1. 8-1 CHAPTER 8 Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM / SML

2. 8-2 Investment returns The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

3. 8-3 What is investment risk? Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment.

4. 8-4 Selected Realized Returns, 1990 – 2007 Average Standard Return Deviation Small-company stocks17.5%33.1% Large-company stocks12.420.3 L-T corporate bonds 6.2 8.6 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2008 Yearbook (Bursa Malaysia, 2008)

5. 8-5 Investment alternatives & Rate of Returns( %) Economy Prob.T-BillHTCollUSRMP Recession 0.15.5%-27.0%27.0% 6.0%-17.0% Below avg 0.25.5%-7.0%13.0%-14.0%-3.0% Average 0.45.5%15.0%0.0%3.0%10.0% Above avg 0.25.5%30.0%-11.0%41.0%25.0% Boom 0.15.5%45.0%-21.0%26.0%38.0%

6. 8-6 Investment alternatives & Rate of Returns( %) T-bills will return the promised 5.5%, regardless of the economy- risk-free return Do T-bills promise a completely risk-free return? T-bills do not provide a completely risk-free return, as they are still exposed to inflation.. T-bills are also risky in terms of reinvestment rate risk. However, T-bills are risk-free in the default sense of the word.

7. 8-7 “Reinvestment Risk” 5.5% CF 5.5% CF “reinvest cash inflow at going market rates” Thus, if market rates, may experience income reduction

8. 8-8 “inflation risk” If inflation rate = 8% - funds deposited loses the purchasing power - “inflation risk”

9. 8-9 How do the returns of HT and Coll. behave in relation to the market? HT – Moves with the economy, and has a positive correlation. This is typical. Coll. – Is countercyclical with the economy, and has a negative correlation. This is unusual.

10. 8-10 Calculating the expected return

11. 8-11 Summary of expected returns Expected return HT 12.4% Market 10.5% USR 9.8% T-bill 5.5% Coll. 1.0% HT has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

12. 8-12 12.4 HT’s expected return Expected returns & Standard deviation

13. 8-13 Calculating standard deviation

14. 8-14 (-27-12.4) 2 (0.1) + (-7-12.4) 2 (0.2) (15-12.4) 2 (0.4) + (30-12.4) 2 (0.2) (45-12.4) 2 (0.1) 1/2 6 HT = = 20%

15. 8-15 -7.6%12.4%32.4% Expected returns & Standard deviation

16. 8-16 Standard deviation for each investment

17. 8-17 Comparing standard deviations USR Prob. T - bill HT 0 5.5 9.8 12.4 Rate of Return (%)

18. 8-18 Comments on standard deviation as a measure of risk Standard deviation (σ i ) measures total, or stand-alone, risk. The larger σ i is, the lower the probability that actual returns will be closer to expected returns. Larger σ i is associated with a wider probability distribution of returns.

19. 8-19 Comparing risk and return SecurityExpected return, r Risk, σ T-bills5.5%0.0% HT12.4%20.0% Coll1.0%13.2% USR 9.8%18.8% Market10.5%15.2% ^

20. 8-20 Investor attitude towards risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and a riskless asset, which serves as compensation for investors to hold riskier securities.

21. 8-21 Portfolio construction: Risk and return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections. A portfolio’s expected return is a weighted average of the returns of the portfolio’s component assets.

22. 8-22 Calculating portfolio expected return = expected return = 12.4% = 1.0%

23. 8-23 An alternative method for determining portfolio expected return EconomyProb.HTCollPort. Recession0.1-27.0%27.0% 0.0% *A Below avg0.2-7.0%13.0% 3.0% *B Average0.415.0%0.0%7.5% Above avg0.230.0%-11.0%9.5% Boom0.145.0%-21.0%12.0% *A: 0.5(-27%) + 0.5(27) = 0% *B: 0.5(-7%) + 0.5(13%) = 3%

24. 8-24 Calculating portfolio standard deviation

25. 8-25 Comments on portfolio risk measures σ p = 3.4% is much lower than the σ i of either stock (σ HT = 20.0%; σ Coll. = 13.2%). Therefore, the portfolio provides the average return of component stocks, but lower than the average risk. Why? Negative correlation between stocks. Combining stocks in a portfolio generally lowers risk.

26. 8-26 Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0) -10 15 25 15 0 -10 Stock W 0 Stock M -10 0 Portfolio WM

27. 8-27 Returns distribution for two perfectly positively correlated stocks (ρ = 1.0) Stock M 0 15 25 -10 Stock M’ 0 15 25 -10 Portfolio MM’ 0 15 25 -10

28. 8-28 Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Diversifiable Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

29. 8-29 Creating a portfolio: Beginning with one stock and adding randomly selected stocks to portfolio σ p decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. Expected return of the portfolio would remain relatively constant. Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, σ p tends to converge to  20%.

30. 8-30 Breaking down sources of risk Diversifiable risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification. Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta.

31. 8-31 Beta Measures a stock’s market risk, and shows a stock’s volatility relative to the market. If beta = 1.0, the security is just as risky as the average stock. If beta > 1.0, the security is riskier than average. If beta < 1.0, the security is less risky than average. Most stocks have betas in the range of 0.5 to 1.5.

32. 8-32 Calculating betas Well-diversified investors are primarily concerned with how a stock is expected to move relative to the market in the future. A typical approach to estimate beta is to run a regression of the security’s past returns against the past returns of the market. The slope of the regression line is defined as the beta coefficient for the security.

33. 8-33 Illustrating the calculation of beta... riri _ rMrM _ - 505101520 20 15 10 5 -5 -10 Regression line: r i = -2.59 + 1.44 r M ^^ Yearr M r i 115% 18% 2 -5-10 312 16

34. 8-34 Comparing expected returns and beta coefficients Security Expected Return Beta HT 12.4% 1.32 Market 10.5 1.00 USR 9.8 0.88 T-Bills 5.5 0.00 Coll. 1.0-0.87 Riskier securities have higher returns, so the rank order is OK.

35. 8-35 Can the beta of a security be negative? Yes, if the correlation between Stock i and the market is negative (i.e., ρ i,m < 0). If the correlation is negative, the regression line would slope downward, and the beta would be negative. However, a negative beta is highly unlikely.

36. 8-36 Beta coefficients for HT, Coll, and T-Bills riri _ kMkM _ - 20 0 20 40 40 20 -20 HT: b = 1.30 T-bills: b = 0 Coll: b = -0.87

37. 8-37 Capital Asset Pricing Model (CAPM) Model linking risk and required returns. CAPM suggests that there is a Security Market Line (SML) that states that a stock’s required return equals the risk-free return plus a risk premium. r i = r RF + (r M – r RF ) b i

38. 8-38 The Security Market Line (SML): Calculating required rates of return SML: r i = r RF + (r M – r RF ) b i r i = r RF + (RP M ) b i Assume the r RF = 5.5% and RP M = 5.0%.

39. 8-39 What is the market risk premium (RP M )? Additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk. Varies from year to year, but most estimates suggest that it ranges between 4% and 8% per year.

40. 8-40 Calculating required rates of return r HT = 5.5% + (5.0%)(1.32) = 5.5% + 6.6%= 12.10% r M = 5.5% + (5.0%)(1.00)= 10.50% r USR = 5.5% + (5.0%)(0.88)= 9.90% r T-bill = 5.5% + (5.0%)(0.00)= 5.50% r Coll = 5.5% + (5.0%)(-0.87)= 1.15%

41. 8-41 Illustrating the Security Market Line.. Coll.. HT T-bills. USR SML r M = 10.5 r RF = 5.5 -1 0 1 2. SML: r i = 5.5% + (5.0%) b i r i (%) Risk, b i

42. 8-42 Expected vs. Required returns

43. 8-43 An example: Equally-weighted two-stock portfolio Create a portfolio with 50% invested in HT and 50% invested in Collections. The beta of a portfolio is the weighted average of each of the stock’s betas. b P = w HT b HT + w Coll b Coll b P = 0.5 (1.32) + 0.5 (-0.87) b P = 0.225

44. 8-44 Calculating portfolio required returns The required return of a portfolio is the weighted average of each of the stock’s required returns. r P = w HT r HT + w Coll r Coll r P = 0.5 (12.10%) + 0.5 (1.2%) r P = 6.6% Or, using the portfolio’s beta, CAPM can be used to solve for expected return. r P = r RF + (RP M ) b P r P = 5.5% + (5.0%) (0.225) r P = 6.6%

45. 8-45 Factors that change the SML What if investors raise inflation expectations by 3%, what would happen to the SML? SML 1 r i (%) SML 2 0 0.5 1.01.5 13.5 10.5 8.5 5.5  I = 3% Risk, b i

46. 8-46 Y = C + mx ri = rf + (Rm - Rf)b RPm SML line - Inflation is captured by rf - Inflation - rf - Risk factor is captured by (Rm – Rf) - Risk factor - (Rm – Rf)

47. 8-47 Factors that change the SML What if investors’ risk aversion increased, causing the market risk premium to increase by 3%, what would happen to the SML? SML 1 r i (%) SML 2 0 0.5 1.01.5 13.5 10.5 5.5  RP M = 3% Risk, b i