Lecture 11 - Return, risk, and the security market line. The following will be discussed in this chapter: 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.
Lecture 11 Return, Risk, and the Security Market Line © 2003 The McGrawHill Companies, Inc. All rights reserved 13.2 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 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 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 E ( R) n pi Ri i McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.4 Example: Expected Returns ã Supposeyouhavepredictedthefollowing returns for stocks C and T in three possible states of nature. What are the expected returns? – – – – State Boom Normal Recession Probability 0.3 0.5 ??? C 0.15 0.10 0.02 T 0.25 0.20 0.01 ã RC=.3(.15)+.5(.10)+.2(.02)=.099=9.99% ã RT=.3(.25)+.5(.20)+.2(.01)=.177=17.7% McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.5 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 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.6 Example: Variance and Standard Deviation • Consider the previous example. What are the variance and standard deviation for each stock? • Stock C = .3(.15.099)2 + .5(.1.099)2 + .2(.02.099)2 = .002029 = .045 • Stock T = .3(.25.177)2 + .5(.2.177)2 + .2(.01.177)2 = .007441 = .0863 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.7 Another Example • Consider the following information: – – – – – State Boom Normal Slowdown Recession Probability 25 50 15 10 ABC, Inc .15 08 04 .03 • What is the expected return? • Whatisthevariance? ã Whatisthestandarddeviation? McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.8 Portfolios ã Aportfolioisacollectionofassets • An asset’s risk and return is important in how it affects the risk and return of the portfolio • The riskreturn tradeoff for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.9 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 McGrawHill/Irwin •DCLK: 2/15 = .133 •KO: 3/15 = .2 •INTC: 4/15 = .267 •KEI: 6/15 = .4 © 2003 The McGrawHill Companies, Inc. All rights reserved 13.10 Portfolio Expected Returns • The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio E ( RP ) m w j E(R j ) j • 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 McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.20 Diversification ã Portfoliodiversificationistheinvestmentin severaldifferentassetclassesorsectors ã Diversificationisnotjustholdingalotof assets • Diversification can reduce the variability of returns without a reduction in expected returns – This reduction in risk arises if worse than expected returns from one asset are offset by better than expected returns from another • The risk that cannot be diversified away is calledsystematicrisk McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.21 Diversifiable Risk ã Theriskthatcanbeeliminatedbycombining assetsintoaportfolio • Often considered the same as unsystematic, unique or assetspecific risk • If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.22 Systematic Risk Principle • There is a reward for bearing risk • There is not a reward for bearing risk unnecessarily • The expected return on a risky asset depends only on that asset’s systematic risk since unsystematic risk can be diversified away McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.23 Measuring Systematic Risk • We use the beta coefficient to measure systematic risk • 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 more systematic risk than the overall market McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.24 Total versus Systematic Risk • Consider the following information: Standard Deviation – Security C 20% – Security K 30% Beta 1.25 0.95 • Which security has more total risk? • Which security has more systematic risk? • Whichsecurityshouldhavethehigher expectedreturn? McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.25 Example: Portfolio Betas ã Consider the following example – Security – DCLK – KO – INTC – KEI Weight 133 167 Beta 3.69 0.64 1.64 1.79 ã Whatistheportfoliobeta? ã 133(3.69)+.2(.64)+.167(1.64)+.4(1.79)= 1.61 McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.26 Beta and the Risk Premium • Remember that the risk premium = expected return – riskfree rate • The higher the beta, the greater the risk premiumshouldbe ã Canwedefinetherelationshipbetweenthe riskpremiumandbetasothatwecanestimate theexpectedreturn? YES! McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.27 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 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.28 Reward-to-Risk Ratio: Definition and Example • The rewardtorisk ratio is the slope of the line illustrated in the previous example – Slope = (E(RA) – Rf) / ( A – 0) – Rewardtorisk ratio for previous example = (20 – 8) / (1.6 – 0) = 7.5 • What if an asset has a rewardtorisk ratio of 8 (implying that the asset plots above the line)? • What if an asset has a rewardtorisk ratio of 7 (implying that the asset plots below the line)? McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.29 Market Equilibrium ã Inequilibrium,allassetsandportfoliosmust havethesamerewardưtoưriskratioandtheyall mustequaltherewardưtoưriskratioforthe market E ( RA ) R f A McGrawHill/Irwin E ( RM R f ) M © 2003 The McGrawHill Companies, Inc. All rights reserved 13.30 Security Market Line • The security market line (SML) is the representation of market equilibrium • The slope of the SML is the rewardtorisk ratio: (E(RM) – Rf) / M • ButsincethebetaforthemarketisALWAYS equaltoone,theslopecanberewritten ã Slope=E(RM)Rf=marketriskpremium McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.31 The Capital Asset Pricing Model (CAPM) • The capital asset pricing model 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 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.32 Factors Affecting Expected Return • Pure time value of money – measured by the riskfree rate • Reward for bearing systematic risk – measuredbythemarketriskpremium ã Amountofsystematicriskmeasuredbybeta McGrawưHill/Irwin â2003TheMcGrawưHillCompanies,Inc.Allrightsreserved 13.33 Example - CAPM • Consider the betas for each of the assets given earlier. If the riskfree rate is 4.5% and the market risk premium is 8.5%, what is the expected return for each? Security DCLK Beta Expected Return 3.69 4.5 + 3.69(8.5) = 35.865% 64 4.5 + .64(8.5) = 9.940% INTC 1.64 4.5 + 1.64(8.5) = 18.440% KEI 1.79 4.5 + 1.79(8.5) = 19.715% KO McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved 13.34 Figure 13.4 McGrawHill/Irwin © 2003 The McGrawHill Companies, Inc. All rights reserved ... have purchased securities in the following amounts. What are your portfolio weights in each security? – – – – $2000? ?of? ?DCLK $3000? ?of? ?KO $4000? ?of? ?INTC $6000ofKEI McGrawưHill/Irwin ãDCLK:2/15=.133 ãKO:3/15=.2 ãINTC:4/15=.267 ãKEI:6/15=.4... • 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 riskreturn tradeoff for a portfolio is measured by the portfolio expected return and ... 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 McGrawưHill/Irwin