Introduction to Risk, Return, and The Opportunity Cost of Capital Principles of Corporate Finance Eighth Edition Chapter 7 Introduction to Risk, Return, and The Opportunity Cost of Capital Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved

Topics Covered Over a Century of Capital Market History Measuring Portfolio Risk Calculating Portfolio Risk Beta and Unique Risk Diversification & Value Additivity

The Value of an Investment of $1 in 1900 13

The Value of an Investment of $1 in 1900 Real Returns 13

Average Market Risk Premia (by country) Risk premium, % Country

Stock Market Index Returns Rates of Return 1900-2003 Stock Market Index Returns Percentage Return Year Source: Ibbotson Associates 14

Measuring Risk Histogram of Annual Stock Market Returns # of Years

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.

Measuring Risk Coin Toss Game-calculating variance and standard deviation

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.” 18

Measuring Risk 19

Measuring Risk 20

Measuring Risk 21

Portfolio Risk The variance of a two stock portfolio is the sum of these four boxes 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is: 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

Portfolio Risk Example Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

Portfolio Risk In real life, the correlation coefficient is 0.4 Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 0.4 and calculate the portfolio variance. 19

Portfolio Risk 19

Portfolio Risk To calculate portfolio variance add up the boxes The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N To calculate portfolio variance add up the boxes STOCK STOCK

Copyright 1996 by The McGraw-Hill Companies, Inc Beta and Unique Risk 1. Total risk = diversifiable risk + market risk 2. Market risk is measured by beta, the sensitivity to market changes beta Expected return market 10% - + +10% stock Copyright 1996 by The McGraw-Hill Companies, Inc -10%

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.

Beta and Unique Risk

Beta and Unique Risk Covariance with the market Variance of the market

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