The last couple of months in finance industry can be summarized in two words — chaos and uncertainty. The aptness of this laconic description is all too evident. The sub-prime crisis where everybody lost, the dizzying commodity price movements, the pink slip syndrome, the spectacular bank busts and the gargantuan bail-outs all vouch for it.
The financial meltdown is such a rich topic with reasons and ramifications so overarching that all self-respecting columnists will be remiss to let it slide. Μετά από όλα, a columnist who keeps his opinions to himself is a columnist only in his imagination. I too will share my views on causes and effects of this turmoil that is sure to affect our lives more directly than anybody else’s, but perhaps in a future column.
The chaos and uncertainty I want to talk about are of different kind — the physics kind. The terms chaos and uncertainty have a different and specific meanings in physics. How those meanings apply to the world of finance is what this column is about.
Symmetries and Patterns
Physicists are a strange bunch. They seek and find symmetries and patterns where none exists. I remember once when our brilliant professor, Lee Smolin, described to us how the Earth could be considered a living organism. Using insightful arguments and precisely modulated articulation, Lee made a compelling case that the Earth, όντως, satisfied all the conditions of being an organism. The point in Lee’s view was not so much whether or the Earth was literally alive, but that thinking of it as an organism was a viable intellectual pattern. Once we represent the Earth in that model, we can use the patterns pertaining to organism to draw further predictions or conclusions.
Expanding on this pattern, I recently published a column presenting the global warming as a bout of fever caused by a virus (us humans) on this host organism. Don’t we plunder the raw material of our planet with the same abandon with which a virus usurps the genetic material of its host? In addition to fever, typical viral symptoms include sores and blisters as well. Looking at the cities and other eye sores that have replaced pristine forests and other natural landscapes, it is not hard to imagine that we are indeed inflicting fetid atrocities to our host Earth. Can’t we think of our city sewers and the polluted air as the stinking, oozing ulcers on its body?
While these analogies may sound farfetched, we have imported equally distant ideas from physics to mathematical finance. Why would stock prices behave anything like a random walk, unless we want to take Bush’s words (ότι “Wall Street got drunk”) literally? Αλλά σοβαρά, Brownian motion has been a wildly successful model that we borrowed from physics. Ξανά, once we accept that the pattern is similar between molecules getting bumped around and the equity price movements, the formidable mathematical machinery and physical intuitions available in one phenomenon can be brought to bear on the other.
Looking at the chaotic financial landscape now, I wonder if physics has other insights to offer so that we can duck and dodge as needed in the future. Of the many principles from physics, chaos seems such a natural concept to apply to the current situation. Are there lessons to be learned from chaos and nonlinear dynamics that we can make use of? May be it is Heisenberg’s uncertainty principle that holds new insights.
Perhaps I chose these concepts as a linguistic or emotional response to the baffling problems confronting us now, but let’s look at them any way. It is not like the powers that be have anything better to offer, είναι?
In physics, chaos is generally described as our inability to predict the outcome of experiments with arbitrarily close initial conditions. Για παράδειγμα, try balancing your pencil on its tip. Σαφώς, you won’t be able to, and the pencil will land on your desktop. Τώρα, note this line along which it falls, and repeat the experiment. Regardless of how closely you match the initial conditions (of how you hold and balance the pencil), the outcome (the line along which it falls) is pretty much random. Although this randomness may look natural to us — μετά από όλα, we have been trying to balance pencils on their tips ever since we were four, if my son’s endeavours are anything to go by — it is indeed strange that we cannot bring the initial conditions close enough to be confident of the outcome.
Even stranger is the fact that similar randomness shows up in systems that are not quite as physical as pencils or experiments. Take, για παράδειγμα, the socio-economic phenomenon of globalization, which I can describe as follows, admittedly with an incredible amount of over-simplification. Long time ago, we used to barter agricultural and dairy products with our neighbours — λένε, a few eggs for a litre (or was it pint?) of milk. Our self-interest ensured a certain level of honesty. We didn’t want to get beaten up for adding white paint to milk, για παράδειγμα. These days, thanks to globalization, people don’t see their customers. A company buys milk from a farmer, adds god knows what, makes powder and other assorted chemicals in automated factories and ships them to New Zealand and Peru. The absence of a human face in the supply chain and in the flow of money results in increasingly unscrupulous behaviour.
Increasing chaos can be seen in the form of violently fluctuating concentrations of wealth and fortunes, increasing amplitudes and frequency of boom and bust cycles, exponential explosion in technological innovation and adaptation cycles, and the accelerated pace of paradigm shifts across all aspects of our lives.
It is one thing to say that things are getting chaotic, quite another matter to exploit that insight and do anything useful with it. I won’t pretend that I can predict the future even if (rather, especially if) I could. Ωστόσο,, let me show you a possible approach using chaos.
One of the classic examples of chaos is the transition from a regular, laminar flow of a fluid to a chaotic, turbulent flow. Για παράδειγμα, when you open a faucet slowly, if you do it carefully, you can have a pretty nice continuous column of water, thicker near the top and stretched thinner near the bottom. The stretching force is gravity, and the cohesive forces are surface tension and inter-molecular forces. As you open the faucet still further, ripples begin to appear on the surface of the column which, at higher rates of flow, rip apart the column into complete chaos.
In a laminar flow, macroscopic forces tend to smooth out microscopic irregularities. Like gravity and surface tension in our faucet example, we have analogues of macroscopic forces in finance. The stretching force is probably greed, and the cohesive ones are efficient markets.
There is a rich mathematical framework available to describe chaos. Using this framework, I suspect one can predict the incidence and intensity of financial turmoils, though not their nature and causes. Ωστόσο,, I am not sure such a prediction is useful. Imagine if I wrote two years ago that in 2008, there would be a financial crisis resulting in about one trillion dollar of losses. Even if people believed me, would it have helped?
Usefulness is one thing, but physicists and mathematicians derive pleasure also from useless titbits of knowledge. What is interesting about the faucet-flow example is this: if you follow the progress two water molecules starting off their careers pretty close to each other, in the laminar case, you will find that they end up pretty much next to each other. But once the flow turns turbulent, there is not telling where the molecules will end up. Παρομοίως, in finance, suppose two banks start off roughly from the same position — say Bear Stearns and Lehman. Under normal, laminar conditions, their stock prices would track similar patterns. But during a financial turbulence, they end up in totally different recycle bins of history, as we have seen.
If whole financial institutions are tossed around into uncertain paths during chaotic times, imagine where two roughly similar employees might end up. Με άλλα λόγια, don’t feel bad if you get a pink slip. There are forces well beyond your control at play here.
Uncertainty Principle in Quantitative Finance
The Heisenberg uncertainty principle is perhaps the second most popular theme from physics that has captured the public imagination. (The first one, φυσικά, is Einstein’s E = mc2.) Λέει κάτι φαινομενικά απλή — you can measure two complementary properties of a system only to a certain precision. Για παράδειγμα, αν προσπαθώ να καταλάβω όταν ένα ηλεκτρόνιο είναι (μετρούν τη θέση του, that is) περισσότερο και με μεγαλύτερη ακρίβεια, η ταχύτητα του γίνεται σταδιακά όλο και πιο αβέβαιο (ή, η μέτρηση ορμής γίνεται ασαφής).
Quantitative finance has a natural counterpart to the uncertainty principle — risks and rewards. When you try to minimize the risks, the rewards themselves go down. If you hedge out all risks, you get only risk-free returns. Since risk is the same as the uncertainty in rewards, the risk-reward relation is not quite the same as the uncertainty principle (που, as described in the box, deals with complementary variables), but it is close enough to draw some parallels.
To link the quantum uncertainty principle to quantitative finance, let’s look at its interpretation as observation altering results. Does modelling affect how much money we can make out of a product? This is a trick question. The answer might look obvious at first glance. Φυσικά, if we can understand and model a product perfectly, we can price it right and expect to reap healthy rewards. Έτσι, βέβαιος, modelling affects the risk-reward equation.
Αλλά, a model is only as good as its assumptions. And the most basic assumption in any model is that the market is efficient and liquid. The validity of this assumption (ή η έλλειψη αυτής) is precisely what precipitated the current financial crisis. If our modelling effort actually changes the underlying assumptions (usually in terms of liquidity or market efficiency), we have to pay close attention to the quant equivalent of the uncertainty principle.
Look at it this way — a pyramid scheme is a perfectly valid money making model, but based on one unfortunate assumption on the infinite number of idiots at the bottom of the pyramid. (Ερχόμενοι να σκεφτούμε ότι, the underlying assumption in the sub-prime crisis, though more sophisticated, may not have been that different.) Similar pyramid assumptions can be seen in social security schemes, επίσης. We know that pyramid assumptions are incorrect. But at what point do they become incorrect enough for us to change the model?
There is an even more insidious assumption in using models — that we are the only ones who use them. In order to make a killing in a market, we always have to know a bit more than the rest of them. Once everybody starts using the same model, I think the returns will plummet to risk-free levels. Why else do you think we keep inventing more and more complex exotics?
The current financial crisis has been blamed on many things. One favourite theory has been that it was brought about by the greed in Wall Street — the so-called privatization of profits and socialization of losses. Incentive schemes skewed in such a way as to encourage risk taking and limit risk management must take at least part of the blame. A more tempered view regards the turmoil as a result of a risk management failure or a regulatory failure.
This column presents my personal view that the turmoil is the inevitable consequence of the interplay between opposing forces in financial markets — risk and rewards, speculation and regulation, risk taking and risk management and so on. To the extent that the risk appetite of a financial institute is implemented through a conflict between such opposing forces, these crises cannot be avoided. Χειρότερος, the intensity and frequency of similar meltdowns are going to increase as the volume of transactions increases. This is the inescapable conclusion from non-linear dynamics. Μετά από όλα, such turbulence has always existed in the real economy in the form cyclical booms and busts. In free market economies, selfishness and the inherent conflicts between selfish interests provide the stretching and cohesive forces, setting the stage for chaotic turbulence.
Physics has always been a source of talent and ideas for quantitative finance, much like mathematics provides a rich toolkit to physics. In his book, Τα όνειρα της Τελικής Θεωρία, Nobel Prize winning physicist Steven Weinberg marvels at the uncanny ability of mathematics to anticipate physics needs. Παρομοίως, quants may marvel at the ability of physics to come up with phenomena and principles that can be directly applied to our field. Για μένα, it looks like the repertoire of physics holds a few more gems that we can employ and exploit.
Box: Heisenberg’s Uncertainty Principle
Where does this famous principle come from? It is considered a question beyond the realms of physics. Before we can ask the question, πρέπει να εξετάσουμε τι πραγματικά λέει η αρχή. Εδώ είναι μερικές πιθανές ερμηνείες:
Η πρώτη άποψη είναι σήμερα δημοφιλής και έχει σχέση με τη λεγόμενη ερμηνεία της Κοπεγχάγης της κβαντομηχανικής. Ας το αγνοήσετε για να μην είναι πολύ ανοιχτή σε συζητήσεις.
Η δεύτερη ερμηνεία είναι γενικά κατανοητή ως μια πειραματική δυσκολία. Αλλά αν η έννοια της πειραματικής εγκατάστασης επεκτείνεται για να συμπεριλάβει το αναπόφευκτο άνθρωπο παρατηρητή, φτάνουμε στην τρίτη άποψη της αντίληψης περιορισμού. Κατά την άποψη αυτή, στην πραγματικότητα είναι δυνατό να “αντλώ” η αρχή της αβεβαιότητας, based on how human perception works.
Ας υποθέσουμε ότι χρησιμοποιούμε μια δέσμη φωτός μήκους κύματος να τηρούν το σωματίδιο. Η ακρίβεια στη θέση που μπορούμε να ελπίζουμε ότι θα επιτευχθεί είναι της τάξης των . Με άλλα λόγια, . Στην κβαντομηχανική, η ορμή του κάθε φωτόνιο στη δέσμη φωτός είναι αντιστρόφως ανάλογη με το μήκος κύματος. Τουλάχιστον ένα φωτόνιο ανακλάται από το σωματίδιο, έτσι ώστε να μπορούμε να το δούμε. Έτσι, από την κλασική νόμο για τη διατήρηση, the momentum of the particle has to change by at least this amount() από ό, τι ήταν πριν από τη μέτρηση. Έτσι, μέσω της αντιληπτικής επιχειρήματα, παίρνουμε κάτι παρόμοιο με την αρχή της αβεβαιότητας του Heisenberg
Μπορούμε να κάνουμε αυτό το επιχείρημα αυστηρότερη, και να πάρετε μια εκτίμηση της αξίας της σταθεράς. Η ανάλυση ενός μικροσκοπίου δίνεται από τον εμπειρικό τύπο , όπου είναι το αριθμητικό άνοιγμα, το οποίο έχει μέγιστη τιμή του ενός. Έτσι, η καλύτερη χωρική ανάλυση είναι . Κάθε φωτόνιο στη δέσμη φωτός έχει μια δυναμική , που είναι η αβεβαιότητα στην ορμή των σωματιδίων. Έτσι παίρνουμε , περίπου μία τάξη μεγέθους μεγαλύτερη από την κβαντική μηχανική όριο.
Μέσω πιο αυστηρή στατιστική επιχειρήματα, που σχετίζονται με τη χωρική ανάλυση και η αναμενόμενη ορμή που μεταφέρεται, μπορεί να είναι δυνατόν να εξαχθεί η αρχή της αβεβαιότητας του Heisenberg μέσω αυτής της συλλογιστικής.
Αν λάβουμε υπόψη τη φιλοσοφική άποψη ότι η πραγματικότητα μας είναι μια γνωστική μοντέλο των αντιληπτικών ερεθισμάτων μας (η οποία είναι η μόνη άποψη που έχει νόημα για μένα), τέταρτο μου ερμηνεία της αρχής της αβεβαιότητας είναι μια γνωστική περιορισμός επίσης κατέχει ένα κομμάτι του νερού.
|Σχετικά με το Συγγραφέας |
Ο συγγραφέας είναι ένας επιστήμονας από το Ευρωπαϊκό Οργανισμό Πυρηνικών Ερευνών (CERN), who currently works as a senior quantitative professional at Standard Chartered in Singapore. More information about the author can be found at his blog: http//www.Thulasidas.com. Οι απόψεις που εκφράζονται σε αυτή τη στήλη είναι μόνο προσωπικές απόψεις του, οι οποίες δεν έχουν επηρεαστεί από παράγοντες της επιχείρησης ή του πελάτη σχέσεις της επιχείρησης.