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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]

Why Is a Bank a Safe Place to Put Money?


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.
One mitigation strategy has been the introduction of trading curbs, also known as "circuit breakers", which are a trading halt in the cash market and the corresponding trading halt in the derivative markets triggered by the halt in the cash market, all of which are affected based on substantial movements in a broad market indicator. Since their inception, circuit breakers have been modified to prevent both speculative gains and dramatic losses within a small time frame.[43]

Why Do Stock Market Crashes Happen?


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Even they know that the markets go through cycles. And right now, the markets are volatile. 2018 was a roller coaster ride that ended with a minor crash. The S&P 500 ended the year 6.5% in the red and the Nasdaq ended the year down 4.3%. Moreover, it was the worst December to hit Wall Street since the Great Depression, with tech stocks ending a nine-year winning streak.


Stock market crashes are 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:[1] a prolonged period of rising stock prices and excessive economic optimism, a market where P/E ratios (Price-Earning ratio) exceed long-term averages, and extensive use of margin debt and leverage by market participants. Other aspects such as wars, large-corporation hacks, changes in federal laws and regulations, and natural disasters of highly economically productive areas may also influence a significant decline in the stock market value of a wide range of stocks. All such stock drops may result in the rise of stock prices for corporations competing against the affected corporations.
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.

What Was the United States Response to 9 11?


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]

What Was the Biggest Cause of the Great Depression?


On August 24, 1921, the Dow Jones Industrial Average stood at a value of 63.9. By September 3, 1929, it had risen more than sixfold, touching 381.2. It would not regain this level for another 25 years. By the summer of 1929, it was clear that the economy was contracting, and the stock market went through a series of unsettling price declines. These declines fed investor anxiety, and events came to a head on October 24, 28, and 29 (known respectively as Black Thursday, Black Monday, and Black Tuesday).
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]

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.


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.
On Black Monday, the Dow Jones Industrial Average fell 38.33 points to 260, a drop of 12.8%. The deluge of selling overwhelmed the ticker tape system that normally gave investors the current prices of their shares. Telephone lines and telegraphs were clogged and were unable to cope. This information vacuum only led to more fear and panic. The technology of the New Era, previously much celebrated by investors, now served to deepen their suffering.
Research at the New England Complex Systems Institute has found warning signs of crashes using new statistical analysis tools of complexity theory. This work suggests that the panics that lead to crashes come from increased mimicry in the market. A dramatic increase in market mimicry occurred during the whole year before each market crash of the past 25 years, including the recent financial crisis. When investors closely follow each other's cues, it is easier for panic to take hold and affect the market. This work is a mathematical demonstration of a significant advance warning sign of impending market crashes.[19][20]
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