Tests of nonuniversality of the stock return distributions in an emerging market

Abstract

There is convincing evidence showing that the probability distributions of stock returns in mature markets exhibit power-law tails and both the positive and negative tails conform to the inverse cubic law. It supports the possibility that the tail exponents are universal at least for mature markets in the sense that they do not depend on stock market, industry sector, and market capitalization. We investigate the distributions of intraday returns at different time scales ( Δt=1, 5, 15, and 30 min) of all the A-share stocks traded in the Chinese stock market, which is the largest emerging market in the world. We find that the returns can be well fitted by the q-Gaussian distribution and the tails have power-law relaxations with the exponents increasing with Δt and being well outside the Lévy stable regime for individual stocks. We provide statistically significant evidence showing that, at small time scales Δt<15 min, the exponents logarithmically decrease with the turnover rate and increase with the market capitalization. When Δt>15 min, no conclusive evidence is found for a possible dependence of the tail exponent on the turnover rate or the market capitalization. Our findings indicate that the intraday return distributions at small time scales are not universal in emerging stock markets but might be universal at large time scales.

Statistical properties of derivatives: A journey in term structures

“…It was observed for several financial markets (stocks, stock indexes, exchange rates, interest rates, and the nearest delivery dates of commodities), different time scales (investigations where carried on time intervals varying from minutes to months), and different time periods [7,8,6,34]. In more specific studies, several authors observed that the tail exponent remains outside the Lévy stable domain, within a range of 3 to 5, for symmetric as well as for asymmetric tails [35,36]. As also shown in [37], the estimate of the exponent can be sensitive to the time scale, and µ is lower for high-frequency data, compared to the figures obtained with weekly or monthly time series.…”

Stock Returns Versus Trading Volume: Is the Correspondence More General?

“…These individual decisions taken together define very complex behaviour of the financial markets [1][2][3][4][5] and lead to such characteristics of the financial data as multifractality [6][7][8][9][10][11], long memory, nonlinear correlations [9,12,13], the leverage effect [14,15], fat tails of financial data fluctuations [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], known together as the financial stylized facts.…”

Distinguishing manipulated stocks via trading network analysis

“…For the first category of financial data, the traditional research approach is to employ the probability distribution functions in order to analyze statistical properties of various variables [1,2,3,4,5,6,7,8,9,10,11,12,13,14] and to employ correlation functions to study the cross correlation among different variables [15,16,17,18,19,20,21]. A power-law distribution has been found in many variables, such as price fluctuations, trading volume and the number of trades.…”