CFA二级-阶段总结与重点精讲-数量

阶段总结与重点精讲直播即将开始L2–QuantitativeMethod1QuantitativeMethodweight:StudySession1-2StudySession3StudySession4Ethics&ProfessionalStandards10%-15%5%-10%15%-20%5%-15%15%-25%10%-20%5%-15%5%-10%5%-10%QuantitativeMethodsEconomicsStudySession5-6StudySession7-8StudySessionStudySession12-13StudySession14StudySession15StudySession16-17FinancialReportingandAnalysisCorporateFinanceEquityFixedIncomeDerivativeInvestmentAlternativeInvestmentPortfolioManagementWeights:100%2QuantitativeMethodContents:➢Studysession3:QuantitativeMethodsfor✓Reading6:FintechInvestmentManagement(★)✓Reading7:CorrelationandRegression(★★)✓Reading8:MultipleRegressionandIssuesinRegressionAnalysis(★★★)✓Reading9:Analysis(★★★)✓Reading10:Excerptfrom“Probabilisticapproaches:scenarioanalysis,decisiontrees,andsimulations”(★)3QuantitativeMethod:➢与2018年相比，2019年的考纲有如下变化：✓新增Reading6:FintechinInvestmentManagement。✓在Reading8中新增了3条关于“MachineLearning”的考纲。4QuantitativeMethodReading7:Correlationregression:1.Correlation2.Simplelinearregression3.5QuantitativeMethodCorrelationScatterplotsCovariancecorrelationtestingofcorrelationH:ρ=0,H:0arn-2t-test:df=n-2;t=1-r2Decisionrule:rejectHift>+t,t<-tcriticalcritical0Limitationstocorrelationanalysis6QuantitativeMethodSimplelinearregressionAssumptionssimplelinearregressionOrdinaryleastsquares(OLS)regressionSimplelinearregressionY=b+bX+εi=1,i01iiInterpretationbb10SignificancetestforaregressioncoefficientH:b=H:b≠001a1ˆb-bt=1s1t-test:df=n-2;ˆb1Rejectionofnullhypothesistheregressionissignificantlyfromzero.7QuantitativeMethodSimplelinearregressionConfidenceintervalforaregressioncoefficientˆˆˆb(ts)orb-(ts)bb+(ts)1cˆ1cˆ11cˆbbb111Iftheconfidenceintervaldoesincludezero,thenullhypothesis(H:b=0)isrejected.01Predictedvaluedependentvariableˆˆˆ+bX01pˆˆˆY(ts)orY-(ts)YY+(ts)cfcfcfLimitationsregressionanalysis8QuantitativeMethodReading8:Multipleregressionandissuesinregression1.Multipleregression2.3.Issuesinregression9QuantitativeMethodMultipleregressionAssumptionsofmultiplelinearregressionMultiplelinearregressionY=b+bX+bX+...+bX+εi011i22ikkiiHypothesistestingofregressionConfidenceintervalforaregressioncoefficientPredictingthedependentvariableˆˆˆˆˆˆˆˆY+bX+bXbXi011i22ikki10QuantitativeMethodtablesofmultipleregressiondfkkn-k-1)-RegressionErrorn-k-1n-12=RSS/SSTF=withdfkn-k-111QuantitativeMethod2AdjustedR2F-statisticsH:b=b=b=…=b=0H:leastb≠0(j=1tok)0123kajRejectionofHthatleastoneindependentvariable,0theawhole,makesasignificantcontributiontoexplainthedependentvariable.12QuantitativeMethodIssuesinregressionofassumptionsHeteroskedasticity()Serialcorrelation(Autocorrelation,)Multicollinearity()Qualitativeindependentvariablevariable,)Ncategories→n-1variablesInterpretationregressionMisspecification()Qualitativedependentvariable13QuantitativeMethodHeteroskedasticity对自变量的不同观察值，其残差的方差不相同。无条件异方差：方差不同，但和自变量无关条件异方差：方差不同并且和自变量有关14QuantitativeMethodEffects•Residualscatterplots•Breuschnχ²-testConditional↓,HeteroskedasticityIerrorH:noheteroskedasticity0Positiveserialcorrelation↓,•Residualscatterplots•testIerrorH:noserialcorrelationNegativeserialcorrelation↑0≤DW≤d:positivecorrelationIIerrorL↑•t-testssignificant,F-testMulticollinearityIIerrorsignificantandhigh15QuantitativeMethodReading9:1.models2.Autoregressivemodels3.Randomwalk4.evaluation16QuantitativeMethodmodelsLineartrendmodels:constantchangeamountwithtime.y=b+bt+εt01tLog-lineartrendmodels:constantgrowthratewithtime.Ln(y)=b+bt+εyε)01tt01tt17QuantitativeMethodAutoregressivemodelsCovariancestationaryAutoregressivex=b+bx+εx=b+bx+bx+...+bx+εt01tt012ptChainruleforecastingDetectingandcorrectingautocorrelation&seasonalityreversionMean-revertinglevelb01-bx=t118QuantitativeMethodRandomwalkRandomwalkandrandomwalkwithadriftx=x+x=b+x+tttt0tttestforunitrootx-x=b+gx+εwhere:g=b-1tt-101t-1t11H:g=0;H:g<0;01a1IffailtorejectH,thereisaunitrootthetimeseriesis0First19QuantitativeMethodModelevaluationcriterion:thesmallestfortheout-of-sampledata.ReliabilityvsinstabilityAutoregressiveConditionalHeteroskedasticityRegressionwithtwotimeseriesCointegration20QuantitativeMethodReadingExcerptfrom“ProbabilisticApproaches:ScenarioDecisionandSimulations”ComparingprobabilisticapproachesSelectivevs.fullriskanalysis.risk:discretevs.continuous.21QuantitativeMethodReading6:FintechofmachinelearningSupervisedlearning:makesuseoflabeledtrainingdata.Regression:targetvariableiscontinuous.Classification:targetvariableiscategoricalorordinal.Unsupervisedlearningdoesuseoflabeledtrainingdata.22QuantitativeMethodMachinelearningalgorithmsPenalizedregressionSupervisedlearningRandomforestsNeuralnetworksClusteringalgorithmsDimensionreductionUnsupervisedlearning23QuantitativeMethodFintechinInvestmentManagementBasicsof