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    Stock Market Crash

    At the beginning of 2008, stock markets are quite turbulent, which brings us back into considerations about crashes. We do not mean that the present stock market situation is comparable to an academic crash, not at all... But, in period of turbulence, it is always a good point to come back to fundamentals... We intend to present some simple and fundamental ideas about crashes and outliers, which may put some light on the present market status.

    In this document, we intend to give a simple presentation of these common but always intriguing market moves that are crashes. Indeed, the characterization of large stock market moves, especially large negative price drops, is of profound importance for risk management. One has always to consider the huge risk in front of high returns. The complex trajectory of stock market prices is the faithful reflection of the continuous flow of news that are interpreted and digested by analysts and traders. Accordingly, large market losses can result from really bad surprises. It is a fact there are shocks generated by external news or events, as Sept. 11 2001, which can move stock market prices and create strong bursts of volatility.

    However, this is only part of the story. A key issue is to check whether large losses (or crashes) may result more fundamentally from an internal origin lying in the dynamics of the stock market itself. Then, the external news would only act as triggers but not as the decisive factors for crashes. Which means that some other news or events would have had the same consequences on the market.

    This internal origin of crashes requires the investigation of signs of instabilities to be found in the market dynamics. Then, we need to survey carefully the history of crashes and make it clear whether we can identify some common features.

    First, we intend to show by examples that crashes are parts of the financial market life... One should not over-emphasize their importance. Then, we propose to examine some common characteristics of crashes that give some hints for investing decisions when those specific features are taking place.

    An important motivation for studying stock market crashes is that they are always unforeseen for most people, especially economists. Out claim is that, if we are well prepared, we can at least keep safe and protect our capital. Let remember these two famous analysis:

    (1) "In a few months, I expect to see the stock market much higher than today." Those words were pronounced by Irving Fisher, America's distinguished and famous economist, Professor of Economics at Yale University, 14 days before Wall Street crashed on Black Tuesday, October 29, 1929.

    (2) "A severe depression such as 1920-21 is outside the range of probability. We are not facing a protracted liquidation." This was the analysis just after the crash of 1929 by the Harvard Economic Society to its subscribers. The Society closed its doors in 1932.

    Note that we do not enter in this document into the academic debate of the proper definition of crashes. We consider as crashes large losses over short period of time, for example a loss of more than 10 to 15% over one month. In addition, during this period, we often observe a strong enhancement of volatility with some daily returns of -6% and others of +4%. The general mood of analysts and investors is also an interesting issue to observe to characterise crashes: during these periods, the pessimism is large enough to generate some panic and then collective "crowd" behaviour of many interacting agents on the market. Of course, in case of a daily return of -20%, followed by other losses in the next days, we enter into the pure academic definition of crashes and nobody will contest it!

    1- A Brief History of crashes (key examples)

    Between 1585 and 1650, Amsterdam became the chief commercial emporium owing to the growing commercial activity in newly discovered America. The years of tulip speculation fell within a period of great prosperity in the republic of the Netherlands. The tulip was imported into Western Europe from Turkey since 1554. What we now call the "tulip mania" of the seventeenth century was the "sure thing" investment during the period from mid-1500s to 1636, before its devastating end in 1637. People became too confident that this "sure thing" would always make them money and, at its peak, the participants mortgaged their houses and businesses to trade tulips. Before the crash, any suggestion that the price of tulips was irrational was dismissed by all the participants. The crisis came unexpectedly. On February 4th, 1637, the possibility of the tulips becoming definitely unsalable was mentioned for the first time. Bulbs worth tens of thousand of US dollars (in present value) in early 1637 became valueless a few months later. This is a remarkable event in history, where all features of modern crashes can be identified, as we shall see in the next examples.

    Let describe now the most famous crash, the one of October 1929. After this Godzilla, the US banking industry underwent the biggest structural changes of its history, as a new era of government regulation began, with Roosevelt's New Deal. The Oct. 1929 crash presents the remarkable features associated with crashes. First, it was unforeseen. The most renowned economic forecasting institutes in America at the time failed to predict that a crash and a depression were forthcoming. A second general feature exemplified by the Oct. 1929 event is that the financial collapse happened when macroeconomic news look good. The political mood before the Oct. 1929 crash was also optimistic. In November 1928, Herbert Hoover was elected President of the US in a landslide, and his election set off the greatest increase in stock buying to that date. Less than a year after the election, Wall Street crashed.

    Another example. From the opening on October 14, 1987 through the market close on October 19, major indexes of market valuation in the United States declined by 30% or more. Furthermore, all major world markets declined substantially in the month. The US was not the first to decline sharply. Non-Japanese Asian markets began a severe decline on October 19, 1987, their time, and this decline was echoed first on a number of European markets, then in North American, and finally in Japan. In local currency units, the minimum decline was in Austria

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