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

Micro Forecasts

Asset Expected Return $(\%)$ Beta Residual Standard Deviation $(\%)$

Stock A $251\mathrm{.}264$

Stock B $222\mathrm{.}074$

Stock C $211\mathrm{.}163$

Stock D $161\mathrm{.}058$

Macro Forecasts

Asset Expected Return $(\%)$ Standard Deviation $(\%)$

T$-$bills $120$

Passive equity portfolio $2025$

Required:

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

Compute the proportion in the active portfolio and the passive index.

What is the Sharpe ratio for the optimal portfolio?

By how much did the position in the active portfolio improve the Sharpe ratio compared to a purely passive index strategy?

What should be the exact makeup of the complete portfolio $($including the risk$-$free asset$)$ for an investor with a coefficient of risk aversion of $3\mathrm{.}2?$