Question

1. The risk-free rate, the average returns, standard deviations, betas, and residual standard deviations for three funds and the S&P 500. Std De. Beta Residual Std. Dev. Fund Avg. 18 25 20 15 30 35 25 20 1.3 1.4 1.2 1.0 1.5 2.5 3.0 S&P 500 Risk-free 1) Figure out a fund with the highest Jensen's alpha. (20points) 2) Figure out the information ratio for Fund C.(15points)

Answer 1

Jensen's alpha = Portfolio Return − [Risk Free Rate + Portfolio Beta * (Market Return − Risk Free Rate)]

Fund A = 18 - [5 + 1.3(15 - 5)] = 0

Fund B = 25 - [5 + 1.4(15 - 5)] = 6

Fund C = 20 - [5 + 1.2(15 - 5)] = 3

Fund B has the highest Jensen's Alpha i.e. 6

Information Ratio of Fund C

Information Ratio = (Portfolio Return - Benchmark Return)/Tracking Error

where Tracking Error is the standard deviation of difference between portfolio return and benchmark return

Tracking Error = 20 - 15 = 5%

= (20 - 15)/(20 - 15) = 1

Fund C has an Information Ratio of 1.

Important : If the information ratio is between 0.4 and 0.6, it is considered to be a good investment, and an information ratio between 0.61 and 1 is considered to be a great investment.

For any query or clarification, please leave a comment.

Formulas The ex-post tracking error formula is the standard deviation of the active returns, given by where rp - b is the active return, i.e., the difference between the portfolio return and the benchmark return.