Principles of Corporate Finance Chapter 7 Introduction to Risk & Return Tenth Edition Slides by Matthew Will McGraw Hill/Irwin Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved 8- 2 Topics Covered Over a Century of Capital Market History Measuring Portfolio Risk Calculating Portfolio Risk How Individual Securities Affect Portfolio Risk Diversification & Value Additivity McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 3 The Value of an Investment of $1 in 1900 $100,000 Common Stock $10,000 21,536 US Govt Bonds Dollars T-Bills $1,000 176 66 $100 $10 2007 19 00 19 10 19 20 19 30 19 40 19 50 19 60 19 70 19 80 19 90 20 00 $1 Start of Year McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 4 The Value of an Investment of $1 in 1900 Real Returns $1,000 914 Equities Bonds Bills Dollars $100 $10 7.48 2.82 2007 19 00 19 10 19 20 19 30 19 40 19 50 19 60 19 70 19 80 19 90 20 00 $1 Start of Year McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 5 Equity Market Risk (by country) 40 35 30 25 20 15 McGraw Hill/Irwin Germany (ex 1922/3) Italy Japan Norway France Average Belgium Sweden S Africa Netherlands Spain Ireland UK 23.58 23.64 23.8 24.93 21.51 21.64 22.28 22.71 22.71 23.35 Denmark USA Switzerland 18.93 19.79 16.64 17.88 Australia 10 5 0 33.66 34.17 27.91 29.24 Canada Standard Deviation of Annual Returns, % Average Risk (1900-2006) Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 6 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. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 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.” McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 8 Portfolio standard deviation Measuring Risk Unique risk Market risk 0 5 10 15 Number of Securities McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 9 Portfolio Risk Example Suppose you invest 60% of your portfolio in WalMart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The expected return on your portfolio is: Expected Return (.60 10) (.40 15) 12% McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 10 Portfolio Risk Example Suppose you invest 60% of your portfolio in Wal-Mart and 40% in IBM. The expected dollar return on your Wal-Mart stock is 10% and on IBM is 15%. The standard deviation of their annualized daily returns are 19.8% and 29.7%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. Portfolio Variance [(.60) 2 x(19.8) 2 ] [(.40) 2 x(29.7) 2 ] 2(.40x.60x 19.8x29.7) 564.5 Standard Deviation 564.5 23.8 % McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 11 Portfolio Risk Expected Portfolio Return (x 1 r1 ) ( x 2 r2 ) Portfolio Variance x12σ 12 x 22σ 22 2( x1x 2ρ 12σ 1σ 2 ) McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 12 Portfolio Risk Example Stocks ABC Corp Big Corp s 28 42 Correlation Coefficient = .4 % of Portfolio Avg Return 60% 15% 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Real Standard Deviation: = (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4) = 28.1 CORRECT Return : r = (15%)(.60) + (21%)(.4) = 17.4% McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 13 Portfolio Risk Example Stocks ABC Corp Big Corp s 28 42 Correlation Coefficient = .4 % of Portfolio Avg Return 60% 15% 40% 21% Standard Deviation = weighted avg = 33.6 Standard Deviation = Portfolio = 28.1 Return = weighted avg = Portfolio = 17.4% Let’s Add stock New Corp to the portfolio McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 14 Portfolio Risk Example Stocks Portfolio New Corp Correlation Coefficient = .3 s % of Portfolio 28.1 50% 30 50% Avg Return 17.4% 19% NEW Standard Deviation = weighted avg = 31.80 NEW Standard Deviation = Portfolio = 23.43 NEW Return = weighted avg = Portfolio = 18.20% NOTE: Higher return & Lower risk How did we do that? DIVERSIFICATION McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 15 Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes Expected stock return beta +10% -10% - 10% +10% -10% Copyright 1996 by The McGraw-Hill Companies, Inc McGraw Hill/Irwin Expected market return Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved 8- 16 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. McGraw Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved