Optional Extra Credit Assignment

This assignment is worth 100 points. In Calculating the assignments course score, I use the total points earned, divided by the total points possible from the Connect assignments (which does not include this assignment.) The solution, in the form of a Word document should be emailed to me by 11/26/22.

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

Expect rate Beta relative to M Standard deviation of the

of return regression (on VI) residuals

A 20% 1.5 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 W = 1, and W. to be determined. What are W and W,?

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 W 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 W. You can do it using calculus or by plotting the ratio for various W and selecting the optimum visually.

5. For your choice of We, what is the expected profit if the notional investment in A is S1 million?

6. Assuming a normal distribution, what is the chance that the arbitrage strategy will end-up in a loss?

Answer all questions please