Large stock market price drawdowns are outliers

Anders Johansen, Didier Sornette

Abstract

ABSTRACT

Drawdowns (loss from the last local maximum to the next local minimum) offer a more natural measure of real market risks than variance, value-at-risk (VAR) or other measures based on fixed time scale distributions of returns. Here we extend considerably our previous analysis of drawdowns by analyzing the major financial indexes, the major currencies, gold and the 20 largest US companies in terms of capitalization as well as nine other companies chosen at random. Approximately 98% of the distributions of drawdowns are well represented by an exponential distribution (or a minor modification with a slightly fatter tail), while the few largest drawdowns occur at a significantly faster rate than predicted by the exponential distribution. This is confirmed by extensive testing on surrogate data. Very large drawdowns thus belong to a class of their own and call for a specific amplification mechanism. Drawups (gain from the last local minimum to the next local maximum) exhibit similar behavior in only about half the markets examined.