1. You are thinking about investing in one of the following mutual funds, MassMu

Question

1. 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 MassMutuVanguardS&P5; 25% 30% Average Return Beta Standard Deviation 15% 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 using market index as benchmark (i.e. set standard deviation to market level). 3) Calculate the T2 measure of MassMutual and Vanguard using market index as benchmark i.e. set beta to market level). 4) Calculate the M2 measure of MassMutual using Vanguard as benchmark (i.e. set standard deviation of MassMutual to Vanguard level) 5) Calculate the T2 measure of Vanguard using MassMutual as benchmark (i e. set beta of Vanguard to MassMutual level).

Explanation / Answer

Sharpe ratio = (Mean Return from Portfolio – Riskfree rate)/Standard deviation of Portfolio Return

Jensen ratio= Expected Return from portfolio– ( Riskfree rate + Beta of portfolio* ( Market Return – Riskfree rate))

Treynor ratio= (Expected Return of portfolio – Riskfree rate)/Beta of portfolio

Msquare Measure = Riskfree rate + Sharpe ratio * Market Standard deviation

Tsquare Measure = Portfolio Return – Market Return/ Beta of portfolio

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1

Mass Mutual

Sharpe ratio = (Mean Return from Massmutual – Riskfree rate)/Standard deviation of Massmutual Return

= (30% - 5%)/28% = 0.89286

Jensen ratio= Expected Return from Massmutual – ( Riskfree rate + Beta of Massmutual * ( Market Return – Riskfree rate))

= 30% - (5% + 2 *(15% - 5%) = 5% = 0.05

Treynor ratio= (Expected Return of Massmutual – Riskfree rate)/Beta of Massmutual

= (30% - 5%)/2 = 0.125

Vanguard

Sharpe ratio = (Mean Return from Vanguard – Riskfree rate)/Standard deviation of Vanguard Returns

= (25%-5%)/18% = 1.11111

Jensen ratio= Expected Return from Vanguard– ( Riskfree rate + Beta of Vanguard* ( Market Return – Riskfree rate))

= 25% - (5% + 1.8 *(15%-5%) = 2% = 0.02

Treynor ratio= (Expected Return of Vanguard – Riskfree rate)/Beta of Vanguard

= (25% - 5%)/1.8 = 0.11111

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2

Massmutual

Msquare Measure = Riskfree rate + Sharpe ratio of Massmutual * Market Standard deviation

= 5% + 0.89286 * 13% = 16.60718 % = 0.16607

Vanguard

Msquare Measure = Riskfree rate + Sharpe ratio of Vanguard * Market Standard deviation

= 5% + 1.11111 * 13% = 19.44443% = 0.19444

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Massmutual

Tsquare Measure = Return from Massmutual – Market Return/ Beta of market

= 30% - 15%/1 = 15% = 0.15

Vanguard

Tsquare Measure = Return from Vanguard – Market Return/ Beta of market

= 25%- 15%/ 1 = 10% = 0.10

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Massmutual

Msquare Measure = Riskfree rate + Sharpe ratio of Massmutual * Vanguard Standard deviation

= 5% + 0.89286 * 18% = 21.07148% = 0.21071

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Vanguard

Tsquare Measure = Return from Vanguard – Market Return/ Beta of Massmutual

= (25% - 15%)/2 = 5% = 0.05

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