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1、Chapter06-EfficientDiversificationCHAPTER06EFFICIENTDIVERSIFICATION1.Solongasthecorrelationcoefficientisnot1.0,theportfoliowillcontaindiversificationbenefits.Anyothercombinationwillcauseadiversificationbenefitsincethestandarddeviationwillfall,relativetothereturnonthepo
2、rtfolio.Otherwise,theriskandreturnwillchangeinunison.2.Thecovariancewiththeotherassetsismoreimportant.Diversificationisaccomplishedviacorrelationwithotherassets.Covariancehelpsdeterminethatnumber.3.a.andb.willbothhavethesameimpactofincreasingthesharpemeasurefrom.40to.4
3、5.4.Theexpectedreturnoftheportfoliowillbeimpactediftheassetallocationischanged.Sincetheexpectedreturnoftheportfolioisthefirstiteminthenumeratorofthesharperatio,theratiowillbechanged.5.Impactontotalvariancea.Bothwillhavethesameimpact.Thetotalvariancewillincreasefrom.18t
4、o.1989b.Anincreaseinbeta,however,increasesthecorrelationcoefficientandthuscreatesmorediversificationbenefit.6.a.Withoutdoinganymath,thesevererecessionisworseandtheboomisbetter.Thus,thereappearstobeahighervariance,yetthemeanisprobablythesamesincethespreadisequallylarger
5、onboththehighandlowside.Themeanreturn,however,shouldbehighersincethereishigherprobabilitygiventothehigherreturns.b.Calculationofmeanreturnandvarianceforthestockfund:6-14Chapter06-EfficientDiversificationa.Calculationofcovariance:Covariancehasincreasedbecausethestockret
6、urnsaremoreextremeintherecessionandboomperiods.Thismakesthetendencyforstockreturnstobepoorwhenbondreturnsaregood(andviceversa)evenmoredramatic.2.a.Onewouldexpectvariancetoincreasebecausetheprobabilitiesoftheextremeoutcomesarenowhigher.b.Calculationofmeanreturnandvarian
7、ceforthestockfund:6-14Chapter06-EfficientDiversificationa.CalculationofcovarianceCovariancehasdecreasedbecausetheprobabilitiesofthemoreextremereturnsintherecessionandboomperiodsarenowhigher.Thisgivesmoreweighttotheextremesinthemeancalculation,thusmakingtheirdeviationfr
8、omthemeanlesspronounced.2.Theparametersoftheopportunitysetare:E(rS)=15%,E(rB)=9%,sS=32%,sB=23%,r=0.15,rf=5.5%Fromthes
