$17.$ A portfolio manager summarizes the input from the macro and micro forecasters in the follow$-$ing table:Macro ForecastsAsset Expected Return $(\%)$ Standard Deviation $(\%)$T$-$bills $80$Passive equity portfolio $1623$Micro ForecastsAsset Expected Return $(\%)$ Beta Residual Standard Deviation $(\%)$Stock A $201\mathrm{.}358$Stock B $181\mathrm{.}871$Stock C $170\mathrm{.}760$Stock D $121\mathrm{.}055$a$.$ Calculate expected excess returns, alpha values, and residual variances for these stocks.b$.$ Construct the optimal risky portfolio.c$.$ What is the Sharpe ratio for the optimal portfolio?d$.$ By how much did the position in the active portfolio improve the Sharpe ratio compared to apurely passive index strategy?e$.$ What should be the exact makeup of the complete portfolio $($including the risk$-$free asset$)$ foran investor with a coefficient of risk aversion of $2\mathrm{.}8?$