Using Benford's Law to catch corporate cheats

Investors wanting to dodge the next Enron, or just outperform the market, might want to pay particular attention to the first digits, and only the first digits, in numbers in company accounts.

Called Benford's Law, after the physicist who discovered it in 1938, it describes a well observed fact: in naturally occurring sets of numbers of sufficient size the first digits are not evenly distributed. Lower numbers predominate: 1 is the first digit in a number almost 30 per cent of the time while 9 begins less than 5 per cent of numbers. As the US Internal Revenue Service uses Benford's Law to sniff out tax cheats, or at least to narrow the field to better channel resources, why not do something similar with the data produced by companies to represent their performance?

Deutsche Bank has done just that, applying Benford's Law to company financial statements and coming up with results which are, at least in the aggregate, compelling.

A data set which does not conform to Benford's Law may well indicate that something is not right. This may be fraud, or may be mistakes or misstatements. In any event all of these leave investors operating at a disadvantage when compared to investing in a company with accurate reports.

Deutsche crunched the numbers on Russell 3000 companies and found that a Benford distribution applies to almost every balance sheet and income statement item, from annual sales to accounts receivables to net income. Similar data was found for global firms.

But companies that do not show conformity to natural number distribution also show a marked divergence in how they perform for their investors.

"Stocks with potential accounting irregularities underperform the market significantly," quantitative strategists at Deutsche Bank led by Yin Luo wrote in a March report.