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PS3Answers - P roblem 1 Security A B Part 1 Exp Ret 12 20...

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Problem 1) Security Exp Ret ST Dev A 12% 15% B 20% 45% Part 1 The question asks for portfolio weights spaced 10% apart, but 5% gives a better grid for the graph. Exp Ret -1 -0.5 0 0.5 1 0.00% 20.00% 45.00% 45.00% 45.00% 45.00% 45.00% 5.00% 19.60% 42.00% 42.38% 42.76% 43.13% 43.50% 10.00% 19.20% 39.00% 39.77% 40.53% 41.27% 42.00% 15.00% 18.80% 36.00% 37.18% 38.32% 39.42% 40.50% 20.00% 18.40% 33.00% 34.60% 36.12% 37.59% 39.00% 25.00% 18.00% 30.00% 32.04% 33.96% 35.77% 37.50% 30.00% 17.60% 27.00% 29.51% 31.82% 33.97% 36.00% 35.00% 17.20% 24.00% 27.01% 29.72% 32.20% 34.50% 40.00% 16.80% 21.00% 24.56% 27.66% 30.45% 33.00% 45.00% 16.40% 18.00% 22.16% 25.65% 28.73% 31.50% 50.00% 16.00% 15.00% 19.84% 23.72% 27.04% 30.00% 55.00% 15.60% 12.00% 17.64% 21.87% 25.40% 28.50% 60.00% 15.20% 9.00% 15.59% 20.12% 23.81% 27.00% 65.00% 14.80% 6.00% 13.77% 18.52% 22.29% 25.50% 70.00% 14.40% 3.00% 12.28% 17.10% 20.84% 24.00% 75.00% 14.00% 0.00% 11.25% 15.91% 19.49% 22.50% 80.00% 13.60% 3.00% 10.82% 15.00% 18.25% 21.00% 85.00% 13.20% 6.00% 11.05% 14.43% 17.15% 19.50% 90.00% 12.80% 9.00% 11.91% 14.23% 16.22% 18.00% 95.00% 12.40% 12.00% 13.27% 14.43% 15.50% 16.50% 100.00% 12.00% 15.00% 15.00% 15.00% 15.00% 15.00% 150.00% 8.00% 45.00% 38.97% 31.82% 22.50% 0.00% x Mean-Standard Deviation Frontiers
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Part 2 For perfect negative correlation we have: Hence, Hence, the miniminum variance portfolio has 25% invested in asset B and 75% invested in asset A. You can also read this off the above chart. See also the framed box in the table in part 1. Part 3 For perfect positive correlation we have: Hence, Hence, invest 150% in asset A and -50% in asset B. This requires that you can sell asst B short. If you cannot, invest 100% in asset A and nothing in asset B. Part 4 No short sales restrictions: In both cases (perfect positive and perfect negative correlation) the variance of the minimum variance portfolio is zero. Expected returns are: rho = +1 E(R) = 1.5*0.12-0.5*.20 = 0.08, = 8.00% rho=-1 E(R) = 0.75*0.12+0.25*0.20 = 14.00% Since the variance of the portfolios that we created is zero and the expected return is higher then the 5% return earned on the t-bill, we are offered an arbitrage opportunity. We will choose to buy either of the portfolios constructed above and sell the t-bill. This arbitrage portfolio will earn a positive profit with no risk. Consequently, when the two assets are perfectly positively correlated we will hold asset A long and short asset B. When the assets are perfectly negatively correlated we will hold both assets long.
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