CHAPTER 8 Risk and Rates of Return

1. CHAPTER 8Risk and Rates of Return • Stand-alone risk (statistics review) • Portfolio risk (investor view) -- diversification important • Risk & return: CAPM/SML (market equilibrium)

2. Risk is viewed primarily from the stockholder perspective • Management cares about risk because stockholders care about risk. • If stockholders like or dislike something about a company (like risk) it affects the stock price. • Risk affects the discount rate for future returns -- directly affecting the multiple (P/E ratio) • Thus, the concern is still about the stock price. • Stockholders have portfolios of investments – they have stock in more than just one company and a great deal of flexibility in which stocks they buy.

3. What is investment risk? • Investment risk pertains to the uncertainty regarding the rate of return. • Especially when it is less than the expected (mean) return. • The greater the chance of low or negative returns, the riskier the investment.

4. Return = dividend + capital gain or loss • Dividends are relatively stable • Stock price changes (capital gains/losses) are the major uncertain component • There is a range of possible outcomes and a likelihood of each -- a probability distribution.

5. Expected Rate of Return • The mean value of the probability distribution of possible returns • It is a weighted average of the outcomes, where the weights are the probabilities

6. Expected Rate of Return(k hat)

7. Investment Alternatives

8. Why is the T-billreturn independent of the economy? Will return be 8% regardless of the economy?

9. Do T-bills really promise acompletely 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.

10. Do the returns of HT and Coll.move with or counter to theeconomy? • High Tech: With. Positive correlation. Typical. • Collections: Countercyclical. Negative correlation. Unusual.

11. Calculate the expected rate ofreturn for each alternative: ^ k = expected rate of return ^ ^ kHT = (-22%)0.1 + (-2%)0.20 + (20%)0.40 + (35%)0.20 + (50%)0.1 = 17.4%

12. Calculate others on your own ^ HT appears to be the best, but is it really?

13. What’s the standard deviationof returns for each alternative?  = standard deviation

14. Normal Distribution

15. In a sample of observations • One often assumes that data are from an approximately normally distributed population. then • about 68.26% of the values are at within 1 standard deviation away from the mean, • 95.46% of the values are within two standard deviations and • 99.73% lie within 3 standard deviations.

16. ^ T-bills= 0.0%. Coll = 13.4%. USR = 18.8%. M = 15.3%. HT = 20.0%.

17. 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.

18. Expected Returns vs. Risk: *Return looks low relative to 

19. Coefficient of variation (CV): Standardized measure of dispersion about the expected value: Shows risk per unit of return.

20. Portfolio Risk & Return Assume a two-stock portfolio with $50,000 in HighTech and $50,000 in Collections. Calculate kp and p.

21. Portfolio Return,kp ^ ^ kp is a weighted average: ^ kp = 0.5(17.4%) + 0.5(1.7%) = 9.6% ^ ^ ^ kp is between kHT and kCOLL.

22. Alternative Method: ^ kp = (3.0%)0.1 + (6.4%)0.20 + (10.0%)0.4 + (12.5%)0.20 + (15.0%)0.1 = 9.6%

23. = 3.3%

24. p = 3.3% is much lower than that of either stock (20% and 13.4%). • p = 3.3% is also lower than avg. of HT and Coll, which is 16.7%. • Portfolio provides avg. return but lower risk. • Reason: diversification. • Negative correlation is present between HT and Coll but is not required to have a diversification effect

25. General Statements about risk: • Most stocks are positively correlated. rk,m 0.65. • You still get a lot of diversification effect at .65 correlation • 35% for an average stock. • Combining stocks generally lowers risk.

26. What would happen to theriskiness of a 1-stockportfolio as more randomlyselected stocks were added? • p would decrease because the added stocks would not be perfectly correlated

27. p % 35 20 0 Company Specific risk Total Risk, P Market Risk 10 20 30 40 ...... 1500+ # stocks in portfolio

28. 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 20% = M .

29. Decomposing Risk—Systematic (Market) and Unsystematic (Business-Specific) Risk • Fundamental truth of the investment world • The returns on securities tend to move up and down together • Not exactly together or proportionately • Events and Conditions Causing Movement in Returns • Some things influence all stocks (market risk) • Political news, inflation, interest rates, war, etc. • Some things influence only particular firms (business-specific risk) • Earnings reports, unexpected death of key executive, etc. • Some things affect all companies within an industry • A labor dispute, shortage of a raw material

30. Total = Market + Firm specificrisk risk risk Market risk is that part of a security’s risk that cannot be eliminated by diversification. Firm-specific risk is that part of a security’s risk which can be eliminated with diversification.

31. By forming portfolios, we can eliminate nearly half the riskiness of individual stocks (35% vs. 20%). • (actually35% vs. 20% is a 43%reduction)

32. CAPM -- Capital Asset Pricing Model 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. NO! • Stand-alone risk as measured by a stock’s or CV is not important to well-diversified investors. • Rational, risk averse investors are concerned with p , which is based on market risk.

34. Beta measures a stock’s market risk. It shows a stock’s volatility relative to the market. • Beta shows how risky a stock is when the stock is held in a well-diversified portfolio. • The higher beta, the higher the expected rate of return.

35. How are betas calculated? • Run a regression of past returns on Stock i versus returns on the market. • The slope coefficient is the beta coefficient.

36. 20 15 10 5 -5 0 5 10 15 20 -5 -10 ki = -2.59 + 1.44 kM Illustration of beta = slope: Regression line . . Year kM ki 1 15% 18% 2 -5 -10 3 12 16 .

37. Find beta: • Statistics program or spreadsheet regression • Find someone’s estimate of beta for a given stock on the web • Generally use weekly or monthly returns, with at least a year of data

38. If beta = 1.0, average risk stock. (The ‘market’ portfolio has a beta of 1.0.) • 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. • Some ag. related companies have betas less than 0.5

39. =1, get the market expected return • <1, earn less than the market expected return • >1, get an expected return greater than the market

40. Can a beta be negative? Answer: Yes, if the correlation between ki and kM is negative. Then in a “beta graph” the regression line will slope downward. Negative beta -- rare

41. ki 40 20 -20 0 20 40 kM -20 b = 1.29 HT b=0 T-bills Coll b = -0.86

42. Riskier securities have higher returns, so the rank order is O.K.

43. Given the beta of a stock, a theoretical required rate of return can be calculated. • The Security Market Line (SML) is used. • SML: ki = kRF + (kM - kRF)bi MRP MRP= market risk premium

44. ki = kRF + (kM - kRF)bi

45. For Term Projects • Use KRF = 2.0%; this is the 10 year treasury rate. Often it is argued to use a shorter term rate, but we are going to use 2.0%. • Use MRP = 5%. This is MRP, not KM. • The historical average MRP is about 5%. • Find your own beta from the web • On Yahoo Finance look up your company and then the “key statistics” tab on the left will give you their beta

46. Use the SML to calculatethe requiredreturns (for the example) • Assume kRF = 8%. • Note that kM = kM is 15%. • MRP = kM - kRF = 15% - 8% = 7% SML: ki = kRF + (kM - kRF)bi . ^

47. Required rates of return: kHT = 8.0% + (15.0% - 8.0%) 1.29 = 8.0% + (7%)1.29 = 8.0% + 9.0% = 17.0% kM = 8.0% + (7%)1.00 = 15.0% kUSR = 8.0% + (7%)0.68 = 12.8% kTbill = 8.0% + (7%)0.00 = 8.0% kColl = 8.0% + (7%)(-0.86) = 2.0%

48. Calculate beta for a portfolio with 50% HT and 50% Collections: Portfolio Beta bP = weighted average of the betas of the stocks in the portfolio = 0.5(bHT) + 0.5(bColl) = 0.5(1.29) + 0.5(-0.86) = 0.22 . Weights are the proportions invested in each stock.

49. The required return on the HT/Coll. portfolio is: kP = Weighted average k = 0.5(17%) + 0.5(2%) = 9.5% . Or use SML for the portfolio: kP = kRF + (kM - kRF) bP = 8.0% + (15.0% - 8.0%) (0.22) = 8.0% + 7%(0.22) = 9.5% .

50. Using Beta—The Capital Asset Pricing Model (CAPM) • The CAPM helps us determine how stock prices are set in the market Developed in 1950s and 1960s by Harry Markowitz and William Sharpe • The CAPM's Approach People won't invest unless a stock's expected return is at least equal to their required return The CAPM attempts to explain how investors' required returns are determined