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

What are the alphas of portfolios A and B?

Create an arbitrage portfolio from the above assets with the weight W_A = 1, and W_B to be determined. What are W_M and W_F?

Write algebraic expressions for the expected arbitrage profit and the standard deviation, assuming the correlation between the residuals is -0.2.

The best choice for W_B 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_B. You can do it using calculus or by plotting the ratio for various W_B and selecting the optimum visually.

For your choice of W_B, what is the expected profit if the notional investment in A is

$1 million?

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