CHAPTER 9 Risk and Rates of Return

1. CHAPTER 9Risk 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 Expected 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% Note: you can work the variance calculation in either decimal or percentage

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 (2013) • Use KRF = 3.0%; this is a bit more than the current 10 year treasury rate of 2.75%. Sometimes analysts use a shorter term rate and short term treasuries are still extremely low, but we are going to use 3.0%. • 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. The Bottom Line on Riskfree Rates   Using a long term government rate (even on a coupon bond) as the riskfree rate on all of the cash flows in a long term analysis will yield a close approximation of the true value. For short term analysis, it is entirely appropriate to use a short term government security rate as the riskfree rate.   The riskfree rate that you use in an analysis should be in the same currency that your cashflows are estimated in. •  In other words, if your cashflows are in U.S. dollars, your riskfree rate has to be in U.S. dollars as well. •  If your cash flows are in Euros, your riskfree rate should be a Euro riskfree rate.   The conventional practice of estimating riskfree rates is to use the government bond rate, with the government being the one that is in control of issuing that currency. In US dollars, this has translated into using the US treasury rate as the riskfree rate. In May 2009, for instance, the ten-year US treasury bond rate was 3.5%.

47. 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 . ^

48. 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%

49. 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.

50. 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% .