Question

Given the performance of 3 mutual funds and S&P500 over the past 15 years in table below:

Return and Risk data for 4 equity mutual funds, 15 year period

Mutual Fund	Average Return %	Standard Deviation %	Beta	R 2
1	15.86	12.85	1.10	.34
2	22.09	15.27	1.42	.79
3	18.39	14.82	0.65	.39
S&P 500	16.35	12.44	1.0	1.0

And assuming that current and average of past 15 years risk free rate is 7.96 %, expected market return is 16.35 % and using a market risk premium of 8.39% (16.35 -7.96) for the 15 year period, estimate:

a. Sharpe ratios of all 3 funds and S&P 500. Which fund has the highest risk adjusted performance according to Sharpe measure? Which of the above funds have beaten the market? (15 points)
b. Treynor of all 3 funds and S&P 500. Which fund has the highest risk adjusted performance according to Treynor measure? Which of the above funds have beaten the market? (15 points)
c. Jensen’s alpha for fund 1?(15 points)
d. Which fund is exposed to most nonsystematic risk? (15 points)

Put the answers of a, b, c in the Table by copy/pasting the table below into the answer box:

Mutual Fund	Sharpe	Treynor	Jensen
1
2			No need
3			No Need
S&P 500			No need

Answer 1

Sharpe ratio of Mutual fund 1 = (Return of Fund 1 - Risk free rate) / Standard Deviation  of Fund 1

Sharpe ratio of Mutual fund 1 = (15.86% - 7.96%) / 12.85%

Sharpe ratio of Mutual fund 1 = 0.6148

Sharpe ratio of Mutual fund 2 = (Return of Fund 2 - Risk free rate) / Standard Deviation of Fund 2

Sharpe ratio of Mutual fund 2 = (22.09% - 7.96%) / 15.27%

Sharpe ratio of Mutual fund 2 = 0.9253

Sharpe ratio of Mutual fund 3 = (Return of Fund 3 - Risk free rate) / Standard Deviation of Fund 3

Sharpe ratio of Mutual fund 3 = (18.39% - 7.96%) / 14.82%

Sharpe ratio of Mutual fund 3 = 0.7038

Sharpe ratio of S&P 500 = (Return of S&P 500 - Risk free rate) / Standard Deviation of S&P 500  

Sharpe ratio of S&P 500 = (16.35% - 7.96%) / 12.44%

Sharpe ratio of S&P 500 = 0.6744

Fund 2 & 3 have beaten the market based on Sharpe ratio

Treynor ratio of Mutual fund 1 = (Return of Fund 1 - Risk free rate) / Beta of Fund 1

Treynor ratio of Mutual fund 1 = (15.86% - 7.96%) / 1.10

Treynor ratio of Mutual fund 1 = 0.0718

Treynor ratio of Mutual fund 2 = (Return of Fund 2 - Risk free rate) / Beta of Fund 2

Treynor ratio of Mutual fund 2 = (22.09% - 7.96%) / 1.42

Treynor ratio of Mutual fund 2 = 0.0995

Treynor ratio of Mutual fund 3 = (Return of Fund 3 - Risk free rate) / Beta of Fund 3

Treynor ratio of Mutual fund 3 = (18.39% - 7.96%) / 0.65

Treynor ratio of Mutual fund 3 = 0.1605

Treynor ratio of S&P 500 = (Return of S&P 500 - Risk free rate) / Beta of S&P 500

Treynor ratio of S&P 500 = (16.35% - 7.96%) / 1

Treynor ratio of S&P 500 = 0.0839

Fund 2 & 3 have beaten the market based on Treynor ratio

Jensen Alpha for fund 1 = Return of fund 1 - (Risk free rate + Beta * Market risk premium)

Jensen Alpha for fund 1 = 15.86% - (7.96% + 1.1 * 8.39%)

Jensen Alpha for fund 1 = -1.329% or -1.33%

Non systematic risk for Fund 1 = (Standard Deviation  of Fund 1)² - (Beta of Fund 1 * Standard Deviation  of S&P 500)²

Non systematic risk for Fund 1 = (12.85%)² - (1.1 * 12.44%)²

Non systematic risk for Fund 1 = -0.002213

i = -1

Non systematic risk for Fund 1 = 4.70i%

Non systematic risk for Fund 2 = (Standard Deviation  of Fund 2)² - (Beta of Fund 2 * Standard Deviation  of S&P 500)²

Non systematic risk for Fund 2 = (15.27%)² - (1.42 * 12.44%)²

Non systematic risk for Fund 2 = -0.007887

i = -1

Non systematic risk for Fund 2 = 8.88i%

Non systematic risk for Fund 3 = (Standard Deviation  of Fund 1)² - (Beta of Fund 1 * Standard Deviation  of S&P 500)²

Non systematic risk for Fund 3 = (14.82%)² - (0.65 * 12.44%)²

Non systematic risk for Fund 3 = 0.0154249

Non systematic risk for Fund 3 = 12.42%

Fund 3 has the most amount of Non systematic risk

Mutual Fund	Sharpe Ratio	Treynor Ratio	Jensen Alpha
1	0.6148	0.0718	-1.33%
2	0.9253	0.0995	No need
3	0.7038	0.1605	No need
S&P 500	0.6744	0.0839	No need