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.

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T he bottom-line value of an active investment process has two parts: the theoretical value of the alpha skill (the gross paper profit), minus the cost of implementation. The higher the former and the lower the latter, the happier the investor is. Clearly total assets under management (AUM) influence the latter. A strategy might be profitable with a low level of assets under management but unprofitable with more assets-as asset amounts grow, so do transaction costs.Kahn and Shaffer [2005] note that one approach to remedy the size problem is to reduce portfolio turnover. While this is a sensible suggestion, Kahn and Shaffer's work is based on a hypothetical relation between turnover and expected alpha that might be too general to be applicable. In reality, any relation between turnover and expected alpha is not exogenous. It depends on alpha factors, their weights in an alpha model, and the rebalance horizon.We propose an analytic framework for integrating alpha models with portfolio turnover. In practice, many alpha models are not constructed in such an integrated framework. Typically, managers first develop an alpha model (giving little consideration to turnover), and then throw the alpha model into an optimizer, setting turnover constraints to handle the transaction costs. There are two drawbacks to this two-step process: 1) It makes it hard to know the true effectiveness of the alpha model; and 2) it does not let managers adjust the alpha model along the way as AUM grow.To integrate an alpha model with portfolio turnover, we extend work by Qian and Hua [2004] and Sorensen et al. [2004] that provides an optimal solution for Information Horizon, Portfolio Turnover, and Optimal Alpha Models

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