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Problem 3 (20) Three funds' returns follow the market index model as below: Rpt = dp + BpRmt + Ept where Rpt denotes the annual excess returns of the funds and Rmt 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 C 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 s/he 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. Problem 3 (20) Three funds' returns follow the market index model as below: Rpt = dp + BpRmt + Ept where Rpt denotes the annual excess returns of the funds and Rmt 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 C 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 s/he 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