Hedge Funds and Benfords Law
Glyn Holton wrote an article about how to detect fraud in the reports by Hedge Funds: using Benford’s Law.
Benford’s law, also called the first-digit law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one third of the time, and larger numbers occur as the leading digit with less and less frequency as they grow in magnitude, to the point that 9 is the first digit less than one time in twenty. This is based on the observation that real-world measurements are generally distributed logarithmically, thus the logarithm of a set of real-world measurements is generally distributed uniformly.Source: Wikipedia
This characteristic of Benford’s Law can be used to detect fraud, writes Holton. He cites a paper by Nicolas Bollen and Veronika Pool Source: Bollen, Nicolas P.B. and Pool, Veronika Krepely, “Conditional Return Smoothing in the Hedge Fund Industry“. Journal of Financial and Quantitative Analysis.
The authors used statistical analysis to examine the financial reports of Hedge Funds for manipulation. More specifically, they look at reports of Hedge Funds with returns falling close to zero.
Glyn Holton writes:
It indicates the distribution of hedge funds’ returns that happen to fall near zero. The discontinuity Bollen and Pool found is pronounced, and it falls precisely at 0. Wow, isn’t that interesting! Anyone who analyzes data for a living knows there is something profoundly wrong with this distribution. The conclusion is inescapable. Hedge fund managers are inflating their returns to avoid reporting negative returns. The fact that they don’t do so in the months prior to an audit suggests they know what they are doing is wrong.
Holton writes that reports by Hedge Funds can be manipulated in three ways:
- Fraud
- Arbitrary Assumption of Asset Prices in Illiquid Markets
- Cherry-Picking from Brokers reporting higher prices
Pool and Bollen discuss some additional explanations of the statistical discontinuity, but also come to the conclusion that false reporting is the most likely explanation.
Topics of this post: financial regulation, General, glyn holton, hedge fund, Nicolas Bollen, Veronika Pool