Scaling of the distribution of price fluctuations of individual companies

Abstract

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 US companies for the 2-year period 1994-95, and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-year period 1962-96. We study the probability distribution of returns over varying time scales ∆t, where ∆t varies by a factor of ≈ 10 5 -from 5 min up to ≈ 4 years. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent α ≈ 3 -well outside the stable Lévy regime 0 < α < 2. For time scales ∆t ≫ (∆t)× ≈ 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.

Self-organized complexity in economics and finance

“…Gopikrishnan et al (24)(25)(26)(27) recently acquired a data set 3 orders of magnitude larger still (of order 10 9 )-one that records every transaction of every stock. They found that when their data were graphed on log-log paper, the result was linearity.…”

Multifractality in the stock market: price increments versus waiting times

“…for large n. The family of the scaling exponents h(q) can be then obtained by observing the slope of log-log plots of F q vs. n. h(q) can be considered as a generalization of the Hurst exponent H with the equivalence H ≡ h (2). Now the distinction between monofractal and multifractal signals can be performed: if h(q) = H for all q, then the signal under study is monofractal; it is multifractal otherwise.…”

“…The so-called financial stylized facts comprising, among others, the non-negligible fat tails of log-return distributions, volatility clustering and its long-time correlations, anomalous diffusion etc. [2,3,4,5] counter the above-mentioned fundamental assumptions of market dynamics challenging their applicability in practice. That the financial dynamics is more complex than it is commonly assumed can also be inferred from a number of recently-published papers discovering and exploring the multifractal characteristics of data from the stock markets [6,7,8,9,10], the forex markets [7,10,11,12,13] and the commodity ones [14].…”

Statistical properties of daily ensemble variables in the Chinese stock markets

“…Econophysics is an emerging interdisciplinary field, where theories, concepts, and tools borrowed from statistical mechanics, nonlinear sciences, mathematics, and complexity sciences are applied to understand the self-organized complex behaviors of financial markets [2,3,4]. Econophysicists have discovered or rediscovered numerous stylized facts of financial markets [2,5], such as fat tails of return distributions [6,1,7,8,9,10,11,12,13], absence of autocorrelations of returns [2], long memory in volatility [14,15,16], intermittency and multifractality [7,17,18,19], and leverage effect [20,21], to list a few.…”