Optimal Portfolio Choice

Problem

Your uncle asks for investment advice. Currently, he has $$100,000$ invested in portfolio $P$ in

Figure $11\mathrm{.}10,$ which has an expected return of $10\mathrm{.}5\%$ and a volatility of $8\%.$ Suppose the risk$-$

free rate is $5\%,$ and the tangent portfolio has an expected return of $18\mathrm{.}5\%$ and a volatility of

$13\%.$ To maximize his expected return without increasing his volatility, which portfolio would

you recommend? If your uncle prefers to keep his expected return the same but minimize his

risk, which portfolio would you recommend?