This is the fifth presentation for the University of New England Graduate School of Business course GSB711 Managerial Finance, offered by Dr Subba Reddy Yarram. This presentation examines risk, return and the Capital Asset Pricing Model (CAPM).

1. Risk, Return and Capital Asset Pricing Model Topic 05 GSB711 – Managerial Finance Readings: Chapter: Introduction to Risk, Return and the Opportunity Cost of Capital (Pages 220 – 246) Questions: 1, 3, 6, 7 and Problems: 9, 13, 16, 20, 21 and 23. Chapter: Risk, Return and Capital Budgeting (Pages 248 – 273) Questions: 1, 2, 4 and Problems: 6, 7, 9, 10, 13, 16, 17, 21, 25 and 29.

2. Topics Covered Rates of Return: A Review A Century of Capital Market History Measuring Risk Risk & Diversification Measuring Market Risk Beta Risk and Return CAPM Capital Budgeting and Project Risk

3. Rates of Return

4. Rates of Return

5. Rates of Return

6. Nominal vs. Real Rates of Return

7. Dow Jones Industrial Average (The Dow) Value of a portfolio holding one share in each of 30 large industrial firms. Standard & Poor’s Composite Index (The S&P 500) Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues. Market Indexes

8. The Value of an Investment of $1 in 1900 $22,745 Index $192 $69 2008 Source: Ibbotson Associates Year Start

9. Rates of Return Common Stocks (1900-2007) 2007

10. Expected Return

11. What is Risk? Risk, in traditional terms, is viewed as a ‘negative’. Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk, reproduced below, give a much better description of risk The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.

12. Country Risk Premia (%)

13. Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation - Average value of squared deviations from mean. A measure of volatility.

14. Expected Returns Expected returns are based on the probabilities of possible outcomes In this context, “expected” means average if the process is repeated many times The “expected” return does not even have to be a possible return

15. Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of nature. What are the expected returns? State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession ??? 2 1 RC = .3(15) + .5(10) + .2(2) = 9.99% RT = .3(25) + .5(20) + .2(1) = 17.7%

16. Variance and Standard Deviation Variance and standard deviation still measure the volatility of returns Using unequal probabilities for the entire range of possibilities Weighted average of squared deviations

17. Example: Variance and Standard Deviation Consider the previous example. What are the variance and standard deviation for each stock? Stock C 2 = .3(15-9.9)2 + .5(10-9.9)2 + .2(2-9.9)2 = 20.29  = 4.5 Stock T 2 = .3(25-17.7)2 + .5(20-17.7)2 + .2(1-17.7)2 = 74.41  = 8.63

18. Portfolios A portfolio is a collection of assets An asset’s risk and return are important in how they affect the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets

20. KO: 3/15 = .2

21. INTC: 4/15 = .267

23. Example: Expected Portfolio Returns Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? DCLK: 19.69% KO: 5.25% INTC: 16.65% KEI: 18.24% E(RP) = .133(19.69) + .2(5.25) + .167(16.65) + .4(18.24) = 13.75%

24. Portfolio Variance Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm Compute the expected portfolio return using the same formula as for an individual asset Compute the portfolio variance and standard deviation using the same formulas as for an individual asset

25. Coin Toss Game-calculating variance and standard deviation Measuring Risk

26. Histogram of Returns Number of Years Return, percent

27. Risk and Diversification Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

28. Risk and Diversification

29. Risk and Diversification

30. Diversification Portfolio diversification is the investment in several different asset classes or sectors Diversification is not just holding a lot of assets For example, if you own 50 internet stocks, you are not diversified However, if you own 50 stocks that span 20 different industries, then you are diversified

31. 29 Portfolio diversification with additional stocks in a portfolio

32. The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

33. Portfolio diversification and numbers of stocks in a portfolio

34. Diversifiable Risk The risk that can be eliminated by combining assets into a portfolio Often considered the same as unsystematic, unique or asset-specific risk If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away

35. Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk

36. Systematic Risk Principle There is a reward for bearing risk There is not a reward for bearing risk unnecessarily The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away

37. Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient to measure systematic risk What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market

38. Total versus Systematic Risk Consider the following information: Standard Deviation Beta Security C 20% 1.25 Security K 30% 0.95 Which security has more total risk? Which security has more systematic risk? Which security should have the higher expected return?

39. Beta and the Risk Premium Remember that the risk premium = expected return – risk-free rate The higher the beta, the greater the risk premium should be Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES!

40. Stock Market Volatility 1900-2007 Std Dev 2007

41. The Value of Investments Value (August 2004 = 100)

42. Risk and Diversification

43. Risk and Diversification

44. Measuring Market Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

45. Measuring Market Risk Example - Turbo Charged Seafood has the following % returns on its stock, relative to the listed changes in the % return on the market portfolio. The beta of Turbo Charged Seafood can be derived from this information.

46. Example - continued Measuring Market Risk

47. Measuring Market Risk Example - continued When the market was up 1%, Turbo average % change was +0.8% When the market was down 1%, Turbo average % change was -0.8% The average change of 1.6 % (-0.8 to 0.8) divided by the 2% (-1.0 to 1.0) change in the market produces a beta of 0.8.

48. Example - continued Measuring Market Risk

49. Portfolio Betas Diversification decreases variability from unique risk, but not from market risk. The beta of your portfolio will be an average of the betas of the securities in the portfolio. If you owned all of the S&P Composite Index stocks, you would have an average beta of 1.0

50. Betas calculated with price data from January 2003 thru December 2007 Stock Betas

51. Risk and Return Vanguard Explorer Fund return Vanguard Explorer Return (%) Market Return (%)

52. Risk and Return Vanguard Index 500 return Vanguard Return (%) Market Return (%)

53. Measuring Market Risk Market Portfolio Market Risk Premium - Risk premium of market portfolio. Difference between market return and return on risk-free Treasury bills.

54. CAPM - Theory of the relationship between risk and return which states that the expected risk premium on any security equals its beta times the market risk premium. Measuring Market Risk

55. Measuring Market Risk 1.0 Security Market Line - The graphic representation of the CAPM.

56. Capital Asset Pricing Model R = rf + B ( rm - rf ) CAPM

57. Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-2005 30 20 10 0 SML Investors Market Portfolio Portfolio Beta 1.0

58. Testing the CAPM Return vs. Book-to-Market Dollars (log scale) High-minus low book-to-market Small minus big 2007 http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

59. Stock Expected Returns

60. Capital Budgeting & Project Risk We discuss more on capital budgeting in a later topic The project cost of capital depends on the use to which the capital is being put. Therefore, it depends on the risk of the project and not the risk of the company.

61. Capital Budgeting & Project Example - Based on the CAPM, ABC Company has a cost of capital of 17%. [4 + 1.3(10)]. A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used? 1/3 Nuclear Parts Mfr. B=2.0 1/3 Computer Hard Drive Mfr. B=1.3 1/3 Dog Food Production B=0.6 AVG. B of assets = 1.3 Risk

62. Capital Budgeting & Project Risk Example - Based on the CAPM, ABC Company has a cost of capital of 17%. (4 + 1.3(10)). A breakdown of the company’s investment projects is listed below. When evaluating a new dog food production investment, which cost of capital should be used? R = 4 + 0.6 (14 - 4 ) = 10% 10% reflects the opportunity cost of capital on an investment given the unique risk of the project.

63. Alternative Models CAPM emphasizes market as the major determinant of expected return Major criticism from Fama and French in early 1990s Other models take into account other aspects Arbitrage pricing theory and Multi factor models Is beta dead? Long-live beta