#52: Market mathematics

Benford’s Law states that the digits making up numbers in large datasets occur with frequencies which follow a simple pattern and can therefore be predicted. This only applies if the numbers are unrestricted in terms of the range of their values (which certainly applies to stocks…think Wall Street Crash). Numbers beginning with a 1, for example, will occur about 30% of the time.

Today’s idea is to use this phenomenon to get a small edge in stock trading. Specifically, if you are trying to predict movements in an Index as a whole.


If all the stock prices in a given market are analysed, the frequency of numbers with different first (ie most significant) digits can be graphed (in purple). These columns can be expected to follow Benford’s law (blue). Here we see that values with 1 as first digit can be expected to be just about to decrease in frequency, whilst those with first digit 8 are can be expected expected to become more common.

A simple sum of the positive and negative deviations from the Benford distribution will indicate whether the index is set to rise or fall.

Applying this technique on eg a daily basis, for a long time, seems to me to provide an edge, which might well be significant compared to the various sources of noise in the system. It’s also likely however to result in large short-term losses which may make the scheme unworkable for anyone other than a very rich gambling addict (As Richard Branson says “How do you become a millionaire? Become a Billionaire and start an airline”).


  1. A better approach might be to see if the average over a long period is significantly over or under the expected value and examine the deviations to extimate whether the index will rise or fall.

    The average for the first digit benford distribution is approximately 3.44. The average for the first 2 digis benford distribution is approximately 21.

    Do you know where I can find some data to check this out?

  2. I’m a little unsure about the influence of the much-quoted 11% long term increase in stock values, which may make this whole approach applicable only to today’s trading position. You could try talking to http://tinyurl.com/2u3pn they have been helpful in the past. Cheers, P

  3. Correction –2 digit benford mean is approximately 25.

Comments are closed