Question $3(20$ points$)$

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

Their expected returns, standard deviations, and the correlation coefficient are given by

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

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? $(5$ points$)$

c$)$ Suppose the risk$-$free interest rate is $6\%,$ find the tangency portfolio. $(5$ points$)$

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 $A=2.(5$

points$)$