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

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.