Information Ratios and Batting Averages

The information ratio (IR) and the batting average are two commonly quoted measures of investment success, but these measures have shortcomings: The IR contains no information about higher moments, and the batting average contains only directional information. This article demonstrates how the IR and batting average interact and how they can be usefully combined to allow investors to construct a comprehensive picture of the choices they face. The intriguing result is that large batting averages can result in low IRs and, conversely, impressive IRs can be obtained with low batting averages. Furthermore, in choosing between two managers with equivalent IRs, an investor who is averse to blowups should choose the manager with the lower batting average.The information ratio (IR) is a common measure of the success (or failure) of money managers. Conceptually, it is simply the ratio of the excess return (relative to a benchmark) to the excess risk of an investment strategy. Unfortunately, when a fund manager quotes only the IR at the end of some fixed investment horizon, investors in the fund cannot easily ascertain the string of successes and failures that led to that final outcome. Did the manager win or lose most of the bets? A measure of success that addresses this shortcoming of the IR is the “batting average.” It is the percentage of investment decisions that led to a profit. The shortcoming of this measure is that it does not give any information about how much money was made or lost as a result of a particular investment decision.This article demonstrates how the IR and batting average interact and how these two measures of success can be usefully combined to allow investors to construct a comprehensive picture of the manager or fund choices they face.Although the investment strategy used by a particular manager cannot be “reverse engineered,” we show how one can extract a batting average once an IR is specified. Our batting average indicates how often managers must make independent and profitable investment decisions to obtain their stated IRs. It also provides insight into how much mileage has been obtained from the available information.The batting average, which is a function of the number of “at bats,” allows differentiation among managers who are using different investment strategies, because the number of at bats is a good proxy for how often a manager receives information relevant to the implementation of the manager’s strategy.We find that the IR and batting average do not convey equivalent information. Indeed, they often provide seemingly contradictory information. One of our main points is that this confusion arises because success is a multidimensional concept and the IR and batting average measure different components of success. We argue that whereas the IR measures the risk-adjusted returns of a particular strategy, the batting average is a useful proxy for the skewness of the distribution of returns. The batting average, therefore, provides information about the higher moments in a particular distribution of returns, information that cannot be measured by the IR.We first demonstrate that if the payoffs for winning and losing are symmetrical (a win followed by a loss results in zero return), a winning strategy need surpass a batting average of 50 percent by only a tiny margin to generate spectacular IRs—provided the strategy is implemented frequently.Next, we investigate the consequences of assuming the more realistic scenario in which investment decisions have asymmetrical upside and downside returns. Here, we find the intriguing result that large batting averages can result in low IRs and that impressive IRs can be obtained with low batting averages.Finally, we demonstrate that in choosing between two managers with equivalent IRs, an investor who is averse to blowups should choose the manager with the lower batting average. Such investors should be wary of standard marketing messages that go no further than claiming “our fund outperformed our benchmark in 8 of the last 10 years.”Success is a multidimensional concept, and IRs and batting averages approach it from different directions. Used together, the IR and the batting average provide orthogonal and complementary information, allowing investors to effectively disentangle the multitude of choices presented to them by the investment community.