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	–21.8	%	–41.5	%	3	%
2012	25.1		21.2		4
2013	14.1		14.5		2
2014	6.4		8.8		4
2015	–2.22		–5.2		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-?

Answer 1

Year	Fund %	Market %	Risk-Free%
2011	–21.8	–41.5	3
2012	25.1	21.2	4
2013	14.1	14.5	2
2014	6.4	8.8	4
2015	–2.22	–5.2	3

Standard Deviation of Fund
Year (n=5)	Fund	(r- avg)	(r- avg)2
2011	–21.8	-26.116%	682.045
2012	25.1	20.784%	431.974
2013	14.1	9.784%	95.726
2014	6.4	2.084%	4.343
2015	–2.22	-6.536%	42.719
Average	4.316	∑(r-avg)2 =1256.807

Variance of Fund: = = 251.361

Standard Deviation = = 15.85%

Sharpe Ratio = = = = 0.2723

Standard Deviation of Market
Year (n=5)	Market	(r- avg)	(r- avg)2
2011	–41.5	-39.3	1544.49
2012	21.2	23.4	547.56
2013	14.5	16.7	278.89
2014	8.8	11	121
2015	–5.2	-3	9
Average	-2.2	∑(r-avg)2=2500.94

Variance of Market: = = 500.188

Standard Deviation of Market = = 22.36%

Correlation of Fund with Market = 0.97

Portfolio Beta = = = 0.687

Treynor Ratio = = = 4.3377