Short Question (SQ2) (15\%) 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: RAte=1%+0.5Rmte+AtRBte=2.0%+1.1Rmte+At(Rmte)=20%,(At)=10%,(Bt)=5% where, RAte,RBte, and Rmte denote the excess returns of fund A, fund B, and the S\&P500 index portfolio in year t.(Rmte),(At), and (Bt) denote the standard deviations of Rmte,At and Bt. 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) 21A2, 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%) (b) 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\%)