  We investigate the variety of a portfolio of stocks in normal and extreme
days of market activity. We show that the variety carries information about the
market activity which is not present in the single-index model and we observe
that the variety time evolution is not time reversal around the crash days. We
obtain the theoretical relation between the square variety and the mean return
of the ensemble return distribution predicted by the single-index model. The
single-index model is able to mimic the average behavior of the square variety
but fails in describing quantitatively the relation between the square variety
and the mean return of the ensemble distribution. The difference between
empirical data and theoretical description is more pronounced for large
positive values of the mean return of the ensemble distribution. Other
significant deviations are also observed for extreme negative values of the
mean return.
