Question $8($Optimal complete portfolio $3$pt$)$

A pension fund manager is considering three mutual funds. The first is a stock fund, the second

is a long$-$term government and corporate bond fund, and the third is a T$-$bill money market fund

that yields a rate of $8\%.$ The probability distribution of the risky funds is as follows:

The correlation between the fund returns is $0\mathrm{.}1.$

What are the investment proportions in the minimum$-$variance portfolio of the two risky

funds, and what is the expected value and standard deviation of its rate of return? $(0\mathrm{.}5$pt$)$

Tabulate and draw the investment opportunity set of the two risky funds. Use investment

proportions for the stock fund of $0\%$ to $100\%$ in increments of $20\%.(0\mathrm{.}5$pt$)$

Draw a tangent from the risk$-$free rate to the opportunity set. What is the expected return

and standard deviation of the tangent portfolio? $(1$pt$)$

You have risk aversion coefficient of $4,$ so your utility is

$U=E[r_P]-\frac{4}{2}{}_{r_P}^2.$

What is the optimal complete portfolio that you will hold? Please give the portfolio weight

on risk$-$free asset and the risky assets. $(1$pt$)$