1、5-1CHAPTER 5Risk and Rates of ReturnnStand-alone risknPortfolio risknRisk&return:CAPM/SML5-2Investment returnsThe rate of return on an investment can be calculated as follows:(Amount received Amount invested)Return=_ Amount investedFor example,if$1,000 is invested and$1,100 is returned after one yea
2、r,the rate of return for this investment is:($1,100-$1,000)/$1,000=10%.5-3What is investment risk?nTwo types of investment risknStand-alone risknPortfolio risk nInvestment risk is related to the probability of earning a low or negative actual return.nThe greater the chance of lower than expected or
3、negative returns,the riskier the investment.5-4Probability distributionsnA listing of all possible outcomes,and the probability of each occurrence.nCan be shown graphically.Expected Rate of ReturnRate ofReturn(%)100150-70Firm XFirm Y5-5Selected Realized Returns,1926 2001 Average Standard Return Devi
4、ationSmall-company stocks17.3%33.2%Large-company stocks12.720.2L-T corporate bonds 6.1 8.6L-T government bonds 5.7 9.4U.S.Treasury bills 3.9 3.2Source:Based on Stocks,Bonds,Bills,and Inflation:(Valuation Edition)2002 Yearbook(Chicago:Ibbotson Associates,2002),28.5-6Investment alternativesEconomyProb
5、.T-BillHTCollUSRMPRecession0.18.0%-22.0%28.0%10.0%-13.0%Below avg0.28.0%-2.0%14.7%-10.0%1.0%Average0.48.0%20.0%0.0%7.0%15.0%Above avg0.28.0%35.0%-10.0%45.0%29.0%Boom0.18.0%50.0%-20.0%30.0%43.0%5-7Why is the T-bill return independent of the economy?Do T-bills promise a completely risk-free return?nT-
6、bills will return the promised 8%,regardless of the economy.nNo,T-bills do not provide a risk-free return,as they are still exposed to inflation.Although,very little unexpected inflation is likely to occur over such a short period of time.nT-bills are also risky in terms of reinvestment rate risk.nT
7、-bills are risk-free in the default sense of the word.5-8How do the returns of HT and Coll.behave in relation to the market?nHT Moves with the economy,and has a positive correlation.This is typical.nColl.Is countercyclical with the economy,and has a negative correlation.This is unusual.5-9Return:Cal
8、culating the expected return for each alternative 17.4%(0.1)(50%)(0.2)(35%)(0.4)(20%)(0.2)(-2%)(0.1)(-22.%)kP k k return of rate expected kHTn1iii5-10Summary of expected returns for all alternativesExp returnHT 17.4%Market 15.0%USR 13.8%T-bill 8.0%Coll.1.7%HT has the highest expected return,and appe
9、ars to be the best investment alternative,but is it really?Have we failed to account for risk?5-11Risk:Calculating the standard deviation for each alternativedeviation Standard2Variancei2n1iiP)kk(5-12Standard deviation calculation15.3%18.8%20.0%13.4%0.0%(0.1)8.0)-(8.0 (0.2)8.0)-(8.0 (0.4)8.0)-(8.0 (
10、0.2)8.0)-(8.0(0.1)8.0)-(8.0 P )k (k MUSRHTCollbillsT22222billsTn1ii2i215-13Comparing standard deviationsUSRProb.T-billHT0 8 13.8 17.4 Rate of Return(%)5-14Comments on standard deviation as a measure of risknStandard deviation(i)measures total,or stand-alone,risk.nThe larger i is,the lower the probab
11、ility that actual returns will be closer to expected returns.nLarger i is associated with a wider probability distribution of returns.nDifficult to compare standard deviations,because return has not been accounted for.5-15Comparing risk and returnSecurityExpected returnRisk,T-bills8.0%0.0%HT17.4%20.
12、0%Coll*1.7%13.4%USR*13.8%18.8%Market15.0%15.3%*Seem out of place.5-16Coefficient of Variation(CV)A standardized measure of dispersion about the expected value,that shows the risk per unit of return.k Meandev Std CV 5-17Risk rankings,by coefficient of variation CVT-bill0.000HT1.149Coll.7.882USR1.362M
13、arket1.020nCollections has the highest degree of risk per unit of return.nHT,despite having the highest standard deviation of returns,has a relatively average CV.5-18Illustrating the CV as a measure of relative riskA=B,but A is riskier because of a larger probability of losses.In other words,the sam
14、e amount of risk(as measured by)for less returns.0ABRate of Return(%)Prob.5-19Investor attitude towards risknRisk aversion assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities.nRisk premium the difference between the return on a risky asset a
15、nd less risky asset,which serves as compensation for investors to hold riskier securities.5-20Portfolio construction:Risk and returnAssume a two-stock portfolio is created with$50,000 invested in both HT and Collections.nExpected return of a portfolio is a weighted average of each of the component a
16、ssets of the portfolio.nStandard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.5-21Calculating portfolio expected return9.6%(1.7%)0.5 (17.4%)0.5 kkw k :average weighted a is kpn1iiipp5-22An alternative method for determining p
17、ortfolio expected returnEconomyProb.HTCollRecession0.1-22.0%28.0%Below avg0.2-2.0%14.7%Average0.420.0%0.0%Above avg0.235.0%-10.0%Boom0.150.0%-20.0%9.6%(15.0%)0.10 (12.5%)0.20 (10.0%)0.40 (6.4%)0.20 (3.0%)0.10 kp5-23Calculating portfolio standard deviation and CV0.34 9.6%3.3%CV3.3%9.6)-(15.0 0.10 9.6
18、)-(12.5 0.20 9.6)-(10.0 0.40 9.6)-(6.4 0.20 9.6)-(3.0 0.10 p2122222p5-24Comments on portfolio risk measuresnp=3.3%is much lower than the i of either stock(HT=20.0%;Coll.=13.4%).np=3.3%is lower than the weighted average of HT and Coll.s (16.7%).n Portfolio provides average return of component stocks,
19、but lower than average risk.nWhy?Negative correlation between stocks.5-25General comments about risknMost stocks are positively correlated with the market(k,m 0.65).n 35%for an average stock.nCombining stocks in a portfolio generally lowers risk.5-26Returns distribution for two perfectly negatively
20、correlated stocks(=-1.0)-101515252525150-10Stock W0Stock M-100Portfolio WM5-27Returns distribution for two perfectly positively correlated stocks(=1.0)Stock M01525-10Stock M01525-10Portfolio MM01525-105-28Creating a portfolio:Beginning with one stock and adding randomly selected stocks to portfolion
21、p decreases as stocks added,because they would not be perfectly correlated with the existing portfolio.nExpected return of the portfolio would remain relatively constant.nEventually the diversification benefits of adding more stocks dissipates(after about 10 stocks),and for large stock portfolios,p
22、tends to converge to 20%.5-29Illustrating diversification effects of a stock portfolio#Stocks in Portfolio10 20 30 40 2,000+Company-Specific RiskMarket Risk20 0Stand-Alone Risk,p p(%)355-30Breaking down sources of riskStand-alone risk=Market risk+Firm-specific risknMarket risk portion of a securitys
23、 stand-alone risk that cannot be eliminated through diversification.Measured by beta.nFirm-specific risk portion of a securitys stand-alone risk that can be eliminated through proper diversification.5-31Failure to diversifynIf an investor chooses to hold a one-stock portfolio(exposed to more risk th
24、an a diversified investor),would the investor be compensated for the risk they bear?nNO!nStand-alone risk is not important to a well-diversified investor.nRational,risk-averse investors are concerned with p,which is based upon market risk.nThere can be only one price(the market return)for a given se
25、curity.nNo compensation should be earned for holding unnecessary,diversifiable risk.5-32Capital Asset Pricing Model(CAPM)nModel based upon concept that a stocks required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversi
26、fication.nPrimary conclusion:The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio.5-33BetanMeasures a stocks market risk,and shows a stocks volatility relative to the market.nIndicates how risky a stock is if the stock is held in a well-diversified p
27、ortfolio.5-34Calculating betasnRun a regression of past returns of a security against past returns on the market.nThe slope of the regression line(sometimes called the securitys characteristic line)is defined as the beta coefficient for the security.5-35Illustrating the calculation of beta.ki _kM_-5
28、051015202015105-5-10Regression line:ki=-2.59+1.44 kMYearkM ki 115%18%2-5-10 312 165-36Comments on betanIf beta=1.0,the security is just as risky as the average stock.nIf beta 1.0,the security is riskier than average.nIf beta 1.0,the security is less risky than average.nMost stocks have betas in the
29、range of 0.5 to 1.5.5-37Can the beta of a security be negative?nYes,if the correlation between Stock i and the market is negative(i.e.,i,m 0).nIf the correlation is negative,the regression line would slope downward,and the beta would be negative.nHowever,a negative beta is highly unlikely.5-38Beta c
30、oefficients for HT,Coll,and T-Billski_kM_-20 0 20 404020-20HT:=1.30T-bills:=0Coll:=-0.875-39Comparing expected return and beta coefficientsSecurityExp.Ret.Beta HT 17.4%1.30Market 15.0 1.00USR 13.8 0.89T-Bills 8.0 0.00Coll.1.7-0.87Riskier securities have higher returns,so the rank order is OK.5-40The
31、 Security Market Line(SML):Calculating required rates of returnSML:ki=kRF+(kM kRF)i nAssume kRF=8%and kM=15%.nThe market(or equity)risk premium is RPM=kM kRF=15%8%=7%.5-41What is the market risk premium?nAdditional return over the risk-free rate needed to compensate investors for assuming an average
32、 amount of risk.nIts size depends on the perceived risk of the stock market and investors degree of risk aversion.nVaries from year to year,but most estimates suggest that it ranges between 4%and 8%per year.5-42Calculating required rates of returnnkHT =8.0%+(15.0%-8.0%)(1.30)=8.0%+(7.0%)(1.30)=8.0%+
33、9.1%=17.10%nkM=8.0%+(7.0%)(1.00)=15.00%nkUSR=8.0%+(7.0%)(0.89)=14.23%nkT-bill=8.0%+(7.0%)(0.00)=8.00%nkColl=8.0%+(7.0%)(-0.87)=1.91%5-43Expected vs.Required returnsk)k(Overvalued 1.9 1.7 Coll.k)k(uedFairly val 8.0 8.0 bills-Tk)k(Overvalued 14.2 13.8 USRk)k(uedFairly val 15.0 15.0 Market k)k(dUnderva
34、lue 17.1%17.4%HT k k 5-44Illustrating the Security Market Line.Coll.HTT-bills.USRSMLkM =15 kRF=8-1 0 1 2.SML:ki=8%+(15%8%)i ki(%)Risk,i5-45An example:Equally-weighted two-stock portfolionCreate a portfolio with 50%invested in HT and 50%invested in Collections.nThe beta of a portfolio is the weighted
35、 average of each of the stocks betas.P=wHT HT+wColl Coll P=0.5(1.30)+0.5(-0.87)P=0.2155-46Calculating portfolio required returnsnThe required return of a portfolio is the weighted average of each of the stocks required returns.kP=wHT kHT+wColl kColl kP=0.5(17.1%)+0.5(1.9%)kP=9.5%nOr,using the portfo
36、lios beta,CAPM can be used to solve for expected return.kP=kRF+(kM kRF)P kP=8.0%+(15.0%8.0%)(0.215)kP=9.5%5-47Factors that change the SMLnWhat if investors raise inflation expectations by 3%,what would happen to the SML?SML1ki(%)SML20 0.5 1.01.5181511 8D D I=3%Risk,i5-48Factors that change the SMLnW
37、hat if investors risk aversion increased,causing the market risk premium to increase by 3%,what would happen to the SML?SML1ki(%)SML20 0.5 1.01.5 181511 8D D RPM=3%Risk,i5-49Verifying the CAPM empiricallynThe CAPM has not been verified completely.nStatistical tests have problems that make verificati
38、on almost impossible.nSome argue that there are additional risk factors,other than the market risk premium,that must be considered.5-50More thoughts on the CAPMnInvestors seem to be concerned with both market risk and total risk.Therefore,the SML may not produce a correct estimate of ki.ki=kRF+(kM kRF)i+?nCAPM/SML concepts are based upon expectations,but betas are calculated using historical data.A companys historical data may not reflect investors expectations about future riskiness.
