1. Risk and Return: The Basics  Stand-alone risk  Portfolio risk  Risk and return: CAPM/SML

2. What is investment risk?  Investment risk pertains to the probability of earning less than the expected return.  The greater the chance of low or negative returns, the riskier the investment.

3. Probability distribution Expected Rate of Return Rate of return (%) 100150-70 Firm X Firm Y

4. Investment Alternatives Economy Prob.T-BillABC Mkt Port. Recession 0.1 8.0%-22.0% 28.0% 10.0%-13.0% Below avg. 0.2 8.0 -2.0 14.7 -10.0 1.0 Average 0.4 8.0 20.0 0.0 7.0 15.0 Above avg. 0.2 8.0 35.0 -10.0 45.0 29.0 Boom 0.18.0 50.0 -20.0 30.0 43.0 1.0

5. Why is the T-bill return independent of the economy? Will return the promised 8% regardless of the state of the economy.

6. 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.

7. Do the returns of A and B move with or counter to the economy?  A: With. Positive correlation. Typical.  B: Countercyclical. Negative correlation. Unusual.

8. k =  k i P i. Calculate the expected rate of return on each alternative k = Expected rate of return k A = (-22%)0.10 + (-2%)0.20 + (20%)0.40 + (35%)0.20 + (50%)0.10 = 17.4%. ^ ^ ^ i = 1 n

9. A appears to be the best, but is it really? ^ k A 17.4% Market 15.0 C 13.8 T-bill 8.0 B. 1.7

10. What’s the standard deviation of returns for each alternative?  = Standard deviation.

11.  T-bills = 0.0%.  A = 20.0%.  B =13.4%.  C =18.8%.  M =15.3%.. 1/2     T-bills = 8.0- + - - + - 22 22 2 0102 0402 80 -8001.......  

12. Prob. Rate of Return (%) T-bill C A 0813.817.4

13.  Standard deviation (  i ) measures stand-alone risk.  The larger the  i, the higher the probability that actual returns will be far below the expected return.

14. Coefficient of Variation (CV) Standardized measure of dispersion about the expected value: Shows risk per unit of return. CV = =. Std dev  ^ k Mean

15. 0 A B  A =  B, but A is riskier because larger probability of losses. = CV A > CV B.  ^ k

16. Portfolio Risk and Return Assume a two-stock portfolio with $50,000 in A and $50,000 in B. Calculate k p and  p. ^

17. 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 A and k B. ^ ^ ^ ^ ^^ ^^ k p =   w i k w  n i = 1

18. 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.ABPort. 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

19. = 3.3%.       p = 3.0-9.6 2 2 2 2 2 12 010 64 -96020 100 -96040 125 -96020 150 -96010............. /     CV p = = 0.34. 3.3% 9.6%

20. 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...............

21. Returns Distributions for Two Perfectly Positively Correlated Stocks (r = +1.0) and for Portfolio MM’ Stock M 0 15 25 -10 0 15 25 -10 Stock M’ 0 15 25 -10 Portfolio MM’

22. 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. ^

23. Large 0 15 Prob. 2 1

24. # Stocks in Portfolio 102030 40 2000+ Company Specific Risk Market Risk 35 18 0 Stand-Alone Risk,  p  p (%)

25.  As more stocks are added, each new stock has a smaller risk- reducing impact.   p falls very slowly after about 40 stocks are included. The lower limit for  p is about  M = 18%.

26. Stand-alone Market Firm-specific Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. Firm-specific risk is that part of a security’s stand-alone risk which can be eliminated by proper diversification. risk risk risk = +

27. By forming portfolios, we can eliminate about half the riskiness of individual stocks (35% vs. 18%).

28. 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?

29.  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 portfolio risk, and here the relevant risk of an individual stock is its contribution to the riskiness of a portfolio.

30.  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.

31. CAPM( Capital Asset Pricing Model) Conclusion: zThe relevant riskiness of an individual stock is its contribution to the riskiness of well-diversified portfolio. zCAPM links risk and required rate of return

32.  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. The concept of beta, “b”

33. Yeark M k i 115% 18% 2 -5-10 312 16... kiki _ kMkM _ - 505101520 20 15 10 5 -5 -10 Illustration of beta calculations: Regression line: k i = -2.59 + 1.44 k M ^^

34. Find beta  “By Eye.”  “By Eye.” Plot points, draw in regression line, get slope as b = Rise/Run. The “rise” is the difference in k i, the “run” is the difference in k M. For example, how much does k i increase or decrease when k M increases from 0% to 10%?

35.  Calculator. Enter data points, and calculator does least squares regression: k i = a + bk M = -2.59 + 1.44k M. r = corr. coefficient = 0.997.  In the real world, we would use weekly or monthly returns, with at least a year of data, and would always use a computer or calculator.

36.  If beta = 1.0, average risk.  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.

37. Can a beta be negative? Yes, in theory, if a stock’s returns are negatively correlated with the market. Then in a “beta graph” the regression line will slope downward. In the “real world,” negative beta stocks do not exist.

38. A T-Bills b = 0 kiki _ kMkM _ - 2002040 40 20 -20 b = 1.29 B b = -0.86

39. Use the SML to calculate the required returns.  Assume k RF = 8%.  Note that k M = k M is 15%. (From market portfolio.)  RP M = k M - k RF = 15% - 8% = 7%. SML: k i = k RF + (k M - k RF )b i. ^

40. Required Rates of Return k A = 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 C = 8.0% + (7%)(0.68)= 12.8%. k T-bill = 8.0% + (7%)(0.00)= 8.0%. k B = 8.0% + (7%)(-0.86)= 2.0%.

41. Expected vs. Required Returns ^ ^ ^ ^ A 17.4% 17.0% Undervalued: k > k Market 15.0 15.0 Fairly valued C 13.8 12.8 Undervalued: k > k T-bills 8.0 8.0 Fairly valued B 1.7 2.0 Overvalued: k < k k k

42. .. B. A T-bills. C SML k M = 15 k RF = 8 -1 0 1 2. SML: k i = 8% + (15% - 8%) b i. k i (%) Risk, b i

43. Calculate beta for a portfolio with 50% A and 50% B b p = Weighted average = 0.5(b A ) + 0.5(b B ) = 0.5(1.29) + 0.5(-0.86) = 0.22.

44. The required return on the A/B 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%.

45. If investors raise inflation expectations by 3 percentage points, what would happen to the SML?

46. SML 1 Original situation Required Rate of Return k (%) SML 2 00.51.01.52.0 18 15 11 8 New SML  I = 3%

47. 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?

48. 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  MRP = 3%

49. Has the CAPM been verified through empirical tests?  Not completely. That statistical tests have problems which make verification almost impossible.

50.  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 + ?