Bull run: Inelastic financial markets theory, Black Scholes option pricing and its underlying Gaussian assumption undermining market risks, and the influx of money 

MNK Risk Consulting > Worldwide Economy News > Bull run: Inelastic financial markets theory, Black Scholes option pricing and its underlying Gaussian assumption undermining market risks, and the influx of money 

It’s an overcast day in Paris, which is slowly coming back to life after the August exodus. The leaves have already begun to fall off the Champs-Élysées trees, covering the boulevard in a light autumnal carpet. French politicians are being very French. “La tragédie française” is the headline of Le Point, amid the collapse of yet another government.

The latest prime ministerial defenestration — this time of François Bayrou, after a stint lasting less than a year — is clearly preying on my lunch date, Jean-Philippe Bouchaud. He has recently co-written with his wife Elisabeth Bouchaud — an accomplished physicist turned theatre director — a play based on Albert Camus’ final work, The First Man, and hopes that the writer’s temperate political disposition will resonate again. “I’m very fond of people that try to find compromise. I think we need to hear his voice again, during these troubled times,” Bouchaud sighs. “In France in particular we are bad at finding compromise.”

Playwriting is just a highbrow hobby, however. With his mop of hair, owlish spectacles and academic mien, Bouchaud looks like the French physics professor he used to be, but in fact he chairs one of Europe’s largest, oldest and least-known hedge funds, Capital Fund Management. CFM currently manages $20bn of assets, perhaps small by American standards but big by European ones, and its flagship fund is now closed to new investors, a tell-tale sign of success in the business of managing money.

While hedge funds have long hired former scientists and mathematicians for their brainpower, most remain dominated by traditional traders and analysts who have served apprenticeships at a big bank or fund management house. In contrast, CFM mostly resembles a physics department with a few traders bolted on, and its investment strategies are “quantitative” — entirely systematic, model-driven and emotionless.

The choice of lunch venue is therefore appropriate. For centuries the École Polytechnique has educated France’s engineering elite, and Maison des Polytechniciens is the de facto club for alumni. Nestled on the second floor of the Maison is a small, discreet restaurant called the Le Poulpry, where Bouchaud is already waiting at a corner table despite my early arrival.

A mutual acquaintance had described Bouchaud as “an odd guy but very lovely”, which seems accurate as he gently greets me in softly accented English. But, as I discover, there is one topic that will get him going — which is, fortunately, the main subject that I want to discuss with him.

“I don’t think passive investments create volatility . . . But they might create these long-term — I don’t know if we should call them bubbles — upward trends.”

Bouchaud is both baffled and frustrated by how economics has fallen in thrall to theorists — mathematical, social or political — and become bereft of the rigour of proper sciences, where real-world experiments and experiences actually matter. Nowhere is that clearer than when it comes to the belief that markets are somehow efficient. “It’s all wrong. It’s not weakly wrong — it’s badly wrong,” he argues.

A common view is that the stock market is an emotionless, methodical valuation machine. It runs on vast amounts of information and spits out reasonably accurate guesses for the value of financial securities. Sure, sometimes the machine ingests bad data, or technical factors can cause glitches. But over time, it ensures that prices are roughly fair. As Benjamin Graham, the doyen of financial analysis, once quipped: “In the short run, the market is a voting machine but in the long run, it is a weighing machine.”

However, according to hot new financial theory — dubbed the “inelastic markets hypothesis” — this is utter baloney. Research by Xavier Gabaix of Harvard University and Ralph Koijen from the University of Chicago published in 2021 indicates that inflows and outflows are wildly more impactful on the stock market than previously thought.

This has caused a stir in the cloistered world of financial economics and certain corners of the investment industry. There, some spy an explanation for why the stock market keeps marching higher, almost impervious to bad news: the gush of money into cheap, mindless passive investment strategies. And if those flows ever reverse, the result will be carnage, critics warn.

Bouchaud has become one of the theory’s leading proponents, writing a paper corroborating Gabaix and Koijen’s findings and arguing that it holds for all other markets as well. For him, the inelastic markets hypothesis is akin to the belated recognition of two high priests from an opposing religion that the dynamics that practitioners like Bouchaud see every day are real and influential.

“It’s a game-changer,” he argues. “They’re economists who are listened to by serious economists, which we are not. They’re pure academics and have nothing to sell. And what they’re saying is that they’ve measured something real here.”

Wary of talking about recondite points of financial economics on an empty stomach, I decide to find out more about his life while we wait for our food. We both go for the three-course lunch menu and choose the swordfish steak for our main course, though he chooses the parmesan shortbread with creamy bufala as a starter, while the chickpea hummus and lime-marinated prawns catches my fancy.

I stress my desire to test the limits of the FT’s expense account, but defer to Bouchaud’s superior judgment when it comes to the wine. A quick glance at the menu results in a glass of fine Chablis for me and a red Burgundy for him, both regrettably reasonably priced.

Bouchaud’s impeccable English betrays five formative teenage years living in London in the late 1970s. He loved it, especially the ska and punk scenes that thrived at the time. “Of course you cry when you move, but London was an exciting place,” he reminisces. Less happily — at least nowadays — he also became a Manchester United fan while living in England. I tell him I support Liverpool, and try to stifle my smugness.

Bouchaud didn’t attend l’X — as the École Polytechnique is sometimes called — but he did teach there for nearly a decade. He therefore has an affinity with the Maison des Polytechniciens. Le Poulpry is also close to CFM’s Paris offices. But the main reason he chose the restaurant is “because the food is very good”. The delicate scallop amuse-bouche we are quickly served is certainly a positive omen.

After the French Lycée in London, Bouchaud studied at École Normale Supérieure and received his doctorate in theoretical physics at its Laboratory of Hertzian Spectroscopy. Among his other early papers are page-turners on quantum Boltzmann equations for atomic hydrogen, and a study of the diffusion front on fractals and superlocalisation from linear response requirements. Despite a fascination with physics, I’m afraid to ask even for simple explanations.

He explains his journey from quantum particles to price-to-earnings ratios as we attack our starters. Ironically for a quantitative investor who relies on models, it was a chance encounter with one of high finance’s foundational formulas — and his instant revulsion to it — that first brought Bouchaud into the world of money.

In 1990 Bouchaud and a colleague published a paper on the “anomalous” movement of certain particles. Rather than move in the usual small random steps — known as Brownian motion — these particles occasionally made violent jumps. A banker happened on the paper, and informed Bouchaud that the assumption of Brownian motion also underpinned an enormously popular financial formula developed in the 1970s by famed financial economists Fischer Black, Myron Scholes and Robert Merton.

This Black-Scholes model ushered in a revolution by giving investors a fairly straightforward equation to calculate a fair value for options — a type of financial derivative that gives investors the right to buy or sell a security at a pre-determined price. This may sound mundane to people outside finance, but has helped nurture a multitrillion-dollar global options market, and won Scholes and Merton the 1997 Nobel Prize in economics (Black passed away in 1995 and was therefore ineligible).

However, Bouchaud thought the famed Black-Scholes model was badly flawed, as it rested on an assumption of random, Brownian stock market movements. Most of the time that’s fine, but Bouchaud argued it underplays the dangers of improbably violent movements. This can lull option sellers into a false sense of security and lead them to buy insufficient protection in case the contract suddenly moves against them — they are “unhedged”, in financial argot.

“Black-Scholes was useful and misleading at the same time. It gave a very clear formula for option writers to hedge their position, which could be coded and followed blindly,” he says. “Unfortunately, it tells you that if you do so quickly your risk is zero, which is wrong. Secondly, and perhaps most importantly, it creates feedback loops.” This was one of the causes behind the havoc of the 1987 Black Monday crash, Bouchaud argues.

He therefore wrote a paper on his own findings and shopped it around Paris. One of the people he met was Jean-Pierre Aguilar, a financier who had just started a new quantitative hedge fund then called Capital Futures Management. They decided to work together, and the result is today’s CFM (Aguilar tragically died in a gliding accident in 2009, and Bouchaud is now chair and “chief scientist” at the fund).

The service at Le Poulpry is unusually brisk and attentive by Parisian standards, with the waiter frequently interrupting long explorations of alternative economic modelling and “econophysics” to check that we are completely happy with our food (we are). By now our swordfish steaks have appeared, resplendent on beds of black rice, coconut milk and coriander curry sauce, and we quickly tuck in.

Under-appreciated but dangerous feedback loops are a recurring theme in Bouchaud’s work as a physicist, which specialised in complex systems and their fragilities. He is convinced that money flows carry the same sort of risk in financial markets today.

The controversial Koijen and Gabaix paper was therefore electrifying. The headline takeaway from their dense research is that a $1 investment in the stock market increases its overall value by $5 — and that this is a permanent effect.

Previously, most economists have assumed that any impact from inflows and outflows is either negligible or fleeting, as other traders quickly take advantage of any mispricing that might result. Imagine throwing a pebble into a pond — it will cause ripples but they will quickly fade away. Gabaix-Koijen in effect showed that the pebble somehow increases the size of the pool itself. Their inelastic markets hypothesis therefore represents an assault on the efficient-markets hypothesis advanced by Eugene Fama, which has become almost dogma in swaths of finance in the half-century since it was first proposed.

This is starting to feel like a second-glass-of-wine topic — and the perfectly cooked swordfish steak has been happily demolished — but for once Le Poulpry’s service breaks down: my attempt at ordering another drink fails miserably. Bouchaud seems to have only halfheartedly drunk his wine anyway, so after a few forlorn glances towards the waiters I reluctantly abandon my efforts.

Why does this matter to anyone but a few financial nerds, though? Because “it shows that the whole bull run is because of an influx of money into the market”, Bouchaud argues. And if flows can have such an enormous impact on the way in, just imagine what can happen if it ever goes out again.

What about the secular four-decade decline in interest rates, I protest. What about the technology industry’s engorged corporate profits? Increasingly global companies, with international supply chains and aggressive tax minimisation? The decline in antitrust enforcement? Aren’t all of these far better explanations for the post-2008 stock market bull run? “I’m not saying it’s the only reason, but it’s a substantial reason,” Bouchaud counters. “I’m just saying that this is a thing that has the same order of magnitude to what we’ve witnessed. So it cannot be discarded.”

Given how the hypothesis suggests that money flows leave an outsized footprint on markets, it has naturally become a flashpoint in the ongoing war between traditional “active” investors and cheap passive funds sold by the likes of Vanguard and BlackRock. Bouchaud seems wary of drawing conclusions on this, but argues that the passive investing phenomenon is probably contributing to the inelasticity.

“Maybe people don’t think economic modelling is as important as cancer research, but it is pretty important.”

After all, passive fund inflows push the market higher, which then begets more inflows from greedy investors. At the same time, the winnowing of traditional value-sensitive investment managers means that there are fewer people around to correct even grossly obvious mispricings. “I don’t think passive investments create volatility,” Bouchaud says. “But they might create these long-term — I don’t know if we should call them bubbles — upward trends that persist and give people a sense that it is going to last for ever.”

His enthusiasm for the inelastic markets hypothesis stems in large part because it is — in Bouchaud’s view — a rigorous attempt at understanding the world as it is, rather than the fantastical version that exists in most economists’ models. Given his background, I ask Bouchaud whether he agrees that economists suffer a case of physicist envy. He scoffs.

“I think they have mathematics envy, rather than physics envy. They just want to prove theorems,” he argues. “That’s my main peeve about economists. They seem more interested in solving logical problems and aesthetic puzzles rather than a deep desire to understand what the real driving forces are.”

By now we have moved on to our desserts. Bouchaud goes for a café gourmand — a very French dessert of espresso alongside a selection of petits fours, while I choose the Breton shortbread topped with roasted fig and whipped cream, and also plump for an espresso to cap the meal. It tastes as good as it sounds.

The sugar high spurs me to ask about something that has long bugged me. As fascinating and intellectually stimulating as finance is, isn’t it a societal tragedy that so many of the world’s smartest people now spend their days trying to eke out a few basis points in the zero-sum world of markets, rather than untangling the mysteries of the galaxy?

Bouchaud nods, but disagrees. He recalls how the famous physicist Richard Feynman — one of his heroes — once observed that progress often comes by focusing intensely on cracking even seemingly trivial problems. This can then lead to answering myriad other humble questions. Over time, these begin to add up, and big breakthroughs happen.

“Quant hedge funds are trying very hard to understand some small problems, but by doing so we have developed methods that are much more general,” Bouchaud argues. “Maybe people don’t think economic modelling is as important as cancer research, but it is pretty important.”

Perhaps. I still suspect most people would prefer cancer to be cured than more accurate dynamic stochastic general equilibrium models, even if the latter might indeed improve many lives. But at least Bouchaud seems to be pouring his money back into science and the arts as well.

As we leave, I ask whether he’s nervous about his upcoming theatrical adaptation of Camus, which is due to be performed at next year’s grand Festival d’Avignon. “Of course. It’s a tough world,” he admits, rapping our wooden table for luck. It’s somehow reassuring that even cerebral econophysicists from time to time instinctively resort to everyday habits of superstition, just like the rest of us.

Robin Wigglesworth

Financial Times, Jean-Philippe Bouchaud, Sept’25.