Active Risk and Information Ratio

Edward Qian and Ronald Hua

Volume 2, Number 3, Third Quarter 2004

One of the underlying assumptions of the Fundamental Law of Active Management is that the active risk of an active investment strategy equates estimated tracking error by a risk model. We show there is an additional source of active risk that is unique to each strategy. This strategy risk is caused by variability of the strategy’s information coefficient over time. This implies that true active risk is often different from, and in many cases, significantly higher than the estimated tracking error given by a risk model. We show that a more consistent estimation of information ratio is the ratio of average information coefficient to the standard deviation of information coefficient. We further demonstrate how the interaction between information coefficient and investment opportunity, in terms of cross sectional dispersion of actual returns, influences the IR.We then provide supporting empirical evidence and offer possible explanations to illustrate the practicality of our findings when applied to active portfolio management.