2. 5-1 CHAPTER 8 Risk and Rates of Return Outline Stand-alone return and risk Return Expected return Stand-alone risk Portfolio return and risk Portfolio return Portfolio risk Link Risk & return: CAPM / SML Beta CAPM and computing SML

3. 5-2 I-1: Return: What is my reward of investing?

4. 5-3 Investment returns 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%. The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested

5. 5-4 Rates of Return: stocks HPR = Holding Period Return P 1 = Ending price P 0 = Beginning price D 1 = Dividend during period one Define return? Your gain per dollar investment

6. 5-5 Rates of Return: Example Ending Price = 24 Beginning Price = 20 Dividend = 1 HPR = ( 24 - 20 + 1 )/ ( 20) = 25%

7. 5-6 I-2: Expected return: describe the uncertainty

8. 5-7 Calculating expected return Two scenarios and the concept of expected return Extending to more than two scenarios

9. 5-8 Investment alternatives EconomyProb.T-BillHTCollUSRMP Recession 0.15.5%-27.0%27.0% 6.0%-17.0% weak 0.25.5%-7.0%13.0%-14.0%-3.0% normal 0.45.5%15.0%0.0%3.0%10.0% strong 0.25.5%30.0%-11.0%41.0%25.0% Boom 0.15.5%45.0%-21.0%26.0%38.0%

10. 5-9 Calculating the expected return

11. 5-10 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. 5-11 I-3. Stand-alone risk

13. 5-12 Calculating standard deviation

14. 5-13 Standard deviation for each investment

15. 5-14 Comparing standard deviations USR Prob. T - bill HT 0 5.5 9.8 12.4 Rate of Return (%)

16. 5-15 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.

17. 5-16 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 risk free asset, which serves as compensation for investors to hold riskier securities.

18. 5-17 Comparing risk and return SecurityExpected return, r Risk, σ T-bills5.5%0.0% HT12.4%20.0% Coll*1.0%13.2% USR* 9.8%18.8% Market10.5%15.2% * Seem out of place. ^

19. 5-18 Selected Realized Returns, 1926 – 2001 Average Standard Return Deviation Small-company stocks17.3%33.2% Large-company stocks12.720.2 L-T corporate bonds 6.1 8.6 Source: Based on Stocks, Bonds, Bills, and Inflation: (Valuation Edition) 2002 Yearbook (Chicago: Ibbotson Associates, 2002), 28.

20. 5-19 Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

21. 5-20 Risk rankings, by coefficient of variation CV T-bill 0.0 HT 1.6 Coll. 13.2 USR 1.9 Market 1.4 Collections has the highest degree of risk per unit of return. HT, despite having the highest standard deviation of returns, has a relatively average CV.

22. 5-21 II: Risk and return in a portfolio

23. 5-22 Portfolio construction: Risk and return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections. Expected return of a portfolio is a weighted average of each of the component assets of the portfolio. Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.

24. 5-23 II-1. Portfolio return

25. 5-24 Calculating portfolio expected return EconomyProb.HTCollPort. Recession0.1-27.0%27.0% weak0.2-7.0%13.0% normal0.415.0%0.0%7.5% strong0.230.0%-11.0% Boom0.145.0%-21.0%

26. 5-25 Calculating portfolio expected return EconomyProb.HTCollPort. Recession0.1-27.0%27.0%0.0% weak0.2-7.0%13.0%3.0% normal0.415.0%0.0%7.5% strong0.230.0%-11.0%9.5% Boom0.145.0%-21.0%12.0%

27. 5-26 An alternative method for determining portfolio expected return

28. 5-27 II-2. Portfolio risk and beta

29. 5-28 Calculating portfolio standard deviation and CV

30. 5-29 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%). σ p = 3.4% is lower than the weighted average of HT and Coll.’s σ (16.6%). Therefore, the portfolio provides the average return of component stocks, but lower than the average risk. Why? Negative correlation between stocks.

31. 5-30 Returns distribution for two perfectly negatively correlated stocks (ρ = -1.0) -10 15 40 15 0 -10 Stock W 0 Stock M -10 0 Portfolio WM

32. 5-31 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

33. 5-32 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%.

34. 5-33 Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Company-Specific Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35

35. 5-34 Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

36. 5-35 Beta Measures a stock’s market risk, and shows a stock’s volatility relative to the market. Indicates how risky a stock is if the stock is held in a well-diversified portfolio. Portfolio beta is a weighted average of its individual securities’ beta

37. 5-36 Calculating betas Run a regression of past returns of a security against past returns on the market. The slope of the regression line is defined as the beta coefficient for the security.

38. 5-37 Comments on beta 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.

39. 5-38 III: CAPM

40. 5-39 What risk do we care? Stand alone? Risk that can not be diversified?

41. 5-40 Capital Asset Pricing Model (CAPM) Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.

42. 5-41 Capital Asset Pricing Model (CAPM) Model linking risk and required returns. CAPM suggests that a stock’s required return equals the risk-free return plus a risk premium that reflects the stock’s risk after diversification. r i = r RF + (r M – r RF ) b i Risk premium RP: additional return to take additional risk The market (or equity) risk premium is (r M – r RF )

43. 5-42 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%

44. 5-43 Applying CAPM Portfolio beta: Beta of a portfolio is a weighted average of its individual securities’ betas. Computing other variables: risk free rate, market return, market risk premium Computing the difference of return between two stocks. Computing price in the future when current price is given

45. 5-44 CAPM in a graph: 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

46. 5-45 Applying CAPM in real world(optional) Total Risk vs. Beta. An experiment The difference between commonly referred risk and beta (Are these high beta stocks really high beta) High risk( total risk), low beta stock can hedge your portfolio (reduce portfolio risk)

47. 5-46 Problems with CAPM (optional) Measurement error of beta Empirical relationship between beta and return is weak Size and Book-to-market factors Momentum

48. 5-47 Optional: diversification in real world Stock Index ETF Style: Value vs. Growth Style: Small vs. Big Performance, Risk, Expense(0.1% is low, 0.5% is about average) Examples: Vanguard Small Cap Value ETF VBR Small growth: VBK Large value: VTV Large growth: VUG

49. 5-48 diversification in real world Foreign ETF:RBL Pros: More diversification Low PE ratio cons Higher risk Higher expense: 0.6% vs. 0.1% Higher spread Poor prior performance