  This paper investigates the common intuition suggesting that during crises
the shape of the financial market clearly differentiates from that of random
walk processes. In this sense, it challenges the analysis of the nature of
financial markets proposed by Fama and his associates. For this, a geometric
approach is proposed in order to define the patterns of change of the market
and a measure of multivariate kurtosis is used in order to test deviations from
multinormality. The emergence of crises can be measured in this framework,
using all the available information about the returns of the stocks under
consideration and not only the index representing the market.
