Circuit Breakers and the Tail Index of Equity Returns

Abstract

Using the tail index of returns on U.S. equities as a summary measure of extreme behavior, we examine changes in the equity markets surrounding the development of program trading for portfolio insurance, the crash of 1987, and the subsequent introduction of circuit breakers and other changes in market architecture. Recently-developed tests for the null of constancy of the tail index, versus the alternative of a change at an unknown date, permit inference on changes in extreme behavior over a long time period while allowing for second-moment dependence in the return data. We find strong evidence of a decrease in the tail index (increase in the probability of extreme events) around the beginning of large-scale program trading, and weaker, but still substantial, evidence of further significant change in the tail index following the introduction of circuit breakers. Point estimates of the tail index suggest that the tail index may have roughly regained pre-program trading levels. More generally, the results tend to suggest that long samples of U.S. equity returns should not be treated as samples from a single distribution function, particularly in examining extremes.