B40.2302 Class #3

1. B40.2302 Class #3 • BM6 chapters 7, 8, 9 • Based on slides created by Matthew Will • Modified 9/23/2001 by Jeffrey Wurgler

2. Principles of Corporate Finance Brealey and Myers Sixth Edition • Introduction to Risk, Return, and the Opportunity Cost of Capital Slides by Matthew Will, Jeffrey Wurgler Chapter 7 Irwin/McGraw Hill • The McGraw-Hill Companies, Inc., 2000

3. Topics Covered • 72 Years of Capital Market History • Measuring Risk • Portfolio Risk and Diversification • Beta and Unique Risk • Diversification and Value Additivity

4. The Value of an Investment of $1 in 1926 Real returns 613 203 6.15 4.34 1.58 Index 1 Year End Source: Ibbotson Associates

5. Returns 1926-1997 Percentage Return Year • Source: Ibbotson Associates

6. Measuring Risk Two standard measures of risk: Variance - Average value of squared deviations from mean. Standard Deviation – Square root of variance, I.e. square root of average value of squared deviations from mean.

7. Measuring Risk Example: Calculating variance and standard deviation. Suppose four equally-likely outcomes:

8. Measuring Risk Histogram of Annual Stock Market Returns # of Years Return %

9. Measuring Risk Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. Reduces risk but not expected return. Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk” or “idiosyncratic risk” Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “non-diversifiable risk” or “systematic risk”

10. Measuring Risk + …

11. Measuring Risk

12. Measuring Risk

13. Portfolio Risk In the two-asset case,

14. Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of +1.00.

15. Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s. The s.d. of BM returns is 17.1% and the s.d. of McDonald’s is 20.8%. Assume they have a correlation of -1.00.

16. 1 2 3 4 5 6 N 1 2 3 4 5 6 N Portfolio Risk The shaded boxes contain variance terms; the others contain covariance terms. To calculate portfolio variance add up the boxes STOCK STOCK

17. Expected stock return slope = beta 10% Expected - 10% + 10% Market risk premium -10% Copyright 1996 by The McGraw-Hill Companies, Inc Beta and Unique Risk A security’s market risk is measured by beta, its expected sensitivity to the market.

18. Beta and Unique Risk Market Portfolio - Portfolio of all investable assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market. Beta - Sensitivity of a stock’s return to the return on the market portfolio.

19. Beta and Unique Risk Covariance with the market risk premium Variance of the market risk premium

20. Diversification & Value Additivity • Value additivity holds … PV(A,B) = PV(A) + PV(B) • … since investors can diversify on their own • They will not pay extra for firms that diversify • And they will not pay less for firms that do diversify, since they can “undo” its effect on their own account • Note: V.A. assumes no “synergies”

21. Principles of Corporate Finance Brealey and Myers Sixth Edition • Risk and Return Slides by Matthew Will, Jeffrey Wurgler Chapter 8 Irwin/McGraw Hill • The McGraw-Hill Companies, Inc., 2000

22. Topics Covered • Markowitz Portfolio Theory • Risk and Return Relationship • Testing the CAPM • CAPM Alternatives • Consumption CAPM (CCAPM) • Arbitrage pricing theory (APT)

23. Markowitz Portfolio Theory • Can combine individual securities into portfolios that achieve at least a given expected return at the lowest possible variance. • These are called the efficient portfolios. • a.k.a. mean-variance efficient portfolios.

24. Markowitz Portfolio Theory • Portfolio expected return and standard deviation depends on the weights you put on each stock. Portfolio Expected Return (%) 100% McDonald’s 45% McDonald’s, 55% Bristol-Myers-Squibb 100% Bristol-Myers-Squibb Portfolio Standard Deviation (%)

25. Efficient Frontier • Each half egg shell represents the possible combinations of two stocks. • As you add more stocks, you can construct more complex portfolios. • The composite using all securities is the efficient frontier, and the portfolios on the frontier are efficient portfolios. Portfolio Expected Return (%) Portfolio Standard Deviation (%)

26. Efficient Frontier • Lending or Borrowing at the risk-free rate (rf) allows us to achieve combinations that are outside the efficient frontier. • Would never choose T, for example, when could choose S and then borrow or lend S Portfolio Expected Return (%) Lending Borrowing rf T Portfolio Standard Deviation (%)

27. Security Market Line Expected return . rm SML Market Portfolio rf Beta 1.0

28. Security Market Line / CAPM Expected return SML rf Beta 1.0 SML/CAPM: E[ri ] = rf + Bi (E[rm] - rf )

29. Testing the CAPM Beta vs. Average Risk Premium Avg Portfolio Risk Premium 1931-65 SML 30 20 10 0 Beta decile portfolios Market Portfolio Portfolio Beta 1.0

30. Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966-91 30 20 10 0 SML Investors Market Portfolio Portfolio Beta 1.0

31. Testing the CAPM Company Size vs. Average Return Average Return (%) Company size Smallest Largest

32. Testing the CAPM Book-to-Market vs. Average Return Average Return (%) Book-to-Market Ratio Highest Lowest

33. Consumption Betas vs Market Betas Stocks (and other risky assets) Market risk makes wealth uncertain. Standard CAPM Wealth = market portfolio

34. Consumption Betas vs Market Betas Stocks (and other risky assets) Stocks (and other risky assets) Wealth is uncertain Market risk makes wealth uncertain. Consumption CAPM Standard CAPM Wealth Consumption is uncertain Wealth = market portfolio Consumption

35. Arbitrage Pricing Theory • Besides CCAPM, APT is another alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …

36. Arbitrage Pricing Theory • APT, like CCAPM, is an alternative to CAPM • If Return = a + b1*rfactor 1+ b2*rfactor 2 + … • Then Expected Return (risk premium) = = ri – rf = b1*(rfactor 1 - rf) + b2 *(rfactor 2 - rf)+ …

37. Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990 data)

38. Principles of Corporate Finance Brealey and Myers Sixth Edition • Capital Budgeting and Risk Slides by Matthew Will, Jeffrey Wurgler Chapter 9 Irwin/McGraw Hill • The McGraw-Hill Companies, Inc., 2000

39. Topics Covered • Measuring Betas • Capital Structure and COC • Discount Rates for International Projects • Estimating Discount Rates – What if no beta? • Risk and DCF

40. Company Cost of Capital • Value-additivity: Total firm value is the sum of the value of its various assets. • Note each PV on the right is evaluated at its own discount rate

41. Company Cost of Capital • Company’s average cost of capital versus individual project cost of capital. (CAPM) 13 5.5 0 SML Required Return (%) “Company Cost of Capital” Project Beta 1.26 “Average Company Beta”

42. Measuring Betas • The SML shows the equilibrium relationship between expected return and risk (beta) according to the CAPM. • How to measure beta? • Typical approach: Regression analysis

43. Measuring Betas Hewlett-Packard Stock Beta Returns - Jan 88 to Dec 92 Hewlett-Packard return (%) R2 = 0.45 B = 1.70 Slope (beta) estimated from a regression over 60 months of return data. Market return (%)

44. Measuring Betas Hewlett-Packard Stock Beta Returns - Jan 93 - Dec 97 Hewlett-Packard return (%) R2 = 0.35 B = 1.69 Slope (beta) estimated from a regression over 60 months of return data. Market return (%)

45. Measuring Betas AT&T Stock Beta Returns - Jan 88 - Dec 92 R2 = 0.28 B = 0.90 A T & T (%) Slope (beta) estimated from a regression over 60 months of return data. Market return (%)

46. Measuring Betas AT&T Stock Beta Returns - Jan 93 - Dec 97 R2 = 0.17 B = 0.90 A T & T (%) Slope (beta) estimated from a regression over 60 months of return data. Market return (%)

47. Beta Stability % IN SAME % WITHIN ONE RISK CLASS 5 CLASS 5 CLASS YEARS LATER YEARS LATER 10 (High betas) 35 69 9 18 54 8 16 45 7 13 41 6 14 39 5 14 42 4 13 40 3 16 45 2 21 61 1 (Low betas) 40 62 Source: Sharpe and Cooper (1972)

48. Company Cost of Capitalsimple approach The overall company cost of capital is based on the weighted-average beta of the individual asset / project betas. The weights in the weighted average are determined by the % of firm value attached to each asset / project. Example: Say firm value is split as: 1/3 New ventures investment (B=2.0) 1/3 Expand existing business investment (B=1.3) 1/3 Plant efficiency investment (B=0.6) Average asset beta = (1/3)*2.0 + (1/3)*1.3 + (1/3)*0.6 = 1.3 This average beta determines the company cost of capital.

49. Capital Structure & COC • So we’ve established how to estimate the company cost of capital. • If you owned all of firm’s securities – 100% of its equity and 100% of its debt – you would own all its assets • Think of company cost of capital as expected return on this hypothetical portfolio.

50. Capital Structure & COC Company cost of capital =rportfolio = rassets rassets = rdebt (D) + requity (E) (V) (V) Bassets = Bdebt (D) + Bequity (E) (V) (V) IMPORTANT E, D, and V are all market values requity = rf + Bequity ( rm - rf )