The risk free rate is $2\%$

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a$.$ Describe the process used to derive the risky asset weights in the optimal portfolio.

b$.$ Calculate the expected return of the optimal risky portfolio $($write out the equation$).$

c$.$ Calculate the standard deviation of the optimal risky portfolio $($write out the equation$).$

d$.$ Calculate the Sharpe ratio of the optimal risky portfolio $($write out the equation$).$

e$.$ If the highest standard deviation I am willing to accept is $8\%,$

$$ i$.$ How much do I invest in the optimal risky portfolio? How much do I invest in the risk$-$free asset?$$

$$ ii$.$ What is my expected return for this portfolio?

$$ iii.$$ What is the Sharpe ratio of this portfolio?$$

f$.$ If I require an expected return of $10\%$ and can only invest in the stock fund and the bond fund,

$$ i$.$ What are my weights in those two funds?$$

$$ ii$.$ What is the standard deviation of that portfolio?

$$ iii.$$ What is the Sharpe ratio of that portfolio?

g$.$ If my risk aversion parameter is $4\mathrm{.}6,$ how much wealth should I allocate to my optimal risky portfolio and how much to the risk free asset?