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: Expected return Standard deviation Stock fund ( S ) 20% 30% Bond fund ( B ) 12% 15% The correlation between the fund returns is 0.1. 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? 2) Tabulate and draw the investment opportunity set of two risky funds. Use investment proportions for the stock funds of zero to 100% in increments of 20%. 3) Draw a tangent from the risk-free rate to the opportunity set. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. 4) You require that your portfolio yield an expected return of 14% a) What is the standard deviation of your optimal portfolio? b) What is the proportion invested in the T-bill fund and each of two risky funds? 5) If you were to use only the two risky funds, and still require an expected return of 14%, what must be the investment proportions of your portfolio? Compare its standard deviation to that of the optimized portfolio in Problem 4). What do you conclude?