You are thinking about investing in one of the following mutual funds, Mass Mutu

Question

You are thinking about investing in one of the following mutual funds, Mass Mutual 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 ofany of the mutual funds. The T-bill rate is averaged 5% in last 5 years. MassMutual Vanguard S&P500; Index 30% 15% Average Return Beta Standard Deviation 25% 1.8 1896 28% 13% 4) Calculate the following performance measure for both MassMutual and Vanguard: Sharpe measure, Jensen measure, and Treynor measure. By each of the three measures, did MassMutual or Vanguard outperform the market index? a) Calculate the M2 measure of Mass Mutual and Vanguard using market index as benchmark (i.e, set standard deviation to market level). 6) Caleulate the T? measure of Mass Mutual and Vanguard using market index as benchmarik i.e set beta to market level). Calculate the M2 measure of MassMutual using Vanguard as benchmark (i.e. set standard deviation of MassMutual to Vanguard level). Calculate the Ta measure of Vanguard using Mass Mutual as benchmark (i.e. set beta of Vanguard to Mass Mutual level).

Explanation / Answer

1. a.) Mass Mutual

Sharpe= Avg Return-Risk Free Rate/Risk= 30-5/28= 0.89

Jensen= Reurn(portfolio)- ((Risk Free Rate+Beta(Market Return-Risk Free Rate)))= 30-(5+2(15-5))= .05

Treynor= Avg Return- Risk Free Rate/Beta= 30-5/2= 0.12

b.) Vanguard

Sharpe= 25-5/18= .01

Jensen= 25-(5+1(15-5))= 0.1

Treynor= 25-5/1.8= 0.11

Mass Mutual outperforms.

2. M2 =(Rp-Rf/Betap)*Betabenchmark+Rf

Mass Mutual =(30-5/2)*1+5 = 17.5%

Vanguard= (25-5/1.8)* 1+5 = 16.1%

3. T2= Treynor Square

Mass Mutual= 1.44%

Vanguard= 1.21%

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