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1、Chapter06-EfficientDiversificationCHAPTER06EFFICIENTDIVERSIFICATION1.Solongasthecorrelationcoefficientisnot1.0,theportfoliowillcontaindiversificationbenefits.Anyothercombinationwillcauseadiversificationbenefitsincethestandarddeviationwillfall,relative
2、tothereturnontheportfolio.Otherwise,theriskandreturnwillchangeinunison.2.Thecovariancewiththeotherassetsismoreimportant.Diversificationisaccomplishedviacorrelationwithotherassets.Covariancehelpsdeterminethatnumber.3.a.andb.willbothhavethesameimpactofi
3、ncreasingthesharpemeasurefrom.40to.45.4.Theexpectedreturnoftheportfoliowillbeimpactediftheassetallocationischanged.Sincetheexpectedreturnoftheportfolioisthefirstiteminthenumeratorofthesharperatio,theratiowillbechanged.5.Impactontotalvariancea.Bothwill
4、havethesameimpact.Thetotalvariancewillincreasefrom.18to.1989b.Anincreaseinbeta,however,increasesthecorrelationcoefficientandthuscreatesmorediversificationbenefit.6.a.Withoutdoinganymath,thesevererecessionisworseandtheboomisbetter.Thus,thereappearstobe
5、ahighervariance,yetthemeanisprobablythesamesincethespreadisequallylargeronboththehighandlowside.Themeanreturn,however,shouldbehighersincethereishigherprobabilitygiventothehigherreturns.b.Calculationofmeanreturnandvarianceforthestockfund:6-14Chapter06-
6、EfficientDiversificationa.Calculationofcovariance:Covariancehasincreasedbecausethestockreturnsaremoreextremeintherecessionandboomperiods.Thismakesthetendencyforstockreturnstobepoorwhenbondreturnsaregood(andviceversa)evenmoredramatic.2.a.Onewouldexpect
7、variancetoincreasebecausetheprobabilitiesoftheextremeoutcomesarenowhigher.b.Calculationofmeanreturnandvarianceforthestockfund:6-14Chapter06-EfficientDiversificationa.CalculationofcovarianceCovariancehasdecreasedbecausetheprobabilitiesofthemoreextremer
8、eturnsintherecessionandboomperiodsarenowhigher.Thisgivesmoreweighttotheextremesinthemeancalculation,thusmakingtheirdeviationfromthemeanlesspronounced.2.Theparametersoftheopportunitysetare:E(rS)=15%,E(rB)=9%,sS=32%,sB=23%,r=0.15,rf=5.5%Fromthes
