Behavioural Finance · 4 June 2026 · Afternoon Edition
In the early summer of 2007, one of the most actively traded securities anywhere in the world was a right that no calculating owner should have wanted to hold for a minute. The WuLiangYe put warrant, listed in Shenzhen, gave its holder the right to sell shares of the liquor company at a strike the market price had long since left far behind: a standard option-pricing model put the right’s value below five-hundredths of a Chinese cent. The warrant nonetheless traded at around one yuan — two thousand times its model value — and the entire float changed hands several times a session, day after day, until expiry settled the question in the only way it could.
This was not one aberrant instrument. Wei Xiong and Jialin Yu, who reconstructed the episode in the American Economic Review (“The Chinese Warrants Bubble,” 2011), counted more than a dozen put warrants between 2005 and 2008 that each spent a measurable stretch of life — fifty-four days on average, as long as 165 — in a state of effectively zero fundamental value while trading at an average price of one yuan, with each warrant turning over more than three times per day. The arithmetic was publicly observable the entire time. The expiry dates were printed on the instruments. Every one of them finished at zero.
Behaviour like this looks deranged only if you assume that people price a gamble by its expected value. They do not. A small chance of a large gain is among the most reliably mispriced objects in financial markets — and not primarily because anyone misreads the odds. The odds are often read correctly, then weighted incorrectly in the decision. The formal account of what that does to security prices was given by Nicholas Barberis and Ming Huang in 2008, and its implications are uncomfortable: the same taste that fills a lottery queue also shapes the cross-section of stock returns, and the bill is paid by the people holding the tickets.
The bias: a taste for the ticket
The puzzle is older than behavioural finance. In 1948, Milton Friedman and Leonard Savage opened a famous paper in the Journal of Political Economy with an awkward household fact: the same family that buys insurance — paying a premium to shed risk — also buys lottery tickets, paying a premium to acquire it. No single well-behaved utility curve holds both purchases in one hand; Friedman and Savage bent the curve to fit. The deeper resolution came from Daniel Kahneman and Amos Tversky: people do not act on probabilities at all, but on decision weights — transformed probabilities that systematically diverge from the true ones.
In the 1992 version of their theory, cumulative prospect theory (Journal of Risk and Uncertainty), Tversky and Kahneman estimated the shape of that transformation. It is an inverse-S: small probabilities are inflated, large ones deflated. Their median estimates imply that a one-in-a-hundred chance enters the decision carrying roughly the weight of a one-in-twenty chance — a fivefold overweighting of the rare event. This letter examined the resulting fourfold pattern on 27 May; what matters here is one cell of it: faced with a small probability of a large gain, people are risk-seeking — they will pay more than expected value for the ticket.
In “Stocks as Lotteries” (American Economic Review, 2008), Barberis and Huang took that laboratory regularity and asked what it does to equilibrium prices. If investors evaluate gambles under cumulative prospect theory, then a security whose payoff is positively skewed — a long shot offering a small chance of an enormous outcome — becomes desirable in a way classical theory does not capture: some investors hold it in concentrated positions precisely because concentration preserves the skew diversification would destroy. In equilibrium, the skewed security trades at a premium relative to its expected payoffs and earns a low — possibly negative — average excess return. The dull security, offering no jackpot at all, must compensate its holders with a higher expected return to find owners. Skewness itself becomes a priced characteristic, and the price of skew is paid, continuously, by the people who love it.
The empirical literature soon gave the abstraction a face: Alok Kumar’s “lottery-type” stock — low nominal price, high idiosyncratic volatility, high idiosyncratic skewness, the equity that costs little, jumps around, and occasionally multiplies. It is the closest thing the exchange sells to a scratch card, and it attracts the same customers.
The mechanism: why the tail wags the decision
The overweighting of small probabilities is not a free-floating quirk; it has architecture. The first component is what Kahneman called the possibility effect. The psychological distance between impossible and conceivable is the largest single step on the probability line. Once a jackpot becomes imaginable at all, it is vivid — a winner can be pictured, named, envied — while the modal outcome, a quiet zero, is abstract and unpicturable. Attention flows to the image, and the decision weight follows the attention rather than the arithmetic.
The second component is diminishing sensitivity to magnitude. The felt difference between winning nothing and winning a fortune is enormous; the felt difference between a large fortune and twice that fortune is small. So the presence of a jackpot dominates the decision while its odds recede. This is why the Shenzhen warrants could shed fundamental value by the day without shedding price: the dream component of the price was insensitive to the deterioration of the distribution underneath it.
The third component is narrow framing. A lottery ticket is evaluated as a single, self-contained story — this ticket, this draw, this conceivable win — rather than as the four-hundredth draw in a lifetime sequence, where the law of large numbers would expose the premium. Kahneman and Dan Lovallo (1993) called this treating each gamble as unique rather than as one of a batch; Shlomo Benartzi and Richard Thaler showed the same frame working in reverse on the loss side. Overweighted rare gains and overweighted recent losses are one lens pointed at different tails.
Finally, the taste is self-concentrating. Todd Mitton and Keith Vorkink showed that skewness-preferring households rationally refuse diversification — the only free lunch in finance — because averaging across positions destroys the very skew they are buying; the preference dismantles portfolio construction around the ticket. Nor is the demand evenly spread: Kumar found the appetite for lottery-type stocks rises in downturns and is strongest in the socioeconomic groups that spend most on state lotteries. The exchange’s scratch-card counter and the petrol station’s serve the same queue.
The empirical record
If the long shot is systematically overweighted, the long shot should be systematically expensive — and its subsequent returns should be poor. That is what the data show, in three independent registers.
Kumar’s study “Who Gambles in the Stock Market?” (Journal of Finance, 2009) examined the accounts of more than 70,000 retail investors at a large US discount broker. Lottery-type stocks as a class underperformed their dull counterparts, and the investors who tilted hardest toward them gave up roughly two to three percentage points of return a year relative to otherwise comparable investors. The drag was steepest among lower-income households — the clientele least able to absorb it. The lottery preference, in other words, is regressive twice over: it taxes returns, and it taxes hardest those with the least cushion.
Turan Bali, Nusret Cakici and Robert Whitelaw (“Maxing Out,” Journal of Financial Economics, 2011) found the same pattern with a brutally simple sort. Rank all US stocks each month by their single best daily return of the prior month — the statistic they call MAX, a clean proxy for recent lottery-like behaviour — and the stocks in the most spectacular decile go on to underperform the dullest by more than one per cent per month, roughly 1.18 per cent after four-factor adjustment, robust to controls for size, value, momentum, liquidity and reversal. Read as a practitioner: the most arresting advertisement a stock can run — one sensational day — has functioned, on average, as a warning label. Boyer, Mitton and Vorkink (2010) closed the loop: expected idiosyncratic skewness, estimated in advance, carries the same negative premium. The market charges for the dream before the dream has had its day.
Regulators on two continents have since watched the same preference being manufactured at scale. In the United Kingdom, the Financial Conduct Authority published a research note in November 2022 on the “digital engagement practices” of trading apps — confetti after trades, badges, leaderboards, push alerts, flashing movers lists — and found in a randomised experiment that these features raise trading frequency and risk-taking, most strongly among the young and the less financially literate. The accompanying commentary warned of “problematic, even gambling-like, investor behaviour.” The interface generates vivid jackpots on schedule and feeds them to the weighting function.
In India, the Securities and Exchange Board of India published an updated study in September 2024 of individual activity in exchange-traded equity derivatives — the purest retail expression of manufactured skew, since a deep out-of-the-money weekly index option is structurally a scratch card. The findings: across FY2022 to FY2024, 93 per cent of more than eleven million individual traders lost money; aggregate net losses exceeded ₹1.8 lakh crore, roughly ₹75,000 crore of it in FY2024 alone; the average individual lost about ₹2 lakh including costs; the share of traders under thirty rose from 31 to 43 per cent in a year. Opposite them, SEBI noted, sat proprietary desks and foreign funds running algorithms. The casino metaphor is usually lazy journalism; here it is close to a literal description of the payoff geometry.
Two episodes in the price of hope
The Chinese warrants episode of 2005–2008 deserves its place in every behavioural syllabus because it is the cleanest natural experiment a bubble has ever provided. The warrants were created as sweeteners during the reform of China’s split share structure; short-selling them was effectively impossible, so an investor who thought the price absurd had no instrument with which to say so. The put warrants’ fundamental values were not merely low but publicly computable, in real time, from the underlying share prices; their expiry dates were fixed in advance; and still they traded at an average of one yuan through an average of fifty-four days of effective worthlessness, turning over their float more than three times daily. Much of that turnover was not even a bet on the jackpot but on the next buyer — the resale option that grows wherever opinion diverges and short sales are barred. The clock was the one variable nobody could trade against: as each expiry approached, prices collapsed in the final sessions, and every zero-value warrant expired at exactly zero.
Thirteen years later the same geometry assembled itself in the United States, with an attention engine attached. The Securities and Exchange Commission’s staff report of October 2021 on the January 2021 meme-stock episode records the sequence with bureaucratic calm: GameStop, a loss-making mall retailer below $20 at the start of January, touched an intraday $483 on 28 January; distinct accounts trading it daily rose from about 10,000 early in the month to roughly 900,000 by 27 January; and the stock sat at the intersection of five reinforcing attention machines — extreme price moves, extreme volume, heavy short interest, Reddit mention velocity and saturation media coverage. Around the equity bloomed the option chain, where short-dated, far out-of-the-money calls let a small stake express a pure jackpot thesis — option leverage turns an ordinary share into a ticket with an expiry date, a Shenzhen warrant with better marketing. By mid-February the price was back below $50. The episode is remembered as a populist uprising against short sellers, and partly it was; in distributional terms it was the warrants bubble re-run at NASDAQ scale.
The two episodes rhyme because the structure is the same everywhere it appears: an instrument whose design concentrates payoff into a thin, vivid tail; a crowd whose attention has been synchronised by feed or by neighbour; a price that reflects the dream rather than the distribution; and a terminal date — contractual or attentional — on which the account is settled.
The counter-measures: three disciplines
The instinct, reading all this, is to file it under errors other people make. That is itself the error: the weighting function is the factory setting of the species, triggered by jackpot stories, movers lists and round-number milestones that modern market infrastructure supplies free of charge. The defence is not temperament but procedure — three procedures in particular.
First: seal the aspiration sleeve. Hersh Shefrin and Meir Statman’s behavioural portfolio theory (2000) observed that real investors build portfolios in layers — downside protection below, aspiration above — rather than as one mean-variance whole. The discipline is to formalise the aspiration layer instead of smuggling it: an explicit sleeve of one or two per cent of capital, sized so total loss is immaterial, funded once, never replenished after a wipe-out. A sleeve that can be topped up is not a sleeve but a siphon. Booking its lifetime profit and loss in the annual review converts the dream into a recorded base rate of one’s own.
Second: audit the spike. Most lottery positions are not planned; they arrive on a surge of recent vividness. So screen for the vividness directly, before any purchase whose impulse is younger than a month: What was the stock’s largest one-day gain in the past month — its MAX statistic? Has it been appearing on movers lists and in forum chatter? Is the nominal price small enough to feel like a token rather than a claim? A flag on these questions does not forbid the purchase; it triggers a written expected-value case — base rates first, story second, with the Kumar and Bali, Cakici and Whitelaw spreads as the default prior — and a cooling period measured in weeks before execution. The investor is permitted to conclude yes. In writing, after the wait.
Third: count in decades, not draws. The single vivid draw is the frame in which the weighting function does its damage, so the discipline is to refuse the frame. Translate every candidate position into its contribution to the ten-year compounding of the whole portfolio in the modal case — the 95 per cent of paths where the jackpot does not arrive — and ask the frequency question explicitly: out of a hundred tickets shaped like this one, how many pay? Kahneman and Lovallo’s prescription of the “outside view” is precisely this: treat the decision as one of a batch, because it is. Probability weighting needs a spotlight and a single ticket. A ledger of one hundred faceless tickets returns the tail to its true size.
How the practitioners price the long shot
Charlie Munger gave the canonical practitioner’s statement of all this in a 1994 talk at the University of Southern California, long before the academic literature caught up. “The model I like — to simplify the notion of what goes on in a market for common stocks — is the pari-mutuel system at the racetrack,” he said. At the track the odds are set by the crowd’s own bets, so the question is never “which horse is best?” but “which horse is mispriced by the wagering?” Racetrack data show a persistent favourite–longshot bias: longshots attract systematically more money than their payoff odds justify, favourites less (Richard Thaler and William Ziemba catalogued the evidence in 1988). Munger’s betting posture follows: the mispriced bet is almost never the glamorous longshot, whose value the crowd’s weighting function has already spent — it is occasionally the dull favourite. Hence the practice: bet rarely, bet heavily, only when the crowd’s taste for the ticket has left something solid unattended.
Seth Klarman drew the same boundary from the other side in Margin of Safety (1991), with the parable of the trading sardines: the trader who, on opening a tin from a long-appreciating hoard and finding it rancid, is told by the seller, “You don’t understand. These are not eating sardines, they are trading sardines.” Klarman’s dividing line is the one this essay has been drawing: an investment is underwritten by the cash the asset itself will produce, the boring centre of the distribution; a speculation is underwritten by the mood of the next buyer, the thin tail of the resale. His rule that a position must justify itself on the dull case, any jackpot treated as windfall rather than thesis, is the written expected-value audit in institutional form. Neither man relies on willpower at the moment of temptation; both built the refusal into procedure, years in advance.
Key takeaways
- The taste is priced. Investors overweight small probabilities, so positively skewed securities command a premium and deliver low — even negative — subsequent average excess returns; dull securities must pay their holders more (Barberis and Huang, 2008).
- The best day is a warning label. Stocks in the most spectacular recent-gain decile lagged the dullest by over one per cent a month, about 1.18 per cent after four-factor adjustment (Bali, Cakici and Whitelaw, 2011).
- The clientele pays twice. Those most drawn to lottery-type stocks surrender two to three percentage points a year (Kumar, 2009); SEBI found 93 per cent of eleven million Indian derivatives traders losing ₹1.8 lakh crore over three years.
- The urge is now manufactured. The FCA’s 2022 trading-app experiment showed confetti, badges and movers lists raising trading frequency and risk-taking, strongest among the youngest users.
- The defence is procedural. A sealed, capped aspiration sleeve; a written base-rate audit of any spike-born impulse; the hundred-ticket decade frame. Munger’s rare heavy bet on the mispriced favourite and Klarman’s dull-case underwriting are the same disciplines in practitioner form.
— Manish Goel, FCA / NorthPath Advisory OÜ / Tallinn, Estonia
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