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.
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?

Answer 1

Answer:

Sharpe ratio = 0.20

Treynor ratio = –0.005

Explanation:

Note: See the attached excel file for the calculations of average rate of returns, standard deviations and beta used in the calculation below.

a. Calculation of Sharpe ratio

Sharpe ratio refers to a  investment measurement that employed to measure the an investment actual that has been adjusted for the risk associated with the investment.

Sharpe ratio can be calculated using the following formula:

Sharpe ratio = (Average fund rate - Average Risk Free rate) / Standard deviation of fund rate = (5.46% - 2.40%) / 15.05% = 0.20

a. Calculation of Treynor ratio

Treynor ratio refers to investment measurement that is calculated to show the risk of certain investments after the volatility of the market has been taking into consideration.

Treynor ratio can be calculated using the following formula:

Treynor ratio = (Average market return rate - Average Risk Free rate) / Beta = (1.96% - 2.40%) / 87.53% = –0.005

Download xlsx