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Unformatted text preview: d The reward-to-risk ratio is the slope of the line The illustrated in the previous example illustrated Slope = (E(RA) – Rf) / (β 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 What (implying that the asset plots above the line)? (implying What if an asset has a reward-to-risk ratio of 7 What (implying that the asset plots below the line)? (implying Market Equilibrium Market In equilibrium, all assets and portfolios must In have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market must E ( RA ) − R f βA = E ( RM − R f ) βM Security Market Line Security The security market line (SML) is the The representation of market equilibrium representation The slope of the SML is the reward-to-risk ratio: The (E(RM) – Rf) / β M (E(R But since the beta for the market is ALWAYS But equal to one, the slope can be rewritten equal Slope = E(RM) – Rf = market risk premium The Capital Asset Pricing Model (CAPM) (CAPM) The capital asset pricing model defines the The relationship between risk and return relationship E(RA) = Rf + β A(E(RM) – Rf) If we know an asset’s systematic risk, we can If use the CAPM to determine its expected return use This is true whether we are talking about This financial assets or physical assets financial Factors Affecting Expected Return Return Pure time value of money – measured by Pure the risk-free rate the Reward for bearing systematic risk – Reward measured by the market risk premium measured Amount of systematic risk – measured by Amount beta beta Example - CAPM Example Consider the betas for each of the assets given earlier. Consider If the risk-free rate is 2.13% and the market risk premium is 8.6%, what is the expected return for each? premium Security DCLK KO INTC KEI Beta 2.685 0.195 2.161 2.434 Expected Return 2.13 + 2.685(8.6) = 25.22% 2.13 + 0.195(8.6) = 3.81% 2.13 + 2.161(8.6) = 20.71% 2.13 + 2.434(8.6) = 23.06% Figure 13.4 Figure Comprehensive Problem Comprehensive The risk free rate is 4%, and the required return The on the market is 12%. What is the required return on an asset with a beta of 1.5? return What is the reward/risk ratio? The reward/risk ratio is 8% What is the required return on a portfolio What consisting of 40% of the asset above and the rest in an asset with an average amount of systematic risk? systematic R = .04 + 1.5 x (.12 - .04) = .16 R = (.4 x .16) + (.6 x .12) = .136 (.4...
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- Spring '10