Carol and Su are considering investing in two funds: Fund A and Fund B. So far, they can borrow at risk-free rate or invest in T-bill frictionless. The excess returns of the Funds A and B follow the market index model with the following results: Rt = 1% + 0.5Rmt + Eat Rgt = -2.0% + 1.1Rmt + Eat o(RMt) = 20%, o (Eat) = 10%, o (Ebt) = 5% where, Rt, Rt, and Rmt denote the excess returns of fund A, fund B, and the S&P500 index portfolio in year t. o(Rmt), o (eat), and oebe) denote the standard deviations of RMt, Eat and Ebt. Assume the risk-free rate is 2% per year, the expected return of the S&P500 index portfolio is 12% per year. Expense ratio for both funds is zero. Carol and Su are mean-variance investors with the following utility functions, U = E(r) {A02, where r denotes the return of the investment. Carol's optimal allocation to the risk-free asset and the funds A and B are: (38%, 43%, 19%). Note that investors use the same rounding scheme to construct optimal allocations. (a) What is the risk premium for Fund A? (5%) (6) What is the variance of the returns on Fund A? (5%) ( (C) What must be the optimal allocation to the risk-free asset for Su, if you know Su's risk aversion parameter A is half of Carol's risk aversion parameter? (5%)