The Effect of Performativity in Financial Pricing Models

In the 20^th century, the study of finance underwent a shift from being on the fringe of economics to dominating at the forefront, transforming from a ‘primarily descriptive activity’ to a ‘high-status, analytical, mathematical, Nobel-prize-winning enterprise’. However, the accuracy and success of its theories were called into question when it was suggested that the very nature of making an observation as to the state of a financial system may have a direct impact on its workings. This is known as performativity – it can be argued that this has a significant impact on financial pricing models and should be adjusted for appropriately when observing the success of models and pricing financial instruments.

Most economic models are constructed through making a series of assumptions about individual economic agents and their behaviour, such as whether they act in a manner that will maximise utility, or that their decisions are all completely rational^[1]. However, if you look at the NYSE alone, which is just one of around 80 major stock exchanges^[2], you could observe around three billion trades a day, involving 2,800 companies. With such a huge number of individual components, it seems almost impossible to be able to consider every individual decision that would impact its behaviour when constructing a model of a stock exchange, let alone manage to account for this uncertainty when refining a model. However, the widely celebrated growth and success of financial economics in the twentieth century suggests that there must be a significant factor contributing to the empirical success of these theories, despite our acknowledged ignorance (and the resultant ‘over-simplification’) in most financial pricing models. To explain this, Donald MacKenzie argued that financial theories stand in a ‘feedback relation’ to the systems that they describe, and eventually become a part of the system itself. He described this as the ‘performativity of economics’^[1].

This phenomenon can be observed with an investment philosophy known as Chartism. This method is based on examining financial price charts to identify the formation of specific patterns or shapes, which can then be used to determine the best times to buy or sell certain stocks. For example, a Chartist approach could be used to suggest that a certain security has a floor price of 30, which it should not penetrate whilst operating within normal parameters. This would indicate to traders that if the price of that security were to drop below 30, it is no longer operating within the accepted level of price deviation, meaning that they should sell it before its price continues to fall further^[3]. However, if this idea gains regard within the industry, it means that more and more traders will start selling the security as soon as its price falls below 30, therefore putting further downward pressure on its price. This would provide more validation for Chartist theories, and with more people believing in its accuracy, more traders will put downward pressure on the security’s price, and so on, creating a cycle that leads to an effective ‘self-fulfilling prophecy’ which in turn demonstrates empirical success for the theory^[1]. MacKenzie argued that this process is what creates the feedback loop that performativity suggests.

He also suggested that there are three main ways that a financial theory can influence the agents involved in the system. This includes when it is used by regulators or to make predictions about financial transactions, or by individual actors consciously attempt to make their behaviour conform to, or contradict, how they are expected to behave in accordance with the theory^[1]. This implies, that unlike in theories and models in the natural sciences, a financial model does not provide a static observation of the state of the world, but instead it is actively a part of the system itself, meaning that, in MacKenzie’s words, it is ‘an engine not a camera’ (McKenzie, D. 2008).

It can be intuitively conceived that performativity has a major impact on the functioning of financial markets, since, as described earlier, the behaviour of financial markets are dependent on decisions made by individuals. Economic theory dictates that individuals make their decisions based on the information that is available to them at the time, suggesting that if new information, such as a new investment theory, is revealed to them, then the prior knowledge that informs their decision-making has changed^[5]. This means that there is likely to be an impact on their actions as a result, and consequently also upon the financial market system as a whole. In this way the effects of performativity on a system can be explained, with the introduction of a new theory leading to a change in the outputs of the system itself, showing that the theory has then become a part of, and is now an integral component to, the functioning of the system it intended to just describe (McKenzie, D. 2008).

Furthermore, the effects of performativity on financial pricing models can also be empirically observed through the example of option pricing models. An option is a financial contract which gives the buyer the right, but not the obligation, to trade a specific financial asset at a predetermined price on, or up to, a specified date^[5]. Since they first started trading in the 17^th century, the most important concern in the theory of options is how to determine how much they should cost. Developments in the academic study of finance in the 1950s soon led financial economists to derive the Black-Scholes option pricing equation, which soon became known as the ‘defining achievement of modern financial economics’ due to its widespread observed success and adoption (Mackenzie, D. 2006) . This model was based on certain key assumptions, such as log-normality, no transaction costs and a riskless rate of return, and became widely adopted very quickly after the opening of the first modern organized options exchange in 1973 (Mackenzie, D. 2006).

To begin with, there was a notable level of deviation between the values predicted by the equation and the actual values given by the market, but over time, the model slowly became more and more accurate, predicting almost the exact values observed on the market. This period coincided with an extensive adoption of the equation by traders throughout the industry, even to the point where the most common tool used to price options were paper printouts of Black-Scholes equation values sold by Fischer Black himself, demonstrating perhaps the most literal way a theory can be observed to have become a part of the system that it describes (Mackenzie, D. 2006)  . However, the widespread success of what became known as the ‘Midas Equation’^[6] culminated in the stock market crash of 1987, or ‘Black Monday’; markets lost over 20% of their value in a few hours – an almost impossible event according to the model. This failure led to a systemic rejection of the assumption of log-normality (a vital component of the Black-Scholes Pricing model), and the model then never regaining its previous empirical success (Mackenzie, D. 2006)  .

This suggests that, since no other factors influencing the composition of the model changed, its increased success was linked to and, in line with performativity theory, a direct result of the feedback loop created by more people using the equation to make their investment decisions, which is further supported by its inability to deliver empirical results once use of the model fell out of favour in options markets.

Nevertheless, despite the evidence supporting the significance of the impact of performativity when evaluating financial pricing models, there are still questions left unanswered that it is unable to explain. For example, the reflexivity element of the theory relies on people’s acceptance of it to begin with, which means that a model must have some initial merit to become a part of a system. This can be seen in the options pricing example, as performativity can explain how the theory became more accurate when Black’s formula printouts became widely used in the industry, but not why traders initially chose his product over the fourteen other options pricing services then available – indicating that there are likely other factors that affect whether a model is effective that are not impacted by performativity, and that it cannot compensate for the other components required for a model be a successful method of financial pricing (Mackenzie, D. 2006).

In addition to this, the effects of performativity can be hard to predict; agents may be influenced to make their behaviour conform to any given model, but can also choose to act in a way that actively contradicts its predictions, depending on their (possibly inaccurate) judgement of what is best in the situation. The central pillar of behavioural economics is that ‘humans are irrational’, and so cannot be expected to respond to any new situation in the manner expected of a rational decision-maker (Kahneman, D. and Egan, P. 2011). Across the billions of individual decisions that build financial markets it could even be possible that the variation in performative responses would average out to give a negligible aggregate effect.

Overall, despite the fact that there may be other factors influencing the effectiveness of financial pricing models, and that the cumulative effects of performativity may be hard to predict, it is clear that financial markets are completely built upon the individual decisions of economic agents, and therefore are vulnerable to the effects of any information that is likely to impact the way that these agents make their decisions. The empirical evidence from the colossal success of the Black-Scholes pricing model whilst it was supported by performativity further shows how significant its influence can be, demonstrating how important it is to appropriately account for the effects of performativity when deriving and evaluating financial pricing models going forward.

1. McKenzie, D. (2008). An engine, not a camera. Cambridge: MIT Press.
2. Akerlof, G. (1970). The Market for “Lemons”: Quality Uncertainty and the Market Mechanism. The Quarterly Journal of Economics, 84(3), p.488.
3. Mackenzie, D. (2006). Is Economics Performative? Option Theory and the Construction of Derivatives Markets. Journal of the History of Economic Thought, 28(01), p.29.
4. Kahneman, D. and Egan, P. (2011). Thinking, fast and slow. New York: Random House.