1、1CHAPTER 5Risk and Return2Topics in ChapternBasic return conceptsnBasic risk conceptsnStand-alone risknPortfolio(market)risknRisk and return:CAPM/SML3What are investment returns?nInvestment returns measure the financial results of an investment.nReturns may be historical or prospective(anticipated).
2、nReturns can be expressed in:nDollar terms.nPercentage terms.4An investment costs$1,000 and issold after 1 year for$1,100.Dollar return:Percentage return:$Received -$Invested$1,100 -$1,000 =$100.$Return/$Invested$100/$1,000 =0.10=10%.5What is investment risk?nTypically,investment returns are not kno
3、wn with certainty.nInvestment risk pertains to the probability of earning a return less than that expected.nThe greater the chance of a return far below the expected return,the greater the risk.6Probability Distribution:Which stock is riskier?Why?7Consider the FollowingInvestment AlternativesEcon.Pr
4、ob.T-BillAltaRepoAm F.MPBust 0.10 8.0%-22.0%28.0%10.0%-13.0%Below avg.0.20 8.0-2.0 14.7-10.0 1.0Avg.0.40 8.0 20.0 0.0 7.0 15.0Above avg.0.20 8.0 35.0-10.0 45.0 29.0Boom 0.10 8.0 50.0-20.0 30.0 43.0 1.008What is unique about the T-bill return?nThe T-bill will return 8%regardless of the state of the e
5、conomy.nIs the T-bill riskless?Explain.9Alta Inds.and Repo Men vs.the EconomynAlta Inds.moves with the economy,so it is positively correlated with the economy.This is the typical situation.nRepo Men moves counter to the economy.Such negative correlation is unusual.10Calculate the expected rate of re
6、turn on each alternative.r=expected rate of return.rAlta=0.10(-22%)+0.20(-2%)+0.40(20%)+0.20(35%)+0.10(50%)=17.4%.nr=i=1riPi.11Alta has the highest rate of return.Does that make it best?rAlta17.4%Market15.0Am.Foam13.8T-bill 8.0Repo Men 1.712What is the standard deviationof returns for each alternati
7、ve?=Standard deviation=Variance=2ni=1=(ri r)2 Pi.13=(-22-17.4)20.10+(-2-17.4)20.20 +(20-17.4)20.40+(35-17.4)20.20 +(50-17.4)20.101/2 =20.0%.Standard Deviation of Alta Industries14 T-bills=0.0%.Alta=20.0%.Repo=13.4%.Am Foam=18.8%.Market=15.3%.Standard Deviation of Alternatives15Stand-Alone RisknStand
8、ard deviation measures the stand-alone risk of an investment.nThe larger the standard deviation,the higher the probability that returns will be far below the expected return.16Expected Return versus RiskSecurityExpectedreturnRisk,Alta Inds.17.4%20.0%Market 15.0 15.3Am.Foam 13.8 18.8T-bills 8.0 0.0Re
9、po Men 1.7 13.417Coefficient of Variation(CV)nCV=Standard deviation/expected returnnCVT-BILLS =0.0%/8.0%=0.0.nCVAlta Inds =20.0%/17.4%=1.1.nCVRepo Men =13.4%/1.7%=7.9.nCVAm.Foam =18.8%/13.8%=1.4.nCVM =15.3%/15.0%=1.0.18Expected Return versus Coefficient of VariationSecurityExpectedreturnRisk:Risk:CV
10、Alta Inds 17.4%20.0%1.1Market 15.0 15.31.0Am.Foam 13.8 18.81.4T-bills 8.0 0.00.0Repo Men 1.7 13.47.919Return vs.Risk(Std.Dev.):Which investment is best?20Portfolio Risk and ReturnAssume a two-stock portfolio with$50,000 in Alta Inds.and$50,000 in Repo Men.Calculate rp and p.21Portfolio Expected Retu
11、rnrp is a weighted average(wi is%ofportfolio in stock i):rp=0.5(17.4%)+0.5(1.7%)=9.6%.rp=wiri ni=122Alternative Method:Find portfolio return in each economic stateEconomyProb.AltaRepoPort.=0.5(Alta)+0.5(Repo)Bust 0.10-22.0%28.0%3.0%Below avg.0.20 -2.0 14.7 6.4Average 0.40 20.0 0.0 10.0Above avg.0.20
12、 35.0-10.0 12.5Boom 0.10 50.0-20.0 15.023Use portfolio outcomes to estimate risk and expected returnrp=(3.0%)0.10+(6.4%)0.20+(10.0%)0.40 +(12.5%)0.20+(15.0%)0.10=9.6%.p=(3.0-9.6)20.10+(6.4-9.6)20.20 +(10.0-9.6)20.40+(12.5-9.6)20.20 +(15.0-9.6)20.10)1/2 =3.3%.CVp=3.3%/9.6%=.34.24Portfolio vs.Its Comp
13、onentsnPortfolio expected return(9.6%)is between Alta(17.4%)and Repo(1.7%)nPortfolio standard deviation is much lower than:neither stock(20%and 13.4%).naverage of Alta and Repo(16.7%).nThe reason is due to negative correlation(r)between Alta and Repo.25Bonus Slide:of Two-Stock PortfolioThe subscript
14、s denote Stock 1 and Stock 2.r r1,2 is the correlation between Stock 1 and Stock 2.p=w1212+(1-w1)222+2w2(1-w2)1,21226Bonus Slide:of n-Stock PortfolioThe subscripts denote Stock i and Stock j,for i=1,n and j=1,n.r ri,j is the correlation between Stock i and Stock j.p2=wiwjijijnni=1 j=127Two-Stock Por
15、tfoliosnTwo stocks can be combined to form a riskless portfolio if r=-1.0.nRisk is not reduced at all if the two stocks have r=+1.0.nIn general,stocks have r 0.65,so risk is lowered but not eliminated.nInvestors typically hold many stocks.nWhat happens when r=0?28Adding Stocks to a PortfolionWhat wo
16、uld happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?np would decrease because the added stocks would not be perfectly correlated,but the expected portfolio return would remain relatively constant.291 stock 35%Many stocks 20%30102030 40 2,000 stocksCompa
17、ny Specific(Diversifiable)RiskMarket Risk20%0Stand-Alone Risk,p p35%Risk vs.Number of Stock in Portfolio31Stand-alone risk=Market risk+Diversifiable risknMarket risk is that part of a securitys stand-alone risk that cannot be eliminated by diversification.nFirm-specific,or diversifiable,risk is that
18、 part of a securitys stand-alone risk that can be eliminated by diversification.32ConclusionsnAs more stocks are added,each new stock has a smaller risk-reducing impact on the portfolio.np falls very slowly after about 40 stocks are included.The lower limit for p is about 20%=M.nBy forming well-dive
19、rsified portfolios,investors can eliminate about half the risk of owning a single stock.33Can an investor holding one stock earn a return commensurate with its risk?nNo.Rational investors will minimize risk by holding portfolios.nThey bear only market risk,so prices and returns reflect this lower ri
20、sk.nThe one-stock investor bears higher(stand-alone)risk,so the return is less than that required by the risk.34How is market risk measured for individual securities?nMarket risk,which is relevant for stocks held in well-diversified portfolios,is defined as the contribution of a security to the over
21、all riskiness of the portfolio.nIt is measured by a stocks beta coefficient.For stock i,its beta is:nbi=(ri,M i)/M35How are betas calculated?nIn addition to measuring a stocks contribution of risk to a portfolio,beta also which measures the stocks volatility relative to the market.36Using a Regressi
22、on to Estimate BetanRun a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.nThe slope of the regression line,which measures relative volatility,is defined as the stocks beta coefficient,or b.37Use the historical stock re
23、turns to calculate the beta for PQU.YearMarketPQU1 25.7%40.0%2 8.0%-15.0%3-11.0%-15.0%4 15.0%35.0%5 32.5%10.0%6 13.7%30.0%7 40.0%42.0%8 10.0%-10.0%9-10.8%-25.0%10-13.1%25.0%38Calculating Beta for PQU39What is beta for PQU?nThe regression line,and hence beta,can be found using a calculator with a reg
24、ression function or a spreadsheet program.In this example,b=0.83.40Calculating Beta in PracticenMany analysts use the S&P 500 to find the market return.nAnalysts typically use four or five years of monthly returns to establish the regression line.n Some analysts use 52 weeks of weekly returns.41How
25、is beta interpreted?nIf b=1.0,stock has average risk.nIf b 1.0,stock is riskier than average.nIf b 1.0,stock is less risky than average.nMost stocks have betas in the range of 0.5 to 1.5.nCan a stock have a negative beta?42Finding Beta Estimates on the WebnGo to Thomson ONEBusiness School Edition us
26、ing the information on the card that comes with your book.nEnter the ticker symbol for a“Stock Quote”,such as IBM or Dell,then click GO.43Other Web Sites for BetanGo to http:/nEnter the ticker symbol for a“Stock Quote”,such as IBM or Dell,then click GO.nWhen the quote comes up,select Key Statistics
27、from panel on left.44Expected Return versus Market Risk:Which investment is best?SecurityExpectedReturn(%)Risk,bAlta 17.4 1.29Market 15.0 1.00Am.Foam 13.8 0.68T-bills 8.0 0.00Repo Men 1.7-0.8645Use the SML to calculate eachalternatives required return.nThe Security Market Line(SML)is part of the Cap
28、ital Asset Pricing Model(CAPM).nSML:ri=rRF+(RPM)bi.n ri=rRF+(rM-rRF)bi.nAssume rRF=8%;rM=rM =15%.nRPM=(rM-rRF)=15%-8%=7%.46Required Rates of ReturnnrAlta=8.0%+(7%)(1.29)=17%.nrM=8.0%+(7%)(1.00)=15.0%.nrAm.F.=8.0%+(7%)(0.68)=12.8%.nrT-bill=8.0%+(7%)(0.00)=8.0%.nrRepo=8.0%+(7%)(-0.86)=2.0%.47Expected
29、versus Required Returns(%)Exp.Req.rrAlta 17.4 17.0 Undervalued Market 15.0 15.0 Fairly valuedAm.F.13.8 12.8 UndervaluedT-bills 8.0 8.0 Fairly valuedRepo 1.7 2.0 Overvalued48SML:ri=rRF+(RPM)bi ri=8%+(7%)bi.Repo.AltaT-bills.Am.FoamrM =15 rRF=8-1 0 1 2.ri(%)Risk,biMarket49Calculate beta for a portfolio
30、 with 50%Alta and 50%Repobp=Weighted average=0.5(bAlta)+0.5(bRepo)=0.5(1.29)+0.5(-0.86)=0.22.50Required Return on the Alta/Repo Portfolio?rp=Weighted average r =0.5(17%)+0.5(2%)=9.5%.Or use SML:rp=rRF+(RPM)bp=8.0%+7%(0.22)=9.5%.51SML1Original situationr(%)SML200.51.01.5 Risk,bi181511 8New SML I=3%Im
31、pact of Inflation Change on SML52SML1Original situationr(%)SML2After changeRisk,bi181581.0 RPM=3%Impact of Risk Aversion Change53Has the CAPM been completely confirmed or refuted?nNo.The statistical tests have problems that make empirical verification or rejection virtually impossible.nInvestors required returns are based on future risk,but betas are calculated with historical data.nInvestors may be concerned about both stand-alone and market risk.
