منشاء سقوط در سه بازار سهام ایالات متحده: شوک و حباب

This paper presents an exclusive classification of the largest crashes in Dow Jones industrial average, SP500 and NASDAQ in the past century. Crashes are objectively defined as the top-rank filtered drawdowns (loss from the last local maximum to the next local minimum disregarding noise fluctuations), where the size of the filter is determined by the historical volatility of the index. It is shown that all crashes can be linked to either an external shock, e.g., outbreak of war, or a log-periodic power law (LPPL) bubble with an empirically well-defined complex value of the exponent. Conversely, with one sole exception all previously identified LPPL bubbles are followed by a top-rank drawdown. As a consequence, the analysis presented suggest a one-to-one correspondence between market crashes defined as top-rank filtered drawdowns on one hand and surprising news and LPPL bubbles on the other. We attribute this correspondence to the efficient market hypothesis effective on two quite different time scales depending on whether the market instability the crash represent is internally or externally generated.

The analysis presented here have strengthen the evidence for outliers in the financial markets and that the concept can be used as a objective and quantitative definition of a market crash. Furthermore, we have shown that the existence of outliers in the drawdown distribution is primarily related to the existence of LPPL bubbles prior to the occurrence of these outliers or crashes. In fact, of the 15 largest ε-drawdowns identified as outliers only two did not have prior LPPL bubble and these two outliers could be linked to a specific major historical event (WWI and WWII). In complement, only one (1937) previously identified LPPL bubble was not identified as an outlier. The analysis presented suggests a one-to-one correspondence between market crashes defined as top-rank filtered drawdowns on one hand and surprising news and LPPL bubbles on the other. We attribute this correspondence to the EMH effective on to quite different time scales depending on whether the market instability the crash represent is internally or externally generated. Further work is needed to clarify the role of different coarse-graining methods as well as to arrive at a quantitative choice for ε based on the data. Naturally, the choice of ε should not only be determined by the volatility but should also depend further on the type of market.