Chapter 13 Return, Risk, and the Security Market Line 13-1 McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc All rights reserved Chapter Outline • Expected Returns and Variances • Portfolios • Announcements, Surprises, and Expected Returns • Risk: Systematic and Unsystematic • Diversification and Portfolio Risk • Systematic Risk and Beta • The Security Market Line • The SML and the Cost of Capital: A Preview 13-2 Chapter Outline • Expected Returns and Variances • Portfolios • Announcements, Surprises, and Expected Returns • Risk: Systematic and Unsystematic • Diversification and Portfolio Risk • Systematic Risk and Beta • The Security Market Line • The SML and the Cost of Capital: A Preview 13-3 Expected Returns • Expected returns are based on the probabilities of possible outcomes • In this context, “expected” means average if the process is repeated many times • The “expected” return does not even have to be a possible return n E ( R ) = ∑ pi Ri i =1 13-4 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy What is the probability of “Recession”? State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession ??? 13-5 Probabilities add up to 100% (or 1.0) thus 1.0 – 0.3 – 0.5 =0.2 or 20% Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy What are the expected returns? State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession 0.2 RC =.3(15) +.5(10) +.2(2) =9.9% RT =.3(25) +.5(20) +.2(1) =17.7% 13-6 Example: Expected Returns The three states of the economy still apply to stocks C and T If the risk-free rate (from chapter 12) is 4.15%, what is the risk premium for C & T? RC =.3(15) +.5(10) +.2(2) =9.9% RT =.3(25) +.5(20) +.2(1) =17.7% Stock C’s risk premium: 9.9 - 4.15 =5.75% Stock T’s risk premium: 17.7 - 4.15 =13.55% 13-7 Variance and Standard Deviation • Variance and standard deviation measure the volatility of returns • Using unequal probabilities for the entire range of possible outcomes • Weighted average of squared deviations n σ = ∑ pi ( Ri − E ( R)) 13-8 i =1 Example: Variance and Standard Deviation Considering the previous example of stocks C and T: State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession 0.2 Expected return 9.9% 13-9 17.7% Example: Variance and Standard Deviation What is the variance and standard deviation for C? 13-10 State Probability C T Boom 0.3 15 25 Normal 0.5 10 20 Recession 0.2 Expected return 9.9% 17.7% Stock C σ2 = 3(15-9.9)2 + 5(10-9.9)2 + 2(2-9.9)2 = 20.29 σ = 4.50% Reward-to-Risk Ratio: Definition and Example • The reward-to-risk ratio is the slope of the line illustrated in the previous example • Slope = (E(RA) – Rf) / (βA – 0) • Reward-to-risk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5 • What if an asset has a reward-to-risk ratio of (implying that the asset plots above the line)? • What if an asset has a reward-to-risk ratio of (implying that the asset plots below the line)? 13-63 Market Equilibrium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-torisk ratio for the market E ( RA ) − R f βA 13-64 = E ( RM − R f ) βM Chapter Outline • Expected Returns and Variances • Portfolios • Announcements, Surprises, and Expected Returns • Risk: Systematic and Unsystematic • Diversification and Portfolio Risk • Systematic Risk and Beta • The Security Market Line • The SML and the Cost of Capital: A Preview 13-65 The Capital Asset Pricing Model (CAPM) The capital asset pricing model defines the relationship between risk and return: E(RA) = Rf + βA(E(RM) – Rf) If we know an asset’s systematic risk, we can use the CAPM to determine its expected return This is true whether we are talking about financial assets or physical assets 13-66 Example - CAPM Consider the betas for each of the assets given earlier If the risk-free rate is 4.15% and the market risk premium is 8.5%, What is the expected return for each? Security 13-67 Beta Expected Return DCLK 2.685 4.15 + 2.685(8.5) = 26.97% KO 0.195 4.15 + 0.195(8.5) = 5.81% INTC 2.161 4.15 + 2.161(8.5) = 22.52% KEI 2.434 4.15 + 2.434(8.5) = 24.84% The CAPM 13-68 Quick Quiz How you compute the expected return and standard deviation for an individual asset? For a portfolio? What is the difference between systematic and unsystematic risk? What type of risk is relevant for determining the expected return? Consider an asset with a beta of 1.2, a risk-free rate of 5%, and a market return of 13% 13-69 What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset? Comprehensive Problem The risk free rate is 4%, and the required return on the market is 12% What is the required return on an asset with a beta of 1.5? What is the reward/risk ratio? What is the required return on a portfolio consisting of 40% of the asset above and the rest in an asset with an average amount of systematic risk? 13-70 Terminology • Portfolio • Expected Return • Unsystematic Risk • Systematic Risk • Security Market Line (SML) • Beta • Capital Asset Pricing Model (CAPM) 13-71 Formulas n E ( R ) = ∑ pi Ri Expected return on an i =1 n σ = ∑ pi ( Ri − E ( R)) i =1 m investment Variance of an entire population, not a sample E ( RP ) = ∑ w j E ( R j ) j =1 13-72 Expected return on a portfolio Formulas E ( RA ) − R f βA = E ( RM − R f ) βM Slope = E(RM) – Rf = market risk premium CAPM = E(RA) = Rf + βA(E(RM) – Rf) 13-73 Key Concepts and Skills •Calculate expected returns •Describe the impact of diversification •Define the systematic risk principle •Construct the security market line •Evaluate the risk-return trade-off •Compute the cost of equity using the Capital Asset Pricing Model 13-74 What are the most important topics of this chapter? Measuring portfolio returns Using Std Dev and Variance to measure portfolio risk Diversification can significantly reduce unsystematic risk Beta measures systematic risk 13-75 What are the most important topics of this chapter? The slope of the Security Market Line = the market risk premium The Capital Asset Pricing Model (CAPM) provides us a measurement of a stock’s required rate of return 13-76 Questions? 13-77 [...]... $2000 of DCLK $3000 of KO $4000 of INTC $6000 of KEI 13-18 Example: Portfolio Weights What are your portfolio weights in each security? $2,000 of DCLK $3,000 of KO $4,000 of INTC $6,000 of KEI $15,000 13-19 DCLK: 2/15 = 133 KO: 3/15 = 200 INTC: 4/15 = 267 KEI: 6/15 = 400 15/15 = 1.000 Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns of the... Portfolio Risk • Systematic Risk and Beta • The Security Market Line • The SML and the Cost of Capital: A Preview 13-15 Portfolios • A portfolio is a collection of assets • An asset’s risk and return are important in how they affect the risk and return of the portfolio 13-16 Portfolios •The risk/return tradeoff for a portfolio is measured by the portfolio’s expected return and standard deviation, just... invest 50% of your money in Asset A, what is the expected return for the portfolio in each state of the economy? 13-31 If 50% of the investment is in Asset A, then 50% (100% - 50%) must be invested in Asset B as the total asset allocation must be 100% Example: Portfolio Variance Consider the following information: State Probability A B Boom 4 30% -5% Bust 6 -10% 25% 8 If you invest 50% of your money... return for the portfolio as a whole (considering both states of the economy)? 13-33 Exp portfolio return = 4(12.5) + 6(7.5) = 9.5% Or Exp portfolio return = 5(6) + 5(13) = 9.5% Example: Portfolio Variance Consider the following information: State Probability A B Boom 4 30% -5% Bust 6 -10% 25% 10 What is the variance of the portfolio? Variance of portfolio = 4(12.5-9.5)2 + 6(7.5-9.5)2 =6 13-34 Example:... A B Boom 4 30% -5% Bust 6 -10% 25% 11 What is the standard deviation of the portfolio? Standard deviation = 2.45% 13-35 Another Example Consider the following information: State Probability Boom 25 15% Normal 60 10% Recession 15 5% X Z 10% 9% 10% What are the expected return and standard deviation for a portfolio with an investment of $6,000 in asset X and $4,000 in asset Z? 13-36 ... $2000 of DCLK $3000 of KO $4000 of INTC $6000 of KEI 13-18 Example: Portfolio Weights What are your portfolio weights in each security? $2,000 of DCLK $3,000 of KO $4,000 of INTC $6,000 of KEI... SML and the Cost of Capital: A Preview 13-15 Portfolios • A portfolio is a collection of assets • An asset’s risk and return are important in how they affect the risk and return of the portfolio... and standard deviation measure the volatility of returns • Using unequal probabilities for the entire range of possible outcomes • Weighted average of squared deviations n σ = ∑ pi ( Ri − E ( R))