Consider a standard portfolio choice problem with two risky assets: equity and

risky bond. Their expected returns, standard deviations, and the correlation co$-$

efficient are given by

$[$

$]$

a$)$ Suppose the risk$-$free interest rate is $5\%,$ find the tangency portfolio.

b$)$ Given the $5\%$ risk$-$free interest rate and the utility function of an investor

$E(r_c)-0\mathrm{.}005A{}_c^2,$ where $A=5,$

what are the investor's optimal portfolio weights on the equity and risky bond?

c$)$ Suppose the risk$-$free interest rate is $6\%,$ find the tangency portfolio.

d$)$ Suppose the risk$-$free saving rate is $5\%$ and the risk$-$free borrowing rate is $6\%.$

Find the optimal portfolio weights of equity, risky bond, and safe asset for an

investor with $A=2.$