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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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Alpha 策略全流程","\u002Fzh\u002Fquant\u002F09-case-study","zh\u002Fquant\u002F09-case-study",{"title":1779,"path":1780,"stem":1781},"量化投资文献与软件图谱","\u002Fzh\u002Fquant\u002F10-reading-software-map","zh\u002Fquant\u002F10-reading-software-map",null,{"id":1784,"title":1266,"body":1785,"description":4413,"extension":4414,"features":1782,"hero":1782,"layout":1782,"locale":1782,"meta":4415,"navigation":1782,"path":1267,"published":4417,"seo":4418,"stem":1268,"__hash__":4419},"docs\u002Fzh\u002Fasset-pricing\u002F03-mean-variance\u002Findex.md",{"type":1786,"value":1787,"toc":4391},"minimark",[1788,1792,1796,1799,1803,1871,1874,1877,1896,1899,1917,1920,1923,1969,1972,2233,2403,2562,2707,2711,2714,2718,2721,2724,2727,2730,2733,2736,2739,2742,2745,2748,3153,3156,3159,3162,3165,3169,3172,3389,3392,3815,3818,3992,4029,4033,4036,4043,4046,4049,4132,4135,4168,4171,4185,4188,4385,4388],[1789,1790,1266],"h1",{"id":1791},"第三章均值-方差分析",[1793,1794,1795],"p",{},"第二章从效用函数解释风险厌恶。本章把问题简化成投资者最常用的一张图：横轴是风险，纵轴是预期收益。均值-方差分析的核心不是“方差越低越好”，而是在给定收益下尽量降低风险，或在给定风险下尽量提高收益。",[1793,1797,1798],{},"马科维茨框架看似数学化，实际直觉很朴素：单个资产的风险不等于组合风险。只要资产之间不是完全同涨同跌，组合就可能通过分散化降低波动。后面的 CAPM、市场组合、资本市场线和许多量化组合优化方法，都建立在本章语言之上。",[1800,1801,1802],"h2",{"id":1802},"本章路线",[1804,1805,1806,1819],"table",{},[1807,1808,1809],"thead",{},[1810,1811,1812,1816],"tr",{},[1813,1814,1815],"th",{},"课次",[1813,1817,1818],{},"核心问题",[1820,1821,1822,1831,1839,1847,1855,1863],"tbody",{},[1810,1823,1824,1828],{},[1825,1826,1827],"td",{},"3.1 组合风险",[1825,1829,1830],{},"为什么协方差决定分散化空间？",[1810,1832,1833,1836],{},[1825,1834,1835],{},"3.2 两资产",[1825,1837,1838],{},"权重和相关系数怎样改变风险？",[1810,1840,1841,1844],{},[1825,1842,1843],{},"3.3 有效前沿",[1825,1845,1846],{},"给定风险时，哪些组合拥有最高期望收益？",[1810,1848,1849,1852],{},[1825,1850,1851],{},"3.4 无风险资产",[1825,1853,1854],{},"资本配置线为什么是直线？",[1810,1856,1857,1860],{},[1825,1858,1859],{},"3.5 切点组合",[1825,1861,1862],{},"风险偏好与最优风险组合怎样分离？",[1810,1864,1865,1868],{},[1825,1866,1867],{},"3.6 实践边界",[1825,1869,1870],{},"估计误差、约束和交易成本怎样改变权重？",[1800,1872,1873],{"id":1873},"学习成果",[1793,1875,1876],{},"通过本章学习，你将掌握：",[1878,1879,1880,1884,1887,1890,1893],"ol",{},[1881,1882,1883],"li",{},"马科维茨投资组合理论的数学基础",[1881,1885,1886],{},"如何计算和绘制有效前沿",[1881,1888,1889],{},"无风险资产对投资决策的影响",[1881,1891,1892],{},"分离定理及其经济含义",[1881,1894,1895],{},"实际资产配置的方法和技巧",[1793,1897,1898],{},"读完本章后，你应能完成以下任务：",[1900,1901,1902,1905,1908,1911,1914],"ul",{},[1881,1903,1904],{},"用权重、预期收益向量和协方差矩阵写出组合收益与组合方差。",[1881,1906,1907],{},"解释为什么低相关资产能够降低组合风险。",[1881,1909,1910],{},"在两资产案例中计算组合收益率、方差和最小方差权重。",[1881,1912,1913],{},"区分可行集、有效前沿、最小方差组合和切点组合。",[1881,1915,1916],{},"说明无风险资产如何把弯曲的有效前沿变成资本配置线。",[1800,1918,1919],{"id":1919},"金融与经济动机",[1793,1921,1922],{},"实际投资者很少只持有一只资产。养老金、基金、家族办公室和个人账户都在做同一个决策：如何把财富分配到股票、债券、现金、商品或另类资产中。均值-方差分析给出一个基准回答：如果只关心预期收益和波动率，组合选择就是在收益和风险之间做权衡。",[1804,1924,1925,1935],{},[1807,1926,1927],{},[1810,1928,1929,1932],{},[1813,1930,1931],{},"投资问题",[1813,1933,1934],{},"均值-方差语言",[1820,1936,1937,1945,1953,1961],{},[1810,1938,1939,1942],{},[1825,1940,1941],{},"为什么不要重仓一只股票",[1825,1943,1944],{},"个体风险可以通过分散化降低",[1810,1946,1947,1950],{},[1825,1948,1949],{},"为什么相关系数重要",[1825,1951,1952],{},"组合风险取决于协方差而非单个波动率",[1810,1954,1955,1958],{},[1825,1956,1957],{},"为什么有“核心组合+现金\u002F杠杆”",[1825,1959,1960],{},"无风险资产与切点组合的线性组合",[1810,1962,1963,1966],{},[1825,1964,1965],{},"为什么业绩要看 Sharpe 比率",[1825,1967,1968],{},"每单位总风险获得的超额收益",[1800,1970,1971],{"id":1971},"模型设置与直觉",[1793,1973,1974,1975,2021,2022,2053,2054,2086,2087,2117,2118,2232],{},"设有 ",[1976,1977,1980,2002],"span",{"className":1978},[1979],"katex",[1976,1981,1984],{"className":1982},[1983],"katex-mathml",[1985,1986,1988],"math",{"xmlns":1987},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[1989,1990,1991,1998],"semantics",{},[1992,1993,1994],"mrow",{},[1995,1996,1997],"mi",{},"n",[1999,2000,1997],"annotation",{"encoding":2001},"application\u002Fx-tex",[1976,2003,2007],{"className":2004,"ariaHidden":2006},[2005],"katex-html","true",[1976,2008,2011,2016],{"className":2009},[2010],"base",[1976,2012],{"className":2013,"style":2015},[2014],"strut","height:0.4306em;",[1976,2017,1997],{"className":2018},[2019,2020],"mord","mathnormal"," 个风险资产，预期收益向量为 ",[1976,2023,2025,2040],{"className":2024},[1979],[1976,2026,2028],{"className":2027},[1983],[1985,2029,2030],{"xmlns":1987},[1989,2031,2032,2037],{},[1992,2033,2034],{},[1995,2035,2036],{},"μ",[1999,2038,2039],{"encoding":2001},"\\mu",[1976,2041,2043],{"className":2042,"ariaHidden":2006},[2005],[1976,2044,2046,2050],{"className":2045},[2010],[1976,2047],{"className":2048,"style":2049},[2014],"height:0.625em;vertical-align:-0.1944em;",[1976,2051,2036],{"className":2052},[2019,2020],"，协方差矩阵为 ",[1976,2055,2057,2073],{"className":2056},[1979],[1976,2058,2060],{"className":2059},[1983],[1985,2061,2062],{"xmlns":1987},[1989,2063,2064,2070],{},[1992,2065,2066],{},[1995,2067,2069],{"mathvariant":2068},"normal","Σ",[1999,2071,2072],{"encoding":2001},"\\Sigma",[1976,2074,2076],{"className":2075,"ariaHidden":2006},[2005],[1976,2077,2079,2083],{"className":2078},[2010],[1976,2080],{"className":2081,"style":2082},[2014],"height:0.6833em;",[1976,2084,2069],{"className":2085},[2019],"，组合权重为 ",[1976,2088,2090,2104],{"className":2089},[1979],[1976,2091,2093],{"className":2092},[1983],[1985,2094,2095],{"xmlns":1987},[1989,2096,2097,2102],{},[1992,2098,2099],{},[1995,2100,2101],{},"w",[1999,2103,2101],{"encoding":2001},[1976,2105,2107],{"className":2106,"ariaHidden":2006},[2005],[1976,2108,2110,2113],{"className":2109},[2010],[1976,2111],{"className":2112,"style":2015},[2014],[1976,2114,2101],{"className":2115,"style":2116},[2019,2020],"margin-right:0.0269em;","，且 ",[1976,2119,2121,2153],{"className":2120},[1979],[1976,2122,2124],{"className":2123},[1983],[1985,2125,2126],{"xmlns":1987},[1989,2127,2128,2150],{},[1992,2129,2130,2143,2145,2148],{},[2131,2132,2133,2138],"msup",{},[2134,2135,2137],"mn",{"mathvariant":2136},"bold","1",[2139,2140,2142],"mo",{"mathvariant":2068,"lspace":2141,"rspace":2141},"0em","′",[1995,2144,2101],{},[2139,2146,2147],{},"=",[2134,2149,2137],{},[1999,2151,2152],{"encoding":2001},"\\mathbf{1}'w=1",[1976,2154,2156,2222],{"className":2155,"ariaHidden":2006},[2005],[1976,2157,2159,2163,2207,2210,2215,2219],{"className":2158},[2010],[1976,2160],{"className":2161,"style":2162},[2014],"height:0.7519em;",[1976,2164,2166,2170],{"className":2165},[2019],[1976,2167,2137],{"className":2168},[2019,2169],"mathbf",[1976,2171,2174],{"className":2172},[2173],"msupsub",[1976,2175,2178],{"className":2176},[2177],"vlist-t",[1976,2179,2182],{"className":2180},[2181],"vlist-r",[1976,2183,2186],{"className":2184,"style":2162},[2185],"vlist",[1976,2187,2189,2194],{"style":2188},"top:-3.063em;margin-right:0.05em;",[1976,2190],{"className":2191,"style":2193},[2192],"pstrut","height:2.7em;",[1976,2195,2201],{"className":2196},[2197,2198,2199,2200],"sizing","reset-size6","size3","mtight",[1976,2202,2204],{"className":2203},[2019,2200],[1976,2205,2142],{"className":2206},[2019,2200],[1976,2208,2101],{"className":2209,"style":2116},[2019,2020],[1976,2211],{"className":2212,"style":2214},[2213],"mspace","margin-right:0.2778em;",[1976,2216,2147],{"className":2217},[2218],"mrel",[1976,2220],{"className":2221,"style":2214},[2213],[1976,2223,2225,2229],{"className":2224},[2010],[1976,2226],{"className":2227,"style":2228},[2014],"height:0.6444em;",[1976,2230,2137],{"className":2231},[2019],"。组合预期收益和方差为：",[1976,2234,2237],{"className":2235},[2236],"katex-display",[1976,2238,2240,2281],{"className":2239},[1979],[1976,2241,2243],{"className":2242},[1983],[1985,2244,2246],{"xmlns":1987,"display":2245},"block",[1989,2247,2248,2278],{},[1992,2249,2250,2253,2257,2265,2268,2270,2276],{},[1995,2251,2252],{},"E",[2139,2254,2256],{"stretchy":2255},"false","[",[2258,2259,2260,2263],"msub",{},[1995,2261,2262],{},"R",[1995,2264,1793],{},[2139,2266,2267],{"stretchy":2255},"]",[2139,2269,2147],{},[2131,2271,2272,2274],{},[1995,2273,2101],{},[2139,2275,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[1995,2277,2036],{},[1999,2279,2280],{"encoding":2001},"E[R_p]=w'\\mu",[1976,2282,2284,2359],{"className":2283,"ariaHidden":2006},[2005],[1976,2285,2287,2291,2295,2299,2346,2350,2353,2356],{"className":2286},[2010],[1976,2288],{"className":2289,"style":2290},[2014],"height:1.0361em;vertical-align:-0.2861em;",[1976,2292,2252],{"className":2293,"style":2294},[2019,2020],"margin-right:0.0576em;",[1976,2296,2256],{"className":2297},[2298],"mopen",[1976,2300,2302,2306],{"className":2301},[2019],[1976,2303,2262],{"className":2304,"style":2305},[2019,2020],"margin-right:0.0077em;",[1976,2307,2309],{"className":2308},[2173],[1976,2310,2313,2337],{"className":2311},[2177,2312],"vlist-t2",[1976,2314,2316,2332],{"className":2315},[2181],[1976,2317,2320],{"className":2318,"style":2319},[2185],"height:0.1514em;",[1976,2321,2323,2326],{"style":2322},"top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;",[1976,2324],{"className":2325,"style":2193},[2192],[1976,2327,2329],{"className":2328},[2197,2198,2199,2200],[1976,2330,1793],{"className":2331},[2019,2020,2200],[1976,2333,2336],{"className":2334},[2335],"vlist-s","​",[1976,2338,2340],{"className":2339},[2181],[1976,2341,2344],{"className":2342,"style":2343},[2185],"height:0.2861em;",[1976,2345],{},[1976,2347,2267],{"className":2348},[2349],"mclose",[1976,2351],{"className":2352,"style":2214},[2213],[1976,2354,2147],{"className":2355},[2218],[1976,2357],{"className":2358,"style":2214},[2213],[1976,2360,2362,2366,2400],{"className":2361},[2010],[1976,2363],{"className":2364,"style":2365},[2014],"height:0.9963em;vertical-align:-0.1944em;",[1976,2367,2369,2372],{"className":2368},[2019],[1976,2370,2101],{"className":2371,"style":2116},[2019,2020],[1976,2373,2375],{"className":2374},[2173],[1976,2376,2378],{"className":2377},[2177],[1976,2379,2381],{"className":2380},[2181],[1976,2382,2385],{"className":2383,"style":2384},[2185],"height:0.8019em;",[1976,2386,2388,2391],{"style":2387},"top:-3.113em;margin-right:0.05em;",[1976,2389],{"className":2390,"style":2193},[2192],[1976,2392,2394],{"className":2393},[2197,2198,2199,2200],[1976,2395,2397],{"className":2396},[2019,2200],[1976,2398,2142],{"className":2399},[2019,2200],[1976,2401,2036],{"className":2402},[2019,2020],[1976,2404,2406],{"className":2405},[2236],[1976,2407,2409,2444],{"className":2408},[1979],[1976,2410,2412],{"className":2411},[1983],[1985,2413,2414],{"xmlns":1987,"display":2245},[1989,2415,2416,2441],{},[1992,2417,2418,2429,2431,2437,2439],{},[2419,2420,2421,2424,2426],"msubsup",{},[1995,2422,2423],{},"σ",[1995,2425,1793],{},[2134,2427,2428],{},"2",[2139,2430,2147],{},[2131,2432,2433,2435],{},[1995,2434,2101],{},[2139,2436,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[1995,2438,2069],{"mathvariant":2068},[1995,2440,2101],{},[1999,2442,2443],{"encoding":2001},"\\sigma_p^2=w'\\Sigma w",[1976,2445,2447,2518],{"className":2446,"ariaHidden":2006},[2005],[1976,2448,2450,2454,2509,2512,2515],{"className":2449},[2010],[1976,2451],{"className":2452,"style":2453},[2014],"height:1.2472em;vertical-align:-0.3831em;",[1976,2455,2457,2461],{"className":2456},[2019],[1976,2458,2423],{"className":2459,"style":2460},[2019,2020],"margin-right:0.0359em;",[1976,2462,2464],{"className":2463},[2173],[1976,2465,2467,2500],{"className":2466},[2177,2312],[1976,2468,2470,2497],{"className":2469},[2181],[1976,2471,2474,2486],{"className":2472,"style":2473},[2185],"height:0.8641em;",[1976,2475,2477,2480],{"style":2476},"top:-2.453em;margin-left:-0.0359em;margin-right:0.05em;",[1976,2478],{"className":2479,"style":2193},[2192],[1976,2481,2483],{"className":2482},[2197,2198,2199,2200],[1976,2484,1793],{"className":2485},[2019,2020,2200],[1976,2487,2488,2491],{"style":2387},[1976,2489],{"className":2490,"style":2193},[2192],[1976,2492,2494],{"className":2493},[2197,2198,2199,2200],[1976,2495,2428],{"className":2496},[2019,2200],[1976,2498,2336],{"className":2499},[2335],[1976,2501,2503],{"className":2502},[2181],[1976,2504,2507],{"className":2505,"style":2506},[2185],"height:0.3831em;",[1976,2508],{},[1976,2510],{"className":2511,"style":2214},[2213],[1976,2513,2147],{"className":2514},[2218],[1976,2516],{"className":2517,"style":2214},[2213],[1976,2519,2521,2524,2556,2559],{"className":2520},[2010],[1976,2522],{"className":2523,"style":2384},[2014],[1976,2525,2527,2530],{"className":2526},[2019],[1976,2528,2101],{"className":2529,"style":2116},[2019,2020],[1976,2531,2533],{"className":2532},[2173],[1976,2534,2536],{"className":2535},[2177],[1976,2537,2539],{"className":2538},[2181],[1976,2540,2542],{"className":2541,"style":2384},[2185],[1976,2543,2544,2547],{"style":2387},[1976,2545],{"className":2546,"style":2193},[2192],[1976,2548,2550],{"className":2549},[2197,2198,2199,2200],[1976,2551,2553],{"className":2552},[2019,2200],[1976,2554,2142],{"className":2555},[2019,2200],[1976,2557,2069],{"className":2558},[2019],[1976,2560,2101],{"className":2561,"style":2116},[2019,2020],[1793,2563,2564,2565,2633,2634,2706],{},"直觉上，",[1976,2566,2568,2588],{"className":2567},[1979],[1976,2569,2571],{"className":2570},[1983],[1985,2572,2573],{"xmlns":1987},[1989,2574,2575,2585],{},[1992,2576,2577,2583],{},[2131,2578,2579,2581],{},[1995,2580,2101],{},[2139,2582,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[1995,2584,2036],{},[1999,2586,2587],{"encoding":2001},"w'\\mu",[1976,2589,2591],{"className":2590,"ariaHidden":2006},[2005],[1976,2592,2594,2598,2630],{"className":2593},[2010],[1976,2595],{"className":2596,"style":2597},[2014],"height:0.9463em;vertical-align:-0.1944em;",[1976,2599,2601,2604],{"className":2600},[2019],[1976,2602,2101],{"className":2603,"style":2116},[2019,2020],[1976,2605,2607],{"className":2606},[2173],[1976,2608,2610],{"className":2609},[2177],[1976,2611,2613],{"className":2612},[2181],[1976,2614,2616],{"className":2615,"style":2162},[2185],[1976,2617,2618,2621],{"style":2188},[1976,2619],{"className":2620,"style":2193},[2192],[1976,2622,2624],{"className":2623},[2197,2198,2199,2200],[1976,2625,2627],{"className":2626},[2019,2200],[1976,2628,2142],{"className":2629},[2019,2200],[1976,2631,2036],{"className":2632},[2019,2020]," 是各资产预期收益的加权平均；",[1976,2635,2637,2659],{"className":2636},[1979],[1976,2638,2640],{"className":2639},[1983],[1985,2641,2642],{"xmlns":1987},[1989,2643,2644,2656],{},[1992,2645,2646,2652,2654],{},[2131,2647,2648,2650],{},[1995,2649,2101],{},[2139,2651,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[1995,2653,2069],{"mathvariant":2068},[1995,2655,2101],{},[1999,2657,2658],{"encoding":2001},"w'\\Sigma w",[1976,2660,2662],{"className":2661,"ariaHidden":2006},[2005],[1976,2663,2665,2668,2700,2703],{"className":2664},[2010],[1976,2666],{"className":2667,"style":2162},[2014],[1976,2669,2671,2674],{"className":2670},[2019],[1976,2672,2101],{"className":2673,"style":2116},[2019,2020],[1976,2675,2677],{"className":2676},[2173],[1976,2678,2680],{"className":2679},[2177],[1976,2681,2683],{"className":2682},[2181],[1976,2684,2686],{"className":2685,"style":2162},[2185],[1976,2687,2688,2691],{"style":2188},[1976,2689],{"className":2690,"style":2193},[2192],[1976,2692,2694],{"className":2693},[2197,2198,2199,2200],[1976,2695,2697],{"className":2696},[2019,2200],[1976,2698,2142],{"className":2699},[2019,2200],[1976,2701,2069],{"className":2702},[2019],[1976,2704,2101],{"className":2705,"style":2116},[2019,2020]," 不只是各资产方差的加权平均，还包括资产之间是否一起波动。分散化的力量正来自协方差项。",[2708,2709],"mermaid-diagram",{"code64":2710,"locale":7},"Zmxvd2NoYXJ0IExSCiAgQVsi6LWE5Lqn5pS255uK5Z2H5YC8IG11Il0gLS0+IENbIue7hOWQiOmihOacn+aUtuebiiJdCiAgQlsi5Y2P5pa55beu55+p6Zi1IFNpZ21hIl0gLS0+IERbIue7hOWQiOmjjumZqSJdCiAgRVsi57uE5ZCI5p2D6YeNIHciXSAtLT4gQwogIEUgLS0+IEQKICBDIC0tPiBGWyLmnInmlYjliY3msr8iXQogIEQgLS0+IEY=",[1800,2712,2713],{"id":2713},"关键定义与定理",[2715,2716,2717],"h3",{"id":2717},"可行集",[1793,2719,2720],{},"所有满足权重约束的组合在“风险-收益”平面上形成的集合。",[1793,2722,2723],{},"中文解释：它描述投资者用现有资产能做出的全部组合选择。",[2715,2725,2726],{"id":2726},"有效前沿",[1793,2728,2729],{},"在给定风险下预期收益最高，或在给定预期收益下风险最低的组合集合。",[1793,2731,2732],{},"中文解释：有效前沿是“没有明显浪费”的组合。前沿以下的组合不是不可能，而是被其他组合支配。",[2715,2734,2735],{"id":2735},"最小方差组合",[1793,2737,2738],{},"所有可行组合中方差最低的组合。",[1793,2740,2741],{},"中文解释：如果一个投资者只想最小化波动率，不关心预期收益，就会选择它。",[2715,2743,2744],{"id":2744},"切点组合",[1793,2746,2747],{},"引入无风险资产后，与风险资产有效前沿相切的组合。它最大化 Sharpe 比率：",[1976,2749,2751],{"className":2750},[2236],[1976,2752,2754,2826],{"className":2753},[1979],[1976,2755,2757],{"className":2756},[1983],[1985,2758,2759],{"xmlns":1987,"display":2245},[1989,2760,2761,2823],{},[1992,2762,2763,2776],{},[2764,2765,2766,2774],"munder",{},[1992,2767,2768,2771],{},[1995,2769,2770],{},"max",[2139,2772,2773],{},"⁡",[1995,2775,2101],{},[2777,2778,2779,2808],"mfrac",{},[1992,2780,2781,2787,2790,2792,2795,2803,2805],{},[2131,2782,2783,2785],{},[1995,2784,2101],{},[2139,2786,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[2139,2788,2789],{"stretchy":2255},"(",[1995,2791,2036],{},[2139,2793,2794],{},"−",[2258,2796,2797,2800],{},[1995,2798,2799],{},"r",[1995,2801,2802],{},"f",[2134,2804,2137],{"mathvariant":2136},[2139,2806,2807],{"stretchy":2255},")",[2809,2810,2811],"msqrt",{},[1992,2812,2813,2819,2821],{},[2131,2814,2815,2817],{},[1995,2816,2101],{},[2139,2818,2142],{"mathvariant":2068,"lspace":2141,"rspace":2141},[1995,2820,2069],{"mathvariant":2068},[1995,2822,2101],{},[1999,2824,2825],{"encoding":2001},"\\max_w \\frac{w'(\\mu-r_f\\mathbf{1})}{\\sqrt{w'\\Sigma w}}",[1976,2827,2829],{"className":2828,"ariaHidden":2006},[2005],[1976,2830,2832,2836,2886,2890],{"className":2831},[2010],[1976,2833],{"className":2834,"style":2835},[2014],"height:2.3589em;vertical-align:-0.93em;",[1976,2837,2841],{"className":2838},[2839,2840],"mop","op-limits",[1976,2842,2844,2877],{"className":2843},[2177,2312],[1976,2845,2847,2874],{"className":2846},[2181],[1976,2848,2850,2863],{"className":2849,"style":2015},[2185],[1976,2851,2853,2857],{"style":2852},"top:-2.4em;margin-left:0em;",[1976,2854],{"className":2855,"style":2856},[2192],"height:3em;",[1976,2858,2860],{"className":2859},[2197,2198,2199,2200],[1976,2861,2101],{"className":2862,"style":2116},[2019,2020,2200],[1976,2864,2866,2869],{"style":2865},"top:-3em;",[1976,2867],{"className":2868,"style":2856},[2192],[1976,2870,2871],{},[1976,2872,2770],{"className":2873},[2839],[1976,2875,2336],{"className":2876},[2335],[1976,2878,2880],{"className":2879},[2181],[1976,2881,2884],{"className":2882,"style":2883},[2185],"height:0.7em;",[1976,2885],{},[1976,2887],{"className":2888,"style":2889},[2213],"margin-right:0.1667em;",[1976,2891,2893,2897,3150],{"className":2892},[2019],[1976,2894],{"className":2895},[2298,2896],"nulldelimiter",[1976,2898,2900],{"className":2899},[2777],[1976,2901,2903,3141],{"className":2902},[2177,2312],[1976,2904,2906,3138],{"className":2905},[2181],[1976,2907,2910,3019,3030],{"className":2908,"style":2909},[2185],"height:1.4289em;",[1976,2911,2913,2916],{"style":2912},"top:-2.1833em;",[1976,2914],{"className":2915,"style":2856},[2192],[1976,2917,2919],{"className":2918},[2019],[1976,2920,2923],{"className":2921},[2019,2922],"sqrt",[1976,2924,2926,3010],{"className":2925},[2177,2312],[1976,2927,2929,3007],{"className":2928},[2181],[1976,2930,2933,2984],{"className":2931,"style":2932},[2185],"height:0.9267em;",[1976,2934,2937,2940],{"className":2935,"style":2865},[2936],"svg-align",[1976,2938],{"className":2939,"style":2856},[2192],[1976,2941,2944,2978,2981],{"className":2942,"style":2943},[2019],"padding-left:0.833em;",[1976,2945,2947,2950],{"className":2946},[2019],[1976,2948,2101],{"className":2949,"style":2116},[2019,2020],[1976,2951,2953],{"className":2952},[2173],[1976,2954,2956],{"className":2955},[2177],[1976,2957,2959],{"className":2958},[2181],[1976,2960,2963],{"className":2961,"style":2962},[2185],"height:0.6779em;",[1976,2964,2966,2969],{"style":2965},"top:-2.989em;margin-right:0.05em;",[1976,2967],{"className":2968,"style":2193},[2192],[1976,2970,2972],{"className":2971},[2197,2198,2199,2200],[1976,2973,2975],{"className":2974},[2019,2200],[1976,2976,2142],{"className":2977},[2019,2200],[1976,2979,2069],{"className":2980},[2019],[1976,2982,2101],{"className":2983,"style":2116},[2019,2020],[1976,2985,2987,2990],{"style":2986},"top:-2.8867em;",[1976,2988],{"className":2989,"style":2856},[2192],[1976,2991,2995],{"className":2992,"style":2994},[2993],"hide-tail","min-width:0.853em;height:1.08em;",[2996,2997,3003],"svg",{"xmlns":2998,"width":2999,"height":3000,"viewBox":3001,"preserveAspectRatio":3002},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.08em","0 0 400000 1080","xMinYMin slice",[3004,3005],"path",{"d":3006},"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",[1976,3008,2336],{"className":3009},[2335],[1976,3011,3013],{"className":3012},[2181],[1976,3014,3017],{"className":3015,"style":3016},[2185],"height:0.1133em;",[1976,3018],{},[1976,3020,3022,3025],{"style":3021},"top:-3.23em;",[1976,3023],{"className":3024,"style":2856},[2192],[1976,3026],{"className":3027,"style":3029},[3028],"frac-line","border-bottom-width:0.04em;",[1976,3031,3033,3036],{"style":3032},"top:-3.677em;",[1976,3034],{"className":3035,"style":2856},[2192],[1976,3037,3039,3071,3074,3077,3081,3085,3088,3132,3135],{"className":3038},[2019],[1976,3040,3042,3045],{"className":3041},[2019],[1976,3043,2101],{"className":3044,"style":2116},[2019,2020],[1976,3046,3048],{"className":3047},[2173],[1976,3049,3051],{"className":3050},[2177],[1976,3052,3054],{"className":3053},[2181],[1976,3055,3057],{"className":3056,"style":2162},[2185],[1976,3058,3059,3062],{"style":2188},[1976,3060],{"className":3061,"style":2193},[2192],[1976,3063,3065],{"className":3064},[2197,2198,2199,2200],[1976,3066,3068],{"className":3067},[2019,2200],[1976,3069,2142],{"className":3070},[2019,2200],[1976,3072,2789],{"className":3073},[2298],[1976,3075,2036],{"className":3076},[2019,2020],[1976,3078],{"className":3079,"style":3080},[2213],"margin-right:0.2222em;",[1976,3082,2794],{"className":3083},[3084],"mbin",[1976,3086],{"className":3087,"style":3080},[2213],[1976,3089,3091,3095],{"className":3090},[2019],[1976,3092,2799],{"className":3093,"style":3094},[2019,2020],"margin-right:0.0278em;",[1976,3096,3098],{"className":3097},[2173],[1976,3099,3101,3124],{"className":3100},[2177,2312],[1976,3102,3104,3121],{"className":3103},[2181],[1976,3105,3108],{"className":3106,"style":3107},[2185],"height:0.3361em;",[1976,3109,3111,3114],{"style":3110},"top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;",[1976,3112],{"className":3113,"style":2193},[2192],[1976,3115,3117],{"className":3116},[2197,2198,2199,2200],[1976,3118,2802],{"className":3119,"style":3120},[2019,2020,2200],"margin-right:0.1076em;",[1976,3122,2336],{"className":3123},[2335],[1976,3125,3127],{"className":3126},[2181],[1976,3128,3130],{"className":3129,"style":2343},[2185],[1976,3131],{},[1976,3133,2137],{"className":3134},[2019,2169],[1976,3136,2807],{"className":3137},[2349],[1976,3139,2336],{"className":3140},[2335],[1976,3142,3144],{"className":3143},[2181],[1976,3145,3148],{"className":3146,"style":3147},[2185],"height:0.93em;",[1976,3149],{},[1976,3151],{"className":3152},[2349,2896],[1793,3154,3155],{},"中文解释：所有投资者先持有同一个最佳风险组合，再根据风险承受能力决定借入、贷出或持有多少无风险资产。",[2715,3157,3158],{"id":3158},"两基金分离定理",[1793,3160,3161],{},"在均值-方差框架下，投资者的最终组合可以由两个基金组合而成：无风险资产和切点风险组合。",[1793,3163,3164],{},"中文解释：资产选择和风险偏好可以分开。市场先决定最优风险组合，个人偏好只决定放大或缩小风险敞口。",[1800,3166,3168],{"id":3167},"例子两个资产的分散化","例子：两个资产的分散化",[1793,3170,3171],{},"资产 A 的预期收益为 8%，波动率为 20%；资产 B 的预期收益为 4%，波动率为 10%；两者相关系数为 0。若各投 50%，组合预期收益为：",[1976,3173,3175],{"className":3174},[2236],[1976,3176,3178,3235],{"className":3177},[1979],[1976,3179,3181],{"className":3180},[1983],[1985,3182,3183],{"xmlns":1987,"display":2245},[1989,3184,3185,3232],{},[1992,3186,3187,3189,3191,3197,3199,3201,3204,3207,3210,3213,3216,3218,3220,3223,3225,3227,3230],{},[1995,3188,2252],{},[2139,3190,2256],{"stretchy":2255},[2258,3192,3193,3195],{},[1995,3194,2262],{},[1995,3196,1793],{},[2139,3198,2267],{"stretchy":2255},[2139,3200,2147],{},[2134,3202,3203],{},"0.5",[2139,3205,3206],{},"×",[2134,3208,3209],{},"8",[1995,3211,3212],{"mathvariant":2068},"%",[2139,3214,3215],{},"+",[2134,3217,3203],{},[2139,3219,3206],{},[2134,3221,3222],{},"4",[1995,3224,3212],{"mathvariant":2068},[2139,3226,2147],{},[2134,3228,3229],{},"6",[1995,3231,3212],{"mathvariant":2068},[1999,3233,3234],{"encoding":2001},"E[R_p]=0.5\\times8\\%+0.5\\times4\\%=6\\%",[1976,3236,3238,3302,3321,3341,3359,3379],{"className":3237,"ariaHidden":2006},[2005],[1976,3239,3241,3244,3247,3250,3290,3293,3296,3299],{"className":3240},[2010],[1976,3242],{"className":3243,"style":2290},[2014],[1976,3245,2252],{"className":3246,"style":2294},[2019,2020],[1976,3248,2256],{"className":3249},[2298],[1976,3251,3253,3256],{"className":3252},[2019],[1976,3254,2262],{"className":3255,"style":2305},[2019,2020],[1976,3257,3259],{"className":3258},[2173],[1976,3260,3262,3282],{"className":3261},[2177,2312],[1976,3263,3265,3279],{"className":3264},[2181],[1976,3266,3268],{"className":3267,"style":2319},[2185],[1976,3269,3270,3273],{"style":2322},[1976,3271],{"className":3272,"style":2193},[2192],[1976,3274,3276],{"className":3275},[2197,2198,2199,2200],[1976,3277,1793],{"className":3278},[2019,2020,2200],[1976,3280,2336],{"className":3281},[2335],[1976,3283,3285],{"className":3284},[2181],[1976,3286,3288],{"className":3287,"style":2343},[2185],[1976,3289],{},[1976,3291,2267],{"className":3292},[2349],[1976,3294],{"className":3295,"style":2214},[2213],[1976,3297,2147],{"className":3298},[2218],[1976,3300],{"className":3301,"style":2214},[2213],[1976,3303,3305,3309,3312,3315,3318],{"className":3304},[2010],[1976,3306],{"className":3307,"style":3308},[2014],"height:0.7278em;vertical-align:-0.0833em;",[1976,3310,3203],{"className":3311},[2019],[1976,3313],{"className":3314,"style":3080},[2213],[1976,3316,3206],{"className":3317},[3084],[1976,3319],{"className":3320,"style":3080},[2213],[1976,3322,3324,3328,3332,3335,3338],{"className":3323},[2010],[1976,3325],{"className":3326,"style":3327},[2014],"height:0.8333em;vertical-align:-0.0833em;",[1976,3329,3331],{"className":3330},[2019],"8%",[1976,3333],{"className":3334,"style":3080},[2213],[1976,3336,3215],{"className":3337},[3084],[1976,3339],{"className":3340,"style":3080},[2213],[1976,3342,3344,3347,3350,3353,3356],{"className":3343},[2010],[1976,3345],{"className":3346,"style":3308},[2014],[1976,3348,3203],{"className":3349},[2019],[1976,3351],{"className":3352,"style":3080},[2213],[1976,3354,3206],{"className":3355},[3084],[1976,3357],{"className":3358,"style":3080},[2213],[1976,3360,3362,3366,3370,3373,3376],{"className":3361},[2010],[1976,3363],{"className":3364,"style":3365},[2014],"height:0.8056em;vertical-align:-0.0556em;",[1976,3367,3369],{"className":3368},[2019],"4%",[1976,3371],{"className":3372,"style":2214},[2213],[1976,3374,2147],{"className":3375},[2218],[1976,3377],{"className":3378,"style":2214},[2213],[1976,3380,3382,3385],{"className":3381},[2010],[1976,3383],{"className":3384,"style":3365},[2014],[1976,3386,3388],{"className":3387},[2019],"6%",[1793,3390,3391],{},"组合方差为：",[1976,3393,3395],{"className":3394},[2236],[1976,3396,3398,3504],{"className":3397},[1979],[1976,3399,3401],{"className":3400},[1983],[1985,3402,3403],{"xmlns":1987,"display":2245},[1989,3404,3405,3501],{},[1992,3406,3407,3415,3417,3423,3425,3428,3430,3436,3438,3444,3446,3449,3451,3457,3459,3461,3463,3465,3467,3469,3471,3473,3475,3478,3480,3482,3484,3486,3488,3490,3492,3494,3496,3498],{},[2419,3408,3409,3411,3413],{},[1995,3410,2423],{},[1995,3412,1793],{},[2134,3414,2428],{},[2139,3416,2147],{},[2131,3418,3419,3421],{},[2134,3420,3203],{},[2134,3422,2428],{},[2139,3424,2789],{"stretchy":2255},[2134,3426,3427],{},"20",[1995,3429,3212],{"mathvariant":2068},[2131,3431,3432,3434],{},[2139,3433,2807],{"stretchy":2255},[2134,3435,2428],{},[2139,3437,3215],{},[2131,3439,3440,3442],{},[2134,3441,3203],{},[2134,3443,2428],{},[2139,3445,2789],{"stretchy":2255},[2134,3447,3448],{},"10",[1995,3450,3212],{"mathvariant":2068},[2131,3452,3453,3455],{},[2139,3454,2807],{"stretchy":2255},[2134,3456,2428],{},[2139,3458,3215],{},[2134,3460,2428],{},[2139,3462,2789],{"stretchy":2255},[2134,3464,3203],{},[2139,3466,2807],{"stretchy":2255},[2139,3468,2789],{"stretchy":2255},[2134,3470,3203],{},[2139,3472,2807],{"stretchy":2255},[2139,3474,2789],{"stretchy":2255},[2134,3476,3477],{},"0",[2139,3479,2807],{"stretchy":2255},[2139,3481,2789],{"stretchy":2255},[2134,3483,3427],{},[1995,3485,3212],{"mathvariant":2068},[2139,3487,2807],{"stretchy":2255},[2139,3489,2789],{"stretchy":2255},[2134,3491,3448],{},[1995,3493,3212],{"mathvariant":2068},[2139,3495,2807],{"stretchy":2255},[2139,3497,2147],{},[2134,3499,3500],{},"0.0125",[1999,3502,3503],{"encoding":2001},"\\sigma_p^2=0.5^2(20\\%)^2+0.5^2(10\\%)^2+2(0.5)(0.5)(0)(20\\%)(10\\%)=0.0125",[1976,3505,3507,3573,3659,3742,3806],{"className":3506,"ariaHidden":2006},[2005],[1976,3508,3510,3513,3564,3567,3570],{"className":3509},[2010],[1976,3511],{"className":3512,"style":2453},[2014],[1976,3514,3516,3519],{"className":3515},[2019],[1976,3517,2423],{"className":3518,"style":2460},[2019,2020],[1976,3520,3522],{"className":3521},[2173],[1976,3523,3525,3556],{"className":3524},[2177,2312],[1976,3526,3528,3553],{"className":3527},[2181],[1976,3529,3531,3542],{"className":3530,"style":2473},[2185],[1976,3532,3533,3536],{"style":2476},[1976,3534],{"className":3535,"style":2193},[2192],[1976,3537,3539],{"className":3538},[2197,2198,2199,2200],[1976,3540,1793],{"className":3541},[2019,2020,2200],[1976,3543,3544,3547],{"style":2387},[1976,3545],{"className":3546,"style":2193},[2192],[1976,3548,3550],{"className":3549},[2197,2198,2199,2200],[1976,3551,2428],{"className":3552},[2019,2200],[1976,3554,2336],{"className":3555},[2335],[1976,3557,3559],{"className":3558},[2181],[1976,3560,3562],{"className":3561,"style":2506},[2185],[1976,3563],{},[1976,3565],{"className":3566,"style":2214},[2213],[1976,3568,2147],{"className":3569},[2218],[1976,3571],{"className":3572,"style":2214},[2213],[1976,3574,3576,3580,3584,3614,3617,3621,3650,3653,3656],{"className":3575},[2010],[1976,3577],{"className":3578,"style":3579},[2014],"height:1.1141em;vertical-align:-0.25em;",[1976,3581,3583],{"className":3582},[2019],"0.",[1976,3585,3587,3591],{"className":3586},[2019],[1976,3588,3590],{"className":3589},[2019],"5",[1976,3592,3594],{"className":3593},[2173],[1976,3595,3597],{"className":3596},[2177],[1976,3598,3600],{"className":3599},[2181],[1976,3601,3603],{"className":3602,"style":2473},[2185],[1976,3604,3605,3608],{"style":2387},[1976,3606],{"className":3607,"style":2193},[2192],[1976,3609,3611],{"className":3610},[2197,2198,2199,2200],[1976,3612,2428],{"className":3613},[2019,2200],[1976,3615,2789],{"className":3616},[2298],[1976,3618,3620],{"className":3619},[2019],"20%",[1976,3622,3624,3627],{"className":3623},[2349],[1976,3625,2807],{"className":3626},[2349],[1976,3628,3630],{"className":3629},[2173],[1976,3631,3633],{"className":3632},[2177],[1976,3634,3636],{"className":3635},[2181],[1976,3637,3639],{"className":3638,"style":2473},[2185],[1976,3640,3641,3644],{"style":2387},[1976,3642],{"className":3643,"style":2193},[2192],[1976,3645,3647],{"className":3646},[2197,2198,2199,2200],[1976,3648,2428],{"className":3649},[2019,2200],[1976,3651],{"className":3652,"style":3080},[2213],[1976,3654,3215],{"className":3655},[3084],[1976,3657],{"className":3658,"style":3080},[2213],[1976,3660,3662,3665,3668,3697,3700,3704,3733,3736,3739],{"className":3661},[2010],[1976,3663],{"className":3664,"style":3579},[2014],[1976,3666,3583],{"className":3667},[2019],[1976,3669,3671,3674],{"className":3670},[2019],[1976,3672,3590],{"className":3673},[2019],[1976,3675,3677],{"className":3676},[2173],[1976,3678,3680],{"className":3679},[2177],[1976,3681,3683],{"className":3682},[2181],[1976,3684,3686],{"className":3685,"style":2473},[2185],[1976,3687,3688,3691],{"style":2387},[1976,3689],{"className":3690,"style":2193},[2192],[1976,3692,3694],{"className":3693},[2197,2198,2199,2200],[1976,3695,2428],{"className":3696},[2019,2200],[1976,3698,2789],{"className":3699},[2298],[1976,3701,3703],{"className":3702},[2019],"10%",[1976,3705,3707,3710],{"className":3706},[2349],[1976,3708,2807],{"className":3709},[2349],[1976,3711,3713],{"className":3712},[2173],[1976,3714,3716],{"className":3715},[2177],[1976,3717,3719],{"className":3718},[2181],[1976,3720,3722],{"className":3721,"style":2473},[2185],[1976,3723,3724,3727],{"style":2387},[1976,3725],{"className":3726,"style":2193},[2192],[1976,3728,3730],{"className":3729},[2197,2198,2199,2200],[1976,3731,2428],{"className":3732},[2019,2200],[1976,3734],{"className":3735,"style":3080},[2213],[1976,3737,3215],{"className":3738},[3084],[1976,3740],{"className":3741,"style":3080},[2213],[1976,3743,3745,3749,3752,3755,3758,3761,3764,3767,3770,3773,3776,3779,3782,3785,3788,3791,3794,3797,3800,3803],{"className":3744},[2010],[1976,3746],{"className":3747,"style":3748},[2014],"height:1em;vertical-align:-0.25em;",[1976,3750,2428],{"className":3751},[2019],[1976,3753,2789],{"className":3754},[2298],[1976,3756,3203],{"className":3757},[2019],[1976,3759,2807],{"className":3760},[2349],[1976,3762,2789],{"className":3763},[2298],[1976,3765,3203],{"className":3766},[2019],[1976,3768,2807],{"className":3769},[2349],[1976,3771,2789],{"className":3772},[2298],[1976,3774,3477],{"className":3775},[2019],[1976,3777,2807],{"className":3778},[2349],[1976,3780,2789],{"className":3781},[2298],[1976,3783,3620],{"className":3784},[2019],[1976,3786,2807],{"className":3787},[2349],[1976,3789,2789],{"className":3790},[2298],[1976,3792,3703],{"className":3793},[2019],[1976,3795,2807],{"className":3796},[2349],[1976,3798],{"className":3799,"style":2214},[2213],[1976,3801,2147],{"className":3802},[2218],[1976,3804],{"className":3805,"style":2214},[2213],[1976,3807,3809,3812],{"className":3808},[2010],[1976,3810],{"className":3811,"style":2228},[2014],[1976,3813,3500],{"className":3814},[2019],[1793,3816,3817],{},"组合波动率为：",[1976,3819,3821],{"className":3820},[2236],[1976,3822,3824,3856],{"className":3823},[1979],[1976,3825,3827],{"className":3826},[1983],[1985,3828,3829],{"xmlns":1987,"display":2245},[1989,3830,3831,3853],{},[1992,3832,3833,3839,3841,3845,3848,3851],{},[2258,3834,3835,3837],{},[1995,3836,2423],{},[1995,3838,1793],{},[2139,3840,2147],{},[2809,3842,3843],{},[2134,3844,3500],{},[2139,3846,3847],{},"≈",[2134,3849,3850],{},"11.18",[1995,3852,3212],{"mathvariant":2068},[1999,3854,3855],{"encoding":2001},"\\sigma_p=\\sqrt{0.0125}\\approx11.18\\%",[1976,3857,3859,3916,3982],{"className":3858,"ariaHidden":2006},[2005],[1976,3860,3862,3866,3907,3910,3913],{"className":3861},[2010],[1976,3863],{"className":3864,"style":3865},[2014],"height:0.7167em;vertical-align:-0.2861em;",[1976,3867,3869,3872],{"className":3868},[2019],[1976,3870,2423],{"className":3871,"style":2460},[2019,2020],[1976,3873,3875],{"className":3874},[2173],[1976,3876,3878,3899],{"className":3877},[2177,2312],[1976,3879,3881,3896],{"className":3880},[2181],[1976,3882,3884],{"className":3883,"style":2319},[2185],[1976,3885,3887,3890],{"style":3886},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[1976,3888],{"className":3889,"style":2193},[2192],[1976,3891,3893],{"className":3892},[2197,2198,2199,2200],[1976,3894,1793],{"className":3895},[2019,2020,2200],[1976,3897,2336],{"className":3898},[2335],[1976,3900,3902],{"className":3901},[2181],[1976,3903,3905],{"className":3904,"style":2343},[2185],[1976,3906],{},[1976,3908],{"className":3909,"style":2214},[2213],[1976,3911,2147],{"className":3912},[2218],[1976,3914],{"className":3915,"style":2214},[2213],[1976,3917,3919,3923,3973,3976,3979],{"className":3918},[2010],[1976,3920],{"className":3921,"style":3922},[2014],"height:1.04em;vertical-align:-0.0839em;",[1976,3924,3926],{"className":3925},[2019,2922],[1976,3927,3929,3964],{"className":3928},[2177,2312],[1976,3930,3932,3961],{"className":3931},[2181],[1976,3933,3936,3948],{"className":3934,"style":3935},[2185],"height:0.9561em;",[1976,3937,3939,3942],{"className":3938,"style":2865},[2936],[1976,3940],{"className":3941,"style":2856},[2192],[1976,3943,3945],{"className":3944,"style":2943},[2019],[1976,3946,3500],{"className":3947},[2019],[1976,3949,3951,3954],{"style":3950},"top:-2.9161em;",[1976,3952],{"className":3953,"style":2856},[2192],[1976,3955,3957],{"className":3956,"style":2994},[2993],[2996,3958,3959],{"xmlns":2998,"width":2999,"height":3000,"viewBox":3001,"preserveAspectRatio":3002},[3004,3960],{"d":3006},[1976,3962,2336],{"className":3963},[2335],[1976,3965,3967],{"className":3966},[2181],[1976,3968,3971],{"className":3969,"style":3970},[2185],"height:0.0839em;",[1976,3972],{},[1976,3974],{"className":3975,"style":2214},[2213],[1976,3977,3847],{"className":3978},[2218],[1976,3980],{"className":3981,"style":2214},[2213],[1976,3983,3985,3988],{"className":3984},[2010],[1976,3986],{"className":3987,"style":3365},[2014],[1976,3989,3991],{"className":3990},[2019],"11.18%",[1793,3993,3994,3995,4028],{},"注意它低于两个波动率的简单平均 ",[1976,3996,3998,4015],{"className":3997},[1979],[1976,3999,4001],{"className":4000},[1983],[1985,4002,4003],{"xmlns":1987},[1989,4004,4005,4012],{},[1992,4006,4007,4010],{},[2134,4008,4009],{},"15",[1995,4011,3212],{"mathvariant":2068},[1999,4013,4014],{"encoding":2001},"15\\%",[1976,4016,4018],{"className":4017,"ariaHidden":2006},[2005],[1976,4019,4021,4024],{"className":4020},[2010],[1976,4022],{"className":4023,"style":3365},[2014],[1976,4025,4027],{"className":4026},[2019],"15%","。这不是因为资产 B “低风险”本身，而是因为两个资产不完全同向波动。",[1800,4030,4032],{"id":4031},"可运行例题相关系数决定分散化空间","可运行例题：相关系数决定分散化空间",[1793,4034,4035],{},"保持两个资产各自的收益和波动率不变，只改变相关系数，搜索不允许卖空时的最小方差权重。",[4037,4038],"pyodide",{"code64":4039,"layout":4040,"locale":7,"packages":4041,"title":4042},"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","vertical","numpy","Python：两资产最小方差与相关性",[1793,4044,4045],{},"相关性越高，可利用的分散化空间通常越小。这里的权重使用已知参数；真实投资中均值和协方差都要估计，样本误差可能比公式本身更重要。",[1800,4047,4048],{"id":4048},"学习顺序建议",[1804,4050,4051,4064],{},[1807,4052,4053],{},[1810,4054,4055,4058,4061],{},[1813,4056,4057],{},"小节",[1813,4059,4060],{},"先抓住的问题",[1813,4062,4063],{},"需要特别留意",[1820,4065,4066,4077,4088,4099,4110,4121],{},[1810,4067,4068,4071,4074],{},[1825,4069,4070],{},"3.1 投资组合理论基础",[1825,4072,4073],{},"组合收益与组合风险如何计算",[1825,4075,4076],{},"权重约束、协方差矩阵",[1810,4078,4079,4082,4085],{},[1825,4080,4081],{},"3.2 两资产组合",[1825,4083,4084],{},"分散化从哪里来",[1825,4086,4087],{},"相关系数对风险的影响",[1810,4089,4090,4093,4096],{},[1825,4091,4092],{},"3.3 多资产组合与有效前沿",[1825,4094,4095],{},"哪些组合是有效的",[1825,4097,4098],{},"最小方差组合、有效前沿形状",[1810,4100,4101,4104,4107],{},[1825,4102,4103],{},"3.4 引入无风险资产",[1825,4105,4106],{},"无风险资产如何改变选择空间",[1825,4108,4109],{},"借贷、杠杆、资本配置线",[1810,4111,4112,4115,4118],{},[1825,4113,4114],{},"3.5 资本市场线与分离定理",[1825,4116,4117],{},"为什么切点组合如此重要",[1825,4119,4120],{},"Sharpe 比率、两基金分离",[1810,4122,4123,4126,4129],{},[1825,4124,4125],{},"3.6 资产配置实践",[1825,4127,4128],{},"理论如何进入真实组合",[1825,4130,4131],{},"估计误差、约束、再平衡",[1800,4133,4134],{"id":4134},"常见错误与考试陷阱",[1878,4136,4137,4144,4150,4156,4162],{},[1881,4138,4139,4143],{},[4140,4141,4142],"strong",{},"把组合波动率算成波动率加权平均","：正确做法是先算方差，再开方。",[1881,4145,4146,4149],{},[4140,4147,4148],{},"忽略协方差项","：相关性越高，分散化收益越小；相关性为 1 时没有分散化收益。",[1881,4151,4152,4155],{},[4140,4153,4154],{},"认为有效前沿上的组合都适合自己","：有效只说明不被支配，具体选择仍取决于风险偏好。",[1881,4157,4158,4161],{},[4140,4159,4160],{},"把最小方差组合当成最优组合","：只有极端保守或特定目标下才会选择它。",[1881,4163,4164,4167],{},[4140,4165,4166],{},"低估估计误差","：均值估计误差会让最优权重非常不稳定，实务中需要约束和稳健化。",[1800,4169,4170],{"id":4170},"自测题",[1878,4172,4173,4176,4179,4182],{},[1881,4174,4175],{},"为什么组合风险取决于协方差矩阵，而不是只取决于各资产方差？",[1881,4177,4178],{},"两资产相关系数从 1 降到 0，再降到 -1，有效前沿会怎样变化？",[1881,4180,4181],{},"无风险资产存在时，为什么最大 Sharpe 比率组合成为核心组合？",[1881,4183,4184],{},"如果估计得到某资产预期收益很高，均值-方差优化会如何反应？为什么实务中要谨慎？",[1800,4186,4187],{"id":4187},"答案指引",[1878,4189,4190,4376,4379,4382],{},[1881,4191,4192,4193,4375],{},"组合方差包含 ",[1976,4194,4196,4234],{"className":4195},[1979],[1976,4197,4199],{"className":4198},[1983],[1985,4200,4201],{"xmlns":1987},[1989,4202,4203,4231],{},[1992,4204,4205,4207,4214,4221],{},[2134,4206,2428],{},[2258,4208,4209,4211],{},[1995,4210,2101],{},[1995,4212,4213],{},"i",[2258,4215,4216,4218],{},[1995,4217,2101],{},[1995,4219,4220],{},"j",[2258,4222,4223,4225],{},[1995,4224,2423],{},[1992,4226,4227,4229],{},[1995,4228,4213],{},[1995,4230,4220],{},[1999,4232,4233],{"encoding":2001},"2w_iw_j\\sigma_{ij}",[1976,4235,4237],{"className":4236,"ariaHidden":2006},[2005],[1976,4238,4240,4244,4247,4290,4331],{"className":4239},[2010],[1976,4241],{"className":4242,"style":4243},[2014],"height:0.9305em;vertical-align:-0.2861em;",[1976,4245,2428],{"className":4246},[2019],[1976,4248,4250,4253],{"className":4249},[2019],[1976,4251,2101],{"className":4252,"style":2116},[2019,2020],[1976,4254,4256],{"className":4255},[2173],[1976,4257,4259,4281],{"className":4258},[2177,2312],[1976,4260,4262,4278],{"className":4261},[2181],[1976,4263,4266],{"className":4264,"style":4265},[2185],"height:0.3117em;",[1976,4267,4269,4272],{"style":4268},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[1976,4270],{"className":4271,"style":2193},[2192],[1976,4273,4275],{"className":4274},[2197,2198,2199,2200],[1976,4276,4213],{"className":4277},[2019,2020,2200],[1976,4279,2336],{"className":4280},[2335],[1976,4282,4284],{"className":4283},[2181],[1976,4285,4288],{"className":4286,"style":4287},[2185],"height:0.15em;",[1976,4289],{},[1976,4291,4293,4296],{"className":4292},[2019],[1976,4294,2101],{"className":4295,"style":2116},[2019,2020],[1976,4297,4299],{"className":4298},[2173],[1976,4300,4302,4323],{"className":4301},[2177,2312],[1976,4303,4305,4320],{"className":4304},[2181],[1976,4306,4308],{"className":4307,"style":4265},[2185],[1976,4309,4310,4313],{"style":4268},[1976,4311],{"className":4312,"style":2193},[2192],[1976,4314,4316],{"className":4315},[2197,2198,2199,2200],[1976,4317,4220],{"className":4318,"style":4319},[2019,2020,2200],"margin-right:0.0572em;",[1976,4321,2336],{"className":4322},[2335],[1976,4324,4326],{"className":4325},[2181],[1976,4327,4329],{"className":4328,"style":2343},[2185],[1976,4330],{},[1976,4332,4334,4337],{"className":4333},[2019],[1976,4335,2423],{"className":4336,"style":2460},[2019,2020],[1976,4338,4340],{"className":4339},[2173],[1976,4341,4343,4367],{"className":4342},[2177,2312],[1976,4344,4346,4364],{"className":4345},[2181],[1976,4347,4349],{"className":4348,"style":4265},[2185],[1976,4350,4351,4354],{"style":3886},[1976,4352],{"className":4353,"style":2193},[2192],[1976,4355,4357],{"className":4356},[2197,2198,2199,2200],[1976,4358,4360],{"className":4359},[2019,2200],[1976,4361,4363],{"className":4362,"style":4319},[2019,2020,2200],"ij",[1976,4365,2336],{"className":4366},[2335],[1976,4368,4370],{"className":4369},[2181],[1976,4371,4373],{"className":4372,"style":2343},[2185],[1976,4374],{},"。资产之间同涨同跌会放大组合波动，不同涨跌会抵消部分风险。",[1881,4377,4378],{},"相关系数越低，分散化越强，有效前沿越向左上方弯曲；相关系数为 -1 时，可能构造零风险组合。",[1881,4380,4381],{},"任意无风险资产与风险组合的连线斜率都是 Sharpe 比率。斜率最高的切点组合给每单位风险最高超额收益。",[1881,4383,4384],{},"优化器会倾向给它很高权重，甚至在允许卖空时给出极端杠杆。若预期收益估计噪声大，这种权重可能完全不稳健。",[1800,4386,4387],{"id":4387},"小结与过渡",[1793,4389,4390],{},"本章说明了分散化和有效前沿如何把风险资产组合成更有效的投资机会。下一章的 CAPM 会在此基础上加入市场均衡：如果所有投资者都做均值-方差选择，哪些风险会被补偿，哪些风险会被分散掉？",{"title":10,"searchDepth":4392,"depth":4392,"links":4393},2,[4394,4395,4396,4397,4398,4406,4407,4408,4409,4410,4411,4412],{"id":1802,"depth":4392,"text":1802},{"id":1873,"depth":4392,"text":1873},{"id":1919,"depth":4392,"text":1919},{"id":1971,"depth":4392,"text":1971},{"id":2713,"depth":4392,"text":2713,"children":4399},[4400,4402,4403,4404,4405],{"id":2717,"depth":4401,"text":2717},3,{"id":2726,"depth":4401,"text":2726},{"id":2735,"depth":4401,"text":2735},{"id":2744,"depth":4401,"text":2744},{"id":3158,"depth":4401,"text":3158},{"id":3167,"depth":4392,"text":3168},{"id":4031,"depth":4392,"text":4032},{"id":4048,"depth":4392,"text":4048},{"id":4134,"depth":4392,"text":4134},{"id":4170,"depth":4392,"text":4170},{"id":4187,"depth":4392,"text":4187},{"id":4387,"depth":4392,"text":4387},"马科维茨投资组合理论与资产配置","md",{"sidebar":4416},{"order":4401},true,{"title":1266,"description":4413},"Xgiw2IHdKTwaD30lR4TsDqS9YI_tf7ktVa4rSJ2ioQw",[4421,4423],{"title":1260,"path":1261,"stem":1262,"description":4422,"children":-1},"期望效用理论、风险厌恶与资产选择",{"title":1272,"path":1273,"stem":1274,"description":4424,"children":-1},"CAPM理论、推导与实证检验",1785754746056]