Performativity

A true story that sounds like a paradox: a mathematical formula first remade an entire market into the thing it described, then destroyed that achievement with its own hands fourteen years later. The formula is finance's most famous option pricing model, Black–Scholes. Sociologists coined a word from this case: performativity. A theory is not a camera photographing the world as it is; a theory is an engine, pulling the world toward what it describes.

The term comes from the French sociologist Michel Callon in 1998. His words: economics is not observing how the economy works, it is "performing, shaping and formatting" the economy. His full claim goes further: the economy is not embedded in society, it is embedded in economics. For a market to run, you first need a body of calculating buyers and sellers, plus rules and instruments able to cut a transaction out of its tangle of personal ties. And those rules and instruments are exactly what economics supplies. The textbook "economic man," who recognises nothing but self-interest, is a case in point: to Callon, it is not a false assumption about human nature, but a specification sheet that instruments gradually implement.

The Scottish sociologist Donald MacKenzie then took the crucial next step: grading "theory shapes reality" into four strengths, from "merely being used" through "pulling the world toward itself" to "falsifying itself," so it does not degenerate into a slogan that explains everything. You saw in R06 that classification changes the people classified; this is the theory-level version: a theory changes the world the theory describes.

The story starts in 1973, when two things happened almost together: Black and Scholes published the option pricing formula, and the Chicago Board Options Exchange (CBOE) opened on 26 April. An option is the right to buy or sell a stock at an agreed price in the future, and nobody could say clearly what that right ought to be worth, while the formula supplied an algorithm. At the start, market prices did not match the prices the formula produced, which is to say the formula was "wrong."

What follows is the core of the case. Traders began carrying around the pricing sheets Black printed, quoting off the formula. More importantly, there was arbitrage: whenever the market price deviated from the formula price, someone could buy low and sell high on the difference, and arbitrage itself pushes the market price toward the formula price. So market prices gradually converged on the model. MacKenzie and Millo's 2003 study working through the exchange's historical archives (published in the American Journal of Sociology, cited over 2300 times) traced the full arc: between 1973 and 1987 the fit between model and market kept improving. How good it got, one technical reading can show: the model assumes constant volatility, which means that whatever strike price you pick, the implied volatility you back out should converge to the same number, drawn as a flat line. Before 1987 the market data really did look like that: the implied volatilities backed out from options at different strikes lined up almost flat, and on the eve of the crisis the implied volatility of 10% out-of-the-money puts differed from the rest by only about 1.83 percentage points. The market was very nearly the world the model described. Note the direction of that sentence: it is not that the model accurately described the market, it is that the market was remade by the model into something more and more like the model. That is the strongest of the four grades, Barnesian (named after the sociologist Barry Barnes).

Then came the break. On 19 October 1987 the Dow fell 22.6% (508 points) in a single day, remembered as Black Monday. MacKenzie's 2004 article takes the mechanism apart: a product called portfolio insurance was popular at the time, which was simply Black–Scholes hedging logic turned into automatically executed rules, selling to cut losses by formula as prices fell. The problem was that thousands of accounts were executing the same formula at once: the fall triggered selling, the selling deepened the fall, which triggered more selling, a stampede organised by the formula itself. After the crash the market kept a permanent scar: the implied volatility of low-strike puts turned up sharply, the flat line became the "volatility smile," the market had learned to expect crashes, and the shape has never gone away since. Translated: too many people used the model, and using it made the model false. That is the fourth grade, counterperformativity, the inversion of performativity. MacKenzie and Bamford formalised this class of cases in 2018: a theory can become untrue because too many people believe it.

Critics have drawn three boundaries around the theory. The first comes from the philosopher Mäki in 2013: the word "performative" is borrowed from the philosopher of language Austin's performative utterances, where saying is doing, as in "I now pronounce you married"; but a market converging on a model is not linguistic magic, it is a causal process driven by arbitrage, instruments and interests, so borrow the word carefully. The second comes from Brisset: not every theory can perform successfully, reality resists, and for a theory to fulfil itself it needs institutions, interests and material instruments to cooperate. The third is the sharpest, from Mirowski and Nik-Khah: anyone studying "economists making markets" cannot treat it as a neutral phenomenon and must also ask which economics's market is being made, and in whose interest. Marti and Gond gathered these in 2018 into three testable conditions: the theory must be treated as a script for action, it must have supporting instruments, and there must be no strong counteracting force. With all three present, self-fulfilment happens.

Connecting it back to the red line. Ranking reactivity (R01) studies how people respond after being measured, while performativity studies how a theory makes a world: the former's input is an evaluative number, and it watches the struggles and accountability of the measured; the latter's input is a whole theory plus instruments, and it watches the world being shaped. Espeland and Sauder knew in 2007 that Callon's concept came first and still chose the word reactivity, precisely to keep the validity of the measure and accountability at the centre of the question. The two words are not synonyms, they are two viewing ports on the same machine.

One open question: in MacKenzie's case, what got performed was a formula anyone could read. When the "theory" is an uninterpretable deep model, can the amplifying and inverting grades still be told apart? Can you judge in advance whether a model's spread will amplify or cancel itself? Both questions are marked unresolved in the D6 report.

The one-line takeaway: if enough people use a theory, the world first becomes like it, then gets crushed by it.