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 0.89.

Year	Fund		Market		Risk-Free
2011	–17.60	%	–34.50	%	2	%
2012	25.10		20.50		4
2013	13.40		12.40		2
2014	6.60		8.40		5
2015	–1.80		–4.20		3

Calculate Jensen’s alpha for the fund, as well as its information ratio.

Answer 1

1. Computation of Beta

Beta = Correlation * Standard deviation of Fund / Standard Deviation of Market

Beta = 0.89 * 0.1608 / 0.2151

Beta = 0.6652

Jensen's Alpha = Average Return of Fund - (Average Risk Free Rate + Beta * (Average Market Return - Average Risk Free Rate)

Jensen's Alpha = 5.14% - (3.20% + 0.6652 * (0.52% - 3.20%)

Jensen's Alpha = 3.72%

2. Information Ratio

Information Ratio = Average Market Return - Average Fund Return / Difference in Standard Deviation

Information Ratio = 0.52% - 5.14% / 5.43%

Information Ratio = -0.85