Secrets of the Stock Market's Biggest Winners
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The Dow was already down 20 percent from its September 3 high, according to Yahoo Finance DJIA Historical Prices. That signaled a bear market. In late September, investors had been worried about massive declines in the British stock market. Investors in Clarence Hatry's company lost billions when they discovered he used fraudulent collateral to buy United Steel. A few days later, Great Britain's Chancellor of the Exchequer, Philip Snowden, described America's stock market as "a perfect orgy of speculation." The next day, U.S. newspapers agreed.
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The following day, Black Tuesday, was a day of chaos. Forced to liquidate their stocks because of margin calls, overextended investors flooded the exchange with sell orders. The Dow fell 30.57 points to close at 230.07 on that day. The glamour stocks of the age saw their values plummet. Across the two days, the Dow Jones Industrial Average fell 23%.
Research at the Massachusetts Institute of Technology suggests that there is evidence the frequency of stock market crashes follows an inverse cubic power law.[15] 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.[16] In 1963, Mandelbrot proposed that instead of following a strict random walk, stock price variations executed a Lévy flight.[17] 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.[18] Researchers continue to study this theory, particularly using computer simulation of crowd behaviour, and the applicability of models to reproduce crash-like phenomena.

The mathematical description of stock market movements has been a subject of intense interest. The conventional assumption has been that stock markets behave according to a random log-normal distribution.[9] Among others, mathematician Benoît Mandelbrot suggested as early as 1963 that the statistics prove this assumption incorrect.[10] Mandelbrot observed that large movements in prices (i.e. crashes) are much more common than would be predicted from a log-normal distribution. Mandelbrot and others suggested that the nature of market moves is generally much better explained using non-linear analysis and concepts of chaos theory.[11] 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.[12] George Soros said in late October 1987, 'Mr. Robert Prechter's reversal proved to be the crack that started the avalanche'.[13][14]

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On October 24, many of the world's stock exchanges experienced the worst declines in their history, with drops of around 10% in most indices.[38] In the US, the DJIA fell 3.6%, i.e. not as much as other markets.[39] Instead, both the US dollar and Japanese yen soared against other major currencies, particularly the British pound and Canadian dollar, as world investors sought safe havens. Later that day, the deputy governor of the Bank of England, Charles Bean, suggested that "This is a once in a lifetime crisis, and possibly the largest financial crisis of its kind in human history."[40]