The Statistical Physics of Stock Markets. Thought of the Day 143.0

This video is an Order Routing Animation

The externalist view argues that we can make sense of, and profit from stock markets’ behavior, or at least few crucial properties of it, by crunching numbers and looking for patterns and regularities in certain sets of data. The notion of data, hence, is a key element in such an understanding and the quantitative side of the problem is prominent even if it does not mean that a qualitative analysis is ignored. The point here that the outside view maintains that it provides a better understanding than the internalist view. To this end, it endorses a functional perspective on finance and stock markets in particular.

The basic idea of the externalist view is that there are general properties and behavior of stock markets that can be detected and studied through mathematical lens, and they do not depend so much on contextual or domain-specific factors. The point at stake here is that the financial systems can be studied and approached at different scales, and it is virtually impossible to produce all the equations describing at a micro level all the objects of the system and their relations. So, in response, this view focuses on those properties that allow us to get an understanding of the behavior of the systems at a global level without having to produce a detailed conceptual and mathematical account of the inner ‘machinery’ of the system. Hence the two roads: The first one is to embrace an emergentist view on stock market, that is a specific metaphysical, ontological, and methodological thesis, while the second one is to embrace a heuristic view, that is the idea that the choice to focus on those properties that are tractable by the mathematical models is a pure problem-solving option.

A typical view of the externalist approach is the one provided, for instance, by statistical physics. In describing collective behavior, this discipline neglects all the conceptual and mathematical intricacies deriving from a detailed account of the inner, individual, and at micro level functioning of a system. Concepts such as stochastic dynamics, self-similarity, correlations (both short- and long-range), and scaling are tools to get this aim. Econophysics is a stock example in this sense: it employs methods taken from mathematics and mathematical physics in order to detect and forecast the driving forces of stock markets and their critical events, such as bubbles, crashes and their tipping points. Under this respect, markets are not ‘dark boxes’: you can see their characteristics from the outside, or better you can see specific dynamics that shape the trends of stock markets deeply and for a long time. Moreover, these dynamics are complex in the technical sense. This means that this class of behavior is such to encompass timescales, ontology, types of agents, ecologies, regulations, laws, etc. and can be detected, even if not strictly predictable. We can focus on the stock markets as a whole, on few of their critical events, looking at the data of prices (or other indexes) and ignoring all the other details and factors since they will be absorbed in these global dynamics. So this view provides a look at stock markets such that not only they do not appear as a unintelligible casino where wild gamblers face each other, but that shows the reasons and the properties of a systems that serve mostly as a means of fluid transactions that enable and ease the functioning of free markets.

Moreover the study of complex systems theory and that of stock markets seem to offer mutual benefits. On one side, complex systems theory seems to offer a key to understand and break through some of the most salient stock markets’ properties. On the other side, stock markets seem to provide a ‘stress test’ of the complexity theory. Didier Sornette expresses the analogies between stock markets and phase transitions, statistical mechanics, nonlinear dynamics, and disordered systems mold the view from outside:

Take our personal life. We are not really interested in knowing in advance at what time we will go to a given store or drive to a highway. We are much more interested in forecasting the major bifurcations ahead of us, involving the few important things, like health, love, and work, that count for our happiness. Similarly, predicting the detailed evolution of complex systems has no real value, and the fact that we are taught that it is out of reach from a fundamental point of view does not exclude the more interesting possibility of predicting phases of evolutions of complex systems that really count, like the extreme events. It turns out that most complex systems in natural and social sciences do exhibit rare and sudden transitions that occur over time intervals that are short compared to the characteristic time scales of their posterior evolution. Such extreme events express more than anything else the underlying “forces” usually hidden by almost perfect balance and thus provide the potential for a better scientific understanding of complex systems.

Phase transitions, critical points, extreme events seem to be so pervasive in stock markets that they are the crucial concepts to explain and, in case, foresee. And complexity theory provides us a fruitful reading key to understand their dynamics, namely their generation, growth and occurrence. Such a reading key proposes a clear-cut interpretation of them, which can be explained again by means of an analogy with physics, precisely with the unstable position of an object. Complexity theory suggests that critical or extreme events occurring at large scale are the outcome of interactions occurring at smaller scales. In the case of stock markets, this means that, unlike many approaches that attempt to account for crashes by searching for ‘mechanisms’ that work at very short time scales, complexity theory indicates that crashes have causes that date back months or year before it. This reading suggests that it is the increasing, inner interaction between the agents inside the markets that builds up the unstable dynamics (typically the financial bubbles) that eventually ends up with a critical event, the crash. But here the specific, final step that triggers the critical event: the collapse of the prices is not the key for its understanding: a crash occurs because the markets are in an unstable phase and any small interference or event may trigger it. The bottom line: the trigger can be virtually any event external to the markets. The real cause of the crash is its overall unstable position, the proximate ‘cause’ is secondary and accidental. Or, in other words, a crash could be fundamentally endogenous in nature, whilst an exogenous, external, shock is simply the occasional triggering factors of it. The instability is built up by a cooperative behavior among traders, who imitate each other (in this sense is an endogenous process) and contribute to form and reinforce trends that converge up to a critical point.

The main advantage of this approach is that the system (the market) would anticipate the crash by releasing precursory fingerprints observable in the stock market prices: the market prices contain information on impending crashes and this implies that:

if the traders were to learn how to decipher and use this information, they would act on it and on the knowledge that others act on it; nevertheless, the crashes would still probably happen. Our results suggest a weaker form of the “weak efficient market hypothesis”, according to which the market prices contain, in addition to the information generally available to all, subtle information formed by the global market that most or all individual traders have not yet learned to decipher and use. Instead of the usual interpretation of the efficient market hypothesis in which traders extract and consciously incorporate (by their action) all information contained in the market prices, we propose that the market as a whole can exhibit “emergent” behavior not shared by any of its constituents.

In a nutshell, the critical events emerge in a self-organized and cooperative fashion as the macro result of the internal and micro interactions of the traders, their imitation and mirroring.

 

Suspicion on Consciousness as an Immanent Derivative

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The category of the subject (like that of the object) has no place in an immanent world. There can be no transcendent, subjective essence. What, then, is the ontological status of a body and its attendant instance of consciousness? In what would it exist? Sanford Kwinter (conjuncted here) here offers:

It would exist precisely in the ever-shifting pattern of mixtures or composites: both internal ones – the body as a site marked and traversed by forces that converge upon it in continuous variation; and external ones – the capacity of any individuated substance to combine and recombine with other bodies or elements (ensembles), both influencing their actions and undergoing influence by them. The ‘subject’ … is but a synthetic unit falling at the midpoint or interface of two more fundamental systems of articulation: the first composed of the fluctuating microscopic relations and mixtures of which the subject is made up, the second of the macro-blocs of relations or ensembles into which it enters. The image produced at the interface of these two systems – that which replaces, yet is too often mistaken for, subjective essence – may in turn have its own individuality characterized with a certain rigor. For each mixture at this level introduces into the bloc a certain number of defining capacities that determine both what the ‘subject’ is capable of bringing to pass outside of itself and what it is capable of receiving (undergoing) in terms of effects.

This description is sufficient to explain the immanent nature of the subjective bloc as something entirely embedded in and conditioned by its surroundings. What it does not offer – and what is not offered in any detail in the entirety of the work – is an in-depth account of what, exactly, these “defining capacities” are. To be sure, it would be unfair to demand a complete description of these capacities. Kwinter himself has elsewhere referred to the states of the nervous system as “magically complex”. Regardless of the specificity with which these capacities can presently be defined, we must nonetheless agree that it is at this interface, as he calls it, at this location where so many systems are densely overlaid, that consciousness is produced. We may be convinced that this consciousness, this apparent internal space of thought, is derived entirely from immanent conditions and can only be granted the ontological status of an effect, but this effect still manages to produce certain difficulties when attempting to define modes of behavior appropriate to an immanent world.

There is a palpable suspicion of the role of consciousness throughout Kwinter’s work, at least insofar as it is equated with some kind of internal, subjective space. (In one text he optimistically awaits the day when this space will “be left utterly in shreds.”) The basis of this suspicion is multiple and obvious. Among the capacities of consciousness is the ability to attribute to itself the (false) image of a stable and transcendent essence. The workings of consciousness are precisely what allow the subjective bloc to orient itself in a sequence of time, separating itself from an absolute experience of the moment. It is within consciousness that limiting and arbitrary moral categories seem to most stubbornly lodge themselves. (To be sure this is the location of all critical thought.) And, above all, consciousness may serve as the repository for conditioned behaviors which believe themselves to be free of external determination. Consciousness, in short, contains within itself an enormous number of limiting factors which would retard the production of novelty. Insofar as it appears to possess the capacity for self-determination, this capacity would seem most productively applied by turning on itself – that is, precisely by making the choice not to make conscious decisions and instead to permit oneself to be seized by extra-subjective forces.

Conjuncted: Speculatively Accelerated Capital – Trading Outside the Pit.

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High Frequency Traders (HFTs hereafter) may anticipate the trades of a mutual fund, for instance, if the mutual fund splits large orders into a series of smaller ones and the initial trades reveal information about the mutual funds’ future trading intentions. HFTs might also forecast order flow if traditional asset managers with similar trading demands do not all trade at the same time, allowing the possibility that the initiation of a trade by one mutual fund could forecast similar future trades by other mutual funds. If an HFT were able to forecast a traditional asset managers’ order flow by either these or some other means, then the HFT could potentially trade ahead of them and profit from the traditional asset manager’s subsequent price impact.

There are two main empirical implications of HFTs engaging in such a trading strategy. The first implication is that HFT trading should lead non-HFT trading – if an HFT buys a stock, non-HFTs should subsequently come into the market and buy those same stocks. Second, since the HFT’s objective would be to profit from non-HFTs’ subsequent price impact, it should be the case that the prices of the stocks they buy rise and those of the stocks they sell fall. These two patterns, together, are consistent with HFTs trading stocks in order to profit from non-HFTs’ future buying and selling pressure. 

While HFTs may in aggregate anticipate non-HFT order flow, it is also possible that among HFTs, some firms’ trades are strongly correlated with future non-HFT order flow, while other firms’ trades have little or no correlation with non-HFT order flow. This may be the case if certain HFTs focus more on strategies that anticipate order flow or if some HFTs are more skilled than other firms. If certain HFTs are better at forecasting order flow or if they focus more on such a strategy, then these HFTs’ trades should be consistently more strongly correlated with future non-HFT trades than are trades from other HFTs. Additionally, if these HFTs are more skilled, then one might expect these HFTs’ trades to be more strongly correlated with future returns. 

Another implication of the anticipatory trading hypothesis is that the correlation between HFT trades and future non-HFT trades should be stronger at times when non-HFTs are impatient. The reason is anticipating buying and selling pressure requires forecasting future trades based on patterns in past trades and orders. To make anticipating their order flow difficult, non-HFTs typically use execution algorithms to disguise their trading intentions. But there is a trade-off between disguising order flow and trading a large position quickly. When non-HFTs are impatient and focused on trading a position quickly, they may not hide their order flow as well, making it easier for HFTs to anticipate their trades. At such times, the correlation between HFT trades and future non-HFT trades should be stronger.