10Return and Risk.docx
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10Return and Risk.docx
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10ReturnandRisk
ExerciseforPROJECTINVESTMENTEVALUATION:
Youhavebeenaskedtodevelopabidprice.Thecontractwillbefor8yearsandwillresultinaguaranteedsaleof$9,000peryear.Fixedcostswillbe$550,000peryear.Theequipmentfortheproductionlinehasaninstalledcostof$2,700,000anditcanbesoldfor$450,000attheendoftheproject.Theequipmentwillbedepreciatedstraight-lineoverthe8-yearlifeoftheproject.Youwillneed$800,000inworkingcapitalwhichwillberecoveredattheendoftheproject.Thevariableproductioncostsare$790percanoe.Ifyourtaxrateis34%andthediscountrateis14%,whatisthelowestbidpricethatshouldbesubmittedforthecontract?
(PVIFA8,14%=4.6389)
RETURN&RISK
▪NPVapproach
▪Discountrate
▪Therelationshipbetweenrisklevelsandrequireddiscountrates.
CALCULATINGRETURNS
▪DividendorInterestPayment:
DividendYield=Dt+1
P1
▪CapitalGainorLoss:
CapitalGainYield=Pt+1–Pt
Pt
Return=Dt+1+(Pt+1–Pt)
Pt
EXAMPLE:
CALCULATINGRETURNS
YoupurchasedabondonJanuary1st,2000thathadafacevalueof$1,000,an8%annualcoupon,andannualcompounding.
Youpaid$839.67andyousubsequentlysoldthebondattheendofDecember2000for$822.33.
Whatwasyourpercentrateofreturnfortheyearwiththisinvestment?
HISTORICALRECORD
AVERAGEANNUALRETURNS
1949-97
TYPEOF
INVESTMENTAVERAGERETURN
CanadianCommon
Stocks13.13%
U.SCommonStocks
(inCan$)15.18
LongBonds7.81
TreasuryBills6.09
SmallStocks15.76
INFLATON4.34
ØOvertheperiodfrom1948-97,riskfreeinvestmentsearned6.09%.
ØUsingthisriskfreevalue,wecancalculatetheriskpremiumrequiredforriskierinvestmentsoverthatsameperiod.
AVERAGEANNUALRETURNS
&RISKPREMIUMS
1949-97
TYPEOFAVERAGERISK
INVESTMENTRETURNPREMIUM
CanadianCommon
Stocks13.13%7.04%
U.SCommonStocks
(inCan$)15.189.09
LongBonds7.811.72
SmallStocks15.769.67
TreasuryBills6.090.00
INFLATION4.34-1.75
AVERAGEANNUALRETURNS
&RISKPREMIUMS
1973-97
TYPEOFAVERAGERISK
INVESTMENTRETURNPREMIUM
CanadianCommon
Stocks12.24%3.07%
U.SCommonStocks
(inCan$)16.097.04
LongBonds11.952.90
SmallStocks15.756.70
TreasuryBills9.050.00
INFLATION5.79-3.26
ØSowhatiscorrect?
ØEvenwith72yearsofhighqualitydatafortheUnitedStates,theanalystsacceptthattheriskpremiumcannotbeestimatedexactlyandthatsubtlechangesinourattitudestoriskmightbeoccurringallthetime.
Risk
ØAgain,historyteachesussomeimportantlessons.HistoryrecordshowsthedistributionoftheequityreturnsismuchmorethangovernmentbondsandTreasuryBill.(p.226figure9.4,p.233table9.6,Ross).
TSE100
Squared
YearReturnDeviationDeviation
198811.08-0.77.59
198921.379.5290.63
1990-14.80-26.65710.22
199112.02.17.03
1992-1.43-13.28176.36
199332.5520.70428.49
1994-0.18-12.03144.72
199514.532.687.18
199628.3516.50272.25
199714.983.139.80
Total118.471,840.27
ØTheSTANDARDDEVIATION(σ)ofthereturnsfromassetsisthemostcommonlyusedmeasureofvolatility,whichmeansthebiggertheσthemorevolatile(thelargedistancefrommeanitcovers)itis.
Inyourstatisticsormathematicsclassesyouwillhavelearnedhowtocalculateanduseaverage,variance,andstandarddeviationcalculationstoanalyzeadistribution.Wecanrefreshthoseskillsbydoinganexampleusing10yearsoftheTSEinformation
AverageRateofReturn=118.47=11.85%
10
Variance2=AverageofSquaredDeviations
=SquaredDeviations=1,840.27
t–19
2=204.47
StandardDeviation=SquareRootofVariance
=204.47½=14.30%
ØAdditionalinformation:
theaveragereturnonTreasuryBillsoverthatperiodwas7.67%,sotheRiskPremiumpaidtotheownersofTSE100was4.18%.
ØThehigherthestandarddeviation,thehighertherateofreturn.Risk,asmeasuredbyvolatilityinthisway.
Historicalreturnsandstandarddeviations;
1948-97
InvestmentAvgeReturnStndardDev
Canadian
Commonstocks13.13%16.45%
U.S.Common
Stocks15.18%16.73%
LongBonds7.81%10.47%
SmallCapitalization
Stocks15.76%23.25%
TreasuryBills6.09%4.07%
INFLATION4.34%3.50%
NormalDistribution
(p.235Figure9.10)
Examples:
Whatis68%possibilityfortheannualreturnofCanadiancommonstock1984-1997?
EfficiencyofCapitalMarkets
∙EFFICIENTCAPITALMARKETS:
ØArefinancialmarketsinwhichsecuritypricesreflectallrelevantandavailableinformationaboutassetvalues.
ØIfcapitalmarketsareefficient,thenallsecuritiesarefairlypricedinthelightoftheinformationavailabletotheinvestors.
∙Thinkforamomentwhattheconceptofefficientmarketsmeans:
ØIfallinformationisimmediatelytakenintoaccountinthepriceofeverystock,thentheNPVofallstockswillbedriventozero.Ifthepriceofastockwas“too”lowtheninvestinginthatstockwouldcreateaNPVsituation,investorswouldrushtobuythestock,andthatwoulddrivethepriceuptothelevelwheretheNPVoftheinvestmentwaszero.
ØInanefficientmarket,investorsgetexactlywhattheypayforwhentheybuysecuritiesandfirmsreceiveexactlywhattheirstocksandbondsareworthwhentheysellthem.
∙Infact,theextentoftheefficiencyofthecapitalmarketsisoneofthegreatresearchquestionsofthefinanceindustry.
FormsandEvidenceofMarketEfficiency
▪Theresearchintothedegreeofmarketefficiencyhassetoutthreeformsofmarketefficiencyandempiricalevidencehasbeensoughttoeitheracceptorrejecttheexistenceofanefficientmarket.
▪WeakFormEfficiency
ØStatesthatpricesefficientlyreflectalltheinformationinthepastseriesofstockprices.Inaweakformefficientmarket,itisimpossibletoearnsuperiorreturnssimplybylookingforpatternsinstockprices---inotherwords,pricechangesarerandom.
▪Semi-strongFormEfficiency
ØStatesthatpricesreflectallpublishedinformation.Ifthemarketissemi-strongefficient,itisimpossibletomakeconsistentlysuperiorreturnsjustbyreadingthenewspaper,lookingatannualreports,andanalyzingallofthepublicinformation.
▪StrongFormEfficiency
ØStatesthatstockpriceseffectivelyintegrateALLavailableinformation.
ØStrongformefficiencytellsusthatsuperiorinformationishardtofindbecauseinpursuingsuperiorinformationyouareincompetitionwithmillionsofactive,intelligent,greedyinvestors.
UNSYSTEMATICRISK&
SYSTEMATICRISK
ØWeneedtodistinguishbetweenuniqueorunsystematicrisk(whichcanbediversifiedaway)andmarketorsystematicrisk(whichcannotbe).
ØRemember:
sinceunsystematicriskcanbediversifiedaway,financialmarketswouldhavenoreasontorewardinvestorswithariskpremiumforthattypeofrisk.
ØSincemarketorsystematicriskcannotbeeliminated,investorsexpecttoberewardedforacceptinggreaterlevelsofsuchrisk.
AUTOSTOCK
ScenarioOutcome(O)E(R)-O(E(R)–O)2
Recession-15-21441
Normal+600
Boom+27+21441
E(RAS)=1/3(-15+6+27)=6%
Variance=2=1/3(441)+0+1/3(441)=294
StandardDeviation=AS=17.1%
GOLDSTOCK
ScenarioOutcome(O)E(R)-O((E(R)–O)2
Recession+30-29841
Normal+3-24
Boom-30+31961
E(RGS)=1/3(+30+3-30)=1%
Var=2=1/3(841)+1/3(4)+1/3(961)=602
StandardDeviation=GS=24.5%
PORTFOLIO
(AUTOSTOCK75%;GOLDSTOCK25%)
RateofReturn
ScenarioProbAutoGoldPortfolio
Recession1/3-1530-3.75
Normal1/3+63+5.25
Boom1/3+27-30+12.75
E(R)+6+1+4.75
Variance229460245.5
SD17.1%24.5%6.75%
E(Rp)=1/3*E(Rrec)+1/3*E(Rnorm)+1/3*E(Rbm)
=1/3*-3.75+1/3*5.25+1/3*12.75=4.75%
2p=1/3(-8.5)2+1/3(0.5)2+1/3(8.0)2=45.5
p=6.75%
SUMMARYOFPORTFOLIOS
AUTOSTOCK&GOLDSTOCK
E(Rp)p
A.100%Auto6%17.1%
B.75%Auto;25%Gold4.756.75
C.50%Auto;50%Gold3.53.74
D.25%Auto;75%Gold2.2514.1
E.100%Gold1.24.5
▪TheExpectedReturnoftheportfolioateachstateoftheeconomyissimplytheweightedaverage:
E(Rrecession)=(.75)(-15)+(.25)(30)=-3.75%
▪TheoverallExpectedReturnfortheportfolioisderivedbymultiplyingtheE(R)foreachstateoftheeconomybytheprobabilityofthatoutcome.
E(Rp)=1/3*E(Rr)+1/3*E(Rn)+1/3*E(Rb)
=4.75%
Variance=2p=1/3(E(Rr)–E(Rp))2…..
2p=45.5
StandardDeviation=p=6.75%
EfficientFrontier
▪Minimumvariance(MV):
Itistheportfoliowiththelowestpossiblevariance(standarddeviation).
▪Feasibleset:
theentirecurve(p258,Ross).
▪Efficientset(efficientfrontier):
FromMVtoX
▪Covariance:
Thevarianceofaportfolioisnotsimplytheaveragemeanofallthesecuritiescomposedtheportfolio.
Bothfigure10.1onpage248Rossand
theformulaonpage250Rossshows:
theconceptofcorrelationandofthecovariancebetweenstocks:
apositiverelationshipbetweenthetwosecuritiesincreasesthevariance,whileanegativerelatedtwosecuritiesdecreasesthevariance.
▪Beta:
ØBETACOEFFICIENT():
▪Ameasureoftheamountofsystematicormarketriskpresentinanyparticularriskyassetrelativetotheaverageriskyassetasrepresentedbythemarketportfolio.
▪Page271Table10.7Rossshowstheestimateforthebetaofvariousfirms.
▪TotalRiskversusBeta
THESECURITYMARKETLINE
▪ModernfinancialtheorystatesthatALLinvestmentsMUSTliealongtheSML.
▪LookatFigure10.11onpa
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