  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 return
distribution for each trading day and we find that the symmetry properties of
the ensemble return distribution drastically change in crash and rally days of
the market. We compare these empirical results with numerical simulations based
on the single-index model and we conclude that this model is unable to explain
the behavior of the market in extreme days.
