1. 6 - 1 Copyright © 2001 by Harcourt, Inc.All rights reserved. CHAPTER 6 Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM/SML

2. 6 - 2 Copyright © 2001 by Harcourt, Inc.All rights reserved. What is investment risk? Investment risk pertains to the probability of actually earning a low or negative return. The greater the chance of low or negative returns, the riskier the investment.

3. 6 - 3 Copyright © 2001 by Harcourt, Inc.All rights reserved. Probability distribution Expected Rate of Return Rate of return (%) 100150-70 Firm X Firm Y

4. 6 - 4 Copyright © 2001 by Harcourt, Inc.All rights reserved. Annual Total Returns,1926-1998 AverageStandard ReturnDeviationDistribution Small-company stocks 17.4% 33.8% Large-company stocks 13.2 20.3 Long-term corporate bonds 6.1 8.6 Long-term government 5.7 9.2 Intermediate-term government 5.5 5.7 U.S. Treasury bills 3.8 3.2 Inflation 3.2 4.5

5. 6 - 5 Copyright © 2001 by Harcourt, Inc.All rights reserved. Investment Alternatives (Given in the problem) EconomyProb.T-BillHTCollUSRMP Recession0.18.0%-22.0%28.0%10.0%-13.0% Below avg.0.28.0-2.014.7-10.0 1.0 Average0.48.020.00.07.0 15.0 Above avg.0.28.035.0-10.045.0 29.0 Boom0.18.050.0-20.030.0 43.0 1.0

6. 6 - 6 Copyright © 2001 by Harcourt, Inc.All rights reserved. Why is the T-bill return independent of the economy? Will return the promised 8% regardless of the economy.

7. 6 - 7 Copyright © 2001 by Harcourt, Inc.All rights reserved. Do T-bills promise a completely risk-free return? No, T-bills are still exposed to the risk of inflation. However, not much unexpected inflation is likely to occur over a relatively short period.

8. 6 - 8 Copyright © 2001 by Harcourt, Inc.All rights reserved. Do the returns of HT and Coll. move with or counter to the economy? HT: Moves with the economy, and has a positive correlation. This is typical. Coll: Is countercyclical of the economy, and has a negative correlation. This is unusual.

9. 6 - 9 Copyright © 2001 by Harcourt, Inc.All rights reserved. Calculate the expected rate of return on each alternative: k = expected rate of return. k HT = (-22%)0.1 + (-2%)0.20 + (20%)0.40 + (35%)0.20 + (50%)0.1 = 17.4%. ^ ^

10. 6 - 10 Copyright © 2001 by Harcourt, Inc.All rights reserved. k HT17.4% Market15.0 USR13.8 T-bill8.0 Coll.1.7 HT appears to be the best, but is it really? ^

11. 6 - 11 Copyright © 2001 by Harcourt, Inc.All rights reserved. What’s the standard deviation of returns for each alternative?  = Standard deviation.  = =  =

12. 6 - 12 Copyright © 2001 by Harcourt, Inc.All rights reserved.  T-bills = 0.0%.  HT = 20.0%.  Coll =13.4%.  USR =18.8%.  M =15.3%. 1/2  T-bills =           (8.0 – 8.0) 2 0.1 + (8.0 – 8.0) 2 0.2 + (8.0 – 8.0) 2 0.4 + (8.0 – 8.0) 2 0.2 + (8.0 – 8.0) 2 0.1

13. 6 - 13 Copyright © 2001 by Harcourt, Inc.All rights reserved. Prob. Rate of Return (%) T-bill USR HT 0813.817.4

14. 6 - 14 Copyright © 2001 by Harcourt, Inc.All rights reserved. Standard deviation (  i ) measures total, or stand-alone, risk. The larger the  i, the lower the probability that actual returns will be close to the expected return.

15. 6 - 15 Copyright © 2001 by Harcourt, Inc.All rights reserved. Expected Returns vs. Risk Security Expected return Risk,  HT 17.4% 20.0% Market 15.0 15.3 USR 13.8* 18.8* T-bills 8.0 0.0 Coll. 1.7* 13.4* *Seems misplaced.

16. 6 - 16 Copyright © 2001 by Harcourt, Inc.All rights reserved. Coefficient of Variation (CV) Standardized measure of dispersion about the expected value: Shows risk per unit of return. CV = =. Std dev  ^ k Mean

17. 6 - 17 Copyright © 2001 by Harcourt, Inc.All rights reserved. 0 A B  A =  B, but A is riskier because larger probability of losses. = CV A > CV B.  ^ k

18. 6 - 18 Copyright © 2001 by Harcourt, Inc.All rights reserved. Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in HT and $50,000 in Collections. Calculate k p and  p. ^

19. 6 - 19 Copyright © 2001 by Harcourt, Inc.All rights reserved. Portfolio Return, k p k p is a weighted average: k p = 0.5(17.4%) + 0.5(1.7%) = 9.6%. k p is between k HT and k COLL. ^ ^ ^ ^ ^^ ^^ k p =   w i k i  n i = 1

20. 6 - 20 Copyright © 2001 by Harcourt, Inc.All rights reserved. Alternative Method k p = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40 + (12.5%)0.20 + (15.0%)0.10 = 9.6%. ^ Estimated Return EconomyProb.HTColl.Port. Recession 0.10-22.0% 28.0% 3.0% Below avg. 0.20 -2.0 14.7 6.4 Average 0.40 20.0 0.0 10.0 Above avg. 0.20 35.0 -10.0 12.5 Boom 0.10 50.0 -20.0 15.0

21. 6 - 21 Copyright © 2001 by Harcourt, Inc.All rights reserved. CV p = = 0.34. 3.3% 9.6%  p = = 3.3%. 12/                       (3.0 – 9.6) 2 0.10 + (6.4 – 9.6) 2 0.20 + (10.0 – 9.6) 2 0.40 + (12.5 – 9.6) 2 0.20 + (15.0 – 9.6) 2 0.10

22. 6 - 22 Copyright © 2001 by Harcourt, Inc.All rights reserved.  p = 3.3% is much lower than that of either stock (20% and 13.4%).  p = 3.3% is lower than average of HT and Coll = 16.7%.  Portfolio provides average k but lower risk. Reason: negative correlation. ^

23. 6 - 23 Copyright © 2001 by Harcourt, Inc.All rights reserved. General statements about risk Most stocks are positively correlated. r k,m  0.65.  35% for an average stock. Combining stocks generally lowers risk.

24. 6 - 24 Copyright © 2001 by Harcourt, Inc.All rights reserved. Returns Distribution for Two Perfectly Negatively Correlated Stocks (r = -1.0) and for Portfolio WM 25 15 0 -10 0 0 15 25 Stock WStock MPortfolio WM...............

25. 6 - 25 Copyright © 2001 by Harcourt, Inc.All rights reserved. Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM’ Stock M 0 15 25 -10 Stock M’ 0 15 25 -10 Portfolio MM’ 0 15 25 -10

26. 6 - 26 Copyright © 2001 by Harcourt, Inc.All rights reserved. What would happen to the riskiness of an average 1-stock portfolio as more randomly selected stocks were added?  p would decrease because the added stocks would not be perfectly correlated but k p would remain relatively constant. ^

27. 6 - 27 Copyright © 2001 by Harcourt, Inc.All rights reserved. Large 0 15 Prob. 2 1 Even with large N,  p  20%

28. 6 - 28 Copyright © 2001 by Harcourt, Inc.All rights reserved. # Stocks in Portfolio 102030 40 2,000+ Company Specific Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

29. 6 - 29 Copyright © 2001 by Harcourt, Inc.All rights reserved. As more stocks are added, each new stock has a smaller risk- reducing impact.  p falls very slowly after about 10 stocks are included, and after 40 stocks, there is little, if any, effect. The lower limit for  p is about 20% =  M.

30. 6 - 30 Copyright © 2001 by Harcourt, Inc.All rights reserved. Stand-alone Market Firm-specific Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification, and is measured by beta. Firm-specific risk is that part of a security’s stand-alone risk that can be eliminated by proper diversification. risk risk risk = +

31. 6 - 31 Copyright © 2001 by Harcourt, Inc.All rights reserved. By forming portfolios, we can eliminate about half the riskiness of individual stocks (35% vs. 20%).

32. 6 - 32 Copyright © 2001 by Harcourt, Inc.All rights reserved. If you chose to hold a one-stock portfolio and thus are exposed to more risk than diversified investors, would you be compensated for all the risk you bear?

33. 6 - 33 Copyright © 2001 by Harcourt, Inc.All rights reserved. NO! Stand-alone risk as measured by a stock’s  or CV is not important to a well-diversified investor. Rational, risk averse investors are concerned with  p, which is based on market risk.

34. 6 - 34 Copyright © 2001 by Harcourt, Inc.All rights reserved. There can only be one price, hence market return, for a given security. Therefore, no compensation can be earned for the additional risk of a one-stock portfolio.

35. 6 - 35 Copyright © 2001 by Harcourt, Inc.All rights reserved. Beta measures a stock’s market risk. It shows a stock’s volatility relative to the market. Beta shows how risky a stock is if the stock is held in a well-diversified portfolio.

36. 6 - 36 Copyright © 2001 by Harcourt, Inc.All rights reserved. How are betas calculated? Run a regression of past returns on Stock i versus returns on the market. Returns = D/P + g. The slope of the regression line is defined as the beta coefficient.

37. 6 - 37 Copyright © 2001 by Harcourt, Inc.All rights reserved. Yeark M k i 115% 18% 2 -5-10 312 16... kiki _ kMkM _ - 505101520 20 15 10 5 -5 -10 Illustration of beta calculation: Regression line: k i = -2.59 + 1.44 k M ^^

38. 6 - 38 Copyright © 2001 by Harcourt, Inc.All rights reserved. If beta = 1.0, average stock. If beta > 1.0, stock riskier than average. If beta < 1.0, stock less risky than average. Most stocks have betas in the range of 0.5 to 1.5.

39. 6 - 39 Copyright © 2001 by Harcourt, Inc.All rights reserved. List of Beta Coefficients Stock Beta Merrill Lynch 2.00 America Online 1.70 General Electric 1.20 Microsoft Corp. 1.10 Coca-Cola 1.05 IBM 1.05 Procter & Gamble 0.85 Heinz 0.80 Energen Corp. 0.80 Empire District Electric 0.45

40. 6 - 40 Copyright © 2001 by Harcourt, Inc.All rights reserved. Can a beta be negative? Answer: Yes, if r i, m is negative. Then in a “beta graph” the regression line will slope downward. Though, a negative beta is highly unlikely.

41. 6 - 41 Copyright © 2001 by Harcourt, Inc.All rights reserved. HT T-Bills b = 0 kiki _ kMkM _ - 2002040 40 20 -20 b = 1.29 Coll. b = -0.86

42. 6 - 42 Copyright © 2001 by Harcourt, Inc.All rights reserved. Riskier securities have higher returns, so the rank order is OK. HT 17.4% 1.29 Market 15.0 1.00 USR 13.8 0.68 T-bills 8.0 0.00 Coll. 1.7 -0.86 Expected Risk Security Return (Beta)

43. 6 - 43 Copyright © 2001 by Harcourt, Inc.All rights reserved. Use the SML to calculate the required returns. Assume k RF = 8%. Note that k M = k M is 15%. (Equil.) RP M = k M – k RF = 15% – 8% = 7%. SML: k i = k RF + (k M – k RF )b i. ^

44. 6 - 44 Copyright © 2001 by Harcourt, Inc.All rights reserved. Required Rates of Return k HT = 8.0% + (15.0% – 8.0%)(1.29) = 8.0% + (7%)(1.29) = 8.0% + 9.0%= 17.0%. k M = 8.0% + (7%)(1.00)= 15.0%. k USR = 8.0% + (7%)(0.68)= 12.8%. k T-bill = 8.0% + (7%)(0.00)= 8.0%. k Coll = 8.0% + (7%)(-0.86)= 2.0%.

45. 6 - 45 Copyright © 2001 by Harcourt, Inc.All rights reserved. HT 17.4% 17.0% Undervalued: k > k Market 15.0 15.0 Fairly valued USR 13.8 12.8 Undervalued: k > k T-bills 8.0 8.0 Fairly valued Coll. 1.7 2.0 Overvalued: k < k Expected vs. Required Returns ^ ^ ^ ^ k k

46. 6 - 46 Copyright © 2001 by Harcourt, Inc.All rights reserved... Coll.. HT T-bills. USR SML k M = 15 k RF = 8 -1 0 1 2. SML: k i = 8% + (15% – 8%) b i. k i (%) Risk, b i

47. 6 - 47 Copyright © 2001 by Harcourt, Inc.All rights reserved. Calculate beta for a portfolio with 50% HT and 50% Collections b p = Weighted average = 0.5(b HT ) + 0.5(b Coll ) = 0.5(1.29) + 0.5(-0.86) = 0.22.

48. 6 - 48 Copyright © 2001 by Harcourt, Inc.All rights reserved. The required return on the HT/Coll. portfolio is: k p = Weighted average k = 0.5(17%) + 0.5(2%) = 9.5%. Or use SML: k p = k RF + (k M – k RF ) b p = 8.0% + (15.0% – 8.0%)(0.22) = 8.0% + 7%(0.22) = 9.5%.

49. 6 - 49 Copyright © 2001 by Harcourt, Inc.All rights reserved. If investors raise inflation expectations by 3%, what would happen to the SML?

50. 6 - 50 Copyright © 2001 by Harcourt, Inc.All rights reserved. SML 1 Original situation Required Rate of Return k (%) SML 2 00.5 1.01.5 Risk, b i 18 15 11 8 New SML  I = 3%

51. 6 - 51 Copyright © 2001 by Harcourt, Inc.All rights reserved. If inflation did not change but risk aversion increased enough to cause the market risk premium to increase by 3 percentage points, what would happen to the SML?

52. 6 - 52 Copyright © 2001 by Harcourt, Inc.All rights reserved. k M = 18% k M = 15% SML 1 Original situation Required Rate of Return (%) SML 2 After increase in risk aversion Risk, b i 18 15 8 1.0  RP M = 3%

53. 6 - 53 Copyright © 2001 by Harcourt, Inc.All rights reserved. Has the CAPM been verified through empirical tests? Not completely. Those statistical tests have problems that make verification almost impossible.

54. 6 - 54 Copyright © 2001 by Harcourt, Inc.All rights reserved. Investors seem to be concerned with both market risk and total risk. Therefore, the SML may not produce a correct estimate of k i : k i = k RF + (k M – k RF )b + ?

55. 6 - 55 Copyright © 2001 by Harcourt, Inc.All rights reserved. Also, CAPM/SML concepts are based on expectations, yet betas are calculated using historical data. A company’s historical data may not reflect investors’ expectations about future riskiness.