How Fama Went Wrong: Measures of Multivariate Kurtosis for the Identification of the Dynamics of a N-Dimensional Market

TL;DR

This paper challenges traditional views on market behavior during crises by proposing a geometric approach and a multivariate kurtosis measure to detect deviations from normality across multiple assets.

Contribution

It introduces a novel geometric framework and multivariate kurtosis measure to identify market crises using comprehensive stock return data.

Findings

Crises are associated with significant deviations from multinormality.

Multivariate kurtosis effectively detects market stress.

The approach considers all available stock return information.

Abstract

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.