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).

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.

Hang Seng Index: Trend Persistent (Bull and Bear States)

Figure 1 summarizes the bifurcation parameter for the Hang Seng Index dating back to 1987. During this period there has been very little mean regressive market action. Even recently during the global credit crisis, the Hang Seng did not show the crisis state behavior that the US equity markets exhibited.


Figure 1. The Hang Seng Index has been Trend Persistent

The risk and reward profile of the Hang Seng Index is summarized in Figure 2. The Bull State (when the BP > 10% and R(0) > 0) shows a greater than 50% annualized return with moderate risk. The Bear State (when the BP > 10% and R(0) < 0) shows a -20% annualized return with 32% annualized risk.


Figure 2. The Hang Seng Index Risk Reward Profiles

A short term trend following strategy would appear to be effective in the current environment.

According to Didier Sornette, et. al.: Chinese Equity Bubble: Ready to Burst

July 10, 2009

Amid the current financial crisis, there has been one equity index beating all others: the Shanghai Composite. Our analysis of this main Chinese equity index shows clear signatures of a bubble build up and we go on to predict its most likely crash date: July 17-27, 2009 (20%/80% quantile confidence interval).

ETH Zurich Workshop Presentation: A Financial Market Bifurcation Parameter

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.

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%

International Workshop on Coping with Crises in Complex Socio-Economic Systems

ETH Zurich (Switzerland), June 8-12, 2009
Monday, June 8, 2009:
15:20 - 15:45 CAB G 51
Tonis Vaga: A Financial Market Bifurcation Parameter

Preliminary Program

Poster Presentations

Organizers

Kay Axhausen
Lars-Erik Cederman
Dirk Helbing (Coordinator)
Hans Jürgen Herrmann
Frank Schweitzer
Didier Sornette

Social systems typically feature crises, i.e. unstable and dangerous situations that are characterized by abrupt and large-scale changes. Such disruptions are very hard to predict with any precision and even harder to control. Indeed, crises often convey an impression that key decision makers have lost control and that events unfold in an unstoppable and even catastrophic way. Examples include environmental crises, the collapse of transportation systems, as well as financial and social crises such as poverty, social conflicts or wars.

These and other issues will be addressed during the meeting, which combines elements of an interdisciplinary workshop with a think tank and a summer school for young scientists. Scientists and students interested in participating in this workshop are asked to send an e-mail to Lubos Buzna (lbuzna@ethz.ch) or Amin Mazloumian (amin@gess.ethz.ch) to be included in the e-mail distribution list of this workshop.

I look forward to meeting you!
Dirk Helbing, on behalf of the organizing committee.

CURRENT MARKET: DISORDERED STATE

(click on image to expand)

During the past 12 months the Dow Industrials have had an even lower return and higher risk than the average for prior extremely disordered markets. The high volatility of extremely disordered markets includes large swings both up and down. While the stimulus and bailout programs should provide the credit necessary to eventually restore normal market structure, so far the quantitative evidence is consistent with a disordered market state.

Chaos theory and the current financial crisis

Years ago, in a letter to the editor of Physics Today (February, 1979) we noted that the “market may be considered an open system in which an adequate flow of money will effect a transition from disorder (random walk) to order (cooperative or crowd behavior).” Open systems in the physical sciences require a flow of energy to maintain an ordered state far from thermal equilibrium. For example, a laser requires energy to be pumped continuously to maintain a coherent state. In the financial markets, price stability requires a flow of money or credit. In the Great Depression, credit became scarce as the bubble in stock prices unwound after the "Roaring Twenties." The current credit crisis involves the unwinding of the housing bubble and associated derivative securities.

We define a market “attractor” as a conditional return map, i.e. the average return on the day after a prior day return, R(T-1), that falls into one of five intervals:


small price changes [-0.5% < R(T-1) < +0.5%]
moderate price increases [+0.5% < R(T-1) < +3.5%]
moderate price declines [-0.5% > R(T-1) > -3.5%]
large price increase [+3.5% < R(T-1)]
large price declines [-3.5%] > R(T-1)]

Figure 1 summarizes the average conditional return map for the Dow Jones Industrial Average over the 80 year period from 1929 to 2009. A nonlinear third order polynomial fit is shown and illustrates that the market has been trend persistent on average over this period. The slope of the return map is positive in the region of moderate returns.


Figure 1. Over the past eighty years the Dow Jones Industrial Average has been governed on average by a coherent, trend persistent dynamic.

The conditional return map in Figure 1 illustrates a bistable attractor for the market. Moderate positive returns are followed on average by further positive returns. Similarly, moderate negative returns are followed on average by further negative returns. These drifts are toward dynamic equilibrium points (where the return map crosses zero) far from the market’s long term average daily return.

Next, we identify state transitions from a mean regressive market attractor to a bistable state attractor. First we define a bifurcation parameter as the sum over 200 days of conditional returns following moderate price increases (as defined above), minus the sum over 200 days of conditional returns after moderate price declines. In a mean regressive market, where the return map has a negative slope, this metric is negative whereas in a trend persistent market it is positive. The market attractor bifurcates as this measure crosses zero.

The bifurcation parameter is plotted in Figure 2. The most significant mean regressive markets occurred in the Great Depression era of the 1930s, though there were some wild swings in this indicator. From the 1940s to about 1980, the market was primarily in a trend persistent state and fluctuations of the bifurcation parameter were primarily around a positive mean. The further the bifurcation parameter deviates from zero, the better the opportunities for short term trading: in the Great Depression era a mean reversion strategy would have offered the best chance for success; from 1940 to 1980, a trend following strategy had the odds in its favor. However, more recently with the advent of computerized trading and negotiated commissions, the market has become more efficient, with less opportunity for trading.


Figure 2. The bifurcation parameter is negative in mean reverting market states and positive in trend persistent coherent markets, reflecting the slope of the conditional return map for moderate returns.


Figure 3 illustrates the market return map or attractor for market periods between 1929 and 2009 when the bifurcation parameter is negative. In this situation, moderate positive returns are followed on average by negative returns on the following day; moderate negative returns are followed by positive returns on average.


Figure 3. The market is mean regressive when the slope of the conditional return map and the bifurcation parameter are negative.

Recently the bifurcation parameter has dropped deeply into negative territory. This is an unusual development since this indicator hasn’t fallen this far since the Great Depression era. A short term trading strategy designed to profit from the market’s regression to the mean after moderate returns is appropriate in this market state. A strategy of avoiding equity positions entirely when the bifurcation parameter drops below -10% is illustrated in Figure 4. This straategy would have outperformed a buy and hold both in the Crash of 1929 and also successfully avoided much of the recent market meltdown. However, there is no assurance as to how it will work in the future particularly as it is based on a lagging indicator of market dynamics.


Figure 4. Avoiding mean reverting markets (negative bifurcation parameter) has shown profitable back testing results, but may not work in future markets.

kaoseteooria ja majanduskriis

Leo Võhandu, TTÜ emeriitprofessor



For complete article, click here

Kaos tähendab igapäevakeeles täielikku segadust ja korralagedust. Füüsikas tähendab see mingi süsteemi osiste vastastikust mittelineaarset mõjutamist koos kõigi või peaaegu kõigi süsteemsete liikumiste ebastabiilsusega. Keerulisevõitu väljend on, aga asja olemuse seletab ilusasti ära.

Et füüsikud ja mehaanikud kaoses päris hästi orienteeruvad, siis heietab nii mõnigi lootust, et ehk aitab kaoseteooria meil kriisiolukorrast pääseda. Kiiret lahendust see teooria muidugi pakkuda ei saa, aga üht-teist kasulikku majanduse ja valuutaturgude jaoks võib sealt leida küll.

Kõigepealt märgime, et eesti keeles on ilmunud kahe akadeemiku sulest kaks head ja loetavat raamatut kaoseteooria radadelt. Esimene neist pärineb Tartu Ülikooli mehaanika emeriitprofessori Ülo Lepiku sulest – «Kaos ja kord» (1997). Teise ja hoopis kopsakama raamatu kirjutasid akadeemikud Ülo Lepik ja Jüri Engelbrecht paar aastat hiljem. Selle pealkiri «Kaoseraamat» on küll lühike, aga sisu on see-eest õige huvitav.

...

Kummalisel kombel on just kaks Eestiga tugevalt seotud meest tõestanud, et kaoseteooriast on rikkaks saamise mõttes õige palju kasu.

Veidi vanem neist kahest kannab nime Tõnis Vaga. Usutavasti on ta praegu maailmas kõige tsiteeritum eestlasest majandusteadlane. See on mees, kes 1994. aastal avaldas põhjapaneva ingliskeelse raamatu: Tonis Vaga «Profiting from Chaos» («Kaosest tulu teenimine»). Mul õnnestus see raamat poolkogemata 1995. aastal ühest Tallinna raamatupoest leida ja osta. Alguses arvasin, et on tegu mõne lõunaameeriklasega, kuid järsku taipasin, et selle nime taga võib olla hoopis eestlane Tõnis. Asi sai kohe klaariks, kui vaatasin raamatu pühenduste lehekülge. Üks pühendustest oli tütrele nimega Maie. Nii et oligi eestlane. Pärastine internetikontroll tõestas kah, et tegu on praegu 60-aastase üpris tragi USA eesti kogukonna liikmega.

Vaga on hariduselt füüsik, kuid 1979. aastal avaldas ta ülimalt olulise artikli aktsiaturu hindade kõikumisest ja hiljem ka nn koherentsete turgude teooria, mis mõlemad äratasid majandusteadlaste hulgas suurt tähelepanu. Nii ta asuski oma ideid majanduses realiseerima suurfirma Booz Allen Hamilton vanempartnerina. Muide, Vaga raamatut ei leia te ühestki Eesti raamatukogust, küll aga on see vabalt kõigile kättesaadav Google’i elektronraamatute hulgas.

Teine Eestist pärit mees, kelle kirjutatud raamatud valuutaturgudel kauplemisest USAs õige menukad on, on Alexander Elder. Vagast aasta nooremana sündis ta küll Leningradis, kuid elas Eestis ja õppis Tartus meditsiini. Ta asus tööle kalalaeva arstina. Aafrika ranna lähedal kala püüdes hüppas ta laevalt ära läände ning sai USAs poliitilise varjupaiga. Elder töötas psühhiaatrina New Yorgis ja õpetas muide ka Columbia Ülikoolis.

Psühhiaatrina pakkus valuutaturg talle omamoodi väljakutset ning nüüdseks on ta kirjutanud paraja paki väga menukaid raamatuid valuutaturgudel kauplemisest. Neid raamatuid on tõlgitud 12 keelde. Tartu Ülikooli raamatukogus on Elderi raamatutest olemas viis, Tallinna raamatukogudes mitte ühtegi...

Nonlinear and Chaotic Dynamics and its Application to Historical Financial Markets

Hartmut Kiehling*

For complete article click here.

Abstract: For roughly 15 years, economic research has been involved with chaotic systems. During these years chaos theory took a firm place in science, although the enthusiasm of the first decade was followed by a more subdued kind of consideration. This might be the time to sum up some of the results and to develop some ideas concerning possible applications of chaos theory to economic history (and its theory). Since a good portion of the chaos research that has been done until now deals with financial markets, we will consider that section of economics.

* Address all communications to Hartmut Kiehling, Heerstraße 9, D-81247 München,
Tel. +49-(0)89-8116379, Fax. +49-(0)89-8110189, e-mail: 101520.2007@compu-serve.com, 0898110189@t-online.de.

T. Vaga published his Coherent Market Hypothesis as a nonlinear statistical model. He distinguishes four market phases: random walk, transition, chaotic markets, and coherent markets. Each one is characterized by different kinds of attitudes and the mutual influence of investors. The model follows the psychological theory of social imitation, but is formulated mathematically. 15

Scientific Frontiers and Technical Analysis

Kevin P. Hanley, CMT

Abstract

Are there scientific foundations to Technical Analysis (TA) or is it a pseudo-science? Academia, embracing the Random Walk Theory, the Efficient Market Hypothesis (EMH) and Modern Portfolio Theory (MPT) has argued the latter for some 20 years or more. In fact, according to current orthodoxy, both TA and Fundamental Analysis are fruitless distractions and cannot add value. The advent of Behavioral Science has illuminated some of the flaws in the standard model. Andrew W. Lo’s Adaptive Markets Hypothesis reconciles efficient markets with human behavior by taking an evolutionary perspective. According to Lo, markets are driven by competition, adaptation, and natural selection. What is missing is a more accurate and comprehensive model of the market itself. Chaos and Complex system theories provide a more comprehensive understanding of market behavior. The markets can be seen as chaotic, complex, self-organizing, evolving and adaptive, driven by human behavior and psychology. Patterns in the market are emergent properties. Identifying these patterns has predictive value, but certainties must be left behind; only probabilities remain. TA, shown to be the inductive science of financial markets, is an essential tool for identifying these emergent properties and analyzing their probabilities. Lastly, so that the science of TA may advance, the field must distinguish between scientific, empirically based, market analysis theory and the categories of interpretation and practical trading strategies.