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Solutions to Practice Problems_Week 8_Ch 7_8_11

Solutions to Practice Problems_Week 8_Ch 7_8_11 - CHAPTER 7...

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CHAPTER 7 THE CAPITAL ASSET PRICING MODEL 1. E(r P ) = r f + β P [E(r M ) – r f ] 18 = 6 + β (14 – 6) β P = 12/8 = 1.5 2. If the covariance of the security doubles, then so will its beta and its risk premium. The current risk premium is 14 – 6 = 8%, so the new risk premium would be 16%, and the new discount rate for the security would be 16 + 6 = 22%. If the stock pays a constant perpetual dividend, then we know from the original data that the dividend, D, must satisfy the equation for the present value of a perpetuity: Price = Dividend / Discount rate 50 = D /.14 D = 50 × .14 = \$7.00 At the new discount rate of 22%, the stock would be worth only \$7/.22 = \$31.82. The increase in stock risk has lowered its value by 36.36%. 13. Since the stock's beta is equal to 1.2, its expected rate of return is 6 + 1.2(16 – 6) = 18% E(r) = and .18 = so P 1 = \$53 15. Using the SML: 4 = 6 + β (16 – 6) so β = –2/10 = –.2 17. a. Since the market portfolio by definition has a beta of 1, its expected rate of return is 12%. b. β = 0 means no systematic risk. Hence, the portfolio's expected rate of return in market equilibrium is the risk-free rate, 5%. c. Using the SML, the fair expected rate of return of a stock with β = –0.5 is: E(r) = 5 + (–.5)(12 – 5) = 1.5% The actually expected rate of return, using the expected price and dividend for next year is: E(r) = 44/40 – 1 = .10 or 10% Because the actually expected return exceeds the fair return, the stock is underpriced.

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