Problem 1 (15%) Assume that you are a mean-variance investor. You are given the following data on the market portfolio, the risk-free asset, and funds A and B: Risk-free Market portfolio Fund A Fund B Mean return, E[r] 4% 11% 10% 12% Std. deviation, o 0 18% 12% 25% The correlation of fund A with the market is 0.8, and the correlation of fund B with the market is 0.4. a) If you want to invest all of your money in one fund, will you prefer fund A, fund B, or the market? b) If you are invested in many funds, will you prefer to add fund A or fund B to your holdings? Now suppose that there is another fund C with the mean return of 7% and the standard deviation of 14%. The correlation of fund C with the market is -0.8. c) Suppose you are considering either investing all of your money in a combination of fund C with the market or investing all of your money in fund A. Can you combine fund C and the market in a portfolio that is strictly better than fund A? Problem 1 (15%) Assume that you are a mean-variance investor. You are given the following data on the market portfolio, the risk-free asset, and funds A and B: Risk-free Market portfolio Fund A Fund B Mean return, E[r] 4% 11% 10% 12% Std. deviation, o 0 18% 12% 25% The correlation of fund A with the market is 0.8, and the correlation of fund B with the market is 0.4. a) If you want to invest all of your money in one fund, will you prefer fund A, fund B, or the market? b) If you are invested in many funds, will you prefer to add fund A or fund B to your holdings? Now suppose that there is another fund C with the mean return of 7% and the standard deviation of 14%. The correlation of fund C with the market is -0.8. c) Suppose you are considering either investing all of your money in a combination of fund C with the market or investing all of your money in fund A. Can you combine fund C and the market in a portfolio that is strictly better than fund A