Question $2(20$ points$)$

Consider three investors $A,B,$ and C$.$ Investor A$\text{'}$s risk aversion coefficient ${}_A=4,B\text{'}$s risk

aversion coefficient ${}_B=1\mathrm{.}25,$ and C$\text{'}$s risk aversion coefficient ${}_C=3\mathrm{.}2.$ There are two risky

assets. Suppose the risk$-$free borrowing rate is $7$ percent and the risk$-$free saving rate is $5$

percent. The objective of the three investors is to maximize $E(r_c)-0\mathrm{.}005{}_i{}_c^2,$ where $E(r_c)$

and ${}_c^2$ are the expected return and the variance of an investor's portfolio and $i=A,B,C.$

Investor A finds it optimal to save $25\mathrm{.}6\%$ of his total wealth and invest the rest of his wealth in

the tangency portfolio, and investor B finds it optimal to borrow $15\mathrm{.}8\%$ of her total wealth

$($plus her own money$)$ to invest in the tangency portfolio. What is investor C$\text{'}$s optimal

portfolio weight on the risk$-$free asset?