International-Financial-Management---Bekaert-2e---Solutions---Ch13.doc

International-Financial-Management---Bekaert-2e---Solutions---Ch13.doc

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9

Chapter13:

InternationalCapitalMarketEquilibrium

Chapter 13

InternationalCapitalMarketEquilibrium

QUESTIONS

1.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,weknowthatthevolatilityofthedollarreturnonaJapaneseequityinvestmentis

Vol[r（t+1,¥）+s（t+1）]={Vol[r（t+1,¥）]2+Vol[s（t+1）]2+

2ρVol[r（t+1,¥）]Vol[s（t+1）]}0.5

Clearly,onlywhenthecorrelationisexactly1willtheright-handsidehavetheform

（A2+2AB+B2）0.5=[（A+B）2]0.5=（A+B）

Hence,onlythenwillthevolatilityofthesumbethesumofthevolatilities.Whenthereisperfectcorrelation,thereisnonaturaldiversificationadvantagetohavingexposuretotwosourcesofrisk.However,aslongasρ<1,thetotalvolatilityofthedollarreturntoinvestingintheJapaneseequitymarketwillbelessthanthesumofthetwovolatilities.

2.WhyisthevarianceofaportfolioofinternationallydiversifiedstockslikelytobelowerthanthevarianceofaportfolioofU.S.stocks?

Answer:

Withinternationalstocks,theinvestorcandiversifyawayU.S.-specificsourcesofvolatility（e.g.U.S.–specificbusinesscyclemovements,changesinU.S.monetarypolicy,changesinU.S.interestrates,etc.）.Technically,thevarianceofanequallyweightedportfolioconvergestotheaveragecovariancebetweenthesestockswhenthenumberofstocksgetsverylarge.TheaveragecovarianceamongU.S.stocksishigherthantheaveragecovarianceamongasetofU.S.andinternationalstocks.

3.HowcanyouincreasetheSharperatioofaportfolio?

Whattypeofstockswouldyouhavetoaddtoitinordertodoso?

Answer:

ToincreasetheSharperatioonyourportfolio,youmustaddstocksthatincreasetheexpectedreturnonyourportfolioand/orreducethevolatilityoftheportfolio（forinstance,becausethestocksexhibitlowcorrelationwiththeportfolioyoualreadyhave）.Onewaytothinkoftheproblemistocomputethefollowinghurdlerate,

Hurdlerate=

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,itmaynotbeoptimaltogolongCanadiansecuritiesunlessyoureallybelievetheCanadianstockmarketwillhaveanexpectedreturnh