Chapter 13 Return, Risk, and the Security Market Line Copyright © 2012 by McGraw-Hill Education. All rights reserved. Key Concepts and Skills • • • • • • Know how to calculate expected returns Understand the impact of diversification Understand the systematic risk principle Understand the security market line Understand the risk-return trade-off Be able to use the Capital Asset Pricing Model 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 • “ The return on a risky asset expected in the future.” • Risk premium is defined as “ the difference between the return on a risky investment and that on a risk-free investment.” • Risk premium = Expected return – Risk free rate Expected Returns • Example: If the risk free investments are currently offering 8%. Stock Z offers rate of return 20%. What is stock Z risk premium? • Risk premium = 20% - 8% = 12% 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 13-6 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 Boom Normal Recession Probability 0.3 0.5 ??? C 15% 10 2 T 25% 20 1 • RC = .3(15) + .5(10) + .2(2) = 9.9% • RT = .3(25) + .5(20) + .2(1) = 17.7% 13-7 Variance and Standard Deviation • Variance and standard deviation measure the volatility of returns • Using unequal probabilities for the entire range of possibilities • Weighted average of squared deviations n σ pi ( Ri E ( R )) 2 2 i 1 13-8 Example: Variance and Standard Deviation • Consider the previous example. What are the variance and standard deviation for each stock? • Stock C – 2 = .3(15 - 9.9)2 + .5(10 - 9.9)2 + .2(2 - 9.9)2 = 20.29 – = 4.50% • Stock T – 2 = .3(25 - 17.7)2 + .5(20 - 17.7)2 + .2(1 - 17.7)2 = 74.41 – = 8.63% 13-9 Another Example • Consider the following information: State Boom Normal Slowdown Recession Probability .25 .50 .15 .10 ABC, Inc. (%) 15 8 4 -3 • What is the expected return? • What is the variance? • What is the standard deviation? 13-10 Solution 1) The expected return = (0.25×15) + (0.5×8) + (0.15×4) + (0.1×-3) = 8.05 2) The variance = 0.25(15-8.05)2 + 0.5(8-8.05)2 + 0.15(4-8.05)2 + 0.1(-3-8.05)2 = 26.75 3) The standard deviation = 5.17 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 • The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets 13-12 Portfolio Weights • Portfolio Weight: “The percentage of a portfolio’s total value that is in a particular asset.” • Notice that: the weights have to add up to 1 because all our money is invested in it. Example: Portfolio Weights • Suppose you have $15,000 to invest and you have purchased securities in the following amounts. What are your portfolio weights in each security? – – – – $2000 of DCLK $3000 of KO $4000 of INTC $6000 of KEI •DCLK: 2/15 = .133 •KO: 3/15 = .2 •INTC: 4/15 = .267 •KEI: 6/15 = .4 13-14 Portfolio Expected Returns • The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio m E ( RP ) w j E ( R j ) j 1 • You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities 13-15 Example: Expected Portfolio Returns • Consider the portfolio weights computed previously. If the individual stocks have the following expected returns, what is the expected return for the portfolio? – – – – DCLK: 19.69% KO: 5.25% INTC: 16.65% KEI: 18.24% • E(RP) = .133(19.69) + .2(5.25) + .267(16.65) + .4(18.24) = 15.41% 13-16 Portfolio Weights • N.B.: This says that the expected return on a portfolio is a straightforward combination of the expected returns on the assets in that portfolio. Portfolio Variance • Compute the portfolio return for each state: RP = w1R1 + w2R2 + … + wmRm • Compute the expected portfolio return using the same formula as for an individual asset • Compute the portfolio variance and standard deviation using the same formulas as for an individual asset 13-18 Example 13.3 & 13.4 • Suppose we have the following projections for three stocks: State of the economy Probability of the state of economy Returns if state occurs on stock A Returns if state occurs on stock B Returns if state occurs on stock C Boom 0.4 10% 15% 20% Bust 0.6 8 4 0 Example 13.3 & 13.4 • What would be the expected return if half of the portfolio were in A, with the remainder equally divided between B and C? • What are the standard deviation of the portfolio? Example 13.3 & 13.4 • First calculate the expected returns on the individual stocks as follows: • E(RA) = (0.4×10) + (0.6×8) = 8.8% • E(RB) = (0.4×15) + (0.6×4) = 8.4% • E(RC) = (0.4×20) + (0.6×0) = 8.0% Then, • E(RP) = (0.5×8.8) + (0.25×8.4) + (0.25×8) = 8.5% Example 13.3 & 13.4 • First, calculate the portfolio returns in the two states. (1) The portfolio return when the economy booms is calculated as: • E(RP) = (0.5×10) + (0.25×15) + (0.25×20) = 13.75% Example 13.3 & 13.4 (2) The portfolio return when the economy busts is calculated as: • E(RP) = (0.5×8) + (0.25×4) + (0.25×0) = 5% • E(RP) = (0.4×13.75) + (0.6×5) = 8.5% Example 13.3 & 13.4 • The variance is: σ2P = 0.4 × (0.1375 – 0.085)2 + 0.6 × (0.05 – 0.085) 2 = 0.0018375 • The standard deviation is: σ = 4.3% End of Chapter 13-25