Consider the following information for a mutual fund, the market index, and the

Question

Consider the following information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is .97.

What are the Sharpe and Treynor ratios for the fund? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Treynor ratio

Consider the following information for a mutual fund, the market index, and the risk-free rate. You also know that the return correlation between the fund and the market is .97.

Year Fund Market Risk-Free 2008 –14.99 % –27.5 % 1 % 2009 25.1 19.8 5 2010 12.7 10.3 2 2011 6.8 7.6 4 2012 –1.38 –2.2 3

What are the Sharpe and Treynor ratios for the fund? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Sharpe ratio   

Treynor ratio

Explanation / Answer

Enter all the yearly returns in an excel sheet and

calculate averages of all returns given

Average return of fund = AVERAGE(A1:A5) = 5.65%

Average return of Market = AVERAGE(B1:B5) = 1.60%

Average risk free return = AVERAGE(C1:C5) = 3.00%

Standard deviation of the fund can be calculated as follows

=STDEV.S(A1:A4) = 15.04%

Note: A1 to A5, B1 to B5, C1 to C5 contains annual returns of fund, market and risk free return respectively

Sharpe ratio can be calculated as follows

Sharpe ratio = (Mean fund return Risk-free rate)/Standard deviation of fund return

= (5.65% - 3.00%) / 15.04% = 0.1759

Treynor ratio can be calculated as follows

Treynor ratio = (Mean fund return Risk-free rate)/Beta of fund return

= (5.65% - 3.00%) / 0.97 = 0.0273

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