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.  ...

download pdf of complete paper at:

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

Social Imitation Modell

Social Imitation Modell

Ulf A. Hamster 

Erste Version: 23. März 2009, Aktuell: 14. Juni 2009

Zusammenfassung

Das Ising Modell wird als Markov-Ketten Modell implementiert, was exogen über den Crowding- und Fundamentalverzerrungsparameter gesteuert werden kann, um eine bimodale Verteilung bezüglich der Kaufodere Verkaufsneigung der Agenten zu erzeugen.

1 Einleitung

Coherent Market Hypothesis. Der Aspekt sich gegenseitig beeinflussen- der Agenten wird in der Coherent Market Hypothese (CMH) nach Vaga (1990) aufgegriffen. Die CMH differenziert zwischen effizienten, kohärenten trend- behafteten, chaotischen, instabilen und zurücktreibenden Marktphasen (Schöbel und Veith, 2006, S. 6), welche über die Parameter einer bimodalen Verteilung modelliert wird (Tab. 1). Während Vaga (1990) von einer Renditever- teilung ausgeht, wird i.d.R. die Wahrscheinlichkeit der Anzahl nachfragender vs. anbietender Marktteilnehmer aufgrund gegenseitiger Imitation betrachtet. Wie Shmatov und Smirnov (2005) zeigen, kann letzteres mit Hilfe von Markov-Ketten numerisch implementiert werden (Kap.2).

Interaktion zwischen Agenten. Methodischer Ausgangspunkt ist das Ising Modell zur Beschreibung von Ferromagnetismus, das analog Interaktions- möglichkeiten auf benachbahrte Agenten einschränkt, z.B. Iori (2002) und Sornette und Zhou (2006). Als qualitative Begründungen können Erkenntnisse nicht assozierter empirischer Studien bezüglich Finanzmarktentscheidungen herangezogen werden, z.B. Mund zu Mund Effekt (Hong u. a., 2004, 2005; Brown u. a., 2008), Home Bias Effekt (Huberman, 2001; Massa und Simonov, 2006), und Lokaler Informationsvorteil (Coval und Moskowitz, 2001, 1999; Ivkovic und Weisbenner, 2005), welche als Verkettung von Fehler indi- vidueller Verfügbarkeitsheuristiken (Kuran und Sunstein, 1999) interpretiert werden können.

Heterogene Agenten. Jedoch vernachlässigt das Iori/Ising-Modell wie viele Agenten was tun und wie sie sich gegenseitig beeinflussen, z.B. Unterscheidung der Noise Trader von Fundamentalanlysten (Lux, 1995, 1997), Strate- giewechsel und Markteintritt- & austritt von Agenten (Lux, 1998, S. 149ff.), der Einfluss der Gesamtanzahl der Agenten im Markt (Egenter u. a., 1999), oder individuelle Selbsttäuschung wie Optimismus & Pessimismus (Chen u. a., 2001) Obwohl die Iori-Modelle durch die Nächste Nachbar Einschränkung eine Verfügbarkeitsheuristik impliziert, bilden Lux-Marchesi-Modelle empirische Eigenschaften von Finanzmarktreihen besser ab und sind diesbe- züglich plausibler begründet.

Alzheimer Random Walks and Market Bubbles?

Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks

V. M. Kenkre

An analytic formulation of memory-possessing random walks introduced recently [Cressoni et al., Phys. Rev. Lett. 98, 070603 (2007) and Sch\"utz and Trimper, Phys. Rev. E 70, 045101 (2004)] for Alzheimer behavior and related phenomena is provided along with exact solutions on the basis of Fokker-Planck equations. The solution of a delay-differential equation derived for the purpose is shown to produce log-periodic oscillations and to coincide rather accurately with previously published computer simulation results. Generalizations along several directions are also constructed on the basis of the formalism.

Two remarkable publications have recently appeared on the subject of random walks with memory, one in- volving the ‘elephant walk’ in which the walker chooses steps randomly but is influenced by a perfect memory of steps taken earlier [1], and the other involving an extension of this walk to incorporate partial memory of steps from the beginning up to a time in the past [2]. While an analytical description has been given for the (former) elephant walk, it appears to have been impossible to provide one for the partial memory extension. The significance of the latter is that it has been proposed [2] for the medically important analysis of amnestically in- duced behavior of Alzheimer patients. The authors of Ref. [2] have presented impressive computer simulations of the Alzheimer walk exhibiting log-periodic oscillations in the displacement of the walker, and deduced intriguing conclusions regarding the elements of persistence and what they have called, following Schu ̈tz and Trimper [1], traditional versus reformer behavior of the walker. They have also stated that an analytic solution of their partial memory extension (the Alzheimer walk) remains an open problem. The present Letter is aimed at solving that problem. 

The quote above is from an interesting paper on random walks with either perfect memory (elephant walks) or memory of the past without recent memory (Alzheimer's walks). The latter is given an analytic treatment based on a time dependent Fokker Planck Equation. This is of interest for two reasons: 1. our Coherent Market Hypothesis (CMH) is based on the Fokker Planck Equation; and 2. The log periodic oscillations that occur with Alzheimer's random walks have empirically been found to be precursors to market bubbles and crashes (or at least regime changes) by Didier Sornette, et. al.

The CMH is based on a stationary (time independent) Fokker Planck Equation. Therefore this paper by V. M. Kenkre paves the way for introducing time dependence into the CMH formalism leading to prediction of log periodic oscillations in the financial markets. Clearly this is an important opportunity for research on extending the CMH into time dependent as well as stationary state dynamics.

RELATIVISTIC QUANTUM ECONOPHYSICS – NEW PARADIGMS IN COMPLEX SYSTEMS MODELLING V. Saptsin and V. Soloviev

"Econophysics, or physical economics, already mentioned as a relatively young scientific school, recently celebrated its tenth anniversary. Of course that doesn’t mean that there were no works on the boundary of economics and physics before the econophysics was officially born, howewer the new direction is usually formed only when the certain conditions appear and the necessity to concentrate the scientific forces arises. Quantum econophysics is not an exception. That is why, though the first work according to Gonsales [18], which can be related to the application of quantum mechanical ideas to the economic phenomena, appeared in 1990 [55], we can speak about the birth of the new scientific direction called econophysics only nowadays."

[18] C. P. Goncalves, An Evolutionary Quantum Game Model of Financial Market Dynamics - Theory and Evidence, April 14, 2007, URL http://ma.utexas.edu/mp arc/c/07/07- 89.pdf .

[55] T. Vaga, The Coherent Market Hypothesis, Financial Analysts Journal, November/December, 36–49 ( 1990).

Bubble Hunter

Click on the title to visit the Bubble Hunter Blog, written by:

PIOTR CHWIEJCZAK
I am 33. I graduated from Warsaw University Economist Department in 1996 (M.A.). I spent few years working in several banks as economist/strategist. I was also working as a economic advisor to official bodies Poland and outside Poland. In year 2003/2004 I spent 9 months in Iraq where I was working as advisor to the central banker.

Recent posts include:

The Chinese equity bubble - UPDATE

provides link to more detailed paper by Sornette.

World stock market: approaching trend reversal?

Stanislaw Drozdz and Pawel Oswiencimka in short paper predict that core stocks indexes will face significant correction.

Sugar bubble ready to burst.



"I analyzed sugar#11 future time series between September 2007 and September 3 2009. The y axis is logarithmically scaled so that the exponential function would appear as a straight line. LPPL fit exhibit upward curvature which is clear evidence that the prices were growing “super-exponentially”. The projected crash dates are September 5-15 .It must be noted that a good fit of the model to the data series is not a 100% certainty for a crash, but it clearly points at a bubble formation."

Shanghai Bubble Bursts

According to New Scientist:

"WITH 20/20 hindsight, financial crashes seem inevitable, yet we never see them coming. Now a team of physicists and financiers have bucked the trend by successfully predicting a steep fall in the Shanghai Stock Exchange.

Their model, which employs concepts from the physics of complex atomic systems, was developed by Didier Sornette of the Financial Crisis Observatory in Zurich, Switzerland, and Wei-Xing Zhou of the East China University of Science and Technology in Shanghai."

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).