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4. You are thinking about investing in one of the two mutual funds, MassMutual and Vanguard. You have obtained the following information based on their performance over the last five years. Of course, you can always have the alternative option of investing in S&P 500 index instead of the mutual funds. The T-bill rate is averaged 5% in last 5 years. MassMutual Vanguard S&P500 Index Average Return 30% 25% 15% Beta 2 1.8 1 Standard Deviation 28% 18% 13% a) Calculate the following performance measure for MassMutual, Vanguard and the Index: Sharpe measure, Jensen measure, and Treynor measure. By each of the three measures, did MassMutual or Vanguard outperform the market index? b) Calculate the M measure of MassMutual and Vanguard using market index as benchmark (i.e. set standard deviation to market level). c) Calculate the T measure of MassMutual and Vanguard using market index as benchmark (i.e. set beta to market level). d) Calculate the MP measure of MassMutual using Vanguard as benchmark (i.e. set standard deviation of Mass Mutual to Vanguard level). e) Calculate the T2 measure of Vanguard using MassMutual as benchmark (i.e. set beta of Vanguard to MassMutual level). Formula Sheet For Help -rf -rf o 1) Sharpe measure S=- 2) Treynor measure T= B 3) Jensen measure: a = -E(r) where E(r)=r;+B[E(1M)=r;] = 4) MP and T measure Asset A relative to Asset B (B as the benchmark) M=(SA-SBOB S for Sharpe ratio T2=(TA-TB)BB T for Treynor ratio

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