Please show all work $($formulas etc...$)$ NO EXCEL. Thank you!!

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. The

correlation coefficient between the stock and bond fund is $0\mathrm{.}15,$ the probability distributions of the

securities are shown below. You can use Excel to do this problem.

a$.$ Graph the opportunity set between the stock and bond fund starting with $0\%$ in the stock

fund and increasing it to $100\%$ in increments of $10\%.$ At each weight paring show the

expected return, standard deviation, and Sharpe ratio of the risky portfolio.

b$.$ What is the proportional weight of the risky portfolio in the stock and bond funds which

optimizes the expected Sharpe ratio of the risky portfolio?

c$.$ What is the proportional weight of the risky portfolio in the stock and bond funds which has

the minimum expected variance for the risky portfolio? For this min$-$variance portfolio what

is the expected return and standard deviation of the risky portfolio?