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Principles of Corporate Finance Brealey and Myers Sixth Edition Introduction to Risk, Return, and the Opportunity Cost of Capital Slides by Matthew Will Irwin/McGraw Hill Chapter ©The McGraw-Hill Companies, Inc., 200 7- Topics Covered 72 Years of Capital Market History Measuring Risk Portfolio Risk Beta and Unique Risk Diversification Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- The Value of an Investment of $1 in 1926 5520 Index 1000 S&P Small Cap Corp Bonds Long Bond T Bill 1828 55.38 39.07 10 14.25 0.1 1925 1933 1941 Source: Ibbotson Associates Irwin/McGraw Hill 1949 1957 1965 1973 1981 1989 1997 Year End ©The McGraw-Hill Companies, Inc., 200 7- The Value of an Investment of $1 in 1926 Index 1000 Real returns S&P Small Cap Corp Bonds Long Bond T Bill 613 203 6.15 10 4.34 1.58 0.1 1925 1933 1941 Source: Ibbotson Associates Irwin/McGraw Hill 1949 1957 1965 1973 1981 1989 1997 Year End ©The McGraw-Hill Companies, Inc., 200 7- Rates of Return 1926-1997 Percentage Return 60 40 20 -20 Common Stocks Long T-Bonds T-Bills -40 -60 26 30 35 40 Source: Ibbotson Associates Irwin/McGraw Hill 45 50 55 60 65 70 75 80 85 90 95 Year ©The McGraw-Hill Companies, Inc., 200 7- 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 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- Measuring Risk Coin Toss Game-calculating variance and standard deviation (1) (2) (3) Percent Rate of Return Deviation from Mean Squared Deviation + 40 + 30 900 + 10 0 + 10 - 20 - 30 900 Variance = average of squared deviations = 1800 / = 450 Standard deviation = square of root variance = Irwin/McGraw Hill 450 = 21.2% ©The McGraw-Hill Companies, Inc., 200 7- Measuring Risk Histogram of Annual Stock Market Returns # of Years Return % 50 to 60 40 to 50 30 to 40 20 to 30 10 to 20 to 10 -30 to -20 Irwin/McGraw Hill -10 to -20 to -10 -40 to -30 13 12 11 13 10 -50 to -40 13 12 11 10 ©The McGraw-Hill Companies, Inc., 200 7- Measuring Risk 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.” Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 10 Measuring Risk ( ( )( )( Portfolio rate fraction of portfolio = x of return in first asset + Irwin/McGraw Hill fraction of portfolio in second asset x rate of return on first asset rate of return ) ) on second asset ©The McGraw-Hill Companies, Inc., 200 7- 11 Portfolio standard deviation Measuring Risk 10 15 Number of Securities Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 12 Portfolio standard deviation Measuring Risk Unique risk Market risk 10 15 Number of Securities Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 13 Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes: Stock Stock Stock Irwin/McGraw Hill x 12σ 12 x 1x 2σ 12 x 1x 2ρ 12σ 1σ Stock x 1x 2σ 12 x 1x 2ρ 12σ 1σ x 22σ 22 ©The McGraw-Hill Companies, Inc., 200 7- 14 Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s The expected dollar return on your BM is 10 x 55 = 5.50 and on McDonald’s it is 20 x 45 = 9.90 The expected dollar return on your portfolio is 5.50 + 9300 = 14.50 The portfolio rate of return is 14.50/100 = 145 or 14.5% Assume a correlation coefficient of Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 15 Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s The expected dollar return on your BM is 10 x 55 = 5.50 and on McDonald’s it is 20 x 45 = 9.90 The expected dollar return on your portfolio is 5.50 + 9300 = 14.50 The portfolio rate of return is 14.50/100 = 145 or 14.5% Assume a correlation coefficient of Bristol - Myers Bristol - Myers x 12σ 12 (.55) (17.1) McDonald' s Irwin/McGraw Hill x 1x 2ρ 12σ 1σ .55 .45 1 17.1 20.8 McDonald' s x 1x 2ρ 12σ 1σ .55 .45 1 17.1 20.8 x 22σ 22 (.45) ( 20.8) ©The McGraw-Hill Companies, Inc., 200 7- 16 Portfolio Risk Example Suppose you invest $55 in Bristol-Myers and $45 in McDonald’s The expected dollar return on your BM is 10 x 55 = 5.50 and on McDonald’s it is 20 x 45 = 9.90 The expected dollar return on your portfolio is 5.50 + 9300 = 14.50 The portfolio rate of return is 14.50/100 = 145 or 14.5% Assume a correlation coefficient of Portfolio Valriance [(.55) x(17.1) ] [(.45) x(20.8) ] 2(.55x.45x1x17.1x20.8) 352.10 Standard Deviation 352.1 18.7 % Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 17 Portfolio Risk Expected Portfolio Return (x r1 ) ( x r2 ) Portfolio Variance x 12σ 12 x 22σ 22 2( x 1x 2ρ 12σ 1σ ) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 18 Portfolio Risk The shaded boxes contain variance terms; the remainder contain covariance terms STOCK To calculate portfolio variance add up the boxes N N STOCK Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 19 Beta and Unique Risk Total risk = diversifiable risk + market risk Market risk is measured by beta, the sensitivity to market changes Expected stock return beta -10% +10% - 10% +10% -10% Expected market return Copyright 1996 by The McGraw-Hill Companies, Inc Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 20 Beta and Unique Risk Market Portfolio - Portfolio of all 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/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 21 Beta and Unique Risk im Bi m Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 7- 22 Beta and Unique Risk im Bi m Covariance with the market Variance of the market Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 ... 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 Irwin/McGraw Hill... Portfolio rate fraction of portfolio = x of return in first asset + Irwin/McGraw Hill fraction of portfolio in second asset x rate of return on first asset rate of return ) ) on second asset ©The McGraw-Hill... portfolio is 5.50 + 9300 = 14.50 The portfolio rate of return is 14.50/100 = 145 or 14.5% Assume a correlation coefficient of Bristol - Myers Bristol - Myers x 12σ 12 (.55) (17.1) McDonald' s Irwin/McGraw
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