投资学夏普第二章答案Word文件下载.docx

投资学夏普第二章答案Word文件下载.docx

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asaviolationofthefirstassumption,consideraone-factormodelwherethefactorisgrowthingdp.ifitwerethecasethatasecurityhadapositiverandomerrortermvalueeverytimegdpwashigherthanexpected,thenthefactormodelhasbeenmisspecifiedandshouldbeadjustedtotakeintoaccountthisunexplainedsensitivity.

asaviolationofthesecondassumption,supposethatwheneversecurityahada

positiverandomerrortermvalue,securitybalsohadapositiverandomerrortermvalue,thenthe

factormodelhasbeenmisspecified.inthiscasetheremustbesomesourceofcommonresponsivenessbetweenthetwosecuritiesthathasnotbeencapturedbythefactormodel.5.

bythetermsimilarstockscupidpresumablymeansthattheydisplaysimilarsensitivitiestovariouseconomicandfinancialfactors.ifafactormodeliscorrectlyspecified,thentwostockswithsimilarsensitivitiestothemodelsfactorsshouldgeneratereturnsthatareroughlythesameovertime.intheshortruntheirreturnsmaydifferbythedifferencesinthevaluesoftheirrespectiverandomerrorterms.giventhattheexpectedvalueoftherandomerrortermiszero,overthelong-runonewouldexpecttherandomerrortermtoequalzeroandthustheaveragereturnonthetwosecuritiestobethesame.7.

a.

inaone-factormodel,aportfoliosfactorriskisexpressedasbpf22

?

.since

thesensitivityoftheportfoliotothefactoristheweightedaverageofthecomponentsecuritiessensitivities（withtheirproportionsservingasweights）,then:

factorrisk=（.40?

.20+.60?

3.50）2?

225

=1,069.3

b.

non-factorrisk（expressedas?

ep2istheweightedaverageofthecomponent

securitiesrandomerrortermvariances（withthesquareofthesecuritiesproportionsservingasweights）,then:

non-factorrisk=.402?

49+.602?

100

=43.8

c.thestandarddeviationoftheportfolioisgivenby:

?

ppfepb?

（）/22212

=（1,069.3+43.8）?

=33.4%

9.thecovariancebetweentwosecuritiesinaone-factorworldisgivenby:

ijijf

bb?

2

inthiscase,theequationshouldbesolvedfor

f.thatis:

f

=[

ij/bibj]?

=[（-312.50）/（-0.50?

1.25）]?

=22.4%

10.inaone-factormodelworld,thestandarddeviationofasecurityisgivenby:

iifeib?

forsecuritya:

a=[（.8）2?

（18）2+（25）2]?

=28.9%

forsecurityb:

b=[（1.2）2

（18）2+（15）2]?

=26.3%

11.thenonfactorriskofaportfolioisgivenby:

epiei

in

x?

221

assumingthatthesecuritiesintheportfolioareequal-weighted,theportfoliosnonfactorriskistheaveragenonfactorriskofthesecuritiesdividedbythenumberofportfoliosecurities.thusthenonfactorrisksofthevariousportfoliosare:

10-securityportfolio:

225/10=22.5100-securityportfolio:

225/100=2.251,000-securityportfolio:

225/1,000=0.225

13.inordertocalculatetheexpectedreturnandstandarddeviationofathirty-stock

portfoliobasedonafive-factormodel（withuncorrelatedfactors）,thefollowingparametersmustbeestimated:

zero-factorforeachsecurity30sensitivityofeachsecuritytoeachfactor（5?

30）150varianceoftherandomerrortermforeachsecurity30varianceofeachfactor5expectedvalueofeachfactor5total220ifthefactorsarecorrelated,thentherewillbe（n2-n）factorcovariancesto

estimateinadditiontotheparameterslistedabove.inthiscase,thenumberofadditionalparameterswouldbe（52-5）=20.

14.factorsthoughttopervasivelyaffectsecurityreturnsareusuallyviewedas

macroeconomicormicroeconomicinnature.thetextdiscussedseveralpossiblemacroeconomicfactors.othersuchfactorsmightincludemoneysupplygrowth,thesizeofthebudgetdeficit（orsurplus）,thesizeofthetradedeficit（orsurplus）,orthelevelofconsumerconfidence.microeconomicfactors（oratleastproxiesforthosefactors）thatmightpervasively

influencesecurityreturnsincludedividendyield,earningsgrowthrate,earningsgrowthmomentum（thatis,therateofchangeinearningsgrowth）,bookvalue

-to-priceratio,marketcapitalization,andfinancialleverage.

15.aportfoliossensitivitytoafactoristheweightedaverageofthecomponent

securitiesfactorsensitivities.thereforeinthiscase:

bp1=（.60?

-.20）+（.20?

.50）+（.20?

1.

50）=0.28bp2=（.60?

3.60）+（.20?

10.00）+（.20?

2.20）=4.60bp3=（.60?

0.05）+（.20?

.75）+（.20?

0.30）=0.24

16.inthecontextofafactormodel,theexpectedreturnonsecuritiesisafunctionof

thevaluesexpectedtobeattainedbythefactor（orfactors）.surprisesintheactualoutcomesforthefactorvalueswilldeterminetheactualreturnsearnedonthesecurities,withtheexactnatureofthoseactualreturnsdependingonthestructureofthefactormodel.mathematically,theexpectedreturnonsecuritybasedonasingle-factormodelcan

beexpressedas:

ri=ai+bif

whereriandfaretheexpectedreturnforsecurityiandtheexpectedvalueofthefactor,respectively.

further,realizedreturnsonasecuritycanbeexpressedas:

ri=ai+bif+ei

substituting（ri-bif）foraintheprecedingequationgives:

ri=ri+bi（f-f）+ei

thatis,theactualreturnonthesecurityisafunctionofitsexpectedreturnandthesurprise（orunexpectedchange）inthevalueofthefactor.theunderlyingcorrelationsamongsecuritiesisrepresentedbythesensitivitiesofthesecuritiestosurprisesinthefactorvalue,combinedwiththevolatilityofthefactorvalue.

18.thetime-seriesapproachtofactormodelestimationbeginswiththeassumption

thatthefactorsareknowninadvance.typically,theidentificationofthefactorsproceedsfromananalysisoftheeconomicsofthefirmsinvolved.withthefactorsspecified,historicalinformationconcerningthevaluesofthefactorsandsecurityreturnsarecollectedfromperiodtoperiod.thesedataareusedtoestimatesecuritiessensitivitiestothefactors,thesecuritieszerofactorsanduniquereturns,andthestandarddeviationsoffactorsandtheircorrelations.thecross-sectionalapproachtofactormodelestimationbeginswithestimatesof

thesecurities’sensitivitiestocertainfactors.then,inaparticulartimeperiod,the

valuesofthefactorsareestimatedbasedonthesecuritiesreturnsandtheirsensitivitiestothefactors.byrepeatingtheprocessovermultipletimeperiods,statisticallysignificantestimatesofthefactorsstandarddeviationsandcorrelationscanbecomputed.

thefactoranalysisapproachtofactormodelestimationbeginssimplywithasetofsecuritiesandtheircorrespondingreturns.astatisticalprocedureknownasfactoranalysisisusedtoidentifythenumberofsignificantfactorsandthesecuritiessensitivitiestothosefactorsaswellasthestandarddeviationsofthefactorsandthecorrelationsamongthefactors.

19.securitypricesrepresentinvestors’consensusexpectationsaboutthefuture

prospectsforthefirmsthatissuethesecurities.pastfactorvalueswillalreadybeincorporatedintosecurityprices.thuspastfactorvalueswillhavenoeffectonsecuritypricechangesand,therefor

e,securityreturns.insteaditiswhatinvestorsexpectwillbethevalueoffactorsinthefuturethatshouldberelatedtosecuritypricechangesand,therefore,securityreturns.

22.basedonatwo-factormodel,thevarianceofasecurityis:

iififiiei

bbbbcovff212222212122

1

2

2?

（,）thereforeforthetwosecuritiesinthisproblem:

a

=[（1.5）2?

（20）2]+[（2.6）2?

（15）2]+（2?

1.5?

2.6?

225）+25=4,201

a

=（4,201）?

=64.8%

b

=[（0.7）2?

（20）2]+[（1.2）2?

0.7?

1.2?

225）+16=914

b