Q$3.$ You have $$100$ invested in Portfolio P in the Figure below. It has $E[R_p]=10\mathrm{.}5\%$ and

$SD(R_p)=8\%.$ Assume $r_f=5\%,$ and the tangent portfolio, Portfolio T$,$ has an expected return

of $18\mathrm{.}5\%$ and a volatility of $13\%.$ Note that each black dot represents a portfolio.

a$.$ To maximize your expected return without increasing your volatility, which portfolio

would you invest in$?$ Explain your answer.

b$.$ To keep your expected return the same but minimize your risk, which portfolio would

you invest in$?$ Explain your answer.

c$.$ Which portfolio is not possible to invest in$?$ In other words, which portfolio is impossible

to construct? Explain your answer.