The Clustering of Extreme Movements: Stock Prices and the Weather
Burton G. Malkiel
A striking feature of the United States stock market is the tendency of days with very large movements of stock prices to be clustered together. We define an extreme movement in stock prices as one that can be characterized as a three sigma event; that is, a daily movement in the broad stock-market index that is three or more standard deviations away from the average movement. We find that such extreme movements are typically preceded by, but not necessarily followed by, unusually large stock-price movements. Interestingly, a similar clustering of extreme observations of temperature in New York City can be observed. A particularly robust finding in this paper is that extreme movements in stock prices are usually preceded by larger than average daily movements during the preceding three-day period. This suggests that investors might fashion a market timing strategy, switching from stocks to cash in advance of predicted extreme negative stock returns. In fact, we have been able to simulate market timing strategies that are successful in avoiding nearly eighty percent of the negative extreme move days, yielding a significantly lower volatility of returns. We find, however, that a variety of alternative strategies do not improve an investor’s long-run average return over the return that would be earned by the buy-and-hold investor who simply stayed fully-invested in the stock market.
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