Question

Consider the following 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
2008	–15.2	%	–24.5	%	1	%
2009	25.1		19.5		3
2010	12.4		9.4		2
2011	6.2		7.6		4
2012	–1.2		–2.2		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

	Fund	Market	Risk-free
2008	-15.20%	-24.50%	1%
2009	25.10%	19.50%	3%
2010	12.40%	9.40%	2%
2011	6.20%	7.60%	4%
2012	-1.20%	-2.20%	2%
Average	4.58%	0.76%	2.39%
Std. Dev.	15.05%	16.68%
Sharpe	0.1454
Treynor	0.0250

Calculate Geometric Average Return using following formula:

(1 + R)^5 = (1 + R1) x (1 + R2) x... x (1 + R5)

For Fund, Rp = 4.58% and for Risk-free rate, Rf = 2.39%

Standard deviation can be calculated using STDEV.S function in excel.

Std. Dev. of Fund, SDp = 15.05% and that for Market, SDm = 16.68%

Sharpe Ratio = (Rp - Rf) / SDp = (4.58% - 2.39%) / 15.05% = 0.1454

Beta = Correlation x SDp / SDm = 0.97 x 15.05% / 16.68% = 0.875

Treynor Ratio = (Rp - Rf) / beta = (4.58% - 2.39%) / 0.875 = 0.0250