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

We select the n stocks traded in the New York Stock Exchange and we form a statistical ensemble of daily stock returns for each of the k trading days of our database from the stock price time series. We study the ensemble ret urn distribution for each trading day and we find that the symmetry propert ies of the ensemble return distribution drastically change in crash and ral ly days of the market. In crash and rally days, the distribution becomes as ymmetric. In particular for crashes the positive tail is steeper than the n egative one whereas the reverse is observed in rally days.