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  3. consider the following risky portfolios (a, b, m)

Consider the following risky portfolios (A, B, M) and the riskless asset F: Expect rate...

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Finance

Consider the following risky portfolios (A, B, M) and the riskless asset F: Expect rate of return Beta relative to M Standard deviation of the regression (on M) residuals A 21% 1.6 20% B 15% 1.2 20% M 10% 1 0 F 4% 0 0 1. What are the alphas of portfolios A and B? 2. Create an arbitrage portfolio from the above assets with the weight WA = 1, and WB to be determined. What are WM and WF? 3. Write algebraic expressions for the expected arbitrage profit and the standard deviation, assuming the correlation between the residuals is -0.2. 4. The best choice for WB is the one that maximizes the ratio of expected profit to standard deviation of the profit. Write the algebraic expression for this ratio and find the optimal WB. You can do it using calculus or by plotting the ratio for various WB and selecting the optimum visually. 5. For your choice of WB, what is the expected profit if the notional investment in A is $1 million? 6. Assuming a normal distribution, what is the chance that the arbitrage strategy will end-up in a loss?

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