Benford’s Law and the Stock Market

Abnormal Returns spotted a fascinating article on finance and Bedford’s Law.

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.

The article notes that Benford’s Law has been used to spot financial fraud. It turns out that it’s not so easy to appear being random.

I took all of the closing numbers for the Dow going back to June 8, 1931 which is an even 20,000 points of data. I then broke down all the starting digits and here’s what I got:

First Digit Occurrences
1 7262
2 2236
3 1089
4 961
5 748
6 1114
7 1247
8 2889
9 2454

Since the Dow has never made it to 20,000, there are a lot of readings in the Ones row, but that’s the point of Benford’s Law. According to the law, the Ones should have 30.1% of the readings which is pretty close to what we see (36.31%).

I’m guessing the list is a bit skewed because there are so many readings in the Eights and Nines column. Perhaps if this same test is run in 30 years, we’ll see an even stronger relationship to Benford’s Law.

Posted by on January 22nd, 2011 at 9:22 am


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