Principles of Corporate Finance Seventh Edition Richard A. Brealey Stewart C. Myers Chapter 7 Introduction to Risk, Return, and the Opportunity Cost of Capital Slides by Matthew Will
- Topics Covered 75 Years of Capital Market History Measuring Risk Portfolio Risk Beta and Unique Risk Diversification
- 3 The Value of an Investment of $ in 96 000 Small Cap 640 587 Inde Corp Bonds 0 T Bill S&P 64. 48.9 Long Bond 6.6 0, 95 940 955 970 985 000 Source: Ibbotson Associates Year End
- 4 The Value of an Investment of $ in 96 Real returns 000 Small Cap S&P 660 67 Inde 0 Corp Bonds Long Bond T Bill 6.6 5.0.7 0, 95 940 955 970 985 000 Source: Ibbotson Associates Year End
- 5 Rates of Return 96-000 Percentage Return 60 40 0 0-0 -40-60 6 30 35 40 45 50 55 Common Stocks Long T-Bonds T-Bills 60 65 70 75 80 85 90 95 000 Source: Ibbotson Associates Year
- 6 Average Market Risk Premia (900-000) Risk premium, % 0 9 8 7 6 5 4 3 0 Den 4.3 5. 6 6. 6. 6.5 6.7 7. 7.5 Bel Can Swi Spa UK Ire Neth USA Swe 8 Aus 8.5 Ger 9.9 9.9 0 Fra Jap It Country
- 7 Measuring Risk Variance - Average value of squared deviations from mean. A measure of volatility. Standard Deviation Square root of the variance. A measure of volatility.
- 8 Measuring Risk Coin Toss Game-calculating variance and standard deviation () () (3) Percent Rate of Return Deviation from Mean Squared Deviation + 40 + 30 900 +0 0 0 +0 0 0-0 - 30 900 Variance = average of squared deviations = 800 / 4 = 450 Standard deviation = square of root variance = 450 =.%
Measuring Risk # of Years Histogram of Annual Stock Market Returns 3 0 9 8 7 6 5 4 3 0 4 3 3 3 3 Return % - 9-50 to -40-40 to -30-30 to -0-0 to -0-0 to 0 0 to 0 0 to 0 0 to 30 30 to 40 40 to 50 50 to 60
0 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.
Portfolio Return Portfolio rate of return ( )( ) fraction of portfolio rate of return = in first asset on first asset ( )( ) fraction of portfolio rate of return + in second asset on second asset
Portfolio Risk Portfolio standard deviation 0 Unique risk Market risk 5 0 5 Number of Securities
3 Portfolio Risk The variance of a two stock portfolio is the sum of these four boes Stock Stock Stock = ρ Stock = ρ
4 Portfolio Risk Eample Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The epected dollar return on your CC is 0% 65% = 6.5% and on Reebok it is 0% 35% = 7.0%. The epected return on your portfolio is 6.5 + 7.0 = 3.50%. Assume a correlation coefficient of. Coca - Cola Reebok ρ Coca - Cola = (.65) 3.5 58.5 (3.5) =.65.35 ρ Reebok =.65.35 3.5 58.5 = (.35) (58.5)
5 Portfolio Risk Eample Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The epected dollar return on your CC is 0% 65% = 6.5% and on Reebok it is 0% 35% = 7.0%. The epected return on your portfolio is 6.5 + 7.0 = 3.50%. Assume a correlation coefficient of. Portfolio Variance = [(.65) + [(.35) (3.5) (58.5) + (.65.353.558.5) ] ] =,676.9 Standard Deviation =,676.9 = 4.0 %
6 Portfolio Risk Eample Suppose you invest 65% of your portfolio in Coca-Cola and 35% in Reebok. The epected dollar return on your CC is 0% 65% = 6.5% and on Reebok it is 0% 35% = 7.0%. The epected return on your portfolio is 6.5 + 7.0 = 3.50%. Assume a correlation coefficient of 0.. Portfolio Variance = [(.65) + [(.35) (3.5) (58.5) + (.65.350.3.558.5) ] ] =,006. Standard Deviation =,006. = 3.7 %
7 Portfolio Risk Epected Portfolio Return = ( r ) + ( r ) Portfolio Variance = + + ( ρ )
8 Portfolio Risk Eample Correlation Coefficient =.4 Stocks % of Portfolio Avg Return ABC Corp 8 60% 5% Big Corp 4 40% % Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 8. Return = weighted avg = Portfolio = 7.4% Let s add stock New Corp to the portfolio
9 Portfolio Risk Eample Correlation Coefficient =.3 Stocks % of Portfolio Avg Return Portfolio 8. 50% 7.4% New Corp 30 50% 9% NEW Standard Deviation = weighted avg = 3.80 NEW Standard Deviation = Portfolio = 3.43 NEW Return = weighted avg = Portfolio = 8.0% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION
0 Portfolio Risk The shaded boes contain variance terms; the remainder contain covariance terms. STOCK 3 4 5 6 To calculate portfolio variance add up the boes N 3 4 5 6 N STOCK
Beta and Unique Risk. Total risk = diversifiable risk + market risk. Market risk is measured by beta, the sensitivity to market changes Epected stock return +0% -0% beta - 0% + 0% -0% Epected market return
Beta and Unique Risk Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market inde, 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.
3 Beta and Unique Risk β = i im m Covariance with the market Variance of the market