Fraud Detection Using Benford’s Law
In its latest Report to the Nations, a document summarizing results and presenting conclusions from distributed surveys, the Association of Certified Fraud Examiners (ACFE) estimates that U.S. organizations lose five percent of their annual revenue to fraud. The ACFE also found that the median loss due to an incidence of fraud is roughly $150,000 and the median loss is not proportionate to the size of the organization. Obviously, a large fraud loss for a smaller organization may be more detrimental since its resources are smaller versus a larger organization’s ability to absorb the loss.
An organization’s procedures for detecting fraud are directly related to its fraud detection success. Fraudsters seem to change with an organization’s policies and procedures. Beyond the normal characteristics of a successful fraudster, which would include living beyond their apparent means or they are experiencing financial difficulties, I would add the characteristic of a chameleon. Crafty fraudsters have the ability to adapt to the current situation and be successful. They seem to be able to pass the annual external financial statement audit with flying colors and work around an organization’s ever-changing policies and procedures to prevent fraud. So what is the answer to detecting these crafty criminals?
The theory of Benford’s Law has been around since 1881 but wasn’t applied to financial data until 1989 by Mark Nigrini. The theory is that low-digit numbers 1, 2, and 3 show up more frequently than higher numbers 4 through 9. The chart below represents the percentage of the frequency the first digit should show up in a population:
This theory works well with:
- Sets of numbers that result from mathematical combination of numbers – Results come from two distributions
- Accounts receivable (number sold * price)
- Accounts payable (number bought * price)
- Transaction level data – No need to sample
- Disbursements, sales, expenses
- On large data sets – The more observations, the better
- Full year’s transactions
- Accounts that appear to conform – When the mean of a set of numbers is greater than the median and the skewness is positive
- Most sets of accounting numbers
The theory doesn’t stop at the first digit. Probabilities for 2nd and 3rd digits are also known and using the 1st and 2nd digit together or 1st, 2nd, and 3rd digits together is even more useful in fraud detection. The last two digits are often used to identify fabricated and rounded numbers.
This theory can easy be applied to data sets using excel or other data analysis software. The IRS and other governmental units use it currently to detect fraud. Organizations need to apply this theory on an annual basis to the data they collect or produce. The best part of the theory is that even if the fraudster knows the theory inside and out the fraudster can’t foresee the entire population and his guesses of what numbers to choose to conceal the fraud will most likely be outside of the expected population.
This article is just touching the surface on what Benford’s Law is capable of detecting. Benford’s Law allows organizations to analyze entire sets of data easily and effectively. Is your organization using Benford’s Law to detect fraud?
If you would like assistance using Benford’s Law on the data your organization produces or collects, or if you have any other fraud related questions, please contact Principal, David Hammarberg.
