Symmetry alteration of ensemble return distribution in crash and rally days of financial markets

摘要

We select the $n$ stocks traded in the New York Stock Exchange and we form astatistical ensemble of daily stock returns for each of the $k$ trading days ofour database from the stock price time series. We study the ensemble returndistribution for each trading day and we find that the symmetry properties ofthe ensemble return distribution drastically change in crash and rally days ofthe market. We compare these empirical results with numerical simulations basedon the single-index model and we conclude that this model is unable to explainthe behavior of the market in extreme days.