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
2011	–22.40	%	–42.50	%	3	%
2012	25.10		21.30		5
2013	14.20		14.80		2
2014	6.60		8.80		6
2015	–2.28		–5.20		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

Year	Fund		Market		Risk-Free		Excess Return
2011	-22.40	%	-42.5	%	3	%	20.10
2012	25.10		21.3		5		3.80
2013	14.20		14.8		2		-0.60
2014	6.60		8.8		6		-2.20
2015	-2.28		-5.2		3		2.92
Mean	4.244		-0.56		3.8		4.804
=Item - Mean	-26.64		-41.94				15.30
	20.86		21.86				-1.00
	9.96		15.36				-5.40
	2.36		9.36				-7.00
	-6.52		-4.64				-1.88
Squared	709.902736		1758.963600				233.967616
	434.972736		477.859600				1.008016
	99.121936		235.929600				29.203216
	5.550736		87.609600				49.056016
	42.562576		21.529600				3.549456
Mean of squared	258.422144		516.378400				63.356864
Sq. Root	16.075514	=Std. Dev.	22.723961	=Std. Dev.			7.959703	=Std. Dev.
β = Correlation Coefficient Between Market and Stock × Standard Deviation of Stock Returns/Standard Deviation of Market Returns
=	0.97*16.075514/22.723961	=	0.686203
Jensen's alpha = Portfolio return - [Risk Free Rate + Portfolio Beta * (Market Return - Risk Free Rate)].
	=4.244-(3.8+0.686203*(-0.56-3.8))	=	3.4358
Information ratio Formula = (Rp – Rb) / Tracking error
where,
Rp = Rate of return of the investment portfolio
Rb = Benchmark rate of return
Tracking error = Standard deviation of the excess return with respect to the benchmark rate of return
Tracking Error=	7.959703
Inf. Ratio=	0.6035