Chapter 6 solutions

# Chapter 6 solutions - T HE E CONOMICS OF F INANCIAL M...

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THE ECONOMICS OF FINANCIAL MARKETS R. E. BAILEY Solution Guide to Exercises for Chapter 6 The capital asset pricing model 1. The following information is provided for a stock market: μ j β j Asset 1 6.6% 0.4 Asset 2 9.8% 1.2 Asset 3 12.2% 1.8 Notation: μ j = expected rate of return on asset j ; β j = beta-coefﬁcient for asset j , j = 1 , 2 , 3 . (a) In the context of the Capital Asset Pricing Model (CAPM), deﬁne the ‘beta-coefﬁcient’, β j , corresponding to asset j . Discuss how assets’ beta-coefﬁcients should be interpreted and explain how their values can be obtained in practice. Answer : The beta-coefﬁcient can be deﬁned in any of the following equivalent ways: β j = σ jM σ 2 M = ρ jM σ j σ M σ 2 M = ρ jM σ j σ M , where σ jM is the covariance between the rate of return on asset j and the market rate of return, σ M is the standard deviation of the market rate of return, σ j is the standard deviation of the rate of return on asset j , and ρ jM is the correlation coefﬁcient between the rate of return on asset j and the market rate of return. An asset’s beta-coefﬁcient is a measure of the relationship between its rate of return and the market rate of return. It can be interpreted as a measure of the asset’s risk, relative to the market as a whole. An asset’s beta-coefﬁcient is formally the slope co-efﬁcient on the excess rate of return on the market in a regression of the excess rate of return on asset j on the excess rate of return on the market: r j = r 0 + ( r M - r 0 ) β j + ε j , j = 1 , 2 , ..., n, where ε j is an unobserved random error. It is assumed that E [ ε j | r M ] = 0 , that is, the expected value of the error, conditional upon the rate of return on the market portfolio, is zero. Typically (almost always) beta-coefﬁcients are estimated from data on past rates of return (in the regression described above). (b) Assuming that a risk-free asset is available, explain and interpret the Security Market Line (SML) in the context of the CAPM. Construct the SML from the given information and interpret the values of its coefﬁcients. Answer : The CAPM predicts that: μ j = r 0 + ( μ M - r 0 ) β j , where μ j is the expected rate of return on asset j , μ M is the expected rate of return on the market portfolio, and r 0 is the risk-free rate of return The SML treats μ j as a function of β j and shows how the expected rate of return on each asset differs according to its beta-coefﬁcient. The slope of the SML is then a measure of the market ‘price’ of risk. See ﬁgure 1. The data in the question must satisfy: 0 . 066 = r 0 + 0 . 4( μ M - r 0 ) , and 0 . 098 = r 0 + 1 . 2( μ M - r 0 ) .

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## This note was uploaded on 03/21/2011 for the course ECON 6120 taught by Professor Crabbe during the Spring '11 term at University of Ottawa.

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Chapter 6 solutions - T HE E CONOMICS OF F INANCIAL M...

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