15042,1903],{"className":15043},[1870,2008],[1827,15045,2523],{"className":15046},[1870,1945]," 在实务中危险？\n答案提示：它对 ",[1827,15049,15051,15065],{"className":15050},[1830],[1827,15052,15054],{"className":15053},[1834],[1836,15055,15056],{"xmlns":1838},[1840,15057,15058,15062],{},[1843,15059,15060],{},[1885,15061,2523],{},[1850,15063,15064],{"encoding":1852},"\\mu",[1827,15066,15068],{"className":15067,"ariaHidden":1857},[1856],[1827,15069,15071,15074],{"className":15070},[1861],[1827,15072],{"className":15073,"style":2550},[1865],[1827,15075,2523],{"className":15076},[1870,1945],[1827,15078,15080,15093],{"className":15079},[1830],[1827,15081,15083],{"className":15082},[1834],[1836,15084,15085],{"xmlns":1838},[1840,15086,15087,15091],{},[1843,15088,15089],{},[1885,15090,2600],{"mathvariant":1927},[1850,15092,9862],{"encoding":1852},[1827,15094,15096],{"className":15095,"ariaHidden":1857},[1856],[1827,15097,15099,15102],{"className":15098},[1861],[1827,15100],{"className":15101,"style":2627},[1865],[1827,15103,2600],{"className":15104},[1870]," 的估计误差高度敏感，可能产生杠杆、集中和不可交易持仓。",[2507,15107,15108,15109,15143],{},"因子风险和特异风险有什么区别？\n答案提示：因子风险来自共同暴露 ",[1827,15110,15112,15128],{"className":15111},[1830],[1827,15113,15115],{"className":15114},[1834],[1836,15116,15117],{"xmlns":1838},[1840,15118,15119,15125],{},[1843,15120,15121,15123],{},[1885,15122,5332],{},[1885,15124,3769],{},[1850,15126,15127],{"encoding":1852},"Bf",[1827,15129,15131],{"className":15130,"ariaHidden":1857},[1856],[1827,15132,15134,15137,15140],{"className":15133},[1861],[1827,15135],{"className":15136,"style":4707},[1865],[1827,15138,5332],{"className":15139,"style":5441},[1870,1945],[1827,15141,3769],{"className":15142,"style":3812},[1870,1945],"，会在许多资产间联动；特异风险来自单个资产残差，分散化后可降低。",[2507,15145,15146],{},"主动组合为什么要控制相对基准的因子暴露？\n答案提示：否则主动收益可能主要来自无意的行业、风格或市场 beta，而不是研究团队声称的 alpha。",[2507,15148,15149],{},"怎样判断新增约束是否过强？\n答案提示：比较约束前后的目标值、风险暴露、换手和可交易性；若 alpha 几乎被约束完全消除，需重新审视信号和投资目标。",[1819,15151,15153],{"id":15152},"_78-小结与过渡","7.8 小结与过渡",[1793,15155,15156],{},"组合构建把研究信号变成资金配置。你需要同时尊重三件事：alpha 预测很噪、风险模型不完美、真实交易有约束。下一章会继续沿着资金落地的方向，讨论目标权重如何变成订单，以及价差、冲击和成交不确定性如何改变策略表现。",[13706,15158],{},[1793,15160,15161,3084],{},[1797,15162,15163],{},"参考文献（节选）",[2504,15165,15166,15173,15178,15184,15190,15196],{},[2507,15167,15168,15169],{},"Markowitz, H. (1952). \"Portfolio selection.\" ",[15170,15171,15172],"em",{},"The Journal of Finance.",[2507,15174,15175,15176],{},"Sharpe, W. F. (1964). \"Capital asset prices: A theory of market equilibrium under conditions of risk.\" ",[15170,15177,15172],{},[2507,15179,15180,15181],{},"Ross, S. A. (1976). \"The arbitrage theory of capital asset pricing.\" ",[15170,15182,15183],{},"Journal of Economic Theory.",[2507,15185,15186,15187],{},"Connor, G., & Korajczyk, R. A. (1988). \"Risk and return in an equilibrium APT.\" ",[15170,15188,15189],{},"Journal of Financial Economics.",[2507,15191,15192,15193],{},"Maillard, S., Roncalli, T., & Teiletche, J. (2010). \"The properties of equally weighted risk contribution portfolios.\" ",[15170,15194,15195],{},"The Journal of Portfolio Management.",[2507,15197,15198,15199],{},"Qian, E. (2005). \"Risk parity portfolios: Efficient portfolios through true diversification.\" ",[15170,15200,15201],{},"PanAgora Asset Management White Paper.",{"title":10,"searchDepth":15203,"depth":15203,"links":15204},2,[15205,15210,15215,15216,15220,15224,15225],{"id":1816,"depth":15203,"text":1817,"children":15206},[15207,15209],{"id":1821,"depth":15208,"text":1822},3,{"id":3746,"depth":15208,"text":3747},{"id":4143,"depth":15203,"text":4144,"children":15211},[15212,15213,15214],{"id":4147,"depth":15208,"text":4148},{"id":6391,"depth":15208,"text":6392},{"id":7520,"depth":15208,"text":7521},{"id":9082,"depth":15203,"text":9083},{"id":11264,"depth":15203,"text":11265,"children":15217},[15218,15219],{"id":11268,"depth":15208,"text":11269},{"id":11685,"depth":15208,"text":11686},{"id":12655,"depth":15203,"text":12656,"children":15221},[15222,15223],{"id":12670,"depth":15208,"text":12671},{"id":13277,"depth":15208,"text":13278},{"id":13470,"depth":15203,"text":13471},{"id":13710,"depth":15203,"text":13711,"children":15226},[15227,15228,15229,15230,15231,15232,15233,15234],{"id":13714,"depth":15208,"text":13715},{"id":13826,"depth":15208,"text":13827},{"id":13938,"depth":15208,"text":13939},{"id":14424,"depth":15208,"text":14425},{"id":14458,"depth":15208,"text":14459},{"id":14743,"depth":15208,"text":14744},{"id":14913,"depth":15208,"text":14914},{"id":15152,"depth":15208,"text":15153},"在估计误差、风险暴露、换手、流动性和容量约束下把 alpha 分数转化为组合。","md",{"sidebar":15238},{"order":15239},4,true,{"title":1755,"description":15235},"SkezpjDuvlQvjAhnRQr0lXH0_ysWlFFJ8WVU0FSLTLk",[15244,15246],{"title":1751,"path":1752,"stem":1753,"description":15245,"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。",{"title":1759,"path":1760,"stem":1761,"description":15247,"children":-1},"将目标权重转换为订单，分解价差、延迟、冲击、机会成本与容量限制。",1785754759229]