I have read the following sentence : " The information ratio measures the active management opportunities, and the square of the information ratio indicates our ability to add value " ( In the Grinold's book about Active Portfolio Management).
I do not understand the second part. For me, the information ratio or its square measure the same thing, the possibility of extracting value from the market, on a different scale.
Is the square of the IR like the $R^2$ in statistics for linear regression ( with the fact that quadratic error = variance + square of the biais) ?
Thank you for your help !