A portfolio manager summarizes the input from the macro and micro forecasts in the following table:

Micro Forecasts

Asset	Expected Return (%)	Beta	Residual Standard Deviation (%)
Stock A	20	1.00	60
Stock B	18	2.50	40

Macro Forecasts
Asset	Expected Return (%)	Standard Deviation (%)
T-bills	5	0
Passive Equity Portfolio (m)	12	25

a. Calculate expected excess returns, alpha values, and residual variances for these stocks.

Expected excess return on stock A %

Expected excess return on stock B %

Alpha of stock A %

Alpha of stock B %

Residual variance of stock A

Residual variance of stock B

b. Suppose that the portfolio manager follows the Treynor-Black model, and constructs an active portfolio (p) that consists of the above two stocks. The alpha of the active portfolio (p) is -18%, and its residual standard deviation is 150%.

What is the Sharpe ratio for the optimal portfolio (consisting of the passive equity portfolio and the active portfolio (p))?

How much of the Sharpe ratio is contributed by the active portfolio?

Whats the M² of the optimal portfolio?