CFA+2024++L2数量课后习题及详解.docx

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1、PracticeProblemsThefollowinginformationrelatestoquestions1-5Youareajunioranalystatanassetmanagementirm.Ybursupervisorasksyoutoanalyzethereturndriversforoneoftheirm,sportfolios.Sheasksyoutoconstructaregressionmodeloftheportfoliosmonthlyexcessreturns(RET)againstthreefactors:themarketexcessreturn(MRKT)

2、,avaluefactor(HML),andthemonthlypercentagechangeinavolatilityindex(VIX).Youcollectthedataandruntheregression,andtheresultingmodelisYret=-999+1.817XMRKT+0489XHML+0.037Xy.Youthencreatesomediagnosticchartstohelpdeterminethemodelit.sujmJ SSQUXBoHod%ChangeinvolatilityfactorRETvsMRKTSErUSSB3x20HJodMarket

3、excess returnsRET predicted valuess(snp3J A. Determinethetypeofregressionmodelyoushoulduse.B. 1.ogisticregressionC. SimplelinearregressionD. Multiplelinearregression1. Determinewhichoneofthefollowingstatementsaboutthecoeficientofthevolatilityfactor(VIX)istrue.A. A1.0%increaseinXqxwouldresultina-0.96

4、2%decreaseinYret-B. A0.037%increaseinXvVXWOUIdresultina1.0%increaseinYret-C. A1.0%increaseinXytholdingalltheotherindependentvariablesconstant,wouldresultina0.037%increaseinYRE2. IdentifytheregressionassumptionthatmaybeviolatedbasedonChart1,RETvs.VIX.A. IndependenceoferrorsB. Independenceofindependen

5、tvariablesC. 1.inearitybetweendependentvariableandexplanatoryvariables3. Identifywhichchart,amongCharts2,3,and4,ismostlikelytobeusedtoassesshomoskedasticityA. Chart2B. Chart3C. Chart45. Identifywhichchart,amongCharts2,3,and4,ismostlikelytobeusedtoassessindependenceofindependentvariables.A. Chart2B.

6、Chart3C. Chart41. Ciscorrect.Youshoulduseamultiplelinearregressionmodelsincethedependentvariableiscontinuous(notdiscrete)andthereismorethanoneexplanatoryvariable.Ifthedependentvariablewerediscrete,thenthemodelshouldbeestimatedasalogisticregression.2. Ciscorrect.Thecoeficientofthevolatilityfactor(Xy)

7、is0.037.Itshouldbeinterpretedtomeanthatholdingalltheotherindependentvariablesconstant,a1%increase(decrease)wouldresultina0.037%increase(decrease)inthemonthlyportfolioexcessreturn(V)3. Ciscorrect.Chart1isascatterplotofRETversusVIX.Linearitybetweenthedependentvariableandtheindependentvariablesisanassu

8、mptionunderlyingmultiplelinearregression.AsshowninthefollowingRevisedChart1,therelationshipappearstobemorecurved(i.e.,quadratic)thanlinearSUJruB- O=OjHOd%Changeinvolatilityfactor4. Ciscorrect.Tbassesshomoskedasticitwemustevaluatewhetherthevarianceoftheregressionresidualsisconstantforallobservations.

9、Chart4isascatterplotoftheregressionresidualsversusthepredictedvalues,soitisveryusefulforvisuallyassessingtheconsistencyofthevarianceoftheresidualsacrosstheobservations.Anyclustersofhighand/orlowvaluesoftheresidualsmayindicateaviolationofthehomoskedasticityassumption.5. Biscorrect.Chart3isascatterplo

10、tcomparingthevaluesoftwooftheindependentvariables,MRKTandHML.Thischartwouldmostlikelybeusedtoassesstheindependenceoftheseexplanatoryvariables.EvaluatingRegressionModelFitandInterpretingModelResults1.earningOutcomesThecandidateshouldbeableto: evaluatehowwellamultipleregressionmodelexplainsthedependen

11、tvariablebyanalyzingANOVAtableresultsandmeasuresofgoodnessofit formulatehypothesesonthesigniicanceoftwoormorecoeficientsinamultipleregressionmodelandinterprettheresultsofthejointhypothesistests calculateandinterpretapredictedvalueforthedependentvariable,giventheestimatedregressionmodelandassumedvalu

12、esfortheindependentvariablePracticeProblemsThefollowinginformationrelatestoquestions1-5Youareajunioranalystatanassetmanagementirm.Ybursupervisorasksyoutoanalyzethereturndriversforoneoftheirm,sportfolios.Sheasksyoutoconstructaregressionmodeloftheportfoliosmonthlyexcessreturns(RET)againstthreefactors:

13、themarketexcessreturn(MRKT),avaluefactor(HML),andthemonthlypercentagechangeinavolatilityindex(VIX).Youcollectthedataandruntheregression.Aftercompletingtheirstregression(Model1),youreviewtheANOVAresultswithyoursupervisorThen,sheasksyoutocreatetwomoremodelsbyaddingtwomoreexplanatoryvariables:asizefact

14、or(SMB)andamomentumfactor(MOM).Yburthreemodelsareasfollows:Model1:RETj-bq+ffMRKTz+IjhmlHMLj+byV!X/+/.Model2:RET/=bq+bMRcMRKTj+bMLHML+byVlXbMBSMB/+z.Model3:RETj=bo+ffMRKT/+1hmlHML,+byVlX/+bsMBSMB/+OmomMOM/+/.TheregressionstatisticsandANOVAresultsforthethreemodelsareshowninExhibit1,Exhibit2,andExhibit

15、3.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