Problem $7$ This question deals with the optimal portfolio choice for an investor with mean$-$

variance preferences in a world with two risky securities$,$ and $B,$ and a risk free asset, F$.$ Security

A offers an expected return of $2\%$ and has a standard deviation of return of $2\%.$ Security B has

expected return and standard deviation of $9\%$ and $7\%,$ respectively. The correlation coefficient

between securities $$ and B is $-0\mathrm{.}5.$ The investor can also borrow and lend at a risk free rate of $1\%$

per month.

a$.$ Compute and plot the expected return and standard deviation combinations that the investor

can achieve by combining securities $$ and $B$ into a portfolio.

b$.$ What is the optimal portfolio of risky assets for the investor in such a world?

c$.$ Does the optimal portfolio of risky assets in $($b$)$ depend on the risk preferences of the investor?

Why or why not?