财务管理基础 答案 沈艺峰 沈洪涛im05Risk and Rates of ReturnWord文档格式.docx

财务管理基础 答案 沈艺峰 沈洪涛im05Risk and Rates of ReturnWord文档格式.docx

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Whatwecover,andthewaywecoverit,canbeseenbyscanningBlueprints,Chapter5.Forothersuggestionsaboutthelecture,pleaseseethe“LectureSuggestions”inChapter2,wherewedescribehowweconductourclasses.

DAYSONCHAPTER:

3OF58DAYS（50-minuteperiods）

ANSWERSTOEND-OF-CHAPTERQUESTIONS

5-1a.Theprobabilitydistributionforcompletecertaintyisaverticalline.

b.TheprobabilitydistributionfortotaluncertaintyistheX-axisfrom

-to+.

5-2SecurityAislessriskyifheldinadiversifiedportfoliobecauseofitsnegativecorrelationwithotherstocks.Inasingle-assetportfolio,SecurityAwouldbemoreriskybecauseA>

BandCVA>

CVB.

5-3a.No,itisnotriskless.Theportfoliowouldbefreeofdefaultriskandliquidityrisk,butinflationcoulderodetheportfolio’spurchasingpower.Iftheactualinflationrateisgreaterthanthatexpected,interestratesingeneralwillrisetoincorporatealargerinflationpremium（IP）and--asweshallseeinChapter7--thevalueoftheportfoliowoulddecline.

b.No,youwouldbesubjecttoreinvestmentraterisk.Youmightexpectto“rollover”theTreasurybillsataconstant（orevenincreasing）rateofinterest,butifinterestratesfall,yourinvestmentincomewilldecrease.

c.AU.S.government-backedbondthatprovidedinterestwithconstantpurchasingpower（thatis,anindexedbond）wouldbeclosetoriskless.TheU.S.Treasurycurrentlyissuesindexedbonds.

5-4a.Theexpectedreturnonalifeinsurancepolicyiscalculatedjustasforacommonstock.Eachoutcomeismultipliedbyitsprobabilityofoccurrence,andthentheseproductsaresummed.Forexample,supposea1-yeartermpolicypays$10,000atdeath,andtheprobabilityofthepolicyholder’sdeathinthatyearis2percent.Then,thereisa98percentprobabilityofzeroreturnanda2percentprobabilityof$10,000:

Expectedreturn=0.98（$0）+0.02（$10,000）=$200.

Thisexpectedreturncouldbecomparedtothepremiumpaid.Generally,thepremiumwillbelargerbecauseofsalesandadministrativecosts,andinsurancecompanyprofits,indicatinganegativeexpectedrateofreturnontheinvestmentinthepolicy.

b.Thereisaperfectnegativecorrelationbetweenthereturnsonthelifeinsurancepolicyandthereturnsonthepolicyholder’shumancapital.Infact,theseevents（deathandfuturelifetimeearningscapacity）aremutuallyexclusive.

c.Peoplearegenerallyriskaverse.Therefore,theyarewillingtopayapremiumtodecreasetheuncertaintyoftheirfuturecashflows.Alifeinsurancepolicyguaranteesanincome（thefacevalueofthepolicy）tothepolicyholder’sbeneficiarieswhenthepolicyholder’sfutureearningscapacitydropstozero.

5-5Theriskpremiumonahigh-betastockwouldincreasemore.

RPj=RiskPremiumforStockj=（kM-kRF）bj.

Ifriskaversionincreases,theslopeoftheSMLwillincrease,andsowillthemarketriskpremium（kM-kRF）.Theproduct（kM-kRF）bjistheriskpremiumofthejthstock.Ifbjislow（say,0.5）,thentheproductwillbesmall;

RPjwillincreasebyonlyhalftheincreasein

.

However,ifbjislarge（say,2.0）,thenitsriskpremiumwillrisebytwicetheincreaseinRPM.

5-6AccordingtotheSecurityMarketLine（SML）equation,anincreaseinbetawillincreaseacompany’sexpectedreturnbyanamountequaltothemarketriskpremiumtimesthechangeinbeta.Forexample,assumethattherisk-freerateis6percent,andthemarketriskpremiumis5percent.Ifthecompany’sbetadoublesfrom0.8to1.6itsexpectedreturnincreasesfrom10percentto14percent.Therefore,ingeneral,acompany’sexpectedreturnwillnotdoublewhenitsbetadoubles.

5-7Yes,iftheportfolio’sbetaisequaltozero.Inpractice,however,itmaybeimpossibletofindindividualstocksthathaveanonpositivebeta.Inthiscaseitwouldalsobeimpossibletohaveastockportfoliowithazerobeta.Evenifsuchaportfoliocouldbeconstructed,investorswouldprobablybebetteroffjustpurchasingTreasurybills,orotherzerobetainvestments.

5-8No.Forastocktohaveanegativebeta,itsreturnswouldhavetologicallybeexpectedtogoupinthefuturewhenotherstocks’returnswerefalling.Justbecauseinoneyearthestock’sreturnincreaseswhenthemarketdeclineddoesn’tmeanthestockhasanegativebeta.Astockinagivenyearmaymovecountertotheoverallmarket,eventhoughthestock’sbetaispositive.

SOLUTIONSTOEND-OF-CHAPTERPROBLEMS

5-1

=（0.1）（-50%）+（0.2）（-5%）+（0.4）（16%）+（0.2）（25%）+（0.1）（60%）

=11.40%.

2=（-50%-11.40%）2（0.1）+（-5%-11.40%）2（0.2）+（16%-11.40%）2（0.4）

+（25%-11.40%）2（0.2）+（60%-11.40%）2（0.1）

2=712.44;

=26.69%.

CV=

=2.34.

5-2InvestmentBeta

$35,0000.8

40,0001.4

Total$75,000

bp=（$35,000/$75,000）（0.8）+（$40,000/$75,000）（1.4）=1.12.

5-3kRF=5%;

RPM=6%;

kM=?

kM=5%+（6%）1=11%.

kwhenb=1.2=?

k=5%+6%（1.2）=12.2%.

5-4kRF=6%;

kM=13%;

b=0.7;

k=?

k=kRF+（kM-kRF）b

=6%+（13%-6%）0.7

=10.9%.

5-5a.k=11%;

kRF=7%;

RPM=4%.

k=kRF+（kM–kRF）b

11%=7%+4%b

4%=4%b

b=1.

b.kRF=7%;

b=1.

k=7%+（6%）1

k=13%.

5-6a.

.

=0.1（-35%）+0.2（0%）+0.4（20%）+0.2（25%）+0.1（45%）

=14%versus12%forX.

b.=

=（-10%-12%）2（0.1）+（2%-12%）2（0.2）+（12%-12%）2（0.4）

+（20%-12%）2（0.2）+（38%-12%）2（0.1）=148.8%.

X=12.20%versus20.35%forY.

CVX=X/

X=12.20%/12%=1.02,while

CVY=20.35%/14%=1.45.

IfStockYislesshighlycorrelatedwiththemarketthanX,thenitmighthavealowerbetathanStockX,andhencebelessriskyinaportfoliosense.

5-7a.ki=kRF+（kM-kRF）bi=9%+（14%-9%）1.3=15.5%.

b.1.kRFincreasesto10%:

kMincreasesby1percentagepoint,from14%to15%.

ki=kRF+（kM-kRF）bi=10%+（15%-10%）1.3=16.5%.

2.kRFdecreasesto8%:

kMdecreasesby1%,from14%to13%.

ki=kRF+（kM-kRF）bi=8%+（13%-8%）1.3=14.5%.

c.1.kMincreasesto16%:

ki=kRF+（kM-kRF）bi=9%+（16%-9%）1.3=18.1%.

2.kMdecreasesto13%:

ki=kRF+（kM-kRF）bi=9%+（13%-9%）1.3=14.2%.

5-8Oldportfoliobeta=

（b）+

（1.00）

1.12=0.95b+0.05

1.07=0.95b

1.1263=b.

Newportfoliobeta=0.95（1.1263）+0.05（1.75）=1.15751.16.

AlternativeSolutions:

1.Oldportfoliobeta=1.12=（0.05）b1+（0.05）b2+...+（0.05）b20

1.12=

（0.05）

=1.12/0.05=22.4.

Newportfoliobeta=（22.4-1.0+1.75）（0.05）=1.15751.16.

2.

excludingthestockwiththebetaequalto1.0is22.4-1.0=

21.4,sothebetaoftheportfolioexcludingthisstockisb=21.4/19=1.1263.Thebetaofthenewportfoliois:

1.1263（0.95）+1.75（0.05）=1.15751.16.

5-9Portfoliobeta=

（1.50）+

（-0.50）

+

（1.25）+

（0.75）

bp=（0.1）（1.5）+（0.15）（-0.50）+（0.25）（1.25）+（0.5）（0.75）

=0.15-0.075+0.3125+0.375=0.7625.

kp=kRF+（kM-kRF）（bp）=6%+（14%-6%）（0.7625）=12.1%.

Alternativesolution:

First,calculatethereturnforeachstockusingtheCAPMequation[kRF+（kM-kRF）b],andthencalculatetheweightedaverageofthesereturns.

kRF=6%and（kM-kRF）=8%.

StockInvestmentBetak=kRF+（kM-kRF）bWeight

A$400,0001.5018%0.10

B600,000（0.50）20.15

C1,000,0001.25160.25

D2,000,0000.75120.50

Total$4,000,0001.00

kp=18%（0.10）+2%（0.15）+16%（0.25）+12%（0.50）=12.1%.

5-10WeknowthatbR=1.50,bS=0.75,kM=13%,kRF=7%.

ki=kRF+（kM-kRF）bi=7%+（13%-7%）bi.

kR=7%+6%（1.50）=16.0%

kS=7%+6%（0.75）=11.5

4.5%

5-11

=10%;

bX=0.9;

X=35%.

=12.5%;

bY=1.2;

Y=25%.

kRF=6%;

RPM=5%.

a.CVX=35%/10%=3.5.CVY=25%/12.5%=2.0.

b.Fordiversifiedinvestorstherelevantriskismeasuredbybeta.Therefore,thestockwiththehigherbetaismorerisky.StockYhasthehigherbetasoitismoreriskythanStockX.

c.kX=6%+5%（0.9）

kX=10.5%.

kY=6%+5%（1.2）

kY=12%.

d.kX=10.5%;

=10%.

kY=12%;

=12.5%.

StockYwouldbemostattractivetoadiversifiedinvestorsinceitsexpectedreturnof12.5%isgreaterthanitsrequiredreturnof12%.

e.bp=（$7,500/$10,000）0.9+（$2,500/$10,000）1.2

=0.6750+0.30

=0.9750.

kp=6%+5%（0.975）

kp=10.875%.

f.IfRP