The following data apply to Problems $4$ through $10$: A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term bond fund, and the third is a money market fund that provides a safe return of $8\%.$ The characteristics of the risky funds are as follows:

The correlation between the fund returns is $\mathrm{.}10.$

What are the investment proportions in the minimum$-$variance portfolio of the two risky funds, and what are the expected value and standard deviation of its rate of return?

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 $20\%.$

Draw a tangent from the risk$-$free rate to the opportunity set. What does your graph show for the expected return and standard deviation of the optimal portfolio?