Ch 11 revised - CHAPTER 11 ARBITRAGE PRICING THEORY AND...

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CHAPTER 11: ARBITRAGE PRICING THEORY AND MULTIFACTOR MODELS OF RISK AND RETURN 1. The revised estimate of the expected rate of return on the stock would be the old estimate plus the sum of the products of the unexpected change in each factor times the respective sensitivity coefficient, i.e., revised estimate = 12% + [(1 × 2%) + (0.5 × 3%)] = 15.5% 2. Equation 11.9 applies here: E(r p ) = r f + β P1 [E(r 1 ) - r f ] + β P2 [E(r 2 ) – r f ] We need to find the risk premium (RP) for each of the two factors: RP 1 = [E(r 1 ) - r f ] and RP 2 = [E(r 2 ) - r f ] In order to do so, we solve the following system of two equations with two unknowns: 31 = 6 + (1.5 × RP 1 ) + (2.0 × RP 2 ) 27 = 6 + (2.2 × RP 1 ) + [(–0.2) × RP 2 ] The solution to this set of equations is: RP 1 = 10% and RP 2 = 5% Thus, the expected return-beta relationship is: E(r P ) = 6% + ( β P1 × 10%) + ( β P2 × 5%) 3. The expected return for Portfolio F equals the risk-free rate since its beta equals 0. For Portfolio A, the ratio of risk premium to beta is: (12 - 6)/1.2 = 5 For Portfolio E, the ratio is lower at: (8 – 6)/0.6 = 3.33 This implies that an arbitrage opportunity exists.
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