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.