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. 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 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. 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. George Soros said in late October 1987, 'Mr. Robert Prechter's reversal proved to be the crack that started the avalanche'.
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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For example, the United States has a set of thresholds in place to guard against crashes. If the Dow Jones Industrial Average (DJIA) falls 2,400 points (threshold 2) before 1:00 p.m., the market will be frozen for an hour. If it falls below 3,600 points (threshold 3), the market closes for the day. Other countries have similar measures in place. The problem with this method today is that if one stock exchange closes, shares can often still be bought or sold in other exchanges, which can cause the preventative measures to backfire.
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By July 8, 1932, the Dow was down to 41.22. That was a 90 percent loss from its record-high close of 381.2 on September 3, 1929. It was the worst bear market in terms of percentage loss in modern U.S. history. The largest one-day percentage gain also occurred during that time. On March 15, 1933, the Dow rose 15.34 percent, a gain of 8.26 points, to close at 62.10.
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