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

is a bond fund, and the third is a T$-$bill fund that yields a rate of $8\%.$ The correlation between the

fund returns is $0\mathrm{.}1.$ The expected returns and the standard deviations are as follows:

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

funds?

b$.$ Calculate the expected return and standard deviation of the minimum$-$variance portfolio.

c$.$ Calculate the expected return and standard deviation of portfolios invested in the two risky

funds with weights as follows:

d$.$ Draw the investment opportunity set of the two risky funds and mark the minimum$-$variance

portfolio $($based on parts $b$ and $c).$

e$.$ If you were to use only the two risky funds, and still require an expected return of $14\%.$

Calculate the investment proportions of your portfolio and the standard deviation of the

portfolio.

Take your time on this problem!!