Chapter 5 The Trade-off between Risk and Return

Chapter 5: The Trade-off between Risk and Return Corporate Finance, 3 e Graham, Smart, and Megginson © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Introduction to Risk and Return Valuing risky assets: A task fundamental to financial management Three-step procedure for valuing a risky asset 1. Determine the asset’s expected cash flows. 2. Choose discount rate that reflects asset’s risk. 3. Calculate present value (PV cash inflows PV outflows). This three-step procedure is called discounted cash flow (DCF) analysis. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Risk and Return The return earned on investments represents the marginal benefit of investing. Risk represents the marginal cost of investing. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Three Basic Steps for Valuing a Risky Asset 1. Determine the asset’s expected cash flows. 2. Choose a discount rate that reflect’s the asset’s risk. 3. Calculate the present value. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Historical Return and Risk Decisions must be based on expected return and risk. One simple way to estimate expected return and risk… Assume that expected return and risk going forward will be similar to past values. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. 5

Equity Risk Premium q The difference in equity returns and returns on safe investments q Implies that stocks are riskier than bonds or bills q Volatility of stocks relative to bonds or bills depends on the time horizon over which investment returns are measured q Trade-off always arises between risk and expected return © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Risk Aversion Risk Neutral • Investors seek the highest return without regard to risk. Risk Seeking • Investors have a taste for risk and will take risk even if they cannot expect a reward for doing so. Risk Averse • Investors do not like risk and must be compensated for taking it. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Return on a Single Asset Return - The total gain or loss experienced on an investment over a given period of time © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Arithmetic Versus Geometric Returns • Arithmetic average return: The simple average of annual returns (R 1 + R 2 + R 3 + … + Rt) / t Best estimate of expected return over a single year • Geometric average return: The compound annual return to an investor who bought and held a stock t years [(1+R 1)(1+R 2)(1+R 3)…. (1+Rt)]1/t – 1 © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Arithmetic Versus Geometric Returns An example. . Year Return 2007 -10% 2008 +13% 2009 +17% 2010 + 8% AAR = 7. 00% GAR = 6. 47% © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Probability Distribution q. A probability distribution tells us what outcomes are possible and how likely each outcome is. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Risk of a Single Asset How Do We Measure Risk? A reasonable way to define risk is to focus on the dispersion of returns. • Most common measure is the variance, or its square root, the standard deviation. • Variance equals the expected value of squared deviations from the mean. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Risk of a Single Asset Example: Year Return 2007 -10% 2008 +13% 2009 +17% 2010 +8% Average annual return = 7% © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Expected Return for a Portfolio q Most investors hold multiple-asset portfolios. q Key insight of portfolio theory: Asset return adds linearly, but risk is almost always reduced in a portfolio. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. 14

The Importance of Covariance q Risk reduction is achieved in portfolios because fluctuations in one asset partially off set fluctuations in the other q Risk of a portfolio depends crucially on whether the returns on the portfolio’s components move together or in opposite directions q Covariance: statistical measurement of the comovements of two random variables © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part. 15

Two-Asset Portfolio Standard Deviation Correlation between stocks influences portfolio volatility. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Portfolios of More Than Two Assets q Five-Asset Portfolio Expected return of portfolio is still the average of expected returns of the two stocks. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Portfolio Risk q Variance cannot fall below the average covariance of securities in the portfolio. q Undiversifiable risk (systematic risk, market risk) q Diversifiable risk (unsystematic risk, idiosyncratic risk, or unique risk) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

What is a stock’s beta? Beta is a measure of systematic risk. What if Beta = 1? • What if Beta > 1 or Beta < 1? • • • The stock moves 1% on average when the market moves 1%. An “average” level of risk The stock moves more than 1% on average when the market moves 1%. (Beta > 1) The stock moves less than 1% on average when the market moves 1%. (Beta < 1) © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

Diversifiable and Non-Diversifiable Risk q As number of assets increases, diversification reduces the importance of a stock’s own variance an asset’s covariance with all other assets contributes measurably to overall portfolio return variance. q Only © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

How risky is an individual asset? One Approach: Asset’s Variance or Standard Deviation but… What really matters is systematic risk… how an asset covaries with everything else. Use asset’s beta. © 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.