Can financial market crises be predicted? We propose a Bifurcation Parameter in this regard.
BACKGROUND: Weidlich proposes the Ising Model to describe polarization of opinions in social groups. Haken's model includes the Langevin equation of Brownian motion as a special case and references Weidlich's work as an example of more ordered states in social systems. Vaga applies Weidlich and Haken's state transition concepts to formulate the Coherent Market Hypothesis. Vaga and Nawrocki develop a novel bifurcation parameter and analyze coherent, chaotic, efficient and disordered (crisis) market states.
The Coherent Market Hypothesis provides the theoretical basis for defining a quantitative bifurcation parameter, a potential indicator crisis situations in the financial markets.
The empirical daily conditional return map from 1929 to present illustrates bullish and bearish equilibrium states (where the return map crosses zero). The slope of the conditional return map in the neighborhood of moderate returns is positive with high statistical significance.
The slope of the conditional return (CR) map governs the bifurcation process from the linear, disordered state to the more structured bull and bear states.
The bifurcation parameter is the 200 day sum of conditional returns after moderate positive returns minus the 200 day sum of conditional returns after moderate negative returns. This parameter is related to the slope of the CR map.
The Bifurcation Parameter (BP) has dropped well below -10% in crisis markets such the Crash of 1929 and Great Depression Era. In contrast, the BP didn't drop below -10% at all in the post WW II Era (1946-1975). Since the advent of computerized trading and negotiated commissions in the mid-1970s, the BP has indicated a more efficient market, though recently this indicator has fallen to levels not seen since the Great Depression Era.
In the 1929 to 1939 period, the bifurcation parameter fell well below -10% and remained there on three occasions, each of which resulted in significant market declines
In the 1999 to 2009 period there were two large declines in the Bifurcation Parameter below -10%, one coincided with rising stock prices and the other with a large decline to date.
Periods with a negative BP have a significant negative bias in the conditional return map.
Periods with a BP greater than +10% have a higher degree of bull and bear trend persistence.
Market state definitions can be based solely on the Bifurcation Parameter.
Ordered markets, including both coherent and chaotic states, outperform efficient market periods, while disordered (crisis) markets have underperformed by a large degree.
Ordered markets can be decomposed into coherent bull markets (when the prior day return is >0) or chaotic markets when the prior day return is negative.
Coherent, chaotic, efficient and crisis markets have widely varying risk and reward profiles.
The Crash of 1929 and Great Depression Era was highly volatile.
The post World War II Era enjoyed a high degree of trend persistent, coherent and chaotic markets.
Since the advent of negotiated commissions in 1975, the markets have become more efficient on average.
Returns in coherent and chaotic markets are highly statistically significant. Disordered markets (mean regressive reversals after positive returns) are also statistically significant. However due to the high volatility and relatively limited amount of data, crisis market returns are only significant to the 90% level.
The Bifurcation Parameter provides a statistically significant indicator of the coherent and chaotic market states predicted by the Coherent Market Hypothesis. However, due to the extreme volatility and limited number of crisis markets the significance of this state has only been partially established, i.e. reversals of prior day price advances.
BACKUP CHARTS
The NASDAQ Composite Index exhibited a high degree of coherence from 1971 through the year 2000. It is currently in a disordered state.
The S&P500 Index has exhibited large upside reversals in the recent mean regressive market.
