Singularly Complex. The Catch with Hybrid Finance

BY ABHIJNAN REJ

A Jurassic Park in the Canary Wharf?

On the 6^th of May, 2010, at around 2:45 pm, the Dow fell unusually  rapidly losing over 9% of its total value in a couple of minutes without any perceptible external information input. After a circuit-breaker in the Chicago Mercantile Exchange was switched on for a few seconds, the markets started climbing back up and by 3:00 pm most of the 600 points or so that were lost was regained as traders recalibrated their mental and computational models. There are many conflicting accounts around what might have caused this event—jazzily named the Flash Crash—but almost everybody agrees that high-frequency algorithmic traders had a large role to play. Since algorithms have a much faster reaction time to market movements than humans, at first sight of the unexpectedly hectic buying and selling amidst a large sell-order by Proctor & Gamble, a large number of algorithmic traders decided to exit the market in a classic display of herding behavior (“the herders”) while others continued selling vigorously. At the final reckoning, most of the temporary losses during the couple of hours since the Flash Crash have been attributed to them.

Over the last few years, a small group of experts have built a parallel description of financial markets that go much beyond the orthodox dogma taught in a typical MBA finance course. These researchers have uncovered a very rich set of analogies with ecological and other biological systems which have helped us understand the mechanism behind financial crashes—both Flash and the more prolonged purges—and given us a comprehensive notion of the global human/machine hybrid financial system which is, to use a very bold word, living. Building models and theories that cut across disciplinary boundaries, and through extensive computational modeling, these researchers, including early pioneers of chaos theory such as Robert May and Doyne Farmer, have presented us with a narrative about the future of finance that is, again to use a bold word, alarming. Recognizing that complex systems display unexpected and un-programmed features, these researchers (much like the fictional Dr. Ian Malcolm of Jurassic Park) have argued that introducing financial innovations of increasing complexity (much of which is machine- or high-frequency algorithmically driven) is, more than ever before, making the global financial network fragile and prone to fractures both big and small.

The Need for Speed

More than 70% of equity trades in the US are executed through algorithmic trading. For example, the mathematician-turned-financier James Simons’ Renaissance Technologies, a hedge fund mostly driven by automated trading, manages about 23 billion US dollars--their Nova Fund is completely electronic and potent enough to invite the apocryphal story that on a certain day their trades accounted for 14% of all trades in NASDAQ.

Basically for an algorithmic trader to make a profit, one needs three technical tools- imaginative trading strategies, extremely fast computer programs that can execute those strategies and finally for international funds, cutting-edge communication tools—all three taken together form a formidable weapon to hunt for market mispriced assets, i.e., identical assets selling for two different prices at the same time in two different markets. This is known as an arbitrage opportunity in the finance jargon. The idea is actually quite simple: suppose I know that a certain stock is selling for more in London than in New York at the same time. I’d immediately buy a certain amount of this stock in New York and simultaneously sell it in London pocketing the risk-free difference.

The catch to such a sweet deal is the following: you have to be the first to know of the arbitrage opportunity before all others. Once this information is available to all other traders, they will quickly move in with a similar strategy with the inevitable result that the two prices will converge to one. This is the sacred Efficient Market Hypothesis (EMH) around which much of contemporary finance is built around. It assumes all traders possess the same amount of information at any given point in time, something which is routinely invalidated in the real-world. In practice, the amount of risk-free money you will make through arbitrage is a function of how fast your information channels are (that is, how much more you know about the state of the markets) and how quickly your algorithms can trade. (Often arbitrage opportunities exist only for milliseconds, much smaller than the average human response times.) Increasingly, large funds are beginning to invest in newer technologies that will optimize arbitrage opportunities, including a specially designed chip that prepares and executes trades at 740 nanoseconds and a new transatlantic cable that reduces communication time between Canary Wharf and Wall Street by five milliseconds. These new techniques don’t come cheap, with some estimates of building the transatlantic cable alone running close to a billion dollars. However given the number of arbitrage opportunities, for large banks and funds the price is just right.

For regulators such as the US Securities and Exchange Commission (SEC), such technologies are frightening for many reasons. One, they are simply not equipped to monitor such high speed/high frequency/high-volume trades. Two, they are not sure if such technologies can be used for insider trading, and finally, a recent paper by Neil Johnson and others demonstrate that such ultrafast technologies are in fact making and driving financial black swans such as the Flash Crash and, even more scarily, making large investment banks susceptible to contagion exposure. Simply put, what Johnson and collaborators are arguing is that flash crashes are increasingly becoming more and more common and, in analogy to engineering, these Flash Crash-type micro-fractures are building up to a much larger and violent fractures in the global financial market.

Towards an Ecology of Hybrid Finance

The quest to understand the global human/machine hybrid financial market as an ecological system goes back to the early days of chaos and complexity theory. Indeed both financial markets and ecological systems share many common features, such as spontaneous emergence of unexpected patterns without any exogenous input,in-built fragilities and instabilities driven by increasing complexity. Over the recent years, Didier Sornette of Swiss Federal Institute of Technology Zurich (ETHZ) has become a vocal advocate of this point of view, arguing that crashes and extreme financial events can be best modeled through local interactions and positive feedback loops, and one of the biggest drivers of these crashes are herders and noise traders.

Very recently in January, along with Vladimir Filimonov, Sornette had put forward a very interesting model for flash crashes that draw as much from the study of evolution of human societies as to nuclear engineering. Building on an idea of George Soros about market prices being self-fulfilling prophecies, they have created a model in which a given price data stream can be linearly decomposed into two parts—a  part that depends on the “exogenous”, such as “game-changing” input information of geopolitical or economic nature, and an  “endogenous” part which arises from the self-excitation of the market due to such input information which  triggers a branched cascade of price movements. According to Filimonov and Sornette, it is this endogenous part of the price movement that is responsible for flash crashes. In fact, they go on to suggest a single parameter, n, called the “branching ratio”, in analogy to nuclear processes, whose value determines whether or not we are going into a flash crash regime simply by looking at the price stream over a 10 minutes interval.

The branching ratio measures the internal system dynamics directly. For example, n>0.9 indicates that more than 90% of the price movements can be attributed to the system’s intrinsic dynamics alone; this was precisely the case during the Flash Crash of 2010. Interestingly enough, through the analysis of historical data, Filimonov and Sornette show that the growth of n directly coincides with the rise of high-frequency algorithmic trading. Extrapolating their analysis in light of the news of the upcoming ultra-fast electronic trading devices and accessories such as the transatlantic cable as well as the analysis of Johnson and others presents us with a very worrying picture of finance of the future.

In the past few years, another related set of analysis on the “ecology” of the financial markets addressing similar problems have come from A.G. Haldane of the Bank of England in collaboration with the mathematical biologist and chaos theorist Robert May. In a model published in the science journal Nature last year, they show how, given a sudden external shock, the liquidity crunch cascades through the financial network which is viewed as a random graph (that is, a random collection of nodes representing banks and line segments between nodes that represent inter-banking transactions.) Building on earlier studies in ecology, they conclude that instability and fragility are a direct consequence of increasing complexity and connectivity of the financial network with a few banks (nodes) controlling a large fraction of the total capital in the market. Their view of a financial crash is one of an information cascade where, in the event of external shock, a big failing bank passes its liquidity crunch onto slightly smaller banks that, through all the way down, pass the crunch to the smallest banking/quasi-banking entity and ultimately to individuals--at each step “amplifying the liquidity shock”. A worrying part of the story is that there has been a steady decline in the amount of actual physical or monetary assets that banks have held over the years, severely degenerating their capacity to absorb an external shock or an endogenous perturbation; simply put, a bank might only hold as assets instruments that derive their value from instruments generated by other banks equally susceptible to any crisis! In this era of “post-modern finance”, such destructive closed loops should be the first ones regulators need to break into.

Haldane and May’s research contain several insights. First, they argue that adding each layer of complexity in terms of the introduction of highly-leveraged exotic financial instruments erodes systemic stability by a significant amount and after reaching a critical level of liquidity crunch, the whole network is likely to collapse in one go. Haldane and May (echoing the famous words of Warren Buffet about derivatives being weapons of mass financial destruction) also, understandably enough, hold credit derivatives such as the infamous Credit Default Swap (CDS) responsible for much of the fragility of the financial system; as they aptly note, “CDSs have outpaced Moore’s law of growth”. Second, given that values of derivatives are highly correlated, shocks can propagate smoothly across the entire financial sector making the system very unstable even with large fluctuations in the value of a single derivative. Third, they argue that banks too taken as wholes are highly susceptible to “herding”, which experts such as Didier Sornette have time and again identified as drivers of crashes.

A standard dogma in financial theory is that prices of derivatives of stocks, by definition, depend on the price of the underlying stock in some predictable way and not the other way around (this is the famous Black-Scholes-Merton model), something that has, in practice, turned out to be false. In reality, there are positive feedback loops by which stock prices are influenced by the prices of options that derive their value from these very stocks. (EMH holds that stock prices are random in nature and, if  large informational shocks from the outside are absent,  immune to tinkering by traders. Even though using derivatives to maneuver stock or other assets such as commodities prices is illegal in almost all Western countries, it is nevertheless, as many traders in their private conversations with the author have confided, practiced on a day-to-day basis. Part of the problem in analyzing such positive feedback loops is their mathematical intractability, and given that almost all profitable trading strategies are proprietary, it is unavailable for scrutiny of regulators and investors alike. All of these, taken together, have given us a financial system that is opaque not because of the number of entities involved but by the very fact that as a network it is far from being “linear”. (A more mathematical way of saying this would be that when viewed as a graph, the financial network is not a “tree” but instead has very many loops.)

Haldane and May go on to suggest several policy measures through an ecological lens. First they suggest that regulators stop looking at problems with individual funds and banks alone and start looking at systemic risks, a point also advocated by Sornette. Haldane and May compare this current attitude of regulators to the attitude of public health practitioners who may look at the contagion of infectious diseases as a matter of only isolating a couple of individuals without understanding the terrain in which these diseases may propagate. Haldane and May advocate much higher capital and liquidity requirements on banks that pose the greater threat to the system by the virtue of their higher connectivity and therefore larger “liability” to smaller entities that they are connected to. Second, they push for ``systemic diversity” by means of which shocks do not propagate so evenly in times of crisis. Finally, they call for partitioning the financial markets into modules with the idea in mind that in times of trouble, disturbances can be contained inside a given module and not be allowed to spread beyond that. It must be noted that modularity, especially in the hybrid world, brings with it its own set of problems. For example, a recent study published by Miguel Fortuna and others show non-trivial predator-prey and exclusionary relationships between different modular packages of the Debian Linux operating system. It is not clear whether a similar “life-like” phenomenon will not arise in a modular financial network increasingly driven by algorithms.

It is also important to note that there are dissidents who would ascribe to the picture described above, and yet have a very different view of how it informs regulations. For example, they may claim that in a complex system, too much interference actually increases volatility than decreases it, so the whole business of regulation without understanding the system as a whole might actually make things worse. (Nassim Nicholas Taleb and Mark Blythe also make this excellent point in the realm of geopolitics in their May 2011, Foreign Affairs article.)

Till then, our best bet still is to remember former Defense Secretary Donald Rumsfeld’s charming reformulation of Knightian uncertainty when he asked us to differentiate between the domains of “known unknowns” (where we know what can go wrong) and the “unknown unknowns” (where we do not even know where to look). If ours is to be the true hybrid era, it is the second domain that we ought to pay much more attention to, if not to predict then to simply hedge.

Abhijnan Rej is a Researcher at the Hybrid Reality Institute and on the faculty of the Institute of Mathematics and Applications, Bhubaneswar.