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**Research Story 4: Hedge fund misreporting: Avoiding reporting losses**

After studying smoothing in hedge fund returns (see Research Story 3), I was somewhat unsatisfied. Surely there was clearer and simpler evidence of misreporting in hedge funds. I decided to simply create a histogram of monthly returns, pooled across time and across funds, to see what the data look like. The result was dramatic:

There was a noticeable discontinuity between the two bins bracketing zero, highlighted in bold. The bin to the left includes negative returns the bin to the right includes positive returns, both with absolute value less than 0.19%. The first explanation that comes to mind is the some hedge fund managers might be rounding up returns above zero to avoid reporting losses. And, after some digging, it turns out that this sort of analysis has been used in a variety of other contexts to indicate fraud, including corporate earnings management and elite sumo wrestling.

The sumo wrestling example is especially entertaining. Duggan and Levitt, an a 2002 American Economic Review article, study the frequency with which wrestlers achieve a certain number of wins in tournaments. Each wrestler has 15 bouts per tournament. Those with at least 8 wins move up in the rankings. So there is a big incentive to achieve the 8th victory. Here is the result:

Under the assumption that each wrestler has a 50% chance of winning each bout, the frequency distribution should be normal, with equal probability of 7 or 8 victories per tournament. The low frequency at 7 and high frequency at 8 suggests either that (i) wrestlers try really hard to get the 8th victory, or (ii) wrestlers cheat to get the 8th victory. To test these alternatives, the authors track the subsequent meetings between two wrestlers after one of them won their 8th bout. They found that the following time the same two wrestlers fought, the winner of the first bout lost a high percentage of the time, and then in following meetings no pattern was found. The conclusion is that there was a quid pro quo to allow the wrestler to get his 8th victory.

Similarly, in the hedge fund case, there are numerous alternative explanations for the shape of this distribution, including skill at actually avoiding losses, asymmetry in the payoffs of securities held by the funds, and previously known database problems such as survivorship bias. My coauthor Veronika Pool and I spent about a year designing tests to see if any of these alternatives held up. One test in particular is quite powerful - we simply changed the unit of observation from one month returns to bimonthly returns. All of the other explanations predict that the discontinuity would be present independent of time scale. The misreporting hypothesis, however, predicts that much of the discontinuity would disappear, since any overstatement of returns must at some point be reversed. Here is the result using bimonthly returns:

The resulting paper received significant media attention, including articles in the Wall Street Journal and Forbes. The paper has been downloaded over 1,000 times, and is now forthcoming at the Journal of Finance.