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 .97.

Year	Fund		Market		Risk-Free
2015	−15.2	%	−30.5	%	3	%
2016	25.1		20.1		4
2017	13.0		11.2		2
2018	7.4		8.0		5
2019	−1.56		−3.2		2

What are the Sharpe and Treynor ratios for the fund?

Sharpe=

Treynor=

Answer 1

Year	Fund return in %
2015	-15.2
2016	25.1
2017	13
2018	7.4
2019	-1.56
Average rate of return on funds =Using average function on MS excel	AVERAGE(F720:F724)	5.75
Standard deviation =Using stdevp function in MS excel	STDEVP(F720:F724)	13.58
Year	Market return in %
2015	-30.5	-31.6
2016	20.1	19
2017	11.1	10
2018	8	6.9
2019	-3.2	-4.3
Average rate of return on funds =Using average function on MS excel	AVERAGE(F729:F733)	1.1
Standard deviation =Using stdevp function in MS excel	STDEVP(F729:F733)	17.47
Year	risk free return in %
2015	3
2016	4
2017	2
2018	5
2019	2
Average rate of return on funds =Using average function on MS excel	AVERAGE(F729:F733)	3.2
Beta of fund = (standard deviation of fund/standard deviation of market)*correlation betweend fund and market return	(13.58/17.47)*.97	0.75
required rate of return	risk free rate+(market return-risk free rate)*beta	3.2+(1.1-
Sharpe ratio =	(expected average return-risk free rate)/standard deviation of fund	(5.75-3.2)/13.58	0.1878
Treynor ratio	(expected average return-risk free rate)/beta of fund	(5.75-3.2)/.75	3.4000