Frequency of First Digits
The Chairman
Victor Niederhoffer
11/02/2004
Frequency of First Digits
I find that 14 of the 20 markets and stocks I look at invariably, have the number 1 as their first digit (0 at beginning excluded). This is a instance of Benford's law, first discovered by Simon Newcomb that 30% of the numbers in any list start with 1. It's explained by assuming constant % growth, with a jump from 1 to 2 requiring 100% and 2 to 3 requiring 50% and 3 to 4 , 33% etc. Assuming that the time that an entity stays in a range is proportional to the percentage growth it must take, the explanation becomes plausible. A simulation can show this. And at first one would think it random and non-predictive, the kind of thing that the author says is good for picking up chicks at bars, like the birthday problem. But I have always found that equal arithmetic changes is a much better model for stocks than percentage changes, and this could lead to some opportunities.