2) An insurance 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 one is a risk-free asset that yields a certain rate of 8%. The probability distributions of the risky funds are: Stock fund: E(R) = 20% and variance = 30%. Bond fund: E(R) = 12% and variance= 15%. The correlation coefficient between the fund returns is p= 0.1.

(a) What are the weights of the minimum-variance portfolio proportions? Calculate the expected return and standard deviation of this portfolio.

(b) Derive the tangency portfolio. What is the corresponding reward-to-variability (Sharpe) ratio?