Large Stock Market Price Drawdowns Are Outliers

By Anders Johansen, Didier Sornette. 2000

177 citations recorded by the source corpus.

Drawdowns (loss from the last local maximum to the next local minimum) are essential aspects of risk assessment in investment management. They offer a more natural measure of real market risks than the variance or other cumulants of daily (or some other fixed time scale) distributions of returns. Here, we extend considerably our previous analysis by analyzing the major financial indices, the major currencies, gold, the twenty largest U.S. companies in terms of capitalisation as well as nine others chosen randomly. We find for the major financial markets that approximately 98% of the distributions of drawdowns is well-represented by an exponential (or a minor modification of it with a slightly fatter tail), while the largest to the few ten largest drawdowns are occurring with a significantly larger rate than predicted by the exponential: the largest drops thus constitute genuine outliers. This is confirmed by extensive testing on surrogate data, which unambiguously show that large stock market drops (and crashes) cannot be accounted for by the distribution of returns characterising the smaller market moves. They thus belong to a different class of their own and call for a specific amplification mechanism. A similar scenario is found for the majority of the company stocks analysed. Drawups (gain from the last local minimum to the next local maximum) exhibit a similar behavior in only about half the markets that we examined. In the spirit of Bacon in Novum Organum about 400 years ago, "Errors of Nature, Sports and Monsters correct the understanding in regard to ordinary things, and reveal general forms. For whoever knows the ways of Nature will more easily notice her deviations; and, on the other hand, whoever knows her deviations will more accurately describe her ways," we propose that outliers reveal fundamental properties of the stock market.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/ead105a193c9556eadf89af6cb7345acdc6c2317

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Citations in the corpus

Dragon-Kings, Black Swans and the Prediction of Crises (2009, background): “Details are given in Johansen and Sornette [29-31].”
Critical Market Crashes (2003, unknown): “Johansen and Sornette (2002) have shown that the distribution of drawdowns for independent price increments x is asymptotically an exponential (while the body of the distribution is Gaussian (Mood, 1940)), when the distribution of x does not decay more slowly than an exponential, i.e., belong to…”
Psychological Barriers in Gold Prices (2007, background): “Finally, Johansen and Sornette (2001) have drawn attention to the need for a non-symmetric model of risk in the gold market, a model that would be consistent with the presence of the barriers we have identified here.”
Dragon-kings: Mechanisms, statistical methods and empirical evidence (2012, methodology): “power law distribution of the motion amplitudes, Cabrera and Milton report the existence of maximum characteristic event sizes associated with the onset of fall, quite similarly to financial crashes (Johansen and Sornette, 2001; Sornette, 2003). Like the financial crashes, these maximum sized events”
Characterization of the Frequency of Extreme Earthquake Events by the Generalized Pareto Distribution (2000, methodology): “In the case of financial returns, this was recently documented with a different techniques using “draw downs” or “runs” that allow for a flexible time scale to adapt to the development of local correlations [Johansen and Sornette, 1998; 2000].”
Significance of log-periodic precursors to financial crashes (2001, methodology): “In his section 5, Feigenbaum attempts to show that our detection (Johansen and Sornette 1988b, 2001b) of two populations of drawdowns does not survive his testing procedure.”
On the power of generalized extreme value (GEV) and generalized Pareto distribution (GPD) estimators for empirical distributions of stock returns (2006, background): “butions, which asymptotically decay as x expð xÞ, while Laherrère and Sornette (1999) suggest to fit the distributions of stock returns by the StretchedExponential (SE) law.”
Shocks, Crashes and Bubbles in Financial Markets (2010, methodology): “Many other markets, especially the emergent markets of Asia and Latin America, as well as individual stocks have been analysed previously using pure drawdowns (Johansen and Sornette, 2001b).”