International-Financial-Management---Bekaert-2e---

©2012PearsonEducation,Inc.Chapter13InternationalCapitalMarketEquilibriumQUESTIONS1.IsthevolatilityofthedollarreturntoaninvestmentintheJapaneseequitymarketthesumofthevolatilityoftheJapaneseequitymarketreturninyenplusthevolatilityofyen/dollarexchangeratechanges?Whyorwhynot?Answer:Itisnot.EventhoughthedollarreturnoninvestinginJapaneseequityisapproximatelytheyenreturnontheJapaneseequitymarketplustherateofchangeinthedollar/yenexchangerate,thevolatilityofthissumisnotthesumofthevolatilities.Intuitively,becausetheequityriskandcurrencyriskarenothighlycorrelated,partofthevolatilityoftheindividualcomponentsisdiversifiedaway.Technically,thevarianceofthedollarreturnscanbewrittenasfollows:Var[r(t+1,¥)+s(t+1)]=Var[r(t+1,¥)]+Var[s(t+1)]+2ρVol[r(t+1,¥)]Vol[s(t+1)]wherer(t+1,¥)istheyen-denominatedequityreturn,s(t+1)istherateofchangeinthedollar/yenexchangerate,andρisthecorrelationbetweentheyenequityreturnanddollar/yenexchangeratechanges.Becausevolatility,Vol,isthesquarerootofthevariance,weknowthatthevolatilityofthedollarreturnonaJapaneseequityinvestmentisVol[r(t+1,¥)+s(t+1)]={Vol[r(t+1,¥)]2+Vol[s(t+1)]2+2ρVol[r(t+1,¥)]Vol[s(t+1)]}0.5Clearly,onlywhenthecorrelationisexactly1willtheright-handsidehavetheform(A2+2AB+B2)0.5=[(A+B)2]0.5=(A+B)Hence,onlythenwillthevolatilityofthesumbethesumofthevolatilities.Whenthereisperfectcorrelation,thereisnonaturaldiversificationadvantagetohavingexposuretotwosourcesofrisk.However,aslongasρ1,thetotalvolatilityofthedollarreturntoinvestingintheJapaneseequitymarketwillbelessthanthesumofthetwovolatilities.2.WhyisthevarianceofaportfolioofinternationallydiversifiedstockslikelytobelowerthanthevarianceofaportfolioofU.S.stocks?Answer:Withinternationalstocks,theinvestorcandiversifyawayU.S.-specificsourcesofvolatility(e.g.U.S.–specificbusinesscyclemovements,changesinU.S.monetarypolicy,changesinU.S.interestrates,etc.).Technically,thevarianceofanequallyweightedChapter13:InternationalCapitalMarketEquilibrium©2012PearsonEducation,Inc.2portfolioconvergestotheaveragecovariancebetweenthesestockswhenthenumberofstocksgetsverylarge.TheaveragecovarianceamongU.S.stocksishigherthantheaveragecovarianceamongasetofU.S.andinternationalstocks.3.HowcanyouincreasetheSharperatioofaportfolio?Whattypeofstockswouldyouhavetoaddtoitinordertodoso?Answer:ToincreasetheSharperatioonyourportfolio,youmustaddstocksthatincreasetheexpectedreturnonyourportfolioand/orreducethevolatilityoftheportfolio(forinstance,becausethestocksexhibitlowcorrelationwiththeportfolioyoualreadyhave).Onewaytothinkoftheproblemistocomputethefollowinghurdlerate,Hurdlerate=f*E[r]r+ρVol[r]Vol[r]Inthisequationrfistheriskfreerate,ρisthecorrelationbetweentheportfolioyouhaveandthestockyouwanttoaddtotheportfolio,E[r]andVol[r]aretheexpectedreturnandvolatilityoftheportfolioyouareholding,andVol[r*]isthevolatilityofthestockyouwanttoadd.ThehurdlerateishigherwhentheexistingportfoliohasahighSharperatio,thestockyouareaddingismorevolatile,orthereishighcorrelationbetweenthereturnontheportfolioandthereturnonthestockyouareaddingtotheportfolio.4.WhyisthehurdlerateinSection13.2lowerforJapanthanforCanada?ShouldU.S.investorsstillinvestinCanada?Answer:FromtheformulaintheanswertoQuestion3,weseethatthetwomaindriversofthehurdleratesarethecorrelationsbetweenCanadianandU.S.returnsandbetweenJapaneseandU.S.returns(reportedinExhibit13.6),andthevolatilitiesofCanadianandJapanesereturns(reportedinExhibit13.1).Themostimportantnumberisthecorrelation.OftheG7countries,theCanadianreturnshavethehighestcorrelationwithU.S.returns,whereastheJapanesereturnshavethelowestcorrelation.ItisthisdifferencethatmakesJapanhavethelowesthurdlerateandCanadathehighest.WhetherU.S.investorsshouldstillinvestinCanadadependsontheiropportunityset.ThehurdlerateforCanada,reportedinExhibit13.7,suggeststhateveniftheexpectedreturnonCanadianstockisonlyabitlowerthanthatoftheU.S.,itisstillavaluableinvestmentthatincreasestheSharperatio.However,iftheU.S.investorcaninvestinJapanesesecuritiesfirst,theCanadianhurdleratewillincreaseconsiderably,becausetheU.S.-JapandiversifiedportfoliohasahighSharperatio.Inthatcase,itmaynotbeoptimaltogolongCanadiansecuritiesunlessyoureallybelievetheCanadianstockmarketwillhaveanexpectedreturnhigherthanthehurdlerate,andthuslikelyfarhigherthantheU.S.-Japanportfolio’sexpectedreturn.NotethatthisanswerdependsonthehistoricalnumbersreportedintheExhibits.Sometheoriesofportfoliochoice(suchastheCAPM)postulatethatinvestorsshouldholdportfoliosthatarewelldiversifiedandincludeallsecuritiesinlinewiththeirmarketcapitalizations.5.Whatisthemean-standarddeviationfrontier,andwhatisthemean-variance-efficient(MVE)portfolio?Chapter13:InternationalCapitalMarketEquilibrium©2012PearsonEducation,Inc.3Answer:Themeanstandarddeviationfrontieristhelocusoftheportfoliosinexpectedreturn–standarddeviationspacethathavetheminimumstandarddeviationforeachexpectedreturn.Becausevarianceisthesquaredvalueofstandarddeviation,itisthereforealsooftenreferredtoastheminimum-variancefrontier.TheMVEistheportfolioonthatfrontierthatmaximizestheSharperatio.Itcanbe