1. You are trying to plan your investments for the next year. You have decided that the market will either be strong (a bull market), weak (a bear market) or normal. You think that stocks, bonds, and bills will earn the following returns in these scenarios: Probability Scenario Bull market Normal market Bear market 0.20 0.55 0.25 Stock Bond Return Return 0.25 0.06 0.10 0.04 -0.15 -0.02 Bill Return 0.03 0.03 0.03 You have also decided that you have a risk-aversion (A) of 4. (a) What is the expected return for each of the securities? (b) What is the volatility of each security return? (c) What is the covariance between stock and bond returns? (d) If you combine stocks and bills as an investment, what is your op- timal combination? What is your expected return? What is your portfolio's volatility? (e) If you combine bonds and bills, what is your optimal combination? What is your expected return? What is your portfolio's volatility? (f) If you combine stocks and bonds, what is your optimal combination? What is your expected return? What is your portfolio's volatility? (g) If you combine all three assets in your portfolio, what is your op- timal combination? What is your expected return? What is your portfolio's volatility?