7 1 B 40 2302 Class 3 w
7 - 1 B 40. 2302 Class #3 w BM 6 chapters 7, 8, 9 w Based on slides created by Matthew Will w Modified 9/23/2001 by Jeffrey Wurgler Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Principles of Corporate Finance Brealey and Myers Sixth Edition Introduction to Risk, Return, and the Opportunity Cost of Capital u Slides by Matthew Will, Jeffrey Wurgler Irwin/Mc. Graw Hill Chapter 7 ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 3 Topics Covered w 72 Years of Capital Market History w Measuring Risk w Portfolio Risk and Diversification w Beta and Unique Risk w Diversification and Value Additivity Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 4 The Value of an Investment of $1 in 1926 Real returns 613 Index 203 6. 15 4. 34 1 Source: Ibbotson Associates Irwin/Mc. Graw Hill 1. 58 Year End ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 5 Percentage Returns 1926 -1997 Year Source: Ibbotson Associates Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 7 Measuring Risk Example: Calculating variance and standard deviation. Suppose four equally-likely outcomes: Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 8 Measuring Risk Histogram of Annual Stock Market Returns # of Years Return % Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 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 “nondiversifiable risk” or “systematic risk” Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 10 Measuring Risk +… Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 11 Irwin/Mc. Graw Hill Measuring Risk ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 12 Irwin/Mc. Graw Hill Measuring Risk ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 13 Portfolio Risk In the two-asset case, Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 14 Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in Mc. Donald’s. The s. d. of BM returns is 17. 1% and the s. d. of Mc. Donald’s is 20. 8%. Assume they have a correlation of +1. 00. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 15 Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in Mc. Donald’s. The s. d. of BM returns is 17. 1% and the s. d. of Mc. Donald’s is 20. 8%. Assume they have a correlation of -1. 00. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 16 Portfolio Risk The shaded boxes contain variance terms; the others contain covariance terms. 1 2 3 STOCK To calculate portfolio variance add up the boxes 4 5 6 N 1 2 3 4 5 6 N STOCK Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 17 Beta and Unique Risk A security’s market risk is measured by beta, its expected sensitivity to the market. Expected stock return slope = beta 10% - 10% +10% Expected Market risk premium -10% Copyright 1996 by The Mc. Graw-Hill Companies, Inc Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 19 Beta and Unique Risk Covariance with the market risk premium Variance of the market risk premium Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 20 Diversification & Value Additivity w Value additivity holds … PV(A, B) = PV(A) + PV(B) w … since investors can diversify on their own They will not pay extra for firms that diversify è And they will not pay less for firms that do diversify, since they can “undo” its effect on their own account è Note: V. A. assumes no “synergies” è Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Principles of Corporate Finance Brealey and Myers u Sixth Edition Risk and Return Slides by Matthew Will, Jeffrey Wurgler Irwin/Mc. Graw Hill Chapter 8 ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 22 Topics Covered w Markowitz Portfolio Theory w Risk and Return Relationship w Testing the CAPM w CAPM Alternatives Consumption CAPM (CCAPM) è Arbitrage pricing theory (APT) è Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 23 Markowitz Portfolio Theory w Can combine individual securities into portfolios that achieve at least a given expected return at the lowest possible variance. w These are called the efficient portfolios w a. k. a. mean-variance efficient portfolios. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 24 Markowitz Portfolio Theory u Portfolio expected return and standard deviation depends on the weights you put on each stock. Portfolio Expected Return (%) 100% Mc. Donald’s 45% Mc. Donald’s, 55% Bristol-Myers-Squibb 100% Bristol-Myers-Squibb Portfolio Standard Deviation (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 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 (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 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 Portfolio Expected Return (%) S ing w o rr Bo ing d n Le rf T Irwin/Mc. Graw Hill Portfolio Standard Deviation (%) ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 27 Security Market Line Expected return rm . SML Market Portfolio rf 1. 0 Irwin/Mc. Graw Hill Beta ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 28 Security Market Line / CAPM Expected return SML rf 1. 0 Beta SML/CAPM: E[ri ] = rf + Bi (E[rm] - rf ) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 29 Testing the CAPM Beta vs. Average Risk Premium Avg Portfolio Risk Premium 1931 -65 SML 30 Beta decile portfolios 20 10 Market Portfolio 0 1. 0 Irwin/Mc. Graw Hill Portfolio Beta ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 30 Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966 -91 30 20 SML Investors 10 Market Portfolio 0 1. 0 Irwin/Mc. Graw Hill Portfolio Beta ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 31 Testing the CAPM Company Size vs. Average Return (%) Company size Smallest Irwin/Mc. Graw Hill Largest ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 32 Testing the CAPM Book-to-Market vs. Average Return (%) Book-to-Market Ratio Highest Irwin/Mc. Graw Hill Lowest ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 33 Consumption Betas vs Market Betas Stocks (and other risky assets) Market risk makes wealth uncertain. Standard CAPM Wealth = market portfolio Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 34 Consumption Betas vs Market Betas Stocks (and other risky assets) Wealth is uncertain Market risk makes wealth uncertain. Standard Wealth CAPM Consumption is uncertain Wealth = market portfolio Irwin/Mc. Graw Hill Consumption ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 35 Arbitrage Pricing Theory w Besides CCAPM, APT is another alternative to CAPM Expected Risk Premium =r - rf = Bfactor 1(rfactor 1 Return Irwin/Mc. Graw Hill - rf) + Bf 2(rf 2 - rf) + … = a + bfactor 1(rfactor 1) + bf 2(rf 2) + … ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 36 Arbitrage Pricing Theory w APT, like CCAPM, is an alternative to CAPM w If Return = a + b 1*rfactor 1+ b 2*rfactor 2 + … w Then Expected Return (risk premium) = = ri – rf = b 1*(rfactor 1 - rf) + b 2 *(rfactor 2 - rf) + … Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 37 Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978 -1990 data) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Principles of Corporate Finance Brealey and Myers u Sixth Edition Capital Budgeting and Risk Slides by Matthew Will, Jeffrey Wurgler Irwin/Mc. Graw Hill Chapter 9 ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 39 Topics Covered w Measuring Betas w Capital Structure and COC w Discount Rates for International Projects w Estimating Discount Rates – What if no beta? w Risk and DCF Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 40 Company Cost of Capital w Value-additivity: Total firm value is the sum of the value of its various assets. w Note each PV on the right is evaluated at its own discount rate Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 41 Company Cost of Capital w Company’s average cost of capital versus individual project cost of capital. (CAPM) SML Required Return (%) 13 “Company Cost of Capital” 5. 5 0 1. 26 Irwin/Mc. Graw Hill Project Beta “Average Company Beta” ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 42 Measuring Betas w The SML shows the equilibrium relationship between expected return and risk (beta) according to the CAPM. w How to measure beta? w Typical approach: Regression analysis Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 43 Measuring Betas Returns - Jan 88 to Dec 92 R 2 = 0. 45 B = 1. 70 Hewlett-Packard return (%) Hewlett-Packard Stock Beta Slope (beta) estimated from a regression over 60 months of return data. Market return (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 44 Measuring Betas Returns - Jan 93 - Dec 97 R 2 = 0. 35 B = 1. 69 Hewlett-Packard return (%) Hewlett-Packard Stock Beta Slope (beta) estimated from a regression over 60 months of return data. Market return (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 45 Measuring Betas AT&T Stock Beta R 2 = 0. 28 B = 0. 90 A T & T (%) Returns - Jan 88 - Dec 92 Slope (beta) estimated from a regression over 60 months of return data. Market return (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 46 Measuring Betas AT&T Stock Beta R 2 = 0. 17 B = 0. 90 A T & T (%) Returns - Jan 93 - Dec 97 Slope (beta) estimated from a regression over 60 months of return data. Market return (%) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 47 Beta Stability RISK CLASS % IN SAME CLASS 5 YEARS LATER % WITHIN ONE CLASS 5 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) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Company Cost of Capital 7 - 48 simple approach The overall company cost of capital is based on the weightedaverage 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. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 49 Capital Structure & COC w So we’ve established how to estimate the company cost of capital. w If you owned all of firm’s securities – 100% of its equity and 100% of its debt – you would own all its assets w Think of company cost of capital as expected return on this hypothetical portfolio. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 50 Capital Structure & COC Company cost of capital = rportfolio = rassets = rdebt (D) + requity (E) (V) Bassets = Bdebt (D) + Bequity (E) (V) requity = rf + Bequity ( rm - rf ) Irwin/Mc. Graw Hill IMPORTANT E, D, and V are all market values ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 51 Capital Structure & COC w Changing capital structure can change the risk of the debt relative to the risk of the equity, but does not change the overall risk of the firm. w Changing capital structure therefore does not change the company cost of capital. w Let’s see how changes in capital structure change the costs of equity vs. debt… Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 52 Capital Structure & COC Expected Returns and Betas before refinancing Expected return (%) requity=15 rassets=12. 2 rdebt=8 Bdebt Irwin/Mc. Graw Hill Bassets Bequity ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 53 Capital Structure & COC Expected Returns and Betas after refinancing Expected return (%) requity=14. 3 rassets=12. 2 rdebt=7. 3 Bdebt Irwin/Mc. Graw Hill Bassets Bequity ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 54 Capital Structure & COC w Go from estimated Bequity (say, from regression) and assumed / estimated Bdebt to compute Bassets w This is called unlevering beta w To unlever beta, just remember: Bassets = Bdebt (D) + Bequity (E) (V) Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 55 Irwin/Mc. Graw Hill Pinnacle West Corp. ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 56 Pinnacle West Corp. Requity = rf + Bequity ( rm - rf ) = 4. 5 +. 51(8. 0) = 8. 58% (Used industry average Bequity since PW’s Bequity was measured with lots of error) Rdebt = can estimate as YTM on PW bonds (Bond returns often hard to observe, so hard to estimate Bdebt) = 6. 90 % Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 57 Irwin/Mc. Graw Hill Pinnacle West Corp. ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 58 COC for International Projects w Same principles apply, with complications w If project is owned by US investors, they care more about project’s beta with US market. Not about project’s beta with local market. w The theory is clearest if investors are globally diversified. Then relevant beta is beta with world market. Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
7 - 59 What if can’t calculate Beta? w Suppose a new project doesn’t match the risk of traded securities… how to discount? w Need judgment. General advice: Avoid fudge factors in discount rate. Make unbiased cash flow forecast (i. e. right on average). è Think about determinants of asset betas. Are project cash flows more or less cyclical than usual industry project? è Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Risk and DCF: 7 - 60 Putting it all together Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of. 75, what is the PV of the project? Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
Risk and DCF: 7 - 61 Putting it all together Example Project A is expected to produce CF = $100 mil for each of three years. Given a risk free rate of 6%, a market risk premium of 8%, and an asset beta of. 75, what is the PV of the project? Irwin/Mc. Graw Hill ©The Mc. Graw-Hill Companies, Inc. , 2000
- Slides: 61