Benford’s Law: Are Euro States and US Stocks Cooking The Books?

Thursday, Oct 20 2011 by
Benfords Law Are Euro States and US Stocks Cooking The Books

As we've previously seen, Benford's law – one of the odder practical truths revealed by statistics – is a great tool for identifying fraudulent accounting, a good indicator that's there's something afoot in the footnotes. Now, though, we have a couple of new examples of forensic analysis using the technique, and they don't make comfortable reading if you're long of equities; or indeed anything other than sub-automatic weapons and a bricked-up cave. So on one hand we have evidence suggesting that US corporations are systematically manipulating their accounts, and on the other that the real depth of the issues in the Eurozone are yet to be revealed. If true, we're a long way from resolution of this particular, and peculiar bust.

Benford's Back

To recap: Benford's law says that in naturally occurring data the leading digit is most often 1 and least often 9, descending in frequency as the numbers rise. This doesn't work for all data – human height is distributed according to the familiar Bell curve or normal distribution, for instance – but is common in other areas. In particular Benford's law rules in financial accounting. So, for instance, more companies earn between 100 million and 199 million than between 200 million and 299 million and so on.

Of course, when humans start manipulating and fabricating data they generally try to do so by randomising it. A typical made-up set of numbers will not follow a Benford-style exponential distribution and can therefore be detected. This paper by Durtschi, Hillison and Pacini explains the background and gives a real forensic example:"When the details of the account were inspected, it was apparent that many more refund checks of just over £1,000 had been written than in the previous period ... A subsequent detailed examination of the account, however, uncovered that the financial officer had created bogus shell insurance companies in her own name and was writing large refund checks to those shell companies".The application of Benford's isn't always so simple, though.

When Paul Kedrosky analysed Bernie Madoff's returns he determined:"Bernie Madoff's results, far from being pulled from his hat, showed every sign of having been generated by a randomizing algorithm. My analysis suggested that – based on Benford's Law fit – his results would have passed muster in terms of looking sufficiently random to be real."Basically, Madoff's data so perfectly matched Benford that it should…

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3 Comments on this Article show/hide all

Andrew Butter 22nd Oct '11 1 of 3

Very interesting, but I'm not sure that it's fair to compare the level of incompetence of the EU in general and EU governments specifically with companies that list on leading public stock markets.

The difference is that companies are audited, the EU in Brussels famously didn't get it's audit signed off on numerous occasions and it's internal auditors resign all the time, governments are not rigorously audited and as far as anyone knows the Greek National Accounts were never audited. If governments had to report on their solvency like public companies, then a whole bag of worms would come out, in particular the unsustainability of unfunded liabilities which in UK include all of the crooked PPI schemes that the Labor Government used to put liabilities "off-balance-sheet".

The main reason corporations cook their books is to avoid paying tax, it's no coincidence that 50% of the profits from companies listed on the S&P 500 come from outside USA now, that's not so much "Globalization", as tax-avoidance, it's also a big reason why it makes much more sense to build a new factory in a Special Economic Zone in China and a logistics center in Dubai than in USA or Europe, you book all your losses in the taxable country, and you conceal profits in the tax-free place.

I should know, I worked briefly for Arthur Andersen (I'm proud to say I was fired for calling a senior partner a FFF crook), and I've done outside consulting for all the Big 4 accountants.

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timarr 22nd Oct '11 2 of 3

Hi Andrew

Thanks for bringing this to my attention, I hadn’t spotted that Stockopedia had picked this up. As recorded on my website the economist behind the US market numbers has indicated that they’ve found an error in their numbers, and they’re reworking them. The results will be interesting, because if they indicate that companies aren’t fiddling their figures that will almost be more surprising :)

Of course the two cases listed are very different; the point was to show that there are analysis techniques available to investors to check on the reliability of financial figures: applying Benford analysis to company accounts isn't especially hard (and may be particularly valid for the smaller companies favoured by bulletin board afficionados).  In some senses it’s almost irrelevant why these deviations happen; it’s enough to know that they shouldn’t. If markets properly assessed all the information available then firms would be punished for publishing fake figures: which would be a far more effective way of disciplining them than anything regulators can devise.  It’s not entirely impossible that this might happen: there’s been a collapse in the abnormal returns available by utilising the accrual anomaly, which appears to be directly related to hedge funds exploiting it (as recorded in Death of the Accrual Anomaly).  

On the other hand, if you’re correct that Benford deviations are as a result of tax avoidance you might get the opposite reaction, as investors take this as prudent financial management. To be honest I’m not sure that tax avoidance alone can explain such deviations, because as long as these numbers are derived naturally (i.e. it’s not some human just making them up) then Benford should still apply. 

And as for governments … well, yes. I’m not sure it’s incompetence, though: politicians are having to relearn the hard way that their normal ambiguity gets properly tested by markets. As Richard Feynman said, in a different context: nature cannot be denied.  

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Andrew Butter 22nd Oct '11 3 of 3

I agree that Benford analysis sounds like a very powerful tool, I was very interested to hear about it.

The thrust of my argument was not that public companies don't fiddle their numbers, clearly they do, it was simply that you can't assume it's to defraud their shareholders (not all the time anyway); there are plenty of other reasons to "unrock" the boat.

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About timarr


I'm a UK based technologist (career) and psychologist (academic) with a long-term interest in financial markets, with a particular emphasis (and skill) in how to not make money out of them. When I'm not working or blogging I'm to be found childminding, walking the dog or hiding in the garden shed with a good book :) more »

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