  We find a remarkable time persistence of various proxies for the kurtosis
(p-kurtosis) of the intraday returns distribution for the S&P500 index and this
permits a significant measure of their evolution from 1983 to 2004. There
appears a long time scale dramatic variation of the p-kurtosis uncorrelated
with the variation of the volatility thus falsifying any hypothesis of a
universal shape for the probability distribution of the returns. A large
increase in the kurtosis anticipates the October 87 crash. During the years
1991-2003 it continuously decreases even when the volatility grows during the
dot-com bubble. We propose some speculative interpretations of these results.
