Question $4(30$ points$)$

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

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

Suppose the utility function of an investor is

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

The investor is allowed to borrow or save. $($hint: you are able to answer part $b$ partially an

part $c$ without knowing the answer to part $a.)$

a$)$ Find the largest saving rate that prevents the investor from saving in his or her optim

portfolio. $(15$ points$)$

b$)$ Find the smallest borrowing rate that prevents the investor from borrowing in his or h

optimal portfolio. $(5$ points$)$

c$)$ Suppose the saving rate is smaller than your answer to part a$),$ and the borrowing ra

is larger than your answer to part b$),$ find the investor's optimal portfolio. $(10$ points$)$