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 0.87.

Year	Fund		Market		Risk-Free
2011	–18.20	%	–35.50	%	2	%
2012	25.10		20.60		5
2013	13.50		12.70		2
2014	6.80		8.40		6
2015	–1.86		–4.20		3

Calculate Jensen’s alpha for the fund, as well as its information ratio. (Do not round intermediate calculations. Enter the alpha as a percent rounded to 2 decimal places. Round the ratio to 4 decimal places.)

Answer 1

Jensen's Alpha = Actual return - expected return.

Actual returns are provided.

Expected return is calculated using CAPM as risk-free rate + beta*(market return - risk-free rate)

Beta = correlation *standard deviation of the Fund/standard deviation of the market

(Note: all standard deviations are calculated using the STDEV.P() function in excel.)

Standard deviation of the Fund = 14.59%

Standard deviation of the market = 19.66%

Beta of the Fund = 0.87*(14.59%/19.66%) = 0.65

Information ratio is calculated as the ratio of Jensen's alpha to the standard deviation of Jensen's alpha.

Calculations:

Formula	Fr	Mr	rf	Er = rf + beta*(Mr - rf)	Fr - Er	Jensen's alpha/Stdev of Jensen's alpha
Year	Fund return	Market return	Risk-Free rate	Expected return (using CAPM)	Jensen's alpha	Information ratio
2011	-18.20%	-35.50%	2%	-22.21%	4.01%	1.0298
2012	25.10%	20.60%	5%	15.07%	10.03%	2.5739
2013	13.50%	12.70%	2%	8.91%	4.59%	1.1785
2014	6.80%	8.40%	6%	7.55%	-0.75%	(0.1924)
2015	-1.86%	-4.20%	3%	-1.65%	-0.21%	(0.0542)
Stdev	14.59%	19.66%		Stdev	3.90%