How much do you trust your CFO? Do you think they are doing the right thing? Do you wish there was a way you could check?

Benford’s law is a tool that has been used to detect possible fraudulent accounts. Also known as the law of anomalous numbers, it is the rate at which lower digits will occur in a set of financial statements. The law states that most common digits in the financial numbers found in a set of financial statements are more likely to be lower digits.

A large set of numbers is expected to obey Benford’s law. Most natural distributions, such as Fibonacci sequence, exponential growth and decay or the power of almost any number obey this sequence. A notable failure of Benford’s law is when numbers fall between a regular maximum and minimum. For instance, imagine a sequence of individuals heights measured in feet. Most would be between five and seven feet, violating Benford’s law.

It is estimated that less than 1% of companies engaging in financial fraud are actually caught, whereas 15% of companies may engage in financial fraud annually (see HERE).

With the large amount of data in financial reports, Benford’s law becomes very useful at detecting possible fraud. By measuring the leading digit distribution in a firm’s financial statements and how much they deviate from Benford’s law, higher scores can be used to signal possible financial irregularities. This makes Benford’s law exceptionally useful in studying fraud beyond the companies that are caught.

A recently completed study utilized Benford’s law to detect irregularities in financial statements (see HERE) . It was explicitly interested in the link between CFO gender and possible fraud at the company.

The key argument made by the paper was that there was a correlation between lower Benford scores i.e. reduced risk of fraud and female CFOs. The CFO was utilized for this study as they have the most prominent role in the preparation of financial statements.

Firstly, a score was calculated by taking the absolute value of the actual occurrences of a digit less the predicted occurrences via Benford’s law. Then several regressions were run with different control variables. The simplest regression only included variables indicating the company’s size and positioning in the marketplace such as firms age, firm size, sales growth and more. More complex versions included other variables on management, time-based factors and industry-based factors.

The paper proved there was a statistically significant correlation between lower Benford scores and a female CFO, indicating there is less likely to be fraud when the CFO is female.

Whilst Benford’s law is a useful predictor of fraud, it does have drawbacks. It requires a large sample to provide meaningful results. Furthermore, anomalies do not necessarily mean there has been tampering with the accounts. In particular, for some parts of the data, it is likely to be between a predefined minimum and maximum.

Benford’s Law is used in the investment management industry by quantitative and active managers as a screen for possible fraudulent financial statements.

So, check your books using Benford’s law to make sure there are no statistically improbable irregularities.

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