bkmsol_ch11 - 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. For instance, you can create a Portfolio G with beta equal to 0.6 (the same as E’s) by combining Portfolio A and Portfolio F in equal weights. The expected return and beta for Portfolio G are then: E(r G ) = (0.5 × 12%) + (0.5 × 6%) = 9% β G = (0.5 × 1.2) + (0.5 × 0) = 0.6 Comparing Portfolio G to Portfolio E, G has the same beta and higher return. Therefore, an arbitrage opportunity exists by buying Portfolio G and selling an equal amount of Portfolio E. The profit for this arbitrage will be: 11-1
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r G – r E =[9% + (0.6 × F)] - [8% + (0.6 × F)] = 1% That is, 1% of the funds (long or short) in each portfolio. 4. a.This statement is incorrect. The CAPM requires a mean-variance efficient market portfolio, but APT does not. b. This statement is incorrect. The CAPM assumes normally distributed security returns, but APT does not.
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This note was uploaded on 03/10/2011 for the course FMIS 3601 taught by Professor Vizanko during the Spring '08 term at University of Minnesota Duluth.

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bkmsol_ch11 - CHAPTER 11: ARBITRAGE PRICING THEORY AND...

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