Reflexivity, Coherent Markets, and Financial Instability:

Reconsidering Alternative Explanations for Departures from Generally Accepted Economic and Financial Theory

J. Douglas Barrett
Professor of Quantitative Methods and Chair
Department of Economics and Finance
University of North Alabama
Florence, AL 35632
jdbarrett@una.edu

Peter M. Williams
Professor of Economics
Department of Economics and Finance
University of North Alabama
Florence, AL 35632
pmwilliams@una.edu


ABSTRACT

The current financial crisis has caused a reassessment of many canonical assumptions underpinning traditional theory in economics and finance.  Specifically, the real estate and financial markets have exhibited behavior that belies previously expected conditions.  Nonstandard theories have existed for decades, but have been largely ignored by mainstream academia.  The Reflexivity Theory of Soros, the Coherent Markets Hypothesis of Vaga, and the Financial Instability Hypothesis of Minsky are three potentially viable theories.  The current work is an investigation of these and other alternative theories in economic and financial analysis.


INTRODUCTION

Traditionally, the dominant school of thought in finance is the Efficient Market
Hypothesis (EMH).  (See, e.g., [3].)  In its simplest form, the EMH asserts that market prices reflect all available information.  Theoretically based in mathematics, the EMH is the foundation for much of the inquiry in the discipline.  Empirical studies have shown results that are, at best, mixed.  The recent economic crisis has exacerbated the situation.

The EMH is based on several assumptions.  It asserts that past information does not affect market activity (i.e., the process is “memoryless”), once this information is generally known.  Another assumption is that capital market behavior follows a “random walk.”  Furthermore, with a sufficiently large sample, the returns become well approximated by a normal (Gaussian) distribution.

The purpose of the current study is to discuss issues with the EMH, and highlight the current alternative theories.  In the next section, empirical departures from the aforementioned assumptions for the EMH are discussed.  The succeeding section highlights the list of alternative theories, with a brief description of each.  The paper concludes with a summary and points of convergence for the competing theories.  ...

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http://rwahlers.iweb.bsu.edu/abd2009/Papers/p09_barrett_williams.pdf

Are the Financial Markets Becoming More Efficient?

With the advent of negotiated commissions in 1975 and growing use of increasingly powerful computer based trading systems, the markets appear to be increasingly efficient. One way to measure market efficiency is by examining conditional returns: if conditional returns are trend persistent, profits can be made by betting with the trend; if conditional returns are mean regressive, profits can be had by betting on trend reversals. If conditional returns are too small to profit from, then the markets are efficient.

Our Bifurcation Parameter (BP) is a measure of the degree of trend persistence (when positive) or mean regression (when negative). It is defined as the 200 day sum of daily returns, R(t+1) after prior day returns in the interval 0.5% < R(t) < +3.5% minus the sum of daily returns after previous day returns in the interval -3.5% < R(0) < -0.5%. When this measure is greater than +10%, we consider the market to be trend persistent; when less than -10%, the market is mean regressive. Between these levels, the market is in a relatively efficient state.

Figure 1 illustrates the NASDAQ BP dating back to 1971. For much of this period, the NASDAQ BP was highly trend persistent, and hardly ever mean regressive with respect to daily returns. However, beginning roughly in the year 2000, the NASDAQ has become more efficient and more recently mean regressive, a highly volatile, disordered market state.


Figure 1. The NASDAQ has become more efficient over the past decade and more recently has become mean regressive. (Click on chart to expand).

Figure 2 summarizes the returns for each key market state. The mean regressive state has has the least data and is not statistically significant at the 95% level. The bifurcated bull and bear states are highly statistically significant. Statistical significance is based on excluding the probability that the returns in a particular state are the same as for the efficient state.


Figure 2. The NASDAQ returns in the bull and bear state are statistically significant. (Click on chart to expand).

The Dow Jones Industrial Average has also become more efficient since about 1975. Figure 3 summarizes the Bifurcation Parameter dating back to the Crash of 1929. During the post World War II period the markets were highly trend persistent as the economy boomed. However, in the post 1975 period, the DJIA BP has also steadily declined and currently remains at levels not seen since the Crash of 1929.


Figure 3. The DJIA has become more efficient since 1975 and has recently become highly mean regressive. (Click on chart to expand).

Figure 4 summarizes the returns and their statistical significance for key DJIA market states. The mean regressive state is not statistically significant due to its high volatility and relatively little data. However the DJIA bull and bear states are highly statistically significant.


Figure 4. The DJIA returns in the bull and bear state are statistically significant. (Click on chart to expand).

Japan's NIKKEI Index provides an example of what to expect from an efficient market. It has been efficient on average since about 1991 (based on a quadratic fit to the NIKKEI Bifurcation Parameter). Figure 5 summarizes the NIKKEI Bifurcation Parameter dating back to 1984.


Figure 5. The NIKKEI has been fairly efficient since 1990. (Click on chart to expand).

Figure 6 summarizes the returns and their statistical significance for key NIKKEI market states. The mean regressive state is not statistically significant due to its high volatility and relatively little data. The DJIA bull and bear states are also not statistically significant. Therefore as the markets become more efficient, there will be fewer profitable trading opportunities.


Figure 6. The NIKKEI returns in the bull and bear state are not statistically significant. (Click on chart to expand).

Dow Jones Industrials Remain in Over Reaction, Mean Regressive State

The Bifurcation Parameter (BP) for the Dow Jones Industrial Average (DJIA) remains in negative territory at -38%. This market has been in an over reaction, mean regressive state that has often accompanied crisis markets. The BP is defined here.

Figure 1 summarizes the DJIA BP dating back to the Crash of 1929. For most of this period the BP has been indicating a bifurcated market in which investor sentiment is prone to under react and price is trend persistent. However, with the advent of computerized trading and negotiated commissions in 1975 the markets have become more efficient. An efficient market is defined here as one in which there is neither trend persistence nor mean regression is large enough to provide significant trading opportunities.


Figure 1. The Dow Jones Industrial Average Bifurcation Parameter suggests that the market has become more efficient since 1975. (Click on chart to enlarge).

The average return for the DJIA as a function of the average value of the BP for each market state is summarized in Figure 2. The t-test for each state provides the probability that the returns for a given state are equivalent to those from the efficient market state (when -10% < BP < +10%). Note that the crisis state (BP < -10%) is not statistically significant at the 95% level due to the limited amount of data, the recent market rally and the high volatility of this state. In contrast, the bifurcated bull state (BP >= +10% and R(0) >= 0) is statistically highly significant (p = 1.6E-9). Likewise the bear state (BP < -10% and R(0) < 0) is highly significant (p = 1.5E-5). However, if the markets have become more efficient, then these trend persistent states will be evident less frequently.


Figure 2. The Dow Jones Industrial Average market returns for the bull and bear state have been highly statistically significant. (Click on chart to enlarge).

NASDAQ Remains in Mean Regressive State

The Bifurcation Parameter for the NASDAQ Composite Index slipped back to -22% over the past few weeks (white arrow on the chart). Figure 1 summarizes the average daily return expected from each of the four key market states expected from the Bifurcation Parameter (and prior day return, R(0)).

NASDAQ Composite Index Returns for States Predicted by the NASDAQ Bifurcation Parameter (click on chart to enlarge)

The statistical significance of each state is based on a comparison with the efficient state (when -10% < BP < +10%). The statistical significance of the Crisis Market State is questionable at p = 0.1 which is below the 95% confidence level benchmark and approximately the same as found for the Dow Industrial as briefed in Zurich and shown on the briefing slides for that talk. In contrast, the Bull and Bear states are both highly statistically significant. For the Zurich talk, daily returns were annualized and the t-test was based on comparing each state with the buy and hold benchmark (as opposed to the efficient market state).

NASDAQ Leading the Way Out of Crisis Conditions?

Figure 1 summarizes the bifurcation parameter for the NASDAQ Composite Index. The bifurcation parameter has shown steady improvement and has now risen above the -10% threshold. This suggests that the worst of the mean regressive crisis market may be behind us. While the indicator could fluctuate around current levels and create whipsaw results, the big picture is that there has been steady improvement toward a more efficient market state.


Figure 1. The NASDAQ Index is Becoming Less Mean Regressive

The risk and reward profile of the NASDAQ Index is summarized in Figure 2. The Efficient Market State (-10% < BP < +10%) has exhibited an annualized return of 16% with an annualized volatility of 22%. The prior Bull States (when the BP > 10% and R(0) > 0) show a 60% annualized return with moderate risk. The Bear States (when the BP > 10% and R(0) < 0) show a -30% annualized return with 20% annualized risk.


Figure 2. The NASDAQ Index Risk Reward Profiles

To avoid whip saw trading, look for the Bifurcation Parameter to become positive before changing positions in the current environment. While the NASDAQ has improved, the Dow Jones Industrial Average and the S&P Composite Index remain in the crisis state.

Over Reaction, Disordered Market Continues

We introduce an Efficient Market state, defined as -10% < Bifurcation Parameter < +10%. This represents a market where there isn't much over reaction or under reaction to news. We also update prior coherent and chaotic market state definitions, requiring the Bifurcation Parameter to be >= +10%. Therefore the Coherent and Chaotic markets clearly represent under reaction situations and trend persistent states. We also use the prior day return, R(t) to differentiate between coherent (R(t)>=0) and chaotic (R(t)<0) states. These definitions and associated risk and returns since July 1929 are summmarized as follows:

Coherent Bull Markets
Bifurcation Parameter >= +10%
R(t) >= 0 (prior day return is positive)
RETURN 37.94%
RISK 15.05%
% TIME 24.16%

Efficient Markets
-10% < Bifurcation Parameter < +10%
RETURN 6.16%
RISK 14.85%
% TIME 45.25%

Chaotic Markets
Bifurcation Parameter > +10%
R(t) < 0 (prior day return is negative)
RETURN -13.50%
RISK 17.87%
% TIME 22.15%

Disordered Markets
Bifurcation Parameter < -10%
RETURN -17.17%
RISK 36.65%
% TIME 8.43%