A fund manager has obtained the following information for two securities as below

Security Beta Expected Return Residual Risk

A $1\mathrm{.}216\%20\%$

B $0\mathrm{.}810\%25\%$

The risk free rate is $5\%$ and the market risk premium is $8\%.$ The standard deviation of the market return is $30\%.$

$($a$)$ Calculate the optimal active portfolio and the optimal risky portfolio.

$($b$)$ Suppose your target return is $1\%$ less than the optimal risky portfolio. What is

your optimal investment strategy in the risk$-$free asset, the market portfolio,

and the two securities$?$