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chap010 - Chapter 10 Return and Risk The...

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¤ * Chapter 10: Return and Risk: The Capital-Asset-Pricing Model (CAPM) 10.1 a. R = 0.1 (– 4.5%) + 0.2 (4.4%) + 0.5 (12.0%) + 0.2 (20.7%) = 10.57% b. σ 2 = 0.1 (–0.045 – 0.1057) 2 + 0.2 (0.044 – 0.1057) 2 + 0.5 (0.12 – 0.1057) 2 + 0.2 (0.207 – 0.1057) 2 = 0.0052 σ = (0.0052) 1/2 = 0.072 = 7.20% 10.2 a. R A = (6.3 + 10.5 + 15.6) / 3 = 10.8% R B = (-3.7 + 6.4 + 25.3) / 3 = 9.3% b. σ A 2 = {(0.063 – 0.108) 2 + (0.105 – 0.108) 2 +{(0.156 – 0.108) 2 } / 3 = 0.001446 σ A = (0.001446) 1/2 = 0.0380 = 3.80% σ B 2 = {(– 0.037 – 0.093) 2 +(0.064 – 0.093) 2 +(0.253 – 0.093) 2 } / 3 = 0.014447 σ B = (0.014447) 1/2 = 0.1202 = 12.02% c. Cov(R A ,R B ) = [(.063 – .108) (– .037 – .093) + (.105 – .108) (.064 – .093) + (.156 – .108) (.253 – .093) ] / 3 = .013617 / 3 = .004539 Corr(R A ,R B ) = .004539 / (.0380 x .1202) = .9937 10.3 a. R HB = 0.25 (–2.0) + 0.60 (9.2) + 0.15 (15.4) = 7.33% R SB = 0.25 (5.0) + 0.60 (6.2) + 0.15 (7.4) = 6.08% b. σ HB 2 = 0.25 (– 0.02 – 0.0733) 2 + 0.60 (0.092 – 0.0733) 2 + 0.15 (0.154 – 0.0733) 2 = 0.003363 σ HB = (0.003363) 1/2 = 0.05799 = 5.80% σ SB 2 = 0.25 (0.05 – 0.0608) 2 + 0.60 (0.062 – 0.0608) 2 + 0.15 (0.074 – 0.0608) 2 = 0.000056 σ SB = (0.000056) 1/2 = 0.00749 = 0.75% c. Cov (R HB , R SB ) = 0.25 (– 0.02 – 0.0733) (0.05 – 0.0608) + 0.60 (0.092 – 0.0733) (0.062 – 0.0608) + 0.15 (0.154 – 0.0733) (0.074 – 0.0608) = 0.000425286 Corr (R HB , R SB ) = 0.000425286 / (0.05799 × 0.00749) = 0.9791 10.4 Holdings of Atlas stock = 120 × $50 = $6,000 Holdings of Babcock stock = 150 × $20 = $3,000 Weight of Atlas stock = $6,000 / $9,000 = 2 / 3 Answers to End-of-Chapter Problems B-103
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Weight of Babcock stock = $3,000 / $9,000 = 1 / 3 10.5 a. R P = 0.3 (0.12) + 0.7 (0.18) = 0.162 = 16.2% b. σ P 2 = 0.3 2 (0.09) 2 + 0.7 2 (0.25) 2 + 2 (0.3) (0.7) (0.09) (0.25) (0.2) = 0.033244 σ P = (0.033244) 1/2 = 0.1823 = 18.23% 10.6 a. R P = 0.4 (0.15) + 0.6 (0.25) = 0.21 = 21% σ P 2 = 0.4 2 (0.1) 2 + 0.6 2 (0.2) 2 + 2 (0.4) (0.6) (0.1) (0.2) (0.5) = 0.0208 σ P = (0.0208) 1/2 = 0.1442 = 14.42% b. σ P 2 = 0.4 2 (0.1) 2 + 0.6 2 (0.2) 2 + 2 (0.4) (0.6) (0.1) (0.2) (-0.5) = 0.0112 σ P = (0.0112) 1/2 = 0.1058 = 10.58% c. As the stocks are more negatively correlated, the standard deviation of the portfolio decreases. 10.7 Macrosoft: 100 × $80 = $8,000 Intelligent: 300 × $40 = $12,000 Weight:Macrosoft: $8,000 / $20,000 = 0.4 Intelligent: $12,000 / $20,000 = 0.6 a. R P = 0.4 (0.15) + 0.6 (0.20) = 0.18 = 18% σ P 2 = 0.4 2 (0.08) 2 + 0.6 2 (0.2) 2 + 2 (0.4) (0.6) (0.38) (0.08) (0.20) = 0.0183424 σ P = (0.0183424) 1/2 = 0.1354 = 13.54% b. New weight: Macrosoft: $8,000 / $12,000 = 0.667 Intelligent: $4,000 / $12,000 = 0.333 R P = 0.667 (0.15) + 0.333 (0.20) = 0.1666 = 16.66% σ P 2 = 0.667 2 (0.08) 2 + 0.333 2 (0.2) 2 + 2 (0.667) (0.333) (0.38) (0.08) (0.20) = 0.009984 σ P = (0.009984) 1/2 = 0.09992 = 9.99% 10.8 a. R U = 7% R V = 0.2 (-0.05) + 0.5 (0.10) + 0.3 (0.25) = 0.115 = 11.5% σ U 2 = σ U = 0 σ V 2 = 0.2 (-0.05 - 0.115) 2 + 0.5 (0.10 - 0.115) 2 + 0.3 (0.25 - 0.115) 2 = 0.0110 σ V = (0.0110) 1/2 = 0.105 = 10.5% b. Cov (R U , R V ) = 0.2 (-0.05 - 0.115) (0.07 - 0.07) + 0.5 (0.10 - 0.115) (0.07 - 0.07) + 0.3 (0.25 - 0.115) (0.07 - 0.07) = 0 Corr (R U , R V ) = 0 c. R P = 0.5 (0.115) + 0.5 (0.07) = 0.0925 = 9.25% Answers to End-of-Chapter Problems B-104
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¨ * σ P 2 = 0.5 2 (0.0110) = 0.00275 σ P = (0.00275) 1/2 = 0.0524 = 5.24% 10.9 a. R P = 0.3 (0.10) + 0.7 (0.20) = 0.17 = 17.0% σ P 2 = 0.3 2 (0.05) 2 + 0.7 2 (0.15) 2 = 0.01125 σ P = (0.01125) 1/2 = 0.10607 = 10.61% b. R P = 0.9 (0.10) + 0.1 (0.20) = 0.11 = 11.0% σ P 2 = 0.9 2 (0.05) 2 + 0.1 2 (0.15) 2 = 0.00225 σ P = (0.00225) 1/2 = 0.04743 = 4.74% c. No, I would not hold 100% of stock A because the portfolio in b has higher expected return but less standard deviation than stock A. I may or may not hold 100% of stock B, depending on my preference. 10.10 The expected return on any portfolio must be less than or equal to the return on the stock with the highest return. It cannot be greater than this stock’s return because all stocks with lower returns will pull down the value of the weighted average return. Similarly, the expected return on any portfolio must be greater than or equal to the return of the asset with the lowest return. The portfolio return cannot be less than the lowest return in the portfolio because all higher earning stocks will pull up the value of the weighted average. 10.11 a. R A = 0.4 (0.03) + 0.6 (0.15) = 0.102 = 10.2% R B = 0.4 (0.065) + 0.6 (0.065) = 0.065 = 6.5% σ A 2 = 0.4 (0.03 - 0.102) 2 + 0.6 (0.15 - 0.102) 2 = 0.003456 σ A = (0.003456) 1/2 = 0.05878 = 5.88% σ B 2 = σ B = 0 b. X A = $2,500 / $6,000 = 0.417 X B = 1 - 0.417 = 0.583 R P = 0.417 (0.102) + 0.583 (0.065) = 0.0804 = 8.04% σ P 2 = X A 2 σ A 2 = 0.0006 σ P = (0.0006) 1/2 = 0.0245 = 2.45% c. Amount borrowed = -40 × $50 = -$2,000 X A = $8,000 / $6,000 = 4 / 3 X B = 1 - X A = -1 / 3 R P = (4 / 3) (0.102) + (-1 / 3) (0.065) = 0.1143 = 11.43% σ P 2 = (4 / 3) 2 (0.003456) = 0.006144 σ P = (0.006144) 1/2 = 0.07838 = 7.84% 10.12 The wide fluctuations in the price of oil stocks do not indicate that oil is a poor investment. If oil is purchased as part of a portfolio, what matters is only its beta. Since
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