You are thinking about investing in one of the following 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 any 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%

1) 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?

2) Calculate the M² measure of MassMutual and Vanguard relative to the market index (i.e. set standard deviation to market level).

3) Calculate the T² measure of MassMutual and Vanguard relative to the market index (i.e. set beta to market level).

4) Calculate the M² measure of MassMutual relative to Vanguard (i.e. set standard deviation of MassMutual to Vanguard level).

5) Calculate the T² measure of Vanguard relative to MassMutual (i.e. set beta of Vanguard to MassMutual level).