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A stock market crash is a sudden dramatic decline of stock prices across a significant cross-section of a stock market. Crashes are driven by panic as much as by underlying economic factors. They often follow speculative stock market bubbles.

Stock market crashes are in fact social phenomena where external economic events combine with crowd behavior and psychology in a positive feedback loop where selling by some market participants drives more market participants to sell. Generally speaking, crashes usually occur under the following conditions : a prolonged period of rising stock prices and excessive economic optimism, a market where P/E ratios exceed long-term averages, and extensive use of margin debt and leverage by market participants.

There is no numerically specific definition of a crash but the term commonly applies to steep double-digit percentage losses in a stock market index over a period of several days. Crashes are often distinguished from bear markets by panic selling and abrupt, dramatic price declines. Bear markets are periods of declining stock market prices that are measured in months or years. While crashes are often associated with bear markets, they do not necessarily go hand in hand. The crash of 1987 for example did not lead to a bear market. Likewise, the Japanese Nikkei bear market of the 1990s occurred over several years without any notable crashes.

Mathematical theory and stock market crashes

The mathematical characterisation of stock market movements has been a subject of intense interest. The conventional assumption has been that stock markets behave according to a random Gaussian or "normal" distribution. Among others, mathematician Benoît Mandelbrot suggested as early as 1963 that the statistics prove this assumption incorrect. Mandelbrot observed that large movements in prices (i.e. crashes) are much more common than would be predicted in a normal distribution. Mandelbrot and others suggest that the nature of market moves is generally much better explained using non-linear analysis and concepts of chaos theory. This has been expressed in non-mathematical terms by George Soros in his discussions of what he calls reflexivity of markets and their non-linear movement.

Research at the Massachusetts Institute of Technologymarker suggests that there is evidence the frequency of stock market crashes follows an inverse cubic power law. This and other studies such as Prof. Didier Sornette's work suggest that stock market crashes are a sign of self-organized criticality in financial markets. In 1963, Mandelbrot proposed that instead of following a strict random walk, stock price variations executed a Lévy flight. A Lévy flight is a random walk that is occasionally disrupted by large movements. In 1995, Rosario Mantegna and Gene Stanley analyzed a million records of the S&P 500 market index, calculating the returns over a five year period. Their conclusion was that stock market returns are more volatile than a Gaussian distribution but less volatile than a Lévy flight.

Researchers continue to study this theory, particularly using computer simulation of crowd behaviour, and the applicability of models to reproduce crash-like phenomena.

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