The Market Can Stay Irrational: Noise Trader Risk

There is a standard defence of efficient markets, and generations of students have been taught to deploy it like a magic spell. It goes like this:

"Sure, some investors are idiots. But so what? The moment they push a price away from fair value, sophisticated arbitrageurs will pounce, trade against them, push the price back, and take their money. The idiots lose money, go broke, and exit. The rational traders get rich and dominate. Therefore prices are right, and irrationality is self-correcting."

It is a lovely argument. Milton Friedman made a famous version of it. It sounds like it must be true.

In 1990, De Long, Shleifer, Summers and Waldmann built a model showing that every single step of it can fail, and that the noise traders can not only survive but earn higher returns than the smart money. This is the paper that turned "the market can stay irrational longer than you can stay solvent" from a bar-room saying into economics.

The problem: arbitrage is not free money

The efficient markets defence quietly assumes that when the noise traders push a price too high, you can short it and simply collect the difference when it comes back. Risk-free. Costless. Instant.

But hold on. When exactly does it come back?

You short the overpriced stock today. Tomorrow, the noise traders wake up even more excited than yesterday and push it higher. You are now losing money. Not because you were wrong about the value, but because the crowd got more wrong.

This is the whole paper in one sentence: the unpredictability of the noise traders' future mood is itself a risk. They call it noise trader risk, and it is a risk that would not exist at all if the noise traders were not there. It is a hazard the irrational investors manufacture out of nothing and then leave lying around for everyone to trip over.

The key idea via analogy: betting against the drunk

Picture a poker table with a very drunk, very rich player who bets randomly. Classical theory says: wonderful, sit down, take his money, he'll be broke by dawn.

Now add a real-world constraint. You have to settle up at the end of each hour, and your backers pull your funding if you're down. Suddenly the drunk is dangerous. Not because he plays well, but because he plays unpredictably. He might go on a wild heater for the next hour purely by luck, wiping you out before his luck turns. You know you'd win over a thousand hands. You may not get a thousand hands.

The model formalizes this with a beautifully cold-blooded setup. Arbitrageurs are rational and know the true value. Noise traders have random, shifting misperceptions. And critically, arbitrageurs have finite horizons: they must close out their positions at some point and cannot simply wait forever for value to prevail.

Now the consequences cascade:

1. Mispricing survives, with no fundamental risk at all. This is the sharpest part of the result. The mispricing persists even when the asset's true value is perfectly known and certain. There is no uncertainty about the fundamentals whatsoever. The only risk is what the noise traders will think tomorrow, and that alone is enough to keep the rational money from fully correcting the price. Prices can diverge from value indefinitely.

2. Arbitrageurs, being rational, back off. A rational trader who sees a risk demands compensation for it and takes a smaller position. So the very rationality of the smart money is what stops it from doing its job. Rationality does not mean recklessly pushing prices to fair value. It means sizing your bet for the risk you face, and noise trader risk is a real risk.

3. And now the twist that makes this paper famous: the noise traders can earn higher expected returns than the rational investors.

Read that again, because it is the opposite of what everyone assumes. How can being wrong pay better than being right?

Because the noise traders, when they are collectively bullish, hold more of the risky asset. And that asset now carries an extra risk, the noise trader risk, which they themselves created. Risk gets compensated. So they end up bearing a big load of a risk that pays a premium, and they collect that premium. They are being paid for a danger that they are. It is as if the drunk at the poker table gets a bonus for being drunk, because his drunkenness is what makes the game scary.

This demolishes the Friedman argument. The noise traders do not necessarily go broke. Their aggressiveness can pay them, they survive, they keep trading, and they can persist in the market forever.

4. Rational traders may even join them. Once you know a bubble is being inflated by noise traders and that betting against it is dangerous, the smart play may be to buy alongside them and try to get out first. Rational money does not always oppose the bubble. Sometimes it rides it, which makes the bubble worse. The follow-up literature on rational bubble-riding starts right here.

Why it mattered

• It killed the standard defence of market efficiency. "Arbitrage will fix it" is no longer a valid one-line rebuttal. You now have to explain how much arbitrage capital exists, what horizon it operates on, and what risk it must bear. That is a real conversation instead of a magic spell.
• It is the theoretical ancestor of the limits of arbitrage. Shleifer and Vishny's 1997 paper takes this and adds the killer institutional detail: arbitrageurs manage other people's money, and investors pull that money at exactly the worst moment. Same skeleton, more brutal flesh.
• It gives sentiment a mechanism. If noise trader mood is a priced risk, then measurable proxies for sentiment should predict returns. Lee, Shleifer and Thaler's closed-end fund paper (1991) and the entire investor-sentiment literature (Baker and Wurgler and successors) run on this engine.
• It is the paper you cite when your correct trade is losing money. LTCM's convergence trades were right and still killed the fund. Anyone short dot-com stocks in 1999 was right and got carried out. This model tells you those are not accidents but the predictable operation of a real, priced risk.

The honest limitations

• The model is a toy, deliberately. It uses overlapping generations of two-period-lived investors, one risky asset, one safe asset. The two-period lifespan is what forces the finite horizon that drives everything. That is an assumption, not an observation, and a critic can reasonably ask why real arbitrageurs cannot simply wait.
• The answer to that critique is outside the model. Real arbitrageurs do have finite horizons, but for institutional reasons (margin calls, redemptions, career risk, risk limits) rather than because they die every two periods. Shleifer and Vishny had to write a whole separate paper to supply the reason, which is a tell that this model's central assumption was doing unexplained work.
• Noise traders earning more is a possibility, not a prophecy. The higher-return result holds under specific conditions. Take on too much risk and they get wiped out anyway. The paper shows the survival of the irrational is possible, not guaranteed, and popular summaries routinely overstate this.
• Sentiment remains hard to measure. The theory says noise trader mood is a priced risk factor. Turning that into a number you can trade requires a proxy, and every proxy anyone has proposed is contestable. A beautiful mechanism with a muddy measurement is still a partially unfinished job.

The one-line takeaway

De Long, Shleifer, Summers and Waldmann showed that irrational traders create a risk out of their own unpredictability, which frightens rational arbitrageurs into taking smaller positions, so mispricing can persist indefinitely, and the fools can get paid for the very foolishness that causes it.