One of the more curious statistical anomalies of the universe has turned out to have a range of practical applications in the world of finance. It also turns out to be one of the stranger laws underpinning the stockmarket, although figuring out why is a painful process.
Above all, Benford's Law can be used to spot financial fraudsters because of a psychological quirk that means we humans are dead useless at pretending to be random. All of this comes from a law that was discovered by one man, explained by another and named after a third. Now that's random.
Naturally Bizarre
Take any naturally occurring set of numbers and keep a count of the first digit in the number. A newspaper is an ideal test bed. Most people reckon that each number from 1 to 9 will occur with equal frequency: after all, why would they not? Yet they don't: the number 1 appears almost a third of the time and each subsequent number reduces in frequency. And this, frankly, is bizarre at first flush.
This odd feature of the world was first noted by the polymath Simon Newcomb back in the nineteenth century. 'Polymath', of course, is an old-fashioned way of saying 'smart ass'. Anyway, Newcomb noticed that books of logarithm tables were more worn at the front – where the numbers started with a 1 – than at the back. For those youngsters at the back there, log tables were what we used before someone invented the calculator, devised by John Napier back in the fourteenth century as the bane of schoolchildren for four centuries.
Newcomb figured out the curious nature of Benford's Law, published his observations and then was promptly forgotten about. Frank Benford independently discovered the law in the 1930's and compiled copious examples to make his point. His original data table shows that this distribution of leading integers applies for a vast range of different quantities.
Benford Stockmarkets
In fact it turns out that daily stockmarket returns follow Benford's Law. When Eduardo Ley investigated this in On the Peculiar Distribution of the U.S. Stock Indeces' Digits he observed that:
"The analysis presented here suggests that small changes are more likely than big ones; at the same time, the closer the daily changes are (in absolute value) to 0.1%, the more probable they are too".Which accords…
