Risk and Return.ppt

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1、,CHAPTER 3 Risk and Return,Basic return conceptsBasic risk conceptsStand-alone riskPortfolio (market) riskRisk and return: CAPM/SML,What are investment returns?,Investment returns measure the financial results of an investment.Returns may be historical or prospective (anticipated).Returns can be exp

2、ressed in:Dollar terms.Percentage terms.,What is the return on an investment that costs $1,000 and is soldafter 1 year for $1,100?,Dollar return:,Percentage return:,$ Received - $ Invested $1,100 - $1,000 = $100.,$ Return/$ Invested $100/$1,000 = 0.10 = 10%.,What is investment risk?,Typically, inves

3、tment returns are not known with certainty.Investment risk pertains to the probability of earning a return less than that expected.The greater the chance of a return far below the expected return, the greater the risk.,Probability distribution,Rate ofreturn (%),50,15,0,-20,Stock X,Stock Y,Which stoc

4、k is riskier? Why?,Assume the FollowingInvestment Alternatives,What is unique about the T-bill return?,The T-bill will return 8% regardless of the state of the economy.Is the T-bill riskless? Explain.,Do the returns of HT and Collections move with or counter to the economy?,HT moves with the economy

5、, so it is positively correlated with the economy. This is the typical situation.Collections moves counter to the economy. Such negative correlation is unusual.,Calculate the expected rate of return on each alternative.,r = expected rate of return.,rHT = 0.10(-22%) + 0.20(-2%) + 0.40(20%) + 0.20(35%

6、) + 0.10(50%) = 17.4%.,HT has the highest rate of return. Does that make it best?,What is the standard deviationof returns for each alternative?,HT: = (-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 = 20.0%.,Prob.,Rate of Return (%),T-bill,USR,HT,0,8

7、,13.8,17.4,Standard deviation measures the stand-alone risk of an investment.The larger the standard deviation, the higher the probability that returns will be far below the expected return.Coefficient of variation is an alternative measure of stand-alone risk.,Expected Return versus Risk,Coefficien

8、t 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. RUBBER= 18.8%/13.8%= 1.4.CVM = 15.3%/15.0%= 1.0.,Expected Return versus Coefficient of Variation,Return vs. Risk (Std. Dev.): Which investment is b

9、est?,Portfolio Risk and Return,Assume a two-stock portfolio with $50,000 in HT and $50,000 in Collections.,Calculate rp and p.,Portfolio Return, rp,rp is a weighted average:,rp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.,rp is between rHT and rColl.,rp = wiri,n,i = 1,Alternative Method,rp = (3.0%)0.10 + (6.4%)

10、0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%.,Estimated Return,(More.),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%.p is much lower than:either stock (20% and 13.4%).average of HT and Coll (16.7%).The portfolio provides avera

11、ge return but much lower risk. The key here is negative correlation.,Two-Stock Portfolios,Two stocks can be combined to form a riskless portfolio if r = -1.0.Risk is not reduced at all if the two stocks have r = +1.0. In general, stocks have r 0.65, so risk is lowered but not eliminated.Investors ty

12、pically hold many stocks.What happens when r = 0?,What would happen to therisk of an average 1-stockportfolio as more randomlyselected stocks were added?,p would decrease because the added stocks would not be perfectly correlated, but rp would remain relatively constant.,Large,0,15,Prob.,2,1,1 35% ;

13、 Large 20%.,Return,# Stocks in Portfolio,102030 40 2,000+,Company Specific (Diversifiable) Risk,Market Risk,20 0,Stand-Alone Risk, p,p (%),35,Stand-alone Market Diversifiable,Market risk is that part of a securitys stand-alone risk that cannot be eliminated by diversification.Firm-specific, or diver

14、sifiable, risk is that part of a securitys stand-alone risk that can be eliminated by diversification.,risk risk risk,= + .,Conclusions,As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.p falls very slowly after about 40 stocks are included. The lower limit

15、 for p is about 20% = M .By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.,No. Rational investors will minimize risk by holding portfolios.They bear only market risk, so prices and returns reflect this lower risk.The one-stock investor

16、 bears higher (stand-alone) risk, so the return is less than that required by the risk.,Can an investor holding one stock earn a return commensurate with its risk?,Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overa

17、ll riskiness of the portfolio.It is measured by a stocks beta coefficient. For stock i, its beta is:bi = (riM si) / sM,How is market risk measured for individual securities?,How are betas calculated?,In addition to measuring a stocks contribution of risk to a portfolio, beta also which measures the

18、stocks volatility relative to the market.,Using a Regression to Estimate Beta,Run 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.The slope of the regression line, which measures relative volatility, is defined as the

19、 stocks beta coefficient, or b.,Use the historical stock returns to calculate the beta for KWE.,Calculating Beta for KWE,r,KWE,= 0.83r,M,+ 0.03,R,2,= 0.36,-40%,-20%,0%,20%,40%,-40%,-20%,0%,20%,40%,r,M,r,KWE,What is beta for KWE?,The regression line, and hence beta, can be found using a calculator wi

20、th a regression function or a spreadsheet program. In this example, b = 0.83.,Calculating Beta in Practice,Many analysts use the S&P 500 to find the market return.Analysts typically use four or five years of monthly returns to establish the regression line. Some analysts use 52 weeks of weekly retur

21、ns.,If b = 1.0, stock has average risk.If b 1.0, stock is riskier than average.If b 1.0, stock is less risky than average.Most stocks have betas in the range of 0.5 to 1.5.Can a stock have a negative beta?,How is beta interpreted?,Finding Beta Estimates on the Web,Go to .Enter the ticker symbol for

22、a “Stock Quote”, such as IBM or Dell.When the quote comes up, look in the section on Fundamentals.,Expected Return versus Market Risk,Which of the alternatives is best?,Use the SML to calculate eachalternatives required return.,The Security Market Line (SML) is part of the Capital Asset Pricing Mode

23、l (CAPM). SML: ri = rRF + (RPM)bi .Assume rRF = 8%; rM = rM = 15%.RPM = (rM - rRF) = 15% - 8% = 7%.,Required Rates of Return,rHT = 8.0% + (7%)(1.29)= 8.0% + 9.0%= 17.0%.,rM= 8.0% + (7%)(1.00)= 15.0%.rUSR= 8.0% + (7%)(0.68)= 12.8%.rT-bill= 8.0% + (7%)(0.00)= 8.0%.rColl= 8.0% + (7%)(-0.86)= 2.0%.,Expe

24、cted versus Required Returns,.,.,Coll.,.,HT,T-bills,.,USR,rM = 15 rRF = 8,-1 0 1 2,.,SML: ri = rRF + (RPM) bi ri = 8% + (7%) bi,ri (%),Risk, bi,SML and Investment Alternatives,Market,Calculate beta for a portfolio with 50% HT and 50% Collections,bp= Weighted average= 0.5(bHT) + 0.5(bColl)= 0.5(1.29)

25、 + 0.5(-0.86)= 0.22.,What is the required rate of returnon the HT/Collections 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%.,SML1,Original situation,Required Rate of Return r (%),SML2,00.51.01.52.0,181511 8,New SML, I = 3%,Impact

26、of Inflation Change on SML,rM = 18%rM = 15%,SML1,Original situation,Required Rate of Return (%),SML2,After increasein risk aversion,Risk, bi,1815,8,1.0, RPM = 3%,Impact of Risk Aversion Change,Has the CAPM been completely confirmed or refuted through empirical tests?,No. The statistical tests have problems that make empirical verification or rejection virtually impossible.Investors required returns are based on future risk, but betas are calculated with historical data.Investors may be concerned about both stand-alone and market risk.,