Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch12.docx

Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch12.docx

《Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch12.docx》由会员分享，可在线阅读，更多相关《Fundamentals of Corporate Finance 3rd ed Jonathan Berk Ch12.docx（12页珍藏版）》请在冰豆网上搜索。

FundamentalsofCorporateFinance3rdedJonathanBerkCh12

Chapter12

SystematicRiskandtheEquityRiskPremium

Note:

AllproblemsinthischapterareavailableinMyFinanceLab.Anasterisk（*）indicatesproblemswithahigherlevelofdifficulty.

1.Plan:

Calculateeachinvestment’sweightastheamountinvestedinitasaproportionofthetotalamountinvested.

Execute:

Tidepool:

200⨯$55=$11,000

Madfish:

400⨯$25=$10,000

WeightonTidepool=$11,000/（$11,000+$10,000）=52.38%

WeightonMadfish=$10,000/（$11,000+$10,000）=47.62%

Evaluate:

Youcannottelltheweightsjustbythenumberofshares;whatmattersisthetotaldollaramountsinvestedineachstock.

2.Plan:

Theexpectedreturnonanyportfolioistheweightedaverageoftheexpectedreturns

ofthesecuritiesintheportfolio.Thereforewewillcomputetheweightedaveragereturnonthisportfolio.

Execute:

Evaluate:

Theexpectedreturnonthisportfoliois19.8%.

3.Plan:

Performthecalculationstoanswerthequestionsintheproblem.

Execute:

a.Let

bethenumberofsharesinstocki,then

Thenewvalueoftheportfoliois

b.Return

c.Theportfolioweightsarethefractionofvalueinvestedineachstock

Evaluate:

a.Thenewvalueoftheportfoliois$232,500.

b.Thereturnontheportfoliowas16.25%.

c.Ifyoudonotbuyorsellsharesafterthepricechange,yournewportfolioweightsareGoldFinger51.61%,Moosehead16.13%,andVenture32.26%.

4.Plan:

Computetheweightsoneachinvestmentandthen,matchingthoseweightstotheexpectedreturns,computetheexpectedreturnoftheportfoliousingEq.12.3.

Execute:

$38,000/$85,000=0.447,whichistheweightonthesecondstock.Sincetheweightsmustsumto1,theweightonthefinalstockis（1-0.447-0.25）.

E[R]=（0.25）（0.18）+（0.447）（0.25）+（1-0.447-0.25）（0.22）=0.2234

Evaluate:

Theexpectedreturnoftheportfolioisaweightedaverageoftheexpectedreturnsofthestocks.Thebiggestweightonanyindividualstockinthiscaseisthe44.7%onthestockwitha25%return.

5.Bothcalculationsofexpectedreturnofaportfoliogivethesameanswer.

6.Ifthepriceofonestockgoesup,theotherstockpricealwaysgoesupaswell.Similarly,ifonegoesdown,theotherwillalsobegoingdown.

7.Plan:

UseEqs12.3-12.5toanswerparts（a）and（b）.UseEqs.12.3and12.4toanswerpart（c）.

Execute:

a.

b.

c.

Evaluate:

Evenwithmostoftheportfolio’sweightontheriskierstock,thediversificationeffectbringstheoverallportfolioriskdownbelowaweightedaverageofthetwostandarddeviations.

8.Plan:

CalculatetheexpectedreturnandvolatilityofStockAandStockB.

RealizedReturns

Year

StockA

StockB

2005

-10%

21%

2006

20%

30%

2007

5%

7%

2008

-5%

-3%

2009

2%

-8%

2010

9%

25%

Execute:

Evaluate:

ThereturnonStockAis3.5%withavolatilityof10.60%.ThereturnonStockBis12%withavolatilityof15.65%.

9.Plan:

Calculatethevolatilityofaportfoliothatis70%investedinStockAand30%investedinStockB.

Execute:

Evaluate:

Thevolatilityofaportfolioof70%investedinStockAand30%inStockBis10.51%.

10.Plan:

CalculatetheaveragemonthlyreturnandvolatilityforthestockofColaCo.andGasCo.

Date

ColaCo.

GasCo.

Jan

–10.84%

-6.00%

Feb

2.36%

1.28%

Mar

6.60%

–1.86%

Apr

2.01%

–1.90%

May

18.36%

7.40%

June

–1.22%

-0.26%

July

2.25%

8.36%

Aug

–6.89%

–2.46%

Sep

–6.04%

–2.00%

Oct

13.61%

0.00%

Nov

3.51%

4.68%

Dec

0.54%

2.22%

Execute:

ThemeanforColaCo.is2.02%;themeanforGasCo.is0.79%.

Thestandarddeviation（i.e.,volatility）forColaCo.is8.24%;thestandarddeviationforGasCo.is4.25%.

Evaluate:

ColaCo.hasahighermeanreturn（2.02%）thanGasCo.（0.79%）.ButColaCo.hasmorevolatility（8.24%）thanGasCo.（4.25%）.ThisisconsistentwithFinanceTheory—higherriskisassociatedwithhigheraveragereturn.

11.Allthreemethodshavethesameresult:

Thestandarddeviation（i.e.,volatility）is5.90%.

12.

13.Microsoft’sσ=0.28;Ford’sσ=0.59;ThecorrelationbetweenMicrosoftandFordis0.36,andtheweightsare50%each:

14.Plan:

UseEqs.12.3and12.4tocomputetheexpectedreturnandvolatilityoftheindicatedportfolio.

Execute:

Inthiscase,theportfolioweightsarexj=xw=0.50.FromEq.（12.3）,

Wecantakethesquarerootoftheportfoliovarianceequation（Eq.12.4）,togetthestandarddeviation.

Evaluate:

Theportfoliowouldhaveanexpectedreturnof8.5%andastandarddeviationofreturnof14.1%.Therelativelylowcorrelationcoefficienthelpsreducetheriskoftheportfolio.

15.

Volatilityofportfolioislessifthecorrelationis<1.

16.

17.Plan:

YoumustestimatetheexpectedreturnandvolatilityofeachportfoliocreatedbyaddingStockAorStockB.Youwillselectthatportfoliothatgivesyouthegreatestreturnortheleastvolatility.

Execute:

Theexpectedreturnoftheportfoliowillbethesame（17.4%）ifyoupickAorBbecausebothAandBhavethesameexpectedreturn.Therefore,thechoiceofAorBdependsonhowriskytheportfoliobecomeswhenyouaddAorB.

ForA:

ForB:

Evaluate:

BecausetheportfolioislessriskywhenAisadded,youshouldaddAtotheportfolio.

18.Plan:

StocksBandCareidenticalexceptforthefactthatStockBhasalowercorrelationwithAthanCdoes.GiventhatBandC’sstandarddeviationsarethesame,theonewiththelowercorrelationwithAwillproducealowerportfoliostandarddeviation.Becauseshewillbeputting$100,000ineachstock,herportfoliowillbe50%ineachstock.

Execute:

UsingB:

YoucanconfirmthatthisislowerthanthestandarddeviationofaportfoliowithAandC:

Evaluate:

BychoosingthestockthathasthelowercorrelationwithA,youcanachievethegoalofanexpectedreturnof14%withalowerstandarddeviationthanifyouhadchosenthestockwith

thehighercorrelation.

19.Plan:

Computethetotalmarketvalueofthetotalportfolioandtheweightedpercentthateachindividualstockwouldbeinthemarketportfolio.

Execute:

Totalvalueofthemarket

Stock

PortfolioWeight

A

B

C

D

E

Evaluate:

Themarketportfoliowouldhaveavalueof$1.314billion.StockAwouldbe7.61%ofthemarketportfolio,StockBwouldbe18.26%,StockCwouldbe1.83%,StockDwouldbe3.81%,andStockEwouldbe68.49%.

20.Plan:

Computethetotalmarketvalueofthetotalportfolioandtheweightedpercentthateachindividualstockwouldbeinthemarketportfolio.

Execute:

Totalvalueofallfourstocks

Stock

PortfolioWeight

GoldenSeas

JacobsandJacobs

MAG

PDJB

Evaluate:

Themarketportfoliowouldhaveavalueof$1,380.5billion.GoldenSeaswouldbe0.942%ofthemarketportfolio,JacobsandJacobswouldbe1.992%,MAGwouldbe93.444%,andPDJBwouldbe3.622%.

21.Nothingneedstobedone.Theportfolioisstillvalue-weighted.

22.Plan:

ComputetheexcessreturnsofAppleandProctor&Gamble.

Execute:

a.ThebestguesstoApple’sreturntodayistheproductofthemarketreturnandApple’sbeta.Apple’sreturn

b.P&G’sreturn

Evaluate:

Apple’sexcessreturnis–2.8%,andP&G’sis–1.0%.

23.Plan:

GototheMyFinanceLabWebsiteandaccesstheExcelspreadsheet.Usetheslopefunctiontoestimatetheslopecoefficientofthedata,whichisourestimateofbeta.

Execute:

UsingExcel’sslopefunction,thebetaofNike’sstockis0.64.

Evaluate:

TheestimateofbetaforNikeis0.64.

24.Plan:

GototheMyFinanceLabWebsiteandaccesstheExcelspreadsheet.Usetheslopefunctiontoestimatetheslopecoefficientofthedata,whichisourestimateofbeta.

Execute:

a.SolvingforMicrosoft’sbetausingtheslopefunctioninExcel:

1987–1991:

1.4110

1992–1996:

0.8544

1997–2001:

1.8229

2002–2006:

1.0402

Evaluate:

b.Itdecreasedintheearly1990sasMicrosoftestablisheditselfasthedominantoperatingsoftwarecompanybutincreasedduringtheInternetbubbleinthelate1990s（whentechstocksweresoaring）.Ithassincedecreased.

25.Plan:

ComputetheexpectedreturnforJohnson&Johnson.

Execute:

Evaluate:

TheexpectedreturnforJohnson&Johnsonis14.8%.

26.Thesignoftheriskpremiumforanegativebetastockisnegative.Thisisbecausethenegativebetastockactsas“recessioninsurance,”andthusinvestorsarewillingtopayforthisinsuranceintheformofalowerreturnthantherisk-freerate.

27.Plan:

Thebetaofaportfolioisaweightedaverageofthebetasofthestocksintheportfolios.Theweightsaretheweightsofthestocksintheportfolios.

Execute:

Evaluate:

Becausebetasonlyrepresentnondiversifiablerisk,thereisno“diversificationeffect”onbetafromaportfolio.So,thebetaofaportfolioissimplytheweightedaverageofthebetasofthesecuritiesintheportfolio.

28.

29.Plan:

ComputetheexpectedreturnsofIntelandBoeingaswellastheportfoliobeta.Thencomputetheexpectedreturnoftheportfolio.

Execute:

a.Intel’sExpectedReturn=5%1.8（0.15−0.05）=23%

b.Boeing’sExpectedReturn=5%+1.2（0.15–0.05）=17%

c.PortfolioBeta=（70%）（1.8）+（30%）（1.2）=1.62

d.Portfolio’sExpectedReturn=5%+1.62（0.15–0.05）=21.2%

orPortfolio’sExpectedReturn=（70%）（23%）+（30%）（17%）=21.2%

EvaluateIntel’sexpectedreturnis23%,Boeing’sexpectedreturnis17%,theportfoliobetais1.62,andtheexpectedreturnoftheportfoliois21.2%.

*30.Plan:

Computethenecessarybeta.

Execute:

Returnonthestock=（1.5+122–103）/103=19.9%

For19.9%tobetheexpectedreturnonthesto