Three funds' returns follow the market index model as below: R = ap + Be +ept where Re denotes the annual excess returns of the funds and Regist is the annual excess return on the S&P 500 index. The information about three funds and the S&P 500 index is in the table below. Funds B Fund A Fund B Fund C S&P 500 T-bill Expected return 8% 18% 16% 10% 2% Standard Deviation 20% 60% 40% 20% 0 0.5 2 1.5 1.0 0 A mean-variance investor now considers making optimal allocations of his/her capital in A, B, or portfolios. Please answer the following questions. A) Assume this investor is only allowed to invest in one of the three funds and to invest in T-bill. Which fund will s/he invest? B) Continue on part A. If his/her risk aversion coefficient is 1.5, what is the weight of this fund in his portfolio? C) Assume s/he can access all three funds, and she is considering an equal weighted portfolio of all three funds. S/he asks you to evaluate this equal weighted portfolio. Please calculate this portfolio's beta, alpha, Sharpe ratio