In the 1990s I had a friend who was working for an insurance company fighting fraudulent claims, and he mentioned to me that he’d come across Benford’s law.
The law dates from 1881 and was first proposed by astronomer Simon Newcomb. He didn’t get to name it; it’s named after physicist Frank Benford, which is why some refer to it as the Newcomb-Benford law.
It’s also sometimes called the first-digit law, and the theory is that while you would expect the first digit of a number to be evenly distributed in a suitably large body of data, this is not the case.
The law showed that the first digit is a one more than 30% of the time, a two almost 18% of the time and a three 12.5% of the time. Nine is the first digit of a number just 4.6% of the time. You would think that each of the numbers from one to nine would be the first digit about 11.1% of the time. But no. And checking the law against large bodies of data, it stands up again and again.
My friend told me he planned to use this law to quickly spot possibly fraudulent insurance claims, and it got me wondering about using it for listed companies. Did a company’s set of results comply with Benford’s law? The problem back then was the lack of access to historical results data, and I would have had to crunch the numbers manually, so I shelved it.
The results were simple. All 17 of the known fraudulent or error-strewn companies failed, while 13 of the clean results passed
In 2006 Adrian Saville published a paper on Benford’s law in the South African Journal of Economic and Management Sciences using JSE results data to see if it would work to spot fraud.
He got results from 17 delisted JSE stocks that were known or suspected of producing fraudulent or erroneous results. He also got 17 companies that had clean audited results and ran all the numbers through Benford’s law.
The results were simple. All 17 of the known fraudulent or error-strewn companies failed, while 13 of the clean results passed.
So it spotted 100% of the fraud and flagged a false positive in four of the 17 clean stocks.
Back then the problem was still my ability to manually crunch the data. Now AI has solved this for me.
Using NotebookLM from Alphabet, I uploaded a decade of results from a stock I am interested in and asked it to tell me how often each number from one to nine is the first digit of any number.
The results so far have correlated with the law, and from the research paper we know that if the numbers are flagged as clean, they are clean. If I get a potential failure of the law, the Saville paper shows that it may be a false positive, and more digging could be required.
AI is taking an idea from the late 1800s and enabling investors to easily detect potential fraud.
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