财务管理基础 答案 沈艺峰 沈洪涛im05Risk and Rates of Return.docx
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财务管理基础 答案 沈艺峰 沈洪涛im05Risk and Rates of Return.docx
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财务管理基础答案沈艺峰沈洪涛im05RiskandRatesofReturn
Chapter5
RiskandRatesofReturn
LEARNINGOBJECTIVES
Afterreadingthischapter,studentsshouldbeableto:
∙Definedollarreturnandrateofreturn.
∙Defineriskandcalculatetheexpectedrateofreturn,standarddeviation,andcoefficientofvariationforaprobabilitydistribution.
∙Specifyhowriskaversioninfluencesrequiredratesofreturn.
∙Graphdiversifiableriskandmarketrisk;explainwhichoftheseisrelevanttoawell-diversifiedinvestor.
∙StatethebasicpropositionoftheCapitalAssetPricingModel(CAPM)andexplainhowandwhyaportfolio’sriskmaybereduced.
∙Explainthesignificanceofastock’sbetacoefficient,andusetheSecurityMarketLinetocalculateastock’srequiredrateofreturn.
∙Listchangesinthemarketorwithinafirmthatwouldcausetherequiredrateofreturnonafirm’sstocktochange.
∙IdentifyconcernsaboutbetaandtheCAPM.
∙Explainhowstockpricevolatilityismorelikelytoimplyriskthanearningsvolatility.
LECTURESUGGESTIONS
Riskanalysisisanimportanttopic,butitisdifficulttoteachattheintroductorylevel.Wejusttrytogivestudentsanintuitiveoverviewofhowriskcanbedefinedandmeasured,andleaveatechnicaltreatmenttoadvancedcourses.Ourprimarygoalsaretobesurestudentsunderstand
(1)thatinvestmentriskistheuncertaintyaboutreturnsonanasset,
(2)theconceptofportfoliorisk,and(3)theeffectsofriskonrequiredratesofreturn.
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%;RPM=6%;b=1.
k=kRF+(kM–kRF)b
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
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