ACCA_F9 03

Lecture3IntroductiontoRisk,Return,andTheOpportunityCostofCapitalDrJianChenTheUniversityofGreenwich3-2TopicsCoveredOveraCenturyofCapitalMarketHistoryMeasuringtheRiskofsingleassetsCalculatingreturnandriskofportfolioDiversification&ValueAdditivity3-3Duringtheprevioussession,welearntthattheroleofthefinancialmanageristomakefinancialdecisions:–Identifyfuturecashflows–Discountthemintopresentvalues–AddPVs,minusInvestmentcost–ThisisNPV–NPVdecisionrule•IftheNPVofaninvestment=0,gowiththeinvestment(orproject•NPV0,rejecttheinvestment(orproject)3-4Theproblemisthat,wherewetofindthe“discountrate”–Youcannotfinditbylookingatthebank’sinterestratetable–Ifyouchooseawrongdiscountrate,youwillmakeawrongfinancialdecisionFinanceisastudytofindtherightdiscountrate–Anyreturnisrelatedtoarisk3-5Firstly,welookatthebelowtable:ProjectExpectedreturnExpectedriskA12%15%B8%15%3-6Then,let’slookatthesecondtable:ProjectExpectedreturnExpectedriskA12%23%B12%15%3-7thenwelookatthethirdcaseProjectExpectedreturnExpectedriskA12%22%B8%15%3-8Ourquestionishowtocompromisebetweentheriskandthereturn3-9WeneedscientificdefinitionsofreturnandriskgaincapitaldassetyielpurchasedisassettheatwhichPriceassettheofchangePricepurchasedisassettheatwhichPricereceivedpaymentscashanypurchasedisassettheatwhichPriceperiodsoverthechangePricereceivedpaymentscashAnyr•Thisisso-calledtotalreturnconcept3-10ArithmeticaverageandgeometricaveragedistributionofreturnandriskArithmeticReturnandGeometricReturn–Arithmeticreturn:simplyaveragereturns(usuallyataparticulartimepoint)nrrrrrn...3213-11–Geometricreturn:theaveragereturnoveracertainperiods1)1)...(1)(1)(1(321nnrrrrr3-12Example:ThereturnsofsecurityAoverthepastfiveyearscanbelistedasbelow,calculatearithmeticandgeometricreturn.12%14%-10%-5%19%Arithmeticreturn=Geometricreturn=Theresultsaredifferent.3-13TheValueofanInvestmentof$1in1900$1$10$100$1,000$10,000$100,00019001910192019301940195019601970198019902000StartofYearDollarsCommonStockUSGovtBondsT-Bills21,5361766620073-14TheValueofanInvestmentof$1in1900$1$10$100$1,00019001910192019301940195019601970198019902000StartofYearDollarsEquitiesBondsBills9147.482.822007RealReturns3-15AverageMarketRiskPremia(bycountry)4.855.335.55.956.066.176.456.56.887.527.628.588.818.859.399.7110.2910.9701234567891011DenmarkBelgiumSwitzerlandSpainCanadaNorwayIrelandUKNetherlandsAverageUSASwedenSouthAfricaAustraliaGermanyFranceJapanItalyRiskpremium,%Country3-16DividendYield(1900-2006)0.001.002.003.004.005.006.007.008.009.0010.0019001910192019301940195019601970198019902000DividendYield,%3-17RatesofReturn1900-2006Source:IbbotsonAssociates-60%-40%-20%0%20%40%60%80%190019201940196019802000YearPercentageReturnStockMarketIndexReturns3-18MeasuringRisk1141012201724133204812162024-50to-40-40to-30-30to-20-20to-10-10to00to1010to2020to3030to4040to5050to60Return%#ofYearsHistogramofAnnualStockMarketReturns(1900-2006)3-19EquityMarketRisk(bycountry)16.6417.8818.9319.7921.5121.6422.2822.7122.7123.3523.5823.6423.824.9327.9129.2433.6634.170510152025303540CanadaAustraliaSwitzerlandUSADenmarkUKIrelandSpainNetherlandsSAfricaSwedenBelgiumAverageFranceNorwayJapanItalyGermany(ex1922/3)StandardDeviationofAnnualReturns,%AverageRisk(1900-2006)3-20DowJonesRisk010203040506019001910192019301940195019601970198019902000StandardDeviation,%AnnualizedStandardDeviationoftheDJIAoverthepreceding52weeks(1900–2006)3-21MeasuringRisk–singleassets3-22Variance-Averagevalueofsquareddeviationsfrommean.Ameasureofvolatility.StandardDeviation-Averagevalueofsquareddeviationsfrommean.Ameasureofvolatility.3-23Becausethefuturereturnswillbeonlyoneofthepossibleevents,thereturnsbecomeuncertain.Whenfuturereturnsarenotdetermined,ourpredictiononthefutureisonlyestimationofallthepossibleoutcomesbytheirpossibility”3-24DistributionofreturnandRiskInvestment’sRateofReturnIfstateoccurs(%)StateoftheeconomyPossibilityofoccuranceT-BillBondStockRecession0.2812-15Stayasnormal0.58920booming0.388.53589.4517.53-25ErepresentsExpectationRiskofreturnWeusebothvarianceandstandarddeviationasmeasureofriskThevarianceofreturns=2=3-26AfterclassexerciseCompanyABCpredictsthattherearethreestatesofeconomy,whichdecidestheprofitsoverthenextyear:StateofeconomypossibilityExpectedreturnBooming0.540Normal0.315recession0.2-303-27PortfolioRisk)rx()r(xReturnPortfolioExpected2211)σσρxx(2σxσxVariancePortfolio211221222221213-28ReturnandRiskofaPortfolioReturnofaportfolioLetbeginwithaportfolioconsistingoftwoassets:StockXandStockYIfweinvestwxproportionoftotalwealthintostockXandwyproportionoftotalwealthintostockY,sothatwx+wy=1.Thereturnofportfoliowillbe3-29RiskoftheportfolioTheriskofportfolioismuchmoredifficulttomeasure.Tounderstandtheriskofportfolio,inadditionaltounderstandvariance,weneedtoknowcovariance.WedefinecovarianceasAndfurther,wedefinecorrelationcoefficient(-1xy1)Weusevarianceoftheportfolioasproxyofrisk,whichis:3-30Example:Therearethreepossiblexy0xy1,meansstockXandYpositivecorrelated.-1xy0,meansstockXandYnegativecorrelated,theymoveinoppositedirection.Wecansetupa