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2013 | OriginalPaper | Chapter

2. The “Noisy Chaos” Hypothesis

Author : Yasmine Hayek Kobeissi

Published in: Multifractal Financial Markets

Publisher: Springer New York

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Abstract

The concept of “noisy chaos” is introduced in this chapter, based on the processes of bifurcation, entropy, and convergence which occur at the heart of the instability in the financial markets and take into account the sensitivities of the financial systems. The key here is to identify and measure indicators that allow us to construct a model that accounts for extreme consensus factors (undisseminated information, correlated investment horizons, and high leverage) in estimating market reversals. Instability is a relatively subjective notion. If we think in calendar time, the system is unstable as the daily fluctuations seem erratic when compared to periods of months and years. But if we think in intrinsic time, it is as if we are looking at the week as a year, the day as a month, and the minutes as days… in doing so, and as markets are “self-affine” then the L-stable process can be found at the day level and the erratic fluctuations will be at the seconds level.

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previous chapter Turbulence in the Financial Markets

next chapter The Mind Process

Mandelbrot defines fractals as strange attractors of all deterministic chaotic systems. These objects possess the particularity of having an infinite perimeter while being contained in a finite space. Mandelbrot does not assert that markets are chaotic but that the outcome of any process is sensitive to its starting point (Mandelbrot 2008).

The Australian biologist, Robert May, was one of the first to discover bifurcations in 1976.

This concept is discussed in details in Chap. 4.

Time is characteristic in the sense that it depends on the system in question and varies according to the stock, sector, and microstructure of the market. If the characteristic time of the solar system is 100 million years, then the forecasting time would be 1 month.

Ideas gathered from Pr. D Nawrocki research papers to fine-tune and support the concept of Noisy chaos proposed in this book (Nawrocki 1984).

BE can be thought of the verb "be" referring to the existence/survival of the system.

The function can have the following form: X _(t) = X _(t − 1) + ε, with ε a random Gaussian variable with null average.

Sub-microsecond (or nanosecond) delivery for level 1 markets and end-to-end through put of only 2 microseconds for complex markets. NovaSparks.

In trade layering, orders are entered onto an exchange to artificially improve the price of a stock. Once this is achieved, the orders are then cancelled.

Re. Chap. 1.

This is the spread between the competence of the investors and the complexity of the information. (Nawrocki 1995) (Heiner 1983) (Kaen and Roseman 1986).

It is important to note, however, that the success of the contrarian approach depends on timing, which can only be determined through guesswork. The adoption of Bayesian principles might help as well, where the probability of the occurrence of an event is related to the occurrence or nonoccurrence of an associated event. In this case, it would be wiser to base one’s decisions on the analysis of the roughness and the level of risk in the market.

This large number of small fluctuations is different from those at the base of the Markovian process, of which the effects, while they are of short duration, have been totally integrated into the system.

Under-reaction leads to over-reaction at time T owing to the information ignored due to the prospect and disposition effect. The tendency of some investors to hold on to their losing stocks creates a spread between a stock's fundamental value and its market price, as well as price under-reaction to information.

Boltzmann's constant defines the relation between absolute temperature and the kinetic energy contained in each molecule of an ideal gas. It is named after the Austrian physicist Ludwig Boltzmann (1844–1906), and is equal to the ratio of the gas constant to the Avogadro constant: K = R/NA = 1.3807 × 10^-23 J.K^-1 (joule per Kelvin).

On a macroscopic scale, entropy is a function of thermodynamic variables (such as temperature, pressure, or composition). It is a measure of the energy that is not available for work during a thermodynamic process. A closed system evolves toward a state of maximum entropy.

In statistical mechanics, entropy is a measure of the randomness of the microscopic constituents of a thermodynamic system.

In cosmology, entropy is a hypothetical tendency for the universe to attain a state of maximum homogeneity in which all matter is at a uniform temperature, or a state known as “heat death”.

In data transmission and information theory, entropy is a measure of the loss of information in a transmitted signal or message.

According to M. Barranger " Emerging behavior results from global interaction between the scale's constituents, the combination of structure and emergence leads to self-organization" (Barranger 2000).

To determine the trajectory of a deterministic system, it is enough to know its initial position. For two different initial positions, there are two different trajectories. A system is chaotic if it amplifies, even a little, the initial difference, and attains freedom, however, limited, by its attractor. It is in this amplification of short durations that randomness is found.

Management techniques which are based on the analysis of fixed ratios, like the PER (Price earnings ratio), are often found to be too premature.

Here, it is important to look out for the misrepresented current volume flows due to high-frequency trading (HFT) strategies such as tape trading (filter trading and momentum trading) and statistical trading (statistical arbitrage and technical trading). Volumes emanating from these strategies have to be deducted.

For an in-depth analysis on volume, read Buff Dormeier Investing with Volume Analysis (Dormeier 2011).

Ideas backed and found in (Bookstaber 2011), (Nawrocki and Vaga 2012), (Nawrocki 1984).

As per Dr. Brock book (Brock 2012):

“it turns out that what matters to market prices and volatility is not merely that people’s bets are wrong, but additionally how correlated their mistakes are. It is when most investors are wrong in the same direction that the greatest portfolio adjustments occur, and that prices change the most; for most everyone will either sell or buy, and the price swings accordingly… A classical example of a “correlated mistake” where bets on US house prices as late as 2006. Almost no one assigned high probability to the inconceivable 35 % drop in house prices that transpired. The market response was fast and furious”.

Title: The “Noisy Chaos” Hypothesis
Author: Yasmine Hayek Kobeissi
Publisher: Springer New York
Book: Multifractal Financial Markets
Print ISBN: 978-1-4614-4489-3

Electronic ISBN: 978-1-4614-4490-9

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-1-4614-4490-9_2