Money managers who got blindsided by market manias like GameStop and Bitcoin are turning to ‘econophysics’ to help them avoid the next crash

The work of a Nobel Prize-winning physicist is helping money managers understand the science behind "stonks."
November 30, 2021, 10:00 AM UTC
OF BIRDS AND BULLS: A starling murmuration above a lake in Ireland. Economists have found parallels between starlings’ reactions to one another’s flight patterns and investors’ reactions to one another’s opinions.
Photograph by James Crombie/INPHO

This story is part of Fortune‘s 2022 Investor’s Guide.

Like clockwork, on evenings in late autumn and early winter, a cloud of black specks appears above the Roman skyline. Italians call these winged visitors storni, short for Sturnus vulgaris, or the European starling.

The Tiber River seems to draw the birds into the city. Above St. Peter’s Basilica, they bend, whip, and snake in hypnotic formations. Some evenings the starlings, thousands in number, do their dance high above the Roman Forum, paying no mind to the spot where rival senators offed Julius Caesar. They might then wing it past the prison that held Saint Peter in the final days before his crucifixion. Or maybe they’ll head back toward the river and swoop, dive, and dart above the 11th-century church that houses the Bocca della Verità (Mouth of Truth), where Audrey Hepburn and Gregory Peck filmed that memorable scene in Roman Holiday. The starlings’ journey across the sky seems chaotically random, but you can usually count on a spectacular show.

For decades, in Rome and beyond, scientists have studied the starlings’ murmurations, the technical name for the birds’ whipsaw flight patterns, for clues about group dynamics and the wisdom of crowds—and not just birdbrained crowds. Researchers have settled on “why” the birds murmurate. The seemingly unpredictable movements have a purpose: to confuse predators and even attract more starlings to join the mob. The more tantalizing question: How do they do it? How does a mass of individuals coordinate on the fly to move as one? Figure out the how behind starlings’ collective behavior and, the hope goes, a city can take the needed steps to keep a pooping nuisance away from its historical treasures. 

Economists, central bankers, and Wall Street pros have long been interested in that how question too—only for humans. How do the actions of individuals or small groups trigger the manias, crashes, and crises that ultimately take down markets and poop on the global economy?  

After the 2008–09 global financial crisis, that question took on new urgency. If that debacle taught us anything, it’s that the people we entrusted with our retirement savings were, unlike the starlings, inept at spotting risk on the horizon. Hedge fund king David Einhorn, who famously called (and profited from) the collapse of Lehman Brothers in 2008, savaged Wall Street back then for missing danger sign after danger sign. He argued the big banks and more conventional hedge funds were overly reliant on faulty risk-management tools, comparing them to “an airbag that works all the time, except when you have a car accident.” Einhorn was hardly alone. Following Lehman’s demise, a different group of geeky Wall Street pros emerged to call for a whole new approach to investor risk management. They go by the name of econophysicists.

Econophysicists view the markets as a complex system in which the individual, or “agent,” has the potential to influence the crowd. An agent could be any active market participant: a Pimco pension fund manager, a stock-pumping YouTube bull, or even you with your tech-heavy portfolio, your Twitter boasts, and your penchant for cornering people at dinner parties to defend Tesla’s P/E valuation. 

Adherents of econophysics are fascinated by feedback loops, collective behavior, and cause-and-effect on a grand scale—in short, they’re students of “complexity science.” These techy quants regard talk of inexplicable black-swan events as lazy thinking. And they dismiss efficient-markets true believers—those who assert that an asset’s price is the be-all and end-all metric for predicting risk—as woefully narrow-minded. Instead, they put more emphasis on investors’ actions and interactions. Investors take cues from other investors, they note, and that can lead to surprisingly big jolts in the markets. It doesn’t matter that such jolts are hard to predict: You still have to account for them in your own investment planning. 

Econophysicists borrow a lot from various scientific fields for insights into how individual shocks precipitate big market events. In modeling risk, they might study how epidemics spread through a population. Their algorithms may draw from the statistical models of seismologists to better detect the tremors that can cascade, cascade, cascade into the Big One. And, to understand the collective actions of investors, they’ve been known to take cues from the swarming tactics you find in some corners of the animal kingdom. To them, the starlings’ murmurations are not just a metaphor for the rise of WallStreetBets, meme stonks, and Bitcoin’s 255% rally over the past 12 months. They are a proof point that these phenomena are all around us in nature.

As Jean-Philippe Bouchaud says, the markets’ peculiar murmurations remind us that uncertainty “is in the cards.”

“All these birds, they fly very lousily if they are alone. But collectively they can make these amazing shapes,” says Bouchaud, a French physicist who is chairman of Capital Fund Management, a Paris-based hedge fund with $8.2 billion in assets under management. “This is important because we know that something similar happens in financial markets where suddenly people can believe in one thing. Or the other.” This tension, he adds, “creates movements in the stock markets, or movements in the economy.” And those movements can have huge financial consequences—even for investors who never join the flock. 


There’s no single piece of scientific research that started the econophysicist movement, which dates back to the 1980s. But a 2010 research paper on starlings has become a kind of North Star for this school of thought. It was coauthored by the Italian physicist Giorgio Parisi, one of Bouchaud’s “superheroes.” In October, Parisi was one of three scientists to be awarded the Nobel Prize in Physics. 

In their seminal avian research, Parisi and his colleagues weren’t after the why behind the starlings’ movements, but the how—and they cracked it. They could never have known it then, but their work would prove enormously instructive for the dips, spikes, and to-the-moon predictions that play out almost daily in the markets. 

Over two dozen chilly winter evenings between 2005 and 2007, Parisi’s team set up a field lab on the roof of the vast 19th-century Palazzo Massimo, a museum in Rome’s city center. There they tracked the flight patterns of groups of anywhere from 122 to 4,268 individual starlings looping and sidewinding overhead. Aided by powerful cameras, and 3D modeling and computer-vision software, they tracked and measured the birds’ comings and goings. Over time, an exhilarating finding emerged: Each evening, the movements of this enormous flock were triggered not by a kind of central avian command unit, but rather by individual birds within the flock, even ones on the periphery. You’ve heard of the crypto-inspired DeFi movement, short for “decentralized finance.” Call this “deflock.” 

A lone birdie on the far left of the pack—let’s name him Caesar—could influence the movement of birds he couldn’t possibly see elsewhere in the vast grouping, the researchers observed. Caesar was both influencer and influenced. If Caesar recognized, say, a predatory falcon zipping nearby, he would make a defensive move, darting out of its path. The effect on his immediate neighbors would be nearly instantaneous. Even if they were unaware of the danger, Caesar’s close companions would react by following Caesar’s path. Meanwhile, if a bird on the right—Flavia—dipped lower, others would follow her too—even Caesar. The Caesar-Flavia-Flavia-Caesar interplay would then set off a counterreaction by birds clustered deeper in the flock. Repeat this over and over again, and you get what looks, to the distant observer, like the great random bird whirligig in the sky.

NOB.0122.Giorgio Parisi
FINDING ORDER IN CHAOS: Giorgio Parisi in Rome in October. The Nobel winner’s research has spurred advances in A.I. and climate science as well as in the study of markets.
Alessandro Serranó—Shutterstock

What caught the imagination of those who study the behaviors and dynamics of large groups was this finding: The murmurations of the starlings were “scale-free.” These spontaneous flows could happen in groups of any size, underscoring the power of the individual, even ordinary Caesar, in nudging an entire flock in a certain direction: up, down, right, left, and back again. Just as fascinating: A surprisingly small subset of the whole could have as much influence over the others as the alpha, or leader, bird, or the starling with the most relevant information.

Joachim Klement, an investment strategist at London-based investment bank Liberum Capital, for one, draws analogies between the starlings and stonks. “The Reddit WallStreetBets community—and with that, obviously the GameStop, AMC, and you name it—that is exactly what Parisi describes in his work,” says Klement, who writes the popular Klement on Investing newsletter. “It is one reader reading a Reddit string, and hearing people push a certain stock, jumping on that bandwagon, and so it spreads.” 

Like starlings, he adds, “traders and investors are positioning themselves based on what they see other investors doing. And that gives rise to these extreme swings in equity markets, or in financial markets in general, both positive and negative.” 

In awarding the 73-year-old Roman-born Parisi the Nobel Prize, the Royal Swedish Academy of Sciences cited his decades of work to find and measure “hidden patterns” in complex systems—in essence, his lifelong quest to demystify the chaotic and confusing in an increasingly volatile world. If you’ve ever driven in Rome traffic you can probably fathom Parisi’s determination to unravel entropy. If you’re a hedge fund quant on the wrong side of a Reddit-inspired short-squeeze, you’d hope the Rome city fathers would at least name a street, if not a whole piazza, after him.

Parisi is perhaps best known for his work on a spin glass, a kind of metal alloy that itself has virtually no industrial use. For decades, physicists puzzled over the spin glass’s magnetism: specifically, that the tiny iron atoms in the structure seemed to line up in completely random formations. Parisi figured out the pattern and wrote a groundbreaking mathematical formula to prove it. The research appeared esoteric at the time, but the breakthrough helped scientists from various fields better understand how to detect and measure a hidden order in what appears to be thoroughly random and baffling to the eye—phenomena that are far more disorderly than a meme-stock rally.

Computer scientists credit Parisi’s spin glass work in the 1970s and ’80s for pushing later advances in machine learning and neural networks, and climate scientists hail his contributions in modeling atmospheric turbulence. His legacy became evident this fall in the days after he took home a share of the Nobel Prize. Researcher after researcher at the Santa Fe Institute, a mecca for complexity science and econophysics with multiple investing pros on its board of trustees, took to Twitter to praise Parisi. The starlings, one said, gave us precious insights into how we can measure the small movements, or “perturbations,” capable of triggering larger chain reactions.

Parisi declined to sit down to an interview with Fortune, but he was game to share a few thoughts via email. The first thing he wanted to make clear: “I am not a world’s expert on everything.” He also admitted to being “enormously surprised” that his work in cracking complexity would become so meaningful outside the world of physics. He credits others, including the Nobel laureate Phil Anderson, with bringing complexity science to economics and the markets. But he professed no interest in those disciplines himself.

Still, he has lit a fire under others who have financial passions. Bouchaud, the investment manager, first met Parisi in Paris in the early 1980s. Bouchaud was a young researcher then, and physics was his obsession. He found the spin glass lecture so inspiring he soon began to apply it to finance and the markets. Bouchaud believes the failings of markets—and economics as a whole—is our failure to grasp its innate complexity. For generations, “quant” investors have relied on mathematical models to determine what assets to buy and sell, and when. Manias and irrational leaps and tumbles in prices wreak havoc with their math. Now Bouchaud and others are updating their models to take Parisi’s observations into account and protect themselves from such turbulence. “The methods and ideas that Giorgio invented and developed will no doubt help us in such an endeavor,” Bouchaud wrote in a recent LinkedIn post. “I am sure he would be excited by the challenge.”


The tulip mania that swept through 17th-century Europe. A runaway rally in railway shares two centuries later. The 1929 stock market crash. January’s meme-stock rally. Bitcoin to the moon. Chroniclers have long been fascinated (and confounded) by the speculative bubbles that enrich well-positioned investors and punish those who join the party late. With the benefit of hindsight, the latter get written off as hapless suckers who succumbed to popular delusion and collective madness, but generally we’re none the wiser about how to avoid the next mania. If Parisi has added any insight into these phenomena, it’s the reassurance the tipping points can be more precisely measured, and that we can learn something from them.

At the start of 2021, GameStop was just another loss-making brick-and-mortar retailer socked by COVID lockdown measures. Even pre-pandemic, fewer customers were visiting GameStop’s stores in an era of e-commerce and downloadable video games, and sales were way off. Its stock was languishing. The management team was in disarray. Analysts had all but written off the company. But GameStop had a secret weapon few investors saw coming: its own version of Caesar the starling, who goes by “DeepFuckingValue” on Reddit and “Roaring Kitty” on YouTube. He was Keith Gill, a soft-spoken but risk-loving retail trader with a growing social media following.

Where Wall Street saw a dog in GameStop, Gill saw a winner. Throughout the summer of 2020 and into the autumn, Gill pounded his conviction relentlessly on WallStreetBets, the popular Reddit investor message board, and on his YouTube investing-tips livestream. GME was a can’t-miss, he crowed. Gill had no special knowledge about the stock, or any industry expertise on what it takes to be a winning retail play. He has no investor clients and, as he would later stress to Congress, he’s no financial adviser. Gill was that lone bird on the edge of the flock, day-trading and options-trading in GME, and then pumping the stock to anyone within earshot. 

On Christmas Day, Gill posted a brief YouTube video saying his GameStop holdings were up fivefold since the previous summer. That’s around the time others took up the call, in fast-growing numbers, and their collective messaging quickly started to sync into an unrelentingly bullish feedback loop. 

Before long, the meme-stock murmuration was underway. Gill and his flock’s trumpeting paid off on Jan. 11, 2021, when the retailer announced it had appointed e-commerce wiz Ryan Cohen, the cofounder of pet-supply site Chewy, to its board. Never mind that the company’s business outlook didn’t change a whisker. The way they saw it, the Cohen appointment vindicated their bullish calls. The stock price jumped the next day and within a two-week span was up nearly sevenfold. That, in turn, got Elon Musk’s attention. At the close of trading on Jan. 26, the Tesla CEO and Redditor idol tweeted a single word: “Gamestonk!!” The stock price more than doubled again the following day as 179 million shares traded hands.

The rally dumbfounded Wall Street. It came without a single “buy” recommendation from an accredited expert. More impressively, a number of short-seller heavies, including Andrew Left’s Citron Research and the previously high-flying hedge fund Melvin Capital, bet big against the firm, convinced it would collapse. The investors on the wrong end of the trade lost billions. In the aftermath, Congress called on Gill to testify, and regulators later investigated the various Reddit message boards for signs of market manipulation. In October they ruled it was all aboveboard, and not some concerted effort to crush the hedge funds. “Positive sentiment,” almost all of which was fueled on social media by normal Joe and Jane Robinhood traders, was behind the GameStop liftoff, Securities and Exchange Commission investigators concluded. 

NOB.0122.Jean-Philippe Bouchaud
MODELING FOR MURMURATION: Hedge-fund veteran Jean-Philippe Bouchaud is one of a growing number of investors incorporating econophysics into their risk-model algorithms.
Photograph by Elliott Verdier

There will be more stonks, Bouchaud believes. Extreme market moves may surprise investors (and investment pros), but from an econophysicist’s point of view, there’s almost always a logical explanation behind them. This was hardly the first time a feedback loop among investors had triggered massive swings, Bouchaud points out. Every major rally and crash can be traced to just such a phenomenon—from tulip bulbs to GameStop. 

One major new factor in today’s markets: The individual investor is flush with cash, adding a new wild card. Goldman Sachs calculates U.S. households have amassed an additional $3 trillion in cash assets since the start of the pandemic. Its equity strategists, led by David Kostin, expect households to put that money to use—where else?—“into equities,” they wrote in a recent investor note.

The lesson we should draw from the retail-trader–fueled GameStop rally, says Bouchaud, is that investors are influenced by not only the price of a risk asset but also what others tell them about the price. GameStop at a hundred bucks may sound ludicrous to anyone who follows a traditional price/earnings methodology. But to the investor who spends his day on Reddit, a convincing metric of future market success is just how many upvotes a “$100 GME” discussion string gets. It is that kind of interaction with fellow investors, Bouchaud says, “that can create feedback loops, and crashes and trends and all these things.” 

“But in the case of meme stocks,” he continues, “it’s even stronger, because people interact directly—not only through prices, they actually talk to each other at a massive scale through social media. So, you have these interaction effects multiplied by thousands.”


Wall Street calls GameStop and other such risk assets “story stocks,” and they come with a warning. They’re buzzy and can get quickly overvalued if investor after investor is as attracted to the story behind them—this stock is poised to dominate the EV market, or Bitcoin at $100,000 makes sense in a high-inflation world—as they are to the fundamentals. And in that dynamic, those who hop on the bandwagon late can take their lumps when it drives into a ditch. GME now trades more than 50% below the intraday high of $483 it achieved a few hours after Musk’s infamous tweet—a wipeout of nearly $20 billion in paper wealth. As one investor later chided Musk, “That tweet ruined a bunch of lives … but, whatever right?”

Complexity science won’t necessarily help you sniff out a true contender from the pretenders. Its big limitation is that it’s not predictive. It is “really helpful at explaining certain phenomena,” says Klement, before adding, “explaining them ex post [facto].” Think of it instead as a tool to better understand the “how” behind extreme price volatility—one that could help insulate you from the manias that drive up certain asset prices, and help you tune out (or tune in) the stories that sound too good to be true. 

Investors talk to each other at a massive scale through social media. So you have these interaction effects, multiplied by thousands.

Jean-Philippe Bouchaud, Capital Fund Management

How then should you approach a market in which the retail investor has become such a force, where story stocks abound, and price volatility is on the rise? First, understand that in a world of Reddit, Twitter, and TikTok, this is no passing trend. Second, use that knowledge to insulate yourself against this emerging form of risk. Not all of us are willing to put the narrative about a stock above more classic valuation measures and business fundamentals. But there are plenty of investors out there who will do just that—and their behavior could affect you, even if you don’t buy into the story. When story stocks like Tesla, Bed Bath & Beyond, and Hertz soar or crash, widely owned indexes like the S&P 500 and the Russell 2000 get rattled too. And when either FOMO or fear of the flock leads you to buy or sell when you otherwise wouldn’t, the short-term murmuration can upend your long-term goals.

No investor wants to think of herself as part of some birds-of-a-feather collective. And you’re not, the Parisi school of thought contends. With every trade, you have the power to influence others, and others have the power to influence you. That’s not to say all of you have the power to be the next Roaring Kitty, willing the pack in a certain direction. But through your connections, you’ve proved you can add billions in market value to pandemic-ravaged retailers or run up the price on a poorly drawn sketch of a rock.

Okay, maybe not you, personally. But the number of buyers willing to bid up those risk assets is decidedly not zero. That’s what markets are all about. They’re complex, filled with complex actors. 

Rallies in non-fungible tokens and meme stocks would go on forever “in a conventional, linear world,” explains Liberum’s Klement, himself a former student of astrophysics and mathematics. “But what Parisi showed us, and what complex dynamic systems show us, is [the rally] can also stop out of nothing. The narrative changes, the behavior of individual investors relative to what other investors are doing changes. And that creates a new narrative, and suddenly the murmurations go in a completely different direction. And that’s kind of what you saw with a lot of those meme stocks. It goes through the roof for a couple of days and weeks, and then almost without reason, it just—pop.” 

In Rome, the starlings’ tango in the sky seems to end as abruptly as it begins. With no discernible cue, the birds break ranks and head for the tall maples that line the Tiber. Out of sight, they cackle and coat the sidewalks below in guano. City officials want them out of town. But they always return. Like clockwork. 


How physics could help your portfolio

Complexity science adherents and econophysicists are unfazed by volatile markets. But they see flaws in Wall Street’s traditional risk models and view the rise of small “retail” investors as a formidable force. Here are four insights they offer the civilian investor:

Watch for whales, but don’t ignore the guppy
The rise of the retail investor is one of the single biggest changes to the markets, post-COVID. According to Goldman Sachs, U.S. households own half of the $28 trillion market for highly liquid “cash” equity assets. That’s a $3 trillion jump since the start of the pandemic. Translation: Those investors have a lot of firepower, and they will be a potent source of price volatility. The advice: Don’t underestimate the small fry’s ability to move the markets—and don’t overreact when it happens.

Look at narratives as well as economic fundamentals …
If meme-stock rallies—or even Tesla’s bull run—have taught us anything, it’s that a catchy story can be rocket fuel for a stock. Retail investors are giving these so-called story stocks the power to drive even greater price volatility. 

… And don’t fall in love with forecasts
Don’t put too much faith in stock-price targets and highly specific forecasts, like year-end S&P 500 targets. Complexity science advocates caution that in markets with high price volatility, long-term models—those extending beyond 90 days—tend not to age well. Joachim Klement, a strategist at the investment bank Liberum, says they’re akin to pulling out the calendar in September and predicting the weather on the first Tuesday in January. It’s hard to do in normal times. With climate change, it’s a nearly impossible task.  

Market timing is an even worse idea than it used to be
Econophysics adds more evidence to the case against timing the markets. If uncertainty is “in the cards,” as Jean-Philippe Bouchaud of Capital Fund Management contends, and long-view models have their flaws, why would you think you could beat the markets by anticipating the next big rally or swoon ahead of the pack? The advice: Don’t do it. Anchor your asset allocation, buying and selling decisions, and other strategies around broader goals that short-term swings in prices won’t disrupt.  

A version of this article appears in the December 2021/January 2022 issue of Fortune with the headline, “Following the flock: The science of meme stocks and manias.”