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 22 1.00 40

Stock B 20 2.50 60

Macro Forecasts

Asset Expected Return (%) Standard Deviation (%)

T-bills 7 0

Passive Equity Portfolio (m)12 25

Instruction: Enter your answer as a decimal number rounded to two decimal places for residual variances.

Residual variance of stock A

Residual variance of stock B

Instruction: for part b, enter your response as a decimal number rounded to four decimal places.

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))?

What's the M²of the optimal portfolio?