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 –18.20 % –35.5 % 2 % 2009 25.1 20.6 5 2010 13.5 12.7 2 2011 6.8 8.4 6 2012 –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.) Sharpe ratio Treynor ratio

Answer 1

Calculate the standard deviation of mutual fund and market index using STDEV.S function in excel

Mean of fund=5.068%

Mean of Risk free rate=3.6%

std of fund =STDEV.S(-18.20%,25.10%,13.50%,6.80%,-1.86%)=0.1632

stdof market=STDEV.S(-35.50%,20.60%,12.70%,8.40%,-4.20%)=0.2198

? = Correlation Coefficient × (Standard Deviation of Stock ReturnsBetween Market and StockStandard Deviation of Market Returns)

=0.97*(0.1632/0.2198)=0.72

Sharpe ratio =( fund return-risk free rate)/std of fund

=(5.068-3.6)/0.1632=0.09

Treynor ratio=( fund return-risk free rate)/Beta

=(5.068-3.6)/0.72=0.0204