Ross5eChap12sm

Ross5eChap12sm - Chapter 12 An Alternative View of Risk and...

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Unformatted text preview: Chapter 12: An Alternative View of Risk and Return: The Arbitrage Pricing Theory 2. a. If m is the systematic risk portion of return, then: m = β GNP Δ GNP + β Inflation Δ Inflation + β r Δ Interest rates m = .000586($5,436 – 5,396) – 1.40(3.80% – 3.10%) – .67(10.30% – 9.50%) m = 0.83% b. The unsystematic return is the return that occurs because of a firm specific factor such as the bad news about the company. So, the unsystematic return of the stock is –2.6 percent. The total return is the expected return, plus the two components of unexpected return: the systematic risk portion of return and the unsystematic portion. So, the total return of the stock is: ε + + = m R R R = 9.50% + 0.83% – 2.6% R = 7.73% 4. The beta for a particular risk factor in a portfolio is the weighted average of the betas of the assets. This is true whether the betas are from a single factor model or a multi–factor model. So, the betas of the portfolio are: F 1 = .20(1.20) + .20(0.80) + .60(0.95) F 1 = 0.97 F 2 = .20(0.90) + .20(1.40) + .60(–0.05) F 2 = 0.43 F 3 = .20(0.20) + .20(–0.30) + .60(1.50) F 3 = 0.88 So, the expression for the return of the portfolio is: R i = 5% + 0.97 F 1 + 0.43 F 2 + 0.88 F 3 Which means the return of the portfolio is: R i = 5% + 0.97(5.50%) + 0.43(4.20%) + 0.88(4.90%) R i = 16.45% 6. a. The market model is specified by: ε β + − + = ) ( M M R R R R so applying that to each Stock: Stock A: Answers to End–of–Chapter Problems B–175 A M M A A A R R R R ε β + − + = ) ( R A = 10.5% + 1.2(R M – 14.2%) + ε A Stock B: B M M B B B R R R R ε β + − + = ) ( R B = 13.0% + 0.98(R M – 14.2%) + ε B Stock C: C M M C C C R R R R ε β + − + = ) ( R C = 15.7% + 1.37(R M – 14.2%) + ε C b. Since we don't have the actual market return or unsystematic risk, we will get aformula with those values as unknowns: R P = .30R A + .45R B + .30R C R P = .30[10.5% + 1.2(R M – 14.2%) + ε A ] + .45[13.0% + 0.98(R M – 14.2%) + ε B ] + .25[15.7% + 1.37(R M – 14.2%) + ε C R P = .30(10.5%) + .45(13%) + .25(15.7%) + [.30(1.2) + .45(.98) + .25(1.37)] (R M – 14.2%)+ .30 ε A + .45 ε B + .30 ε C R P = 12.925% + 1.1435(R M – 14.2%) + .30 ε A + .45 ε B + .30 ε C c. Using the market model, if the return on the market is 15 percent and the systematic risk is zero, the return for each individual stock is:...
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Ross5eChap12sm - Chapter 12 An Alternative View of Risk and...

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