Q$4$ The optimal risky portfolio $P^{**}$ has an expected return of $12\mathrm{.}5\%$ and a standard deviation

of $19\%.$ The current risk$-$free rate in the market is $3\mathrm{.}5\%.$

a$.$ Draw the capital allocation line. What is the slope of this line and what does it represent?

Suppose that separation theorem holds, and all investors invest along a common capital

allocation line. Consider two different investors. Aggressive investor A holds an optimal

complete portfolio which has a standard deviation of $25\%.$ Conservative investor $C$ holds an

optimal complete portfolio with a standard deviation of $14\%.$

b$.$ What is the Sharpe Ratio of Investor A and Investor C$\text{'}$s optimal complete portfolio?

c$.$ What is the expected return of Investor A and Investor C$\text{'}$s optimal complete portfolio?

d$.$ What is allocation to risky assets $y**$ for Investor A and Investor C$\text{'}$s optimal complete

portfolio?

e$.$ Derive the implied risk aversion coefficient for Investor A and Investor C$.$

f$.$ Explain why these results are a demonstration of separation theorem.