Reflexivity and Resonance — Beunza & Stark on Quantitative Models and Systemic Risk

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Reflexivity and Fallibility — Beunza & Stark on Models and Systemic Risk

Financial pandemonium

The reasons for financial pandemonium are nearly endless these days. Nassim Taleb and Benoit Mandelbrot will point, for instance, to black-swans and fat-tails to explain the misbehavior of markets, emphasizing the deficiencies in the models and assumptions of mainstream finance.

In Inefficient Markets, Andrei Shhleifer posits instead that it is the twin traits of conservatism and representativeness that lead to investor under- and overreactions. While conservatism assumes that “individuals are slow to change their beliefs in the face of new evidence”, representativeness tends “to view events as typical”, ignoring what the laws of probability might heed. Together, they make for a toxic financial cocktail.

Our animal spirits and confidence multipliers, likewise, have been documented extensively in the literature. In Irrational Exuberance, Robert Shiller writes about herding, imitation, and the contagiousness of human psychology. He tells us that “natural Ponzi schemes” arise in finance because people may grow overconfident and risk-seeking when asset prices rise, and vice versa—fuelling the bubbles and feedback loops we experience every now and then.

Reflexive and embedded

But as Daniel Beunza and David Stark note in their presentation to Freie Universitat, the literature commonly ignores how the “reflexive use of models [can] be a source of systemic risk.” Future theories, they suggest, must consider how our mental and quantitative models incorporate market cues to draw conclusions, and how these conclusions shape our views and models in turn.

One element of this is the concept of embeddedness. It reflects the fact that trading is a rather social and interconnected activity. Before the age of computers, personal networks on the floor drove the decisions and behaviors of traders. Ponzi schemes and pyramid schemes, likewise, spread from friend to friend.

Today, the social networks of financial markets are many times more vast and diffused. Their linkages are drawn not only by personal relations and media networks, but by the quantitative models and theoretical knowhow that people learn, deploy, and share. So we have to pay attention to “new rules of association—aggregation, anonymity, and mediation”, write Beunza and Stark.

Performativity and prophecies

That brings us as well to issues of performativity. As the authors explain, we say that “an economic model is performative when its use improves its predictive ability.” Performativity in economics parallels the performative utterance in philosophy—that a statement or model can change the very reality of the things it refers to.

It is also related to self-fulfilling prophecies. And nowhere is prophecy more visceral than in a bank run. When depositors grow fearful of their institution as an ongoing concern, they may withdraw their funds to safety. If this further depresses the perception of bank solvency, other depositors may withdraw as well, kicking of a “positive feedback loop between beliefs and behavior.” Capital then takes flight and the bank goes under. In turn, depositors can create the very future that they feared in the first place.

A similar case of performativity is found in the history of the Black-Scholes model. You might be surprised to hear, for instance, as Donald MacKenzie and Yuval Millo observe, that the option pricing formula performed rather abysmally during its conception in the 1970s. Their paper suggests that the price of call options at the time was overvalued by around thirty to forty percent. So either Black-Scholes was wrong, the market was horribly inefficient, or a lot of money stood to be made.

Yet despite its lacklustre ability at the time, Black-Scholes provided traders and quants with a new source of innovation and legitimacy. And as the model’s adoption grew alongside the exponential rise in computing power, databases, and trading efficiencies, so too did the model’s predictive power. Disparities between theory and observation closed because more and more people began to use the same model for valuation and arbitrage.

Reflexive modeling

Embeddedness and performativity manifest in many domains. Beunza and Stark point, in particular, to merger arbitrage, where traders try to profit from the price discrepancies between merger targets. Here, much of the trader’s livelihood depends on his or her ability to estimate value and likelihoods. They rely on models, tools, news, analogies, precedence, and history to formulate their views.

Yet despite the risk and uncertainty involved, they may take a position within seconds, minutes or hours of the announcement or market opening. As Buenza and Stark explain, arbitrage is “a game of speed.” Traders face a trade-off between certainty and opportunity. The longer they take to play, the more likely it is that somebody else gets to the mispricing first.

Of course, traders aren’t mindless automatons that jump at every signal or noise. They know that their models and constraints give rise to error. But they also know that other traders have taken positions on the opportunity. “Dissonance” between their own estimates and the market’s position might imply “missing information, incorrect modeling, or a profit opportunity”, says Buenza and Stark.

Arbitrage disasters

“Gaps, disparities, [and] mismatches produce positive friction that stimulates research.” Traders use the market to recheck their hypothesis and explore alternatives. Such a response rule, in principle, should spur informational efficiency and self-correction. But such reflexivity also creates interdependencies between the models and actors involved.

As Buenza and Stark note, if a critical mass of traders fail to see and incorporate crucial information, but continue to use the market for feedback, then false confidence may arise. Blow-ups ensue when traders double down on misinformed odds. “The reflexive use of models, in other words, creates systemic risk.”

For a classic example of arbitrage disaster, Buenza and Stark point to the aborted merger between General Electric and Honeywell in 2001. The proposal unravelled not long after the European Commission announced its disapproval of the merger, which led to nearly $3 billion in losses for the arbitrage funds involved.

According to Buenza and Stark, “the traders were misled by precedent: in the past, the antitrust authorities of the United States and Europe had always coordinated, and the American authorities had already signed on the deal.” Despite media speculation, traders did not believe that European opposition was likely. What’s more, the narrowing spread between the two companies “gave a false sense of confidence to arbitrageurs, leading them to enlarge their positions.”

Dissonance and resonance

Reflexivity in some sense is a double-edged sword. In the first instance, dissonance between the individual and the market spurs new search and research. As Buenza and Stark put it, “reflexive modelling, in other words, can be seen as a form of stereoscopic vision, as in the two-eyed form of vision that characterizes human sight. Just as the human brain gains a third dimension… by the comparison of two flat images (left, right eye), arbitrageurs gain a sense of opportunity and risk.”

This assumes, however, that there is sufficient heterogeneity in the market—that participants, each holding a different piece of information, contribute their view to the puzzle. But “reflexive modeling can also lead to a disastrous form of resonance” when everyone thinks in the same way. Under different conditions, embedded and performative interactions will lead to correction or amplification, divergence or convergence. The market vision is sometimes full of blind spots and illusions.

Black swans and misjudgment

What’s more, in practice, it is not always easy to say whether an event or non-event is a black-swan or a misjudgement of likelihoods. There are countless ways to interpret an outlier or distribution. We should remember, however, that the near-impossible is still possible. And if we happen to find black-swans everywhere—as the seventeenth century Dutch explorers who landed on Western Australia discovered—then our conception and expectations of the world are probably off.

In this way, reflexive modelling is not only a reminder about the fallibility of individuals and crowds, the entanglement of unseen strangers and models, or the value of diversity of opinion. From time to time, it is a reminder that complex feedbacks and unintended consequences can lead an otherwise functioning system into err, instability, and disaster. A future theory of finance and risk must incorporate such interplay into its dynamics and conclusions.

Sources and further reading

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