Consider the following information for a mutual fund, the market index, and the

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 .95.

Calculate Jensen’s alpha for the fund, as well as its information ratio. (Do not round intermediate calculations. Round your Jensen’s alpha answer to 2 decimal places and Information ratio answer to 4 decimal places. Omit the "%" sign in your response.)

Year Fund Market Risk-Free 2008 –15.13 % –25.5 % 2 % 2009 25.1 19.6 4 2010 12.5 9.7 2 2011 6.4 7.6 4 2012 –1.26 –2.2 3

Explanation / Answer

Jensen's alpha = expected portfolio return - (risk free rate + beta*(expected market return - risk free rate))

We will calculate the average returns of the fund and the market. Risk free rate will be the latest figure i.e for 2012 (3%)

Thus expected portfolio return = 5.522%, expected market return = 1.84% and risk free rate = 3%

Now we have to calculate beta. Beta = correlation between the fund and the market*standard deviation of returns of fund/standard deviation of returns of market

standard deviation = [sum of (x - mean)^2/N-1]^1/2 The formual "stdev" can also be used in excel to calculate the standard deviations. I used excel and the values are: standard deviation of fund returns = 15.0438. standard deviation of market returns = 17.1331

Beta = 0.95*15.0438/17.1331 = 0.8342

Jensen's alpha = 5.522 - (3+0.8342*(1.84-3))

= 5.522 - 2.0324

= 3.49%

Information ratio = expected value of the active return/standard deviation of the active return = E(return of fund - return of market)/standard deviation of ((return of fund - return of market)

The formula used in excel: active return = return of fund - return of market

For standard deviation the formula "stdev" has been used in excel.

Thus information ratio = 3.682/4.476742119

= 0.8225

Year Fund return Market return 2008 -15.13 -25.5 2009 25.1 19.6 2010 12.5 9.7 2011 6.4 7.6 2012 -1.26 -2.2 Mean 5.522 1.84

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