A bifurcation model of market returns

Abstract

We propose a bifurcation model of market returns to describe transitions between an ‘over-reaction’ mean regressive state and ‘under-reaction’ trend persistent states. Since July 1929, the Dow Jones Industrial Average has exhibited non-stationary state transition behavior, including: (1) mean regressive behavior during crisis situations during the Great Depression of the 1930s and again in the crisis of 2008 when the availability of credit was interrupted; (2) strongly bifurcated, or trend persistent behavior from the 1940s through 1975; and (3) more efficient behavior since 1975. The bifurcation dynamic evident in the pre-1975 era is somewhat enhanced by conditional volume and moderate volatility. The bifurcation model is used to develop a quantitative measure of the degree of market efficiency, which indicates that the market has become more efficient, i.e. less trend persistent, since 1975 with the advent of negotiated commissions and computerized trading techniques. Similar findings are presented for the S&P 500 index and the CRSP Value Weighted Index, which represent large capitalization markets. Results for the CRSP Equal Weight Index are found to be significantly less efficient and more trend persistent than the larger capitalization CRSP Value Weighted Index.