Rapid Note Inverse cubic law for the distribution of stock price variations

The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period January 1994 – December 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent α ≈ 3, well outside the Lévy regime (0 < α < 2). PACS. 89.90.+n Other areas of general interest to physicists The asymptotic behavior of the increment distribution of economic indices has long been a topic of avid interest [1–6]. Conclusive empirical results are, however, difficult to obtain, since the asymptotic behavior can be obtained only by a proper sampling of the tails, which requires a huge quantity of data. Here, we analyze a database documenting each and every trade in the three major US stock markets, the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), and the National Association of Securities Dealers Automated Quotation (NASDAQ) for the entire 2-year period January 1994 to December 1995 [7]. We thereby extract a sample of approximately 4×10 data points, which is much larger than studied hitherto. We form 1000 time series Si(t), where Si is the market price of company i (i.e. the share price multiplied with the number of outstanding shares), i = 1 . . . 1000 is the rank of the company according to its market price on January 1, 1994. The basic quantity of our study is the relative price change, Gi(t) ≡ lnSi(t+∆t)− lnSi(t) ' Si(t+∆t)− Si(t) Si(t) ,