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Unformatted text preview: THE ECONOMICS OF FINANCIAL MARKETS R. E. BAILEY Solution Guide to Exercises for Chapter 8 Factor models and the arbitrage pricing theory 1. The following information is provided for a stock market in which asset returns respond to two factors: Asset b j 1 b j 2 μ j A 1.2 0.4 16% B 0.8 1.6 26% r 6% Notation : b j 1 and b j 2 for j = A, B denote the responses of the rates of return on assets A and B to the factors; μ j is the expected rate of return on each of the assets; and r is the riskfree rate of return. (a) If the APT holds in this market, calculate the risk premia corresponding to the two fac tors. Answer : The APT predicts: μ i r = λ 1 b i 1 + λ 2 b i 2 for i = A, B, (1) where λ 1 , λ 2 are the two risk premia corresponding to factors 1 and 2, respectively. Hence: μ A r = λ 1 b A 1 + λ 2 b A 2 μ B r = λ 1 b B 1 + λ 2 b B 2 Substituting: . 16 . 06 = λ 1 × 1 . 2 + λ 2 × . 4 . 26 . 06 = λ 1 × . 8 + λ 2 × 1 . 6 Hence: . 10 = 1 . 2 λ 1 + 0 . 4 λ 2 . 20 = . 8 λ 1 + 1 . 6 λ 2 Solving (by whatever method you choose) gives: λ 1 = 0 . 05 , λ 2 = 0 . 10 . (b) Construct a portfolio which gives unit weight to the first factor and zero weight to the second factor. Hence provide an interpretation for the risk premia in the APT....
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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.
 Spring '11
 CRABBE

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