Question $5(10$ marks$)$

Consider the following classic portfolio choice problem. Two assets are available to an investor

at time t$.$ One is riskless, with simple return $R_f$ from time $t$ to $t+1,$ and the other is risky. The

risky asset has simple return $R$ from time $t$ to $t+1.$ The investor puts a share $w$ of his portfolio

into the risky asset. We assume that the investor trades off mean and variance in a linear fashion.

That is$,$ investor maximizes a linear combination of mean and variance, with a positive weight on

mean and a negative weight on variance:

$u=(E[R_p]-\frac{k}{2}{}_p^2)$

a$)(7$ marks$)$ What is the proportion of wealth invested in risky asset?

b$)(8$ marks$)$ Explain two$-$fund separation in relation to your answer in part $($a$).$ What does k

represent and why?Question $3(15$ marks$)$ Consider the following classic portfolio choice problem. Two assets are available to an investor at time t$.$ One is riskless, with simple return R$,$ from time t to t$+1,$ and the other is risky. The risky asset has simple return R from time t to t$+1.$ The investor puts a share w of his portfolio into the risky asset. We assume that the investor trades off mean and variance in a linear fashion. That is$,$ investor maximizes a linear combination of mean and variance, with a positive weight on mean and a negative weight on variance: $--($e$[2.]$ ;) a$)(7$ marks$)$What is the proportion of wealth invested in risky asset? b$)(8$ marks$)$ Explain two$-$fund separation in relation to your answer in part $($a$).$ What does k represent and why?