Empirical Regularities in Stock Market Crashes

When a stock market crash is defined as the period from an index's prior peak until its recovery, crashes demonstrate empirical regularities in their scale and timing. For instance, measures of the duration, maximum decline, and lost value of crashes are very highly correlated. These correlations suggest that crashes belong to well-defined categories based on their size and become increasingly predictable as they progress. Accordingly, I advance four stock market crash categories, which are logarithmic in size. Crashes then range from small scale market disturbances like 'flash crashes' in Category 1 to the Wall Street Crash of 1929, America's sole Category 4. Furthermore, I find that U.S. stock markets are bimodal, switching between crashes and booms, and that this switching is regular. Specifically, I find that either a Category 2 or 3 crash occurs every four years, with a variance of just two years. Moreover, by definition, growth during a crash is close to zero. During boom periods, however, the average annual growth rate is 21.5%. Together, these results suggest a new foundation for examining patterns of returns and other characteristics of stock markets.