Chapter 7. Introduction to Risk, Return, and the Opportunity Cost of Capital. Principles of Corporate Finance. Slides by Matthew Will
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1 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
2 - Topics Covered 75 Years of Capital Market History Measuring Risk Portfolio Risk Beta and Unique Risk Diversification
3 - 3 The Value of an Investment of $ in Small Cap Inde Corp Bonds 0 T Bill S&P Long Bond 6.6 0, Source: Ibbotson Associates Year End
4 - 4 The Value of an Investment of $ in 96 Real returns 000 Small Cap S&P Inde 0 Corp Bonds Long Bond T Bill , Source: Ibbotson Associates Year End
5 - 5 Rates of Return Percentage Return Common Stocks Long T-Bonds T-Bills Source: Ibbotson Associates Year
6 - 6 Average Market Risk Premia ( ) Risk premium, % Den Bel Can Swi Spa UK Ire Neth USA Swe 8 Aus 8.5 Ger Fra Jap It Country
7 - 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 - 8 Measuring Risk Coin Toss Game-calculating variance and standard deviation () () (3) Percent Rate of Return Deviation from Mean Squared Deviation Variance = average of squared deviations = 800 / 4 = 450 Standard deviation = square of root variance = 450 =.%
9 Measuring Risk # of Years Histogram of Annual Stock Market Returns Return % to to to -0-0 to -0-0 to 0 0 to 0 0 to 0 0 to to to to 60
10 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.
11 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
12 Portfolio Risk Portfolio standard deviation 0 Unique risk Market risk Number of Securities
13 3 Portfolio Risk The variance of a two stock portfolio is the sum of these four boes Stock Stock Stock = ρ Stock = ρ
14 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 = 3.50%. Assume a correlation coefficient of. Coca - Cola Reebok ρ Coca - Cola = (.65) (3.5) = ρ Reebok = = (.35) (58.5)
15 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 = 3.50%. Assume a correlation coefficient of. Portfolio Variance = [(.65) + [(.35) (3.5) (58.5) + ( ) ] ] =,676.9 Standard Deviation =,676.9 = 4.0 %
16 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 = 3.50%. Assume a correlation coefficient of 0.. Portfolio Variance = [(.65) + [(.35) (3.5) (58.5) + ( ) ] ] =,006. Standard Deviation =,006. = 3.7 %
17 7 Portfolio Risk Epected Portfolio Return = ( r ) + ( r ) Portfolio Variance = + + ( ρ )
18 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
19 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
20 0 Portfolio Risk The shaded boes contain variance terms; the remainder contain covariance terms. STOCK To calculate portfolio variance add up the boes N N STOCK
21 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
22 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.
23 3 Beta and Unique Risk β = i im m Covariance with the market Variance of the market
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