Question

You have been given the following return 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 0.97. Year Fund Market Risk-Free 2011 –23.0 % –43.5 % 3 % 2012 25.1 21.4 5 2013 14.3 15.1 2 2014 6.8 8.8 6 2015 –2.34 –5.2 2 What are the Sharpe and Treynor ratios for the fund?

Answer 1

Using Excel Formula Calculate Average Return and Standard Deviation of Fund, Market and Risk-Free as follows -

Year	Fund	Market	Risk-Free
2011	-23.0%	-43.5%	3%
2012	25.1%	21.4%	5%
2013	14.3%	15.1%	2%
2014	7%	8.8%	6%
2015	-2.34%	-5.2%	2%
Average Return	=AVERAGE(B2:B6) = 4.172%	=AVERAGE(C2:C6)= -0.6.80%	=AVERAGE(D2:D6)=3.60%
Standard Deviation	=STDEV.S(B2:B6) = 0.18222	=STDEV.S(C2:C6) = 0.258862	=STDEV.S(D2:D6) = 0.01817
Correlation between Fund and Market (Given) = r =	0.97
Variance of Market = (Standard Deviation of market)2*100 = (0.258862)2*100	6.7010%
Covariance of Fund and Market
'= (r*Std deviation of Fund*Std Deviation of Market)*100 = (0.97*0.18222*0.258862)*100	4.5755%
Beta = Covariance of Fund and Market / Variance of Market = 4.5755 / 6.7010	0.6828
Sharpe Ratio
= (Average Return of Fund - Average Return of Risk-Free) / Std Deviation of Fund
= (4.172 - 3.60) / 0.18222
= 0.572 / 0.18222
= 3.1391%
Treynor Ratio
= (Average Return of Fund - Average Return of Risk-Free) / Beta of Fund
= (4.172 - 3.60) / 0.6828
= 0.572 / 0.6828
= 0.8377%