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Chapter 11 introduces you to risk and return. After completing this unit, you should be able to: 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.
Risk and Return Chapter 11 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 ã Understand the risk-return trade-off Copyrightê2007McGrawưHillAustraliaPtyLtd 112 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 Copyright ª 2007 McGrawHill Australia Pty Ltd 113 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 E ( R) n pi Ri i Copyright ª 2007 McGrawHill Australia Pty Ltd 114 Example: Expected Returns • Suppose you have predicted the following returns for shares C and T in three possible states of nature What are the expected returns? – – – – State Boom Normal Recession Probability 0.3 0.5 0.2 C 0.15 0.10 0.02 T 0.25 0.20 0.01 • RC = 3(.15) + 5(.10) + 2(.02) = 099 = 9.99% • RT = 3(.25) + 5(.20) + 2(.01) = 177 = 17.7% Copyright ª 2007 McGrawHill Australia Pty Ltd 115 Variance and Standard Deviation • Variance and standard deviation still measure the volatility of returns • Using unequal probabilities for the entire range of possibilities • Weighted average of squared deviations σ2 n pi ( Ri E ( R)) i Copyright ª 2007 McGrawHill Australia Pty Ltd 116 Example: Variance and Standard Deviation • • • Consider the previous example What are the variance and standard deviation for each share? Share C = 3(.15-.099)2 + 5(.1-.099)2 + 2(.02-.099)2 = 002029 = 045 Share T = 3(.25-.177)2 + 5(.2-.177)2 + 2(.01-.177)2 = 007441 = 0863 Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư7 Another Example ã Consider the following information: – – – – – State Boom Normal Slowdown Recession Probability 25 50 15 10 KBC Ltd 15 08 04 -.03 • What is the expected return? • What is the variance? • What is the standard deviation? Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư8 Portfolios ã A portfolio is a collection of assets • An asset’s risk and return is important in how it affects 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 Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư9 Example: Portfolio Weights ã 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 = INTC: 4/15 = 267 KEI: 6/15 = Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 10 Measuring Systematic Risk ã How we measure systematic risk? • We use the beta coefficient to measure systematic risk • What does beta tell us? – – – A beta of implies the asset has the same systematic risk as the overall market A beta < implies the asset has less systematic risk than the overall market A beta > implies the asset has more systematic risk than the overall market Copyright ª 2007 McGrawHill Australia Pty Ltd 11 29 Table 11.8 Copyright ª 2007 McGrawHill Australia Pty Ltd 11 30 Work the Web Example • Many sites provide betas for companies • Yahoo Finance provides beta, plus a lot of other information under its profile link • Click on the web surfer to go to Yahoo Finance – – Enter a ticker symbol and get a basic quote Click on “profile” Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 31 Total vs Systematic Risk ã Consider the following information: – – Security C Security K Standard Deviation 20% 30% Beta 1.25 0.95 • Which security has more total risk? • Which security has more systematic risk? • Which security should have the higher expected return? Copyright ª 2007 McGrawHill Australia Pty Ltd 11 32 Example: Portfolio Betas • • Consider the previous example with the following four securities – Security Weight Beta – DCLK 133 4.03 – KO 0.84 – INTC 167 1.05 – KEI 0.59 What is the portfolio beta? – 133(4.03) + 2(.84) + 167(1.05) + 4(.59) = 1.12 Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 33 Beta and the Risk Premium ã 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! Copyright ª 2007 McGrawHill Australia Pty Ltd 11 34 Example: Portfolio Expected Returns and Betas 30% Expected Return 25% E(RA) 20% 15% 10% Rf 5% 0% 0.5 1.5 A 2.5 Beta Copyright ª 2007 McGrawHill Australia Pty Ltd 11 35 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)/( 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 (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)? Copyright ª 2007 McGrawHill Australia Pty Ltd 11 36 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 E ( RA ) R f A E ( RM R f ) M Copyright ª 2007 McGrawHill Australia Pty Ltd 11 37 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(RM) – Rf)/ M • But since the beta for the market is ALWAYS equal to one, the slope can be rewritten • Slope = E(RM) – Rf = market risk premium Copyright ª 2007 McGrawHill Australia Pty Ltd 11 38 Capital Asset Pricing Model • The capital asset pricing model (CAPM) defines the relationship between risk and return • E(RA) = Rf + A(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 Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 39 Factors Affecting Expected Return ã Pure time value of money – measured by the risk- free rate • Reward for bearing systematic risk – measured by the market risk premium • Amount of systematic risk – measured by beta Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 40 Example CAPM ã Consider the betas for each of the assets given earlier If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the expected return for each? – – – – – Security DCLK KO INTC KEI Beta 4.03 0.84 1.05 0.59 Expected Return 6.15 + 4.03(9.5) = 44.435% 6.15 + 84(9.5) = 14.13% 6.15 + 1.05(9.5) = 16.125% 6.15 + 59(9.5) = 11.755% Copyright ª 2007 McGrawHill Australia Pty Ltd 11 41 SML and Equilibrium Copyrightê2007McGrawưHillAustraliaPtyLtd 11ư 42 Quick Quiz ã ã ã • 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% – What is the reward-to-risk ratio in equilibrium? – What is the expected return on the asset? Copyright ª 2007 McGrawHill Australia Pty Ltd 11 43 ... asset’s risk and return is important in how it affects the risk and return of the portfolio • The risk- return trade-off for a portfolio is measured by the portfolio expected return and standard... 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... 11ư 35 Reward-to -Risk Ratio: Definition and Example ã The reward-to -risk ratio is the slope of the line illustrated in the previous example – – Slope = (E(RA) – Rf)/( A – 0) Reward-to -risk ratio