The Shleifer Model - How Noise Traders Survive in Markets
For decades, traditional finance people had a simple answer to the noise trader problem. Milton Friedman said it. Eugene Fama said it. Fischer Black said it. The answer was: irrational traders will lose their money to smart traders and disappear.
Simple. Clean. And wrong.
In 1990, a paper by DeLong, Shleifer, Summers, and Waldmann showed that noise traders can not only survive in markets but actually make more money than the rational traders. This chapter from Burton and Shah walks through that model. And it is one of the most important results in behavioral finance.
The Setup: Two Assets That Are Basically the Same
Here’s the thing about the Shleifer model. It starts with a very clever trick.
There are two assets in the model. Both pay the exact same dividend every period. No difference in cash flows. No difference in risk from fundamentals. They are basically the same investment.
But they are structured differently:
Asset S (the safe one) - you can convert it into a consumption good for free, any time. You want to eat instead of invest? Just swap it. And you can swap back. Because of this, the price of Asset S is always 1. Always. It is like cash.
Asset U (the unsafe one) - you cannot just convert it. You have to sell it on the market first, then buy what you want. And here is the important part: there is a fixed supply of Asset U. You can’t just create more.
So both assets pay the same dividend. But one trades freely at a fixed price and the other has to go through the market. This difference is what makes the whole model work.
Think of it like two identical apartments in the same building. One you can sell instantly at a guaranteed price. The other you have to list on the market and hope for buyers. Same apartment. But the market price of the second one can be higher or lower depending on who is buying.
Two Types of Traders
The model has two types of people. That’s it.
Rational traders (arbitrageurs) - they know the true probability distribution of future prices. They understand what Asset U is really worth. They also know about the noise traders and account for their behavior.
Noise traders - they also want to maximize their returns. They are not stupid in some cartoon way. But their expectations are biased. They are systematically too optimistic or too pessimistic about Asset U. They think they know the future distribution of prices, but their estimate of the average is off.
Both types are trying to do the best they can. The difference is that noise traders have wrong beliefs, and those wrong beliefs are not random. They lean in one direction consistently.
One more detail: people in this model live for only two periods. Young people invest. Old people cash out and consume. This is called an “overlapping generations” model. And it matters because it means nobody can wait around forever for prices to correct. You have to sell when you get old. No choice.
Why Arbitrageurs Can’t Just Fix Everything
This is where it gets interesting.
The old argument from Friedman and others was simple. If noise traders push prices away from the correct value, rational traders will take the opposite position and profit when prices snap back. This forces prices back to where they should be. Problem solved.
But the Shleifer model says: not so fast.
What if noise traders push prices even further from the correct value? What if you bet against them and they keep going? You are sitting there with a position that is losing money, and you have to sell at the end of your period because you are getting old. You cannot wait.
This is the limits to arbitrage argument. And it is central to the whole debate between behavioral finance and traditional efficient markets.
Rational traders in this model face risk. Not fundamental risk, because both assets pay the same sure dividend. The risk comes entirely from noise traders. Their unpredictable behavior makes Asset U’s price bounce around. And if you are a rational trader betting that prices will return to normal, you might lose money before that happens.
So rational traders cannot take infinitely large positions. They are scared. Rightfully so. The noise traders create a risk that limits how much the smart money can push back.
The Results
The Shleifer model gives two big conclusions.
Conclusion 1: Two identical assets can have different prices. And the price gap can get wider over time. If noise traders are too optimistic about Asset U, they bid the price up above 1. If they are pessimistic, price goes below 1. And because arbitrageurs cannot fully correct this, the mispricing persists.
This is huge. It means markets can be wrong. Not just for a moment, but in a sustained way. Two things that are fundamentally the same can trade at different prices.
Remember Royal Dutch Shell from the previous chapter? Two shares of the same company, listed on different exchanges, trading at different prices for years. The Shleifer model gives a theoretical explanation for exactly that kind of thing.
Conclusion 2: Noise traders can earn more than rational traders. Under certain conditions, when noise traders are overly optimistic, they end up taking on more risk than arbitrageurs. And sometimes that extra risk pays off. They hold more of the risky asset, and when things go their way, they make more money.
This is the part that traditional finance people really did not like. Because if noise traders can profit, they will not disappear. They will attract followers. New people will see their returns and say “I want to do what they are doing.” And the ranks of noise traders will grow.
Why This Model Changed the Debate
Before 1990, the argument against behavioral finance was basically: sure, some people trade irrationally, but they will lose money and leave the market. Natural selection in finance.
The Shleifer model broke that argument. It showed a logically consistent world where:
- Irrational traders survive
- Irrational traders can outperform rational ones
- Prices stay wrong for extended periods
- Smart money cannot fix everything because of risk
And the model does this with the simplest possible setup. Two identical assets. Two types of traders. No complicated fundamental risk. All the mess comes from noise traders and the limits on what arbitrageurs can do about them.
Now, the model does not explain everything. It does not tell us why noise traders are systematically biased. It just assumes they are. It does not explain what determines the proportion of noise traders versus rational traders in the market. It just shows that the proportion matters for the results.
But as a proof of concept, it was powerful. It said to the efficient market crowd: your assumption that irrational traders will be wiped out is not a logical certainty. Here is a model where they survive and thrive.
The Practical Takeaway
If you invest in real markets, here is what this means for you.
Markets can be wrong. Not just for five minutes. For months or years. Two similar investments can trade at very different prices, and there is no guarantee that the gap will close on your timeline.
And the smart money cannot always save you. Hedge funds and professional traders face the same limits to arbitrage that the Shleifer model describes. They have limited capital, limited time, and the market can stay irrational longer than they can stay solvent. You have probably heard that quote attributed to Keynes. The Shleifer model basically proved it mathematically.
So next time someone tells you that market prices are always right because the smart money would fix any mistakes, remember this model. The smart money is scared too. And sometimes the irrational traders win.
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