Duplex Models of Complex Systems

Summary

Duplex models can portray complex systems with the utmost of simplicity, clarity and efficacy. The drawcards range from the dearth of initial premises to the soundness of final conclusions. The mettle of the binomial approach shows up, for instance, in debunking the welter of myths and misconceptions that pervades the fields of finance and economics. According to the Efficient Market Hypothesis, the marketplace always reflects the totality of information available to the general public. Since every nub of know-what and know-how informs the latest prices, no single actor can improve on the valuation of assets ranging from stocks and bonds to commodities and realties.

One consequence is the lack of trusty cues for forecasting the market: if every clue has been fully utilized, then any move henceforth has to come as a complete surprise. Another fallout lies in the Random Walk Model that pictures the path of the market as a form of Brownian motion whereby the price level is wont to shift in any direction with equal likelihood.

Unfortunately, the Efficient credo abounds with flaws ranging from unreal assumptions and spurious concepts to inconsistent models and faulty conclusions. A counterpoint involves the wave motion of the stock market that belies the premise of utter randomness. As a recourse, a true science ought to build on hard data and staunch precepts, rigorous models and tenable results. To this end, the study at hand represents a small but fundamental step toward a coherent theory of the marketplace.

To underscore the gulf between the mythos and reality, the work plan takes a minimalist approach. For starters, the inquest draws only on a minute fraction of the trove of information freely available at the most popular portal among the investing public. Moreover, the quantitative analysis relies solely on the simplest technique in statistical testing. From a computational stance, the attendant program invokes a skimpy subset of the built-in functions within the core module of the R system: the leading choice of programming language and software platform for data science in disparate domains.

1.  Introduction

A duplex framework provides a lean and elegant way to model the dicey behavior of a complex system regardless of the domain. The crux of the methodology lies in the binomial test—the simplest tool in statistical analysis—for drawing conclusions with the greatest of ease, robustness and confidence. The mettle of the spartan approach shows up, for instance, in profiling the stock market: the epitome of chance and chaos in the world at large.

According to the reigning school of finance and economics, the marketplace is so agile as to process the entirety of information available to the general public at once and employ the facts with perfect wisdom. This glossy image is known as the Efficient Market Hypothesis (EMH). Since the latest prices incorporate the totality of know-what and know-how, no one can improve on the valuation of assets ranging from stocks and bonds to commodities and realties.

As a corollary, the EMH trumpets the absence of cues to predict the price level. If every factoid has already been absorbed, there is nothing left over for portending the market. Ergo, any move henceforth has to come as a complete surprise. Another consequent is the Random Walk Model that pictures the path of each asset as a form of Brownian motion whereby the price level moves up or down with equal likelihood.

The attempts to describe the movement of assets based on the statistical physics of gaseous particles have spawned a deluge of literature that has scant bearing on the reality of the markets. Along with the false foundation of perfect efficiency, the entire edifice of financial economics stands on shaky assumptions and faulty arguments. The slip-ups begin with implicit and primary axioms such as ageless assets, utter rationality, and instantaneous action. The failings also appear in the explicit and secondary concepts such as utility maximization, perfect competition, and diminishing marginal productivity—all of which are empirically invalid and logically unsound (Keen, 2003). Hence the need for a fresh start based on solid data coupled with faithful models of the marketplace.

In short, the regnant school of financial economics stands on a morass of fiction ranging from fanciful assumptions and feigned arguments to faithless models and forced conclusions. As a recourse, a wholesome approach ought to begin with a clean slate by building on hard data and realistic models. To this end, the current report represents a small but fundamental step toward a sound theory of the marketplace.

To underscore the cleavage between the theory and reality, the work plan takes a minimalist approach while using the stock market as a case study. For starters, the inquest employs only a minute fraction of the treasury of information freely available to all comers at the most popular portal amongst the investing public. Moreover, the quantitative analysis relies solely on the simplest technique in hypothesis testing. From a computational stance, the requisite program invokes a sparing subset of the inbuilt functions within the kernel module of the R system: the top choice of programming language and digital platform for data science in the context of scientific assays as well as pragmatic pursuits.

1.1.  Objectives

According to the central tenet of finance and economics, the marketplace is a model of perfection. In particular, the system is so efficient that it absorbs every whiff of information at once, thus leaving no further scent for forecasting the price level. As a corollary, every asset is deemed to move in a thoroughly random and unpredictable fashion.

Given this backdrop, the current study overturns the entrenched doctrine with the utmost of simplicity, clarity and efficacy. For this purpose, the stock market represents the essence of flighty behavior that eludes the mass of practitioners and observers ranging from investors and analysts to academics and policymakers.

A second goal is to demonstrate the power of an elementary tool in statistics for tackling an enigma that has long thwarted myriads of actors ranging from lone investors and fund managers to ivory-tower scholars