BKM_Sol_Ch_7

# BKM_Sol_Ch_7 - Chapter 07 Capital Asset Pricing and...

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Chapter 07 - Capital Asset Pricing and Arbitrage Pricing Theory Chapter 7 Capital Asset Pricing and Arbitrage Pricing Theory 1. a, c and d 2. a. E(r X ) = 5% + 0.8(14% – 5%) = 12.2% α X = 14% – 12.2% = 1.8% E(r Y ) = 5% + 1.5(14% – 5%) = 18.5% α Y = 17% – 18.5% = –1.5% b. (i) For an investor who wants to add this stock to a well-diversified equity portfolio, Kay should recommend Stock X because of its positive alpha, while Stock Y has a negative alpha. In graphical terms, Stock X’s expected return/risk profile plots above the SML, while Stock Y’s profile plots below the SML. Also, depending on the individual risk preferences of Kay’s clients, Stock X’s lower beta may have a beneficial impact on overall portfolio risk. (ii) For an investor who wants to hold this stock as a single-stock portfolio, Kay should recommend Stock Y, because it has higher forecasted return and lower standard deviation than Stock X. Stock Y’s Sharpe ratio is: (0.17 – 0.05)/0.25 = 0.48 Stock X’s Sharpe ratio is only: (0.14 – 0.05)/0.36 = 0.25 The market index has an even more attractive Sharpe ratio: (0.14 – 0.05)/0.15 = 0.60 However, given the choice between Stock X and Y, Y is superior. When a stock is held in isolation, standard deviation is the relevant risk measure. For assets held in isolation, beta as a measure of risk is irrelevant. Although holding a single asset in isolation is not typically a recommended investment strategy, some investors may hold what is essentially a single-asset portfolio (e.g., the stock of their employer company). For such investors, the relevance of standard deviation versus beta is an important issue. 3. E(r P ) = r f + β [E(r M ) – r f ] 20% = 5% + β (15% – 5%) β = 15/10 = 1.5 7-1

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Chapter 07 - Capital Asset Pricing and Arbitrage Pricing Theory 4. If the beta of the security doubles, then so will its risk premium. The current risk premium for the stock is: (13% - 7%) = 6%, so the new risk premium would be 12%, and the new discount rate for the security would be: 12% + 7% = 19% If the stock pays a constant dividend in perpetuity, then we know from the original data that the dividend (D) must satisfy the equation for a perpetuity: Price = Dividend/Discount rate 40 = D/0.13 D = 40 × 0.13 = \$5.20 At the new discount rate of 19%, the stock would be worth: \$5.20/0.19 = \$27.37 The increase in stock risk has lowered the value of the stock by 31.58%. 5. The cash flows for the project comprise a 10-year annuity of \$10 million per year plus an additional payment in the tenth year of \$10 million (so that the total payment in the tenth year is \$20 million). The appropriate discount rate for the project is: r f + β [E(r M ) – r f ] = 9% + 1.7(19% – 9%) = 26% Using this discount rate: NPV = –20 + + = 10 1 t t 26 . 1 10 10 26 . 1 10 = –20 + [10 × Annuity factor (26%, 10 years)] + [10 × PV factor (26%, 10 years)] = 15.64 The internal rate of return on the project is 49.55%.
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## This note was uploaded on 08/25/2009 for the course FNCE 4330 taught by Professor Jianyang during the Fall '09 term at University of Colorado Denver.

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BKM_Sol_Ch_7 - Chapter 07 Capital Asset Pricing and...

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