I have found the Benford’s First-digit law interesting. The law states that in a list of data, the leading digit is distributed in a non-asymmetric way. Basically, he found that there are more “1s” than the other numbers (2 to 9) for the leading digit. This discovery applies to stock prices as well.
I have tabulated some of the figures for the STI components. I did one data set for end-2007 which is the peak of the stock market and another for end-2008, which was near the bottom of the crash.
End 2007 – Before the crash
End 2008 – After the crash
Current 2011 figures
I deliberately chose 3 different periods of time – market peaking, market bottoming and market neutral. It is obviously true that the figures for the digit “1” is the most frequent number despite different market condition. So what if this is the case? Is there any useful applications?
Before I began tabulating, I was thinking if the stock prices distribution would deviate from the Benford’s figures. If true, it can be used as a gauge to see if the market is out of whack and not behaving normally. As such, we would be able to know when to buy and sell. However, the data sets that I created are only had a slight difference. Probably when the sample size is larger, it can be more conclusive.
Here are the distributions versus the standard Benford’s figures.
What I notice is that when the market bottoms, the appearance of digit “1” as the leading number increases. While in 2007, the asymmetry becomes less obvious – other numbers appear more frequently than expected. At current market which is neither too overheated or undervalued, it is closer to the Benford’s figures. As mentioned, the sample size is too small to be conclusive. If more tests can elicit this hypothesis, we should buy when digit “1” appear more often than usual, and sell when the appearance of other numbers increases.