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	–17.0	%	–33.5	%	2	%
2012	25.1		20.4		6
2013	13.3		12.1		2
2014	6.4		8.0		5
2015	–1.74		–3.2		3

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

Answer 1

1) Computation of Portfolio Return and Variance

                              

Year	Return on Market	Return on Fund	Risk Free Rate	Variance of Market	Variance OF Fund
	X	Y	Rf	(X-X)	(Y-Y)
2011	-33.5	-17	2	1173.7476	493.3729
2012	20.4	25.1	6	385.7296	395.5325
2013	12.1	13.3	2	128.5956	65.4157
2014	8	6.4	5	52.4176	1.4113
2015	-3.2	-1.74	3	15.6816	48.3303
Total	3.8	26.06	18	1756.1720	1004.0629
Average Return	X=3.8/5 = 0.76	Y=26.06/5 = 5.212	Rf = 18/5 = 3.6	Var = 1756.1720 /5         = 351.23	Var=1004.06 /5 =200.81

2) Computation Standard Deviation

Standard Deviation (SD) =

Standard Deviation of Market = = 18.74

Standard Deviation of Fund = = 14.17

3) Computation of Beta

Correlation (r) =0.97

Standard Deviation of Market (SDx) = 18.74

Standard Deviation of Fund (SDy) = 14.17

Beta of Fund = r * SDy/SDx

                        = 0.97 * 14.17/18.74

                        = 0.73

4) Computation of Sharpe and Treynor Ratio

Sharpe Ratio =   

                         =                 

                         = 0.12

Treynor Ratio Ratio =

                                      =

                                   = 2.20