The relationship between investor skill and the information ratio, which measures the excess return against the benchmark divided by tracking error, can be described in a fundamental law of active management. This law decomposes the information ratio into the correlation between forecasted and realized returns (i.e., the information coefficient or manager skill) and a number of active positions (e.g., breadth).

Excess risk-adjusted return, in turn, may be generated by making the right decision to over/underweight assets versus the benchmark (i.e., timing) or by taking a larger position in investment decisions that prove correct versus decisions that prove incorrect (i.e., sizing). The author captures manager skill through a binomial return-generating process and decomposes the skill metric to the probability of making correct forecasts and associated rates of return. He notes several practical challenges for investors gathering the data required to calculate the information ratio—for example, fat tails, excess kurtosis, the impact of investment constraints, and data transparency.

A given level of the information ratio can be achieved using a combination of the hit ratio, defined as the proportion of right decisions to total decisions made, and the magnitude of win/loss, calculated as the average return of the winning decisions divided by the negative of the average return of losses. The asset manager can achieve a positive information ratio with a majority of wrong decisions if there is a large enough margin of average profits exceeding average losses. The author also finds, through empirical research, that skill in market timing is about twice as important as skill in sizing.

The author concludes that decomposing risk-adjusted returns into described skill factors can help asset managers better understand the drivers of their active performance and offer potential for process improvement.

The study is based on risk and return characteristics calculated for four major asset classes (equities, bonds, currencies, and commodities) and four investment styles (long-only, momentum, value, and carry strategies). The author analyzes monthly return data from 1972 to 2012 originating from empirical results in other published studies.

He proposes a bimodal return-generating process to capture the effect of manager skill in timing and in size selection. The author subsequently separates the effects of hit and win/loss ratios on the information ratio and analyzes their importance among asset classes and active strategies.

Finally, he runs several robustness tests and relaxes the sample assumptions (e.g., allows for portfolio fat tails and excess kurtosis) to ensure the empirical results are consistent with his key findings.

The fundamental law of active management states that a successful strategy is to play often and to play well. The author offers practical insight on how to implement and overcome operational challenges in both the measurement of the hit ratio and decision breadth.

It may be still difficult, however, for investors to use the proposed theory to appraise fund managers’ performance because of a lack of required data (i.e., manager forecasts are usually not reported to the public) and transparency.

The author offers an unconventional approach to performance attribution for active strategies that will be valuable for fund managers and portfolio managers. Institutional investors who hire managers may wish to request from the manager the analysis described in this article in order to benefit both the investment firm and its clients. Based on this framework, researchers may wish to further investigate and build performance attribution models designed for active strategies.