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13-1 Return, Risk, and the Security Market Line Chapter 13 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

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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

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13-3 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

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13-4 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

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13-5 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. 1. What is the probability of “Recession”? StateProbabilityCT Boom0.31525 Normal0.51020 Recession??? 2 1 Probabilities add up to 100% (or 1.0) thus 1.0 – 0.3 – 0.5 = 0.2 or 20%

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13-6 Example: Expected Returns Suppose you have predicted the following returns for stocks C and T in three possible states of the economy. 2. What are the expected returns? StateProbabilityCT Boom0.31525 Normal0.51020 Recession0.2 2 1 R C =.3(15) +.5(10) +.2(2) = 9.9% R T =.3(25) +.5(20) +.2(1) = 17.7%

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13-7 Example: Expected Returns The three states of the economy still apply to stocks C and T. 3. If the risk-free rate (from chapter 12) is 4.15%, what is the risk premium for C & T? R C =.3(15) +.5(10) +.2(2) = 9.9% R T =.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%

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13-8 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

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13-9 Example: Variance and Standard Deviation StateProbabilityCT Boom0.31525 Normal0.51020 Recession0.2 2 1 Expected return 9.9%17.7% Considering the previous example of stocks C and T:

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13-10 Example: Variance and Standard Deviation StateProbabilityCT Boom0.31525 Normal0.51020 Recession0.2 2 1 Expected return 9.9%17.7% 1. What is the variance and standard deviation for C? Stock C 2 =.3(15-9.9) 2 +.5(10-9.9) 2 +.2(2-9.9) 2 = 20.29 = 4.50%

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13-11 Example: Variance and Standard Deviation StateProbabilityCT Boom0.31525 Normal0.51020 Recession0.2 2 1 Expected return 9.9%17.7% 2. What is the variance and standard deviation for T? Stock T 2 =.3(25-17.7) 2 +.5(20-17.7) 2 +.2(1-17.7) 2 = 74.41 = 8.63%

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13-12 Another Example Consider the following information: StateProbabilityABC, Inc. (%) Boom.2515 Normal.50 8 Slowdown.15 4 Recession.10- 3 1. What is the expected return? E(R) =.25(15) +.5(8) +.15(4) +.1(-3) = 8.05%

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13-13 Another Example Consider the following information: StateProbabilityABC, Inc. (%) Boom.2515 Normal.50 8 Slowdown.15 4 Recession.10- 3 2. What is the variance? Variance = σ 2 =.25(15-8.05) 2 +.5(8-8.05) 2 +.15(4-8.05) 2 +.1(-3-8.05) 2 = 26.7475

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13-14 Another Example Consider the following information: StateProbabilityABC, Inc. (%) Boom.2515 Normal.50 8 Slowdown.15 4 Recession.10- 3 3. What is the standard deviation? Standard Deviation = σ = √ 26.7475 = 5.17%

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13-15 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

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13-16 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

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13-17 Portfolios The risk/return trade-off for a portfolio is measured by the portfolio’s expected return and standard deviation, just as with individual assets Risk Return

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13-18 Example: Portfolio Weights Suppose you have $15,000 to invest and you have purchased securities in the following amounts: $2000 of DCLK $3000 of KO $4000 of INTC $6000 of KEI

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13-19 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 DCLK: 2/15 =.133 KO:3/15 =.200 INTC:4/15 =.267 KEI:6/15 =.400 15/15 = 1.000

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13-20 Portfolio Expected Returns The expected return of a portfolio is the weighted average of the expected returns of the respective assets in the portfolio 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

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13-21 Example: Expected Portfolio Returns Consider the portfolio weights computed previously. The individual stocks have the following expected returns: DCLK:19.69% KO: 5.25% INTC:16.65% KEI: 18.24%

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13-22 Example: Expected Portfolio Returns 1. What is the expected return on this portfolio? ReturnWeight DCLK:19.69%.133 KO: 5.25%.200 INTC:16.65%.267 KEI: 18.24%.400 E(R P ) =.133(19.69) +.2(5.25) +.267(16.65) +.4(18.24) = 15.41%

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13-23 Portfolio Variance Compute the expected portfolio return, the variance, and the standard deviation using the same formula as for an individual asset Compute the portfolio return for each state: R P = w 1 R 1 + w 2 R 2 + … + w m R m

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13-24 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25%

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13-25 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 1. What is the expected return for asset A? Asset A: E(R A ) =.4(30) +.6(-10) = 6%

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13-26 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 2. What is the variance for asset A? Variance(A) =.4(30-6) 2 +.6(-10-6) 2 = 384

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13-27 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 3. What is the standard deviation for asset A? Std. Dev.(A) = 19.6%

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13-28 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 4. What is the expected return for asset B? E(R B ) =.4(-5) +.6(25) = 13%

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13-29 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 5. What is the variance for asset B? Variance(B) =.4(-5-13) 2 +.6(25-13) 2 = 216

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13-30 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 6. What is the standard deviation for asset B? Std. Dev.(B) = 14.7%

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13-31 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 7. If you invest 50% of your money in Asset A, what is the expected return for the portfolio in each state of the economy? 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%

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13-32 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 8. If you invest 50% of your money in Asset A, what is the expected return for the portfolio in a boom period? Portfolio return in boom =.5(30) +.5(-5) = 12.5%

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13-33 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 9. What is the expected return for the portfolio as a whole (considering both states of the economy)? Exp. portfolio return =.4(12.5) +.6(7.5) = 9.5% Or Exp. portfolio return =.5(6) +.5(13) = 9.5%

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13-34 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-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

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13-35 Example: Portfolio Variance Consider the following information: StateProbabilityA B Boom.430%-5% Bust.6-10%25% 11. What is the standard deviation of the portfolio? Standard deviation = 2.45%

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13-36 Another Example Consider the following information: State ProbabilityXZ Boom.2515%10% Normal.6010%9% Recession.155%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?

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13-37 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

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13-38 Expected vs. Unexpected Returns Realized returns are generally not equal to expected returns There is the expected component and the unexpected component At any point in time, the unexpected return can be either positive or negative Over time, the average of the unexpected component is zero

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13-39 Announcements and News Announcements and news contain both an expected component and a surprise component It is the surprise component that affects a stock’s price and therefore its return

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13-40 Announcements and News This surprise is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated

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13-41 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

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13-42 Efficient Markets Efficient markets are a result of investors trading on the unexpected portion of announcements The easier it is to trade on surprises, the more efficient markets should be Efficient markets involve random price changes because we cannot predict surprises

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13-43 Systematic Risk Risk factors that affect a large number of assets Also known as non- diversifiable risk or market risk Includes such things as changes in GDP, inflation, interest rates, etc.

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13-44 Unsystematic Risk Risk factors that affect a limited number of assets Also known as unique risk and asset-specific risk Includes such things as labor strikes, part shortages, etc.

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13-45 Computing Returns Total Return = expected return + unexpected return Unexpected return = systematic portion + unsystematic portion Therefore, total return can be expressed as follows: Total Return = expected return + systematic portion + unsystematic portion

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13-46 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

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13-47 Diversification Portfolio diversification is the investment in several different asset classes or sectors Diversification is not just holding a lot of assets

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13-48 Diversification For example, if you own 5 airline stocks, you are not diversified However, if you own 50 stocks that span 20 different industries, then you are diversified

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13-49 Total Risk Total risk = systematic risk + unsystematic risk The standard deviation of returns is a measure of total risk For well-diversified portfolios, unsystematic risk is very small Consequently, the total risk for a diversified portfolio is essentially equivalent to just the systematic risk

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13-51 The Principle of Diversification Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns This reduction in risk arises because worse-than- expected returns from one asset are offset by better- than-expected returns from another However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion

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13-52 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

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13-53 Measuring Systematic Risk How do we measure systematic risk? We use the beta coefficient What does beta tell us? A beta of 1 implies the asset has the same systematic risk as the overall market A beta < 1 implies the asset has less systematic risk than the overall market A beta > 1 implies the asset has more systematic risk than the overall market

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13-54 Actual Company Betas

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13-55 Work the Web Example Many sites provide betas for companies Yahoo Finance provides beta, plus a lot of other information under its Key Statistics link Click on the web surfer to go to Yahoo Finance Enter a ticker symbol and get a basic quote Click on Key Statistics

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13-56 Total vs. Systematic Risk Consider the following information: Standard DeviationBeta Security C20%1.25 Security K30%0.95 1. Which security has more total risk? K because the standard deviation is greater than C 2. Which security has more systematic risk? C because the beta is larger than K

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13-57 Total vs. Systematic Risk Consider the following information: Standard DeviationBeta Security C20%1.25 Security K30%0.95 3. Which security should have the higher expected return? C because beta measures risk and it’s expected return

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13-58 Example: Portfolio Betas Consider the previous example with the following four securities: SecurityWeightBeta DCLK.1332.685 KO.20.195 INTC.2672.161 KEI.42.434 What is the portfolio beta?.133(2.685) +.2(.195) +.267(2.161) +.4(2.434) = 1.947

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13-59 Beta and the Risk Premium Remember that the risk premium = expected return – risk-free rate The higher the beta, the greater the risk premium should be Can we define the relationship between the risk premium and beta so that we can estimate the expected return? YES!

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13-60 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

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13-61 Example: Portfolio Expected Returns and Betas: The SML RfRf AA E(R A )

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13-62 Security Market Line The security market line (SML) is the representation of market equilibrium The slope of the SML is the reward-to-risk ratio: (E(R M ) – R f ) / M But since the beta for the market is ALWAYS equal to one, the slope can be rewritten: Slope = E(R M ) – R f = market risk premium

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13-63 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(R A ) – R f ) / ( A – 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 8 (implying that the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (implying that the asset plots below the line)?

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13-64 Market Equilibrium In equilibrium, all assets and portfolios must have the same reward-to-risk ratio, and they all must equal the reward-to- risk ratio for the market

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13-65 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

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13-66 The Capital Asset Pricing Model (CAPM) The capital asset pricing model defines the relationship between risk and return: E(R A ) = R f + A (E(R M ) – R f ) 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

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13-67 Example - CAPM Security BetaExpected Return DCLK2.685 4.15 + 2.685(8.5) = 26.97% KO0.1954.15 + 0.195(8.5) = 5.81% INTC2.161 4.15 + 2.161(8.5) = 22.52% KEI2.434 4.15 + 2.434(8.5) = 24.84% 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?

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13-68 The CAPM

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13-69 Quick Quiz How do 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%. What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset?

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13-70 Comprehensive Problem 1.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? 2.What is the reward/risk ratio? 3.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?

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13-71 Terminology Portfolio Expected Return Unsystematic Risk Systematic Risk Security Market Line (SML) Beta Capital Asset Pricing Model (CAPM)

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13-72 Formulas Expected return on an investment Variance of an entire population, not a sample Expected return on a portfolio

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13-73 Formulas Slope = E(R M ) – R f = market risk premium CAPM = E(R A ) = R f + A (E(R M ) – R f )

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13-74 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

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13-75 1.Measuring portfolio returns 2. Using Std. Dev. and Variance to measure portfolio risk 3. Diversification can significantly reduce unsystematic risk 4. Beta measures systematic risk What are the most important topics of this chapter?

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13-76 5. The slope of the Security Market Line = the market risk premium 6. The Capital Asset Pricing Model (CAPM) provides us a measurement of a stock’s required rate of return. What are the most important topics of this chapter?

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