A Mean-Reversion Theory of Stock-Market Crashes

Errors in the perception of mean-reversion expectations can cause stockmarket crashes. This view was proposed by Fischer Black after the stockmarket crash of 1987. I discuss this concept and specify a stock-price model with mean-reversion in returns. Using daily data of the Dow Jones Industrial Average and the S&P500 index I show that mean-reversion in returns is a transient but recurring phenomenon. In the case of the crash of 1987 I show that during the period 1982–1986 mean-reversion was higher than during the nine months prior to the crash. This indicates that meanreversion expectations were underestimated in 1987. This error was disclosed when in the week prior to the crash it became known that a surprisingly high volume of equities was under portfolio insurance and thus hedged against a faster reversion. Simulations of the model with parameter estimates obtained from the two periods show that a crash of 20 percent or more had a probability of about seven percent. Up to five years after the crash, mean-reversion was higher than before. This supports Black’s hypothesis. Contrary to that, the crash of 1929 cannot be explained by a mean-reversion illusion.