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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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By the end of the weekend of November 11, the index stood at 228, a cumulative drop of 40% from the September high. The markets rallied in succeeding months, but it was a temporary recovery that led unsuspecting investors into further losses. The Dow Jones Industrial Average lost 89% of its value before finally bottoming out in July 1932. The crash was followed by the Great Depression, the worst economic crisis of modern times, which plagued the stock market and Wall Street throughout the 1930s.
Tulip Mania (in the mid-1630s) is often considered to be the first recorded speculative bubble. Historically, early stock market bubbles and crashes have also their roots in socio-politico-economic activities of the 17th-century Dutch Republic (the birthplace of the world's first formal stock exchange and market),[3][4][5][6][7] the Dutch East India Company (the world's first formally listed public company), and the Dutch West India Company (WIC/GWIC) in particular. As Stringham & Curott (2015) remarked, "Business ventures with multiple shareholders became popular with commenda contracts in medieval Italy (Greif, 2006, p. 286), and Malmendier (2009) provides evidence that shareholder companies date back to ancient Rome. Yet the title of the world's first stock market deservedly goes to that of seventeenth-century Amsterdam, where an active secondary market in company shares emerged. The two major companies were the Dutch East India Company and the Dutch West India Company, founded in 1602 and 1621. Other companies existed, but they were not as large and constituted a small portion of the stock market (Israel [1989] 1991, 109–112; Dehing and 't Hart 1997, 54; de la Vega [1688] 1996, 173)."[8]
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]
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