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. Risk-Free Year 2011 2012 2013 2014 2015 Fund -17.68 25.1 13.4 6.6 -1.8 Market -34.5% 20.5 12.4 8 .4 -4.2 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

First we need to calculate the standard deviation of the fund and the market:

Years	Fund	Market	(XFund-Average Fund return)2	(XMarket-Average Market Return)2	Risk free asset
2011	-17.60%	-34.50%	5.171076%	12.264004%	0.02
2012	25.10%	20.50%	3.984016%	3.992004%	0.04
2013	13.40%	12.40%	0.682276%	1.411344%	0.02
2014	6.60%	8.40%	0.021316%	0.620944%	0.05
2015	-1.80%	-4.20%	0.481636%	0.222784%	0.03
Sum	25.70%	2.60%	10.3403200%	18.51%	16.00%
n	5	5	5	5	5
Average = Sum/n	5.14%	0.52%			3.20%
n-1			4	4
Variance= sum of (XFund-Average Fund return)2/(n-1)			2.58508%	4.62777%
Standard deviation= square root of variance			16.07818%	21.512252%

Fundaverage return - Risk Free average return Sharpe ratio = O Fund

Sharpe ratio = 5.14 - 3.20 16.07818

Sharpe ratio = 0.121

Fundaverage returns - Risk Free average return Treynor ratio = BFund

beta fund = O fund XP(Fund Market) O Market

correlation coefficient

PFund Market

beta fund =- 16.07818 x 0.97 21.512252 -= 0.72

5.14 - 3.20 Treynor ratio = ? 0.72

Sharpe ratio = 0.027