1、3-1CHAPTER 3 Risk and ReturnnBasic return conceptsnBasic risk conceptsnStand-alone risknPortfolio(market)risknRisk and return:CAPM/SML3-2What are investment returns?nInvestment returns measure the financial results of an investment.nReturns may be historical or prospective(anticipated).nReturns can
2、be expressed in:lDollar terms.lPercentage terms.3-3What is the return on an investment that costs$1,000 and is soldafter 1 year for$1,100?nDollar return:nPercentage return:$Received -$Invested$1,100 -$1,000 =$100.$Return/$Invested$100/$1,000 =0.10=10%.3-4What is investment risk?nTypically,investment
3、 returns are not known 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.3-5Probability distributionRate ofreturn(%)50150-20Stock XStock Yn Which stock is risk
4、ier?Why?3-6Assume the FollowingInvestment AlternativesEconomyProb.T-BillHTCollUSRMPRecession 0.10 8.0%-22.0%28.0%10.0%-13.0%Below avg.0.20 8.0-2.0 14.7-10.0 1.0Average 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 1.003-7What is unique about the T-
5、bill return?nThe T-bill will return 8%regardless of the state of the economy.nIs the T-bill riskless?Explain.3-8Do the returns of HT and Collections move with or counter to the economy?nHT moves with the economy,so it is positively correlated with the economy.This is the typical situation.nCollectio
6、ns moves counter to the economy.Such negative correlation is unusual.3-9Calculate the expected rate of return on each alternative.n1=iiiPr=rr=expected rate of return.rHT=0.10(-22%)+0.20(-2%)+0.40(20%)+0.20(35%)+0.10(50%)=17.4%.3-10n HT has the highest rate of return.n Does that make it best?rHT17.4%
7、Market15.0USR13.8T-bill 8.0Collections 1.73-11What is the standard deviationof returns for each alternative?.Variance deviation Standard 122niiiPrr3-12 T-bills=0.0%.HT=20.0%.Coll=13.4%.USR=18.8%.M=15.3%.12niiiPrrHT:=(-22-17.4)20.10+(-2-17.4)20.20 +(20-17.4)20.40+(35-17.4)20.20 +(50-17.4)20.10)1/2=20
8、.0%.3-13Prob.Rate of Return(%)T-billUSRHT0813.817.43-14nStandard 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.nCoefficient of variation is an alternative measure of stand-alon
9、e risk.3-15Expected Return versus RiskExpectedSecurityreturnRisk,HT 17.4%20.0%Market 15.0 15.3USR 13.8 18.8T-bills 8.0 0.0Collections 1.7 13.43-16Coefficient of Variation:CV=Expected return/standard deviation.CVT-BILLS=0.0%/8.0%=0.0.CVHIGH TECH=20.0%/17.4%=1.1.CVCOLLECTIONS=13.4%/1.7%=7.9.CVU.S.RUBB
10、ER=18.8%/13.8%=1.4.CVM=15.3%/15.0%=1.0.3-17Expected Return versus Coefficient of VariationExpectedRisk:Risk:Securityreturn CVHT 17.4%20.0%1.1Market 15.0 15.31.0USR 13.8 18.81.4T-bills 8.0 0.00.0Collections 1.7 13.47.93-18Return vs.Risk(Std.Dev.):Which investment is best?T-billsColl.MktUSRHT0.0%2.0%4
11、.0%6.0%8.0%10.0%12.0%14.0%16.0%18.0%20.0%0.0%5.0%10.0%15.0%20.0%25.0%Risk(Std.Dev.)Return3-19Portfolio Risk and ReturnAssume a two-stock portfolio with$50,000 in HT and$50,000 in Collections.Calculate rp and p.3-20Portfolio Return,rprp is a weighted average:rp=0.5(17.4%)+0.5(1.7%)=9.6%.rp is between
12、 rHT and rColl.rp=wiri ni=13-21Alternative Methodrp=(3.0%)0.10+(6.4%)0.20+(10.0%)0.40 +(12.5%)0.20+(15.0%)0.10=9.6%.Estimated Return(More.)EconomyProb.HTColl.Port.Recession 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 35.0-10.0 12.5Boom 0.10 50.0-20.0 15.03
13、-22n 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%.n p is much lower than:leither stock(20%and 13.4%).laverage of HT and Coll(16.7%).nThe portfolio provides average return but much lower risk.The key here is negative correlation.3-23Two-Stock PortfoliosnT
14、wo stocks can be combined to form a riskless portfolio if r r=-1.0.nRisk is not reduced at all if the two stocks have r r=+1.0.nIn general,stocks have r r 0.65,so risk is lowered but not eliminated.nInvestors typically hold many stocks.nWhat happens when r r=0?3-24What would happen to therisk of an
15、average 1-stockportfolio as more randomlyselected stocks were added?n p would decrease because the added stocks would not be perfectly correlated,but rp would remain relatively constant.3-25Large015Prob.21 1 35%;Large 20%.Return3-26#Stocks in Portfolio102030 40 2,000+Company Specific(Diversifiable)R
16、iskMarket Risk20 0Stand-Alone Risk,p p(%)353-27Stand-alone Market DiversifiableMarket risk is that part of a securitys stand-alone risk that cannot be eliminated by diversification.Firm-specific,or diversifiable,risk is that part of a securitys stand-alone risk that can be eliminated by diversificat
17、ion.risk risk risk =+.3-28ConclusionsnAs more stocks are added,each new stock has a smaller risk-reducing impact on the portfolio.n p falls very slowly after about 40 stocks are included.The lower limit for p is about 20%=M.nBy forming well-diversified portfolios,investors can eliminate about half t
18、he riskiness of owning a single stock.3-29nNo.Rational investors will minimize risk by holding portfolios.nThey bear only market risk,so prices and returns reflect this lower risk.nThe one-stock investor bears higher(stand-alone)risk,so the return is less than that required by the risk.Can an invest
19、or holding one stock earn a return commensurate with its risk?3-30nMarket risk,which is relevant for stocks held in well-diversified portfolios,is defined as the contribution of a security to the overall riskiness of the portfolio.nIt is measured by a stocks beta coefficient.For stock i,its beta is:
20、bi=(r riM i)/MHow is market risk measured for individual securities?3-31How 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.3-32Using a Regression to Estimate BetanRun a regression with
21、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.3-33Use the historical stock returns to calculate the beta for KWE.Year
22、MarketKWE1 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%3-34Calculating Beta for KWErKWE=0.83rM+0.03R2=0.36-40%-20%0%20%40%-40%-20%0%20%40%rMrKWE3-35What is beta for KWE?nThe regression line,and hence beta,can be found usin
23、g a calculator with a regression function or a spreadsheet program.In this example,b=0.83.3-36Calculating 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 wee
24、ks of weekly returns.3-37nIf 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?How is beta interpreted?3-38Finding Beta Estimates on the WebnGo to .nEnte
25、r the ticker symbol for a“Stock Quote”,such as IBM or Dell.nWhen the quote comes up,look in the section on Fundamentals.3-39Expected Return versus Market Riskn Which of the alternatives is best?ExpectedSecurityreturnRisk,bHT 17.4%1.29Market 15.0 1.00USR 13.8 0.68T-bills 8.0 0.00Collections 1.7-0.863
26、-40Use the SML to calculate eachalternatives required return.nThe Security Market Line(SML)is part of the Capital Asset Pricing Model(CAPM).nSML:ri=rRF+(RPM)bi.nAssume rRF=8%;rM=rM =15%.nRPM=(rM-rRF)=15%-8%=7%.3-41Required Rates of ReturnrHT=8.0%+(7%)(1.29)=8.0%+9.0%=17.0%.rM=8.0%+(7%)(1.00)=15.0%.r
27、USR=8.0%+(7%)(0.68)=12.8%.rT-bill=8.0%+(7%)(0.00)=8.0%.rColl=8.0%+(7%)(-0.86)=2.0%.3-42Expected versus Required ReturnsrrHT 17.4%17.0%Undervalued Market 15.0 15.0 Fairly valuedUSR 13.8 12.8 UndervaluedT-bills 8.0 8.0 Fairly valuedColl 1.7 2.0 Overvalued3-43.Coll.HTT-bills.USRrM =15 rRF=8-1 0 1 2.SML
28、:ri=rRF+(RPM)bi ri=8%+(7%)biri(%)Risk,biSML and Investment AlternativesMarket3-44Calculate beta for a portfolio with 50%HT and 50%Collectionsbp=Weighted average=0.5(bHT)+0.5(bColl)=0.5(1.29)+0.5(-0.86)=0.22.3-45What is the required rate of returnon the HT/Collections portfolio?rp=Weighted average r
29、=0.5(17%)+0.5(2%)=9.5%.Or use SML:rp=rRF+(RPM)bp=8.0%+7%(0.22)=9.5%.3-46SML1Original situationRequired Rate of Return r(%)SML200.51.01.52.0181511 8New SML I=3%Impact of Inflation Change on SML3-47rM =18%rM =15%SML1Original situationRequired Rate of Return(%)SML2After increasein risk aversionRisk,bi1
30、81581.0 RPM=3%Impact of Risk Aversion Change3-48Has the CAPM been completely confirmed or refuted through empirical tests?nNo.The statistical tests have problems that make empirical verification or rejection virtually impossible.lInvestors required returns are based on future risk,but betas are calculated with historical data.lInvestors may be concerned about both stand-alone and market risk.
