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 −18.2 % −35.5 % 2 % 2016 25.1 20.6 5 2017 13.5 12.7 2 2018 6.8 8.4 6 2019 −1.86 −4.2 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

Calculation of Various Informations related to Ratio

Year	MutuaL Fund (F)	Market(M)	Risk Free	(F- F̅)^2	(M-M̅)^2
2015	-18.2	-35.5	2	541.3998	1288.81
2016	25.1	20.6	5	401.281	408.04
2017	13.5	12.7	2	71.09862	151.29
2018	6.8	8.4	6	2.999824	64
2019	-1.86	-4.2	3	47.99718	21.16
Total	25.34	2	18	1064.776	1933.3

Return of Fund (F̅) = ∑F/ n = 25.34/5 = 5.068

Return Of Market (M̅)= ∑M/ n = 2 / 5 = 0.4

Avg Risk Free = 18/5 = 3.6

Standard Deviation of Fund (F) = √ ∑[(F- F̅)]^2/n

= √1064.776/5

= 14.5929

Standard Deviation of Market (M) = √ ∑[(M-M̅)^2]/n

= √1933.3/5

= 19.6636

Beta of Fund = [Standard Deviation of Fund / Standard Deviation of Market ] * Corelation between Fund and market

= (14.5929/19.6636)*0.97 = 0.7198

Sharp Ratio of Fund = ( Return Of fund - Risk Free return ) / Standard Deviation of Fund

= ( 5.068-3.6) / 14.5929

= 0.1006

Treynor Ratio of Fund = ( Return Of fund - Risk Free return ) / Beta of Fund

= ( 5.068-3.6) / 0.7198

= 2.039