CFA+2024++L2数量课后习题及详解.docx

PracticeProblemsThefollowinginformationrelatestoquestions1-5Youareajunioranalystatanassetmanagementirm.Ybursupervisorasksyoutoanalyzethereturndriversforoneoftheirm,sportfolios.Sheasksyoutoconstructaregressionmodeloftheportfolio'smonthlyexcessreturns(RET)againstthreefactors:themarketexcessreturn(MRKT),avaluefactor(HML),andthemonthlypercentagechangeinavolatilityindex(VIX).Youcollectthedataandruntheregression,andtheresultingmodelisYret=-°999+1.817XMRKT+0489XHML+0.037Xy.Youthencreatesomediagnosticchartstohelpdeterminethemodelit.sujmJ SSQUXB°oHod%ChangeinvolatilityfactorRETvsMRKTSErUSSB3x20HJodMarket excess returnsRET predicted valuess(snp3J £A. Determinethetypeofregressionmodelyoushoulduse.B. 1.ogisticregressionC. SimplelinearregressionD. Multiplelinearregression1. Determinewhichoneofthefollowingstatementsaboutthecoeficientofthevolatilityfactor(VIX)istrue.A. A1.0%increaseinXqxwouldresultina-0.962%decreaseinYret-B. A0.037%increaseinXvVXWOUIdresultina1.0%increaseinYret-C. A1.0%increaseinXytholdingalltheotherindependentvariablesconstant,wouldresultina0.037%increaseinYRE2. IdentifytheregressionassumptionthatmaybeviolatedbasedonChart1,RETvs.VIX.A. IndependenceoferrorsB. IndependenceofindependentvariablesC. 1.inearitybetweendependentvariableandexplanatoryvariables3. Identifywhichchart,amongCharts2,3,and4,ismostlikelytobeusedtoassesshomoskedasticityA. Chart2B. Chart3C. Chart45. Identifywhichchart,amongCharts2,3,and4,ismostlikelytobeusedtoassessindependenceofindependentvariables.A. Chart2B. Chart3C. Chart41. Ciscorrect.Youshoulduseamultiplelinearregressionmodelsincethedependentvariableiscontinuous(notdiscrete)andthereismorethanoneexplanatoryvariable.Ifthedependentvariablewerediscrete,thenthemodelshouldbeestimatedasalogisticregression.2. Ciscorrect.Thecoeficientofthevolatilityfactor(Xy)is0.037.Itshouldbeinterpretedtomeanthatholdingalltheotherindependentvariablesconstant,a1%increase(decrease)wouldresultina0.037%increase(decrease)inthemonthlyportfolioexcessreturn(V)3. Ciscorrect.Chart1isascatterplotofRETversusVIX.Linearitybetweenthedependentvariableandtheindependentvariablesisanassumptionunderlyingmultiplelinearregression.AsshowninthefollowingRevisedChart1,therelationshipappearstobemorecurved(i.e.,quadratic)thanlinearSUJruB-× O=OjHOd%Changeinvolatilityfactor4. Ciscorrect.Tbassesshomoskedasticit¾wemustevaluatewhetherthevarianceoftheregressionresidualsisconstantforallobservations.Chart4isascatterplotoftheregressionresidualsversusthepredictedvalues,soitisveryusefulforvisuallyassessingtheconsistencyofthevarianceoftheresidualsacrosstheobservations.Anyclustersofhighand/orlowvaluesoftheresidualsmayindicateaviolationofthehomoskedasticityassumption.5. Biscorrect.Chart3isascatterplotcomparingthevaluesoftwooftheindependentvariables,MRKTandHML.Thischartwouldmostlikelybeusedtoassesstheindependenceoftheseexplanatoryvariables.EvaluatingRegressionModelFitandInterpretingModelResults1.earningOutcomesThecandidateshouldbeableto: evaluatehowwellamultipleregressionmodelexplainsthedependentvariablebyanalyzingANOVAtableresultsandmeasuresofgoodnessofit formulatehypothesesonthesigniicanceoftwoormorecoeficientsinamultipleregressionmodelandinterprettheresultsofthejointhypothesistests calculateandinterpretapredictedvalueforthedependentvariable,giventheestimatedregressionmodelandassumedvaluesfortheindependentvariablePracticeProblemsThefollowinginformationrelatestoquestions1-5Youareajunioranalystatanassetmanagementirm.Ybursupervisorasksyoutoanalyzethereturndriversforoneoftheirm,sportfolios.Sheasksyoutoconstructaregressionmodeloftheportfolio'smonthlyexcessreturns(RET)againstthreefactors:themarketexcessreturn(MRKT),avaluefactor(HML),andthemonthlypercentagechangeinavolatilityindex(VIX).Youcollectthedataandruntheregression.Aftercompletingtheirstregression(Model1),youreviewtheANOVAresultswithyoursupervisorThen,sheasksyoutocreatetwomoremodelsbyaddingtwomoreexplanatoryvariables:asizefactor(SMB)andamomentumfactor(MOM).Yburthreemodelsareasfollows:Model1:RETj-bq+ffMRKTz+IjhmlHMLj+byV!X/+/.Model2:RET/=bq+bMRcMRKTj+bMLHML+byVlX÷bMBSMB/+z.Model3:RETj=bo+ffMRKT/+1>hmlHML,+byVlX/+bsMBSMB/+OmomMOM/+/.TheregressionstatisticsandANOVAresultsforthethreemodelsareshowninExhibit1,Exhibit2,andExhibit3.Exhibit1:ANOVATableforModel1RET尸bo+bRMRKT；+1)hmlHML/+byVIXj+RegressionStatisticsCoeficientStd.Errort-Stat.P-ValueMultipleR0.907Intercept-0.9990.414-2.4110.018R-SqUared0.823MRKT1.8170.12414.6830.000AdjustedR-Sq.0.817HML0.4890.1184.1330.000StandardError3.438VIX0.0370.0182.1220.037Observations96.000ANOVADfSSMSFSigniicanceFRegression35058.4301686.143142.6280.000Residual921087.61811.822Total956146.048Exhibit2:ANOVATableforModel2RET/=o+MRKTMRKTi+bfMLHML