Anomalies Live on the Short Side

Here is a question that ought to have been asked much earlier. A long-short anomaly strategy has two legs: it buys the good stocks and sells the bad ones. Which leg makes the money?

Almost nobody had bothered to check systematically. Robert Stambaugh, Jianfeng Yu and Yu Yuan did, across a broad set of well-known anomalies, and the answer is lopsided enough to change how you think about the entire field: the profit is overwhelmingly on the short side. The stocks you are supposed to buy are barely mispriced at all. It is the stocks you are supposed to sell that are wrong.

And they showed when that happens: after periods when investors have been euphoric.

The problem: mispricing has an asymmetry built into it

The paper's logic starts from a structural fact about markets that is easy to overlook.

Suppose you think a stock is too cheap. What do you do? You buy it. Anyone can buy a stock. It requires only money.

Now suppose you think a stock is too expensive. To correct that, you must sell it short. And shorting is hard:

• You must find shares to borrow, which for small or hot stocks may be impossible or ruinously expensive.
• Many institutions, including most mutual funds and pension funds, are simply forbidden from shorting.
• The losses are theoretically unlimited, and you can be forced to close the position at the worst moment.
• If the stock keeps rising, you face margin calls and possible ruin, even if you are eventually right.

So correcting an underpricing is easy and correcting an overpricing is hard. The asymmetry is not psychological, it is mechanical. It follows that overpricing should be more common and more persistent than underpricing, because the forces that would erase it are hobbled.

This predicts exactly what the authors find: anomalies should have most of their profit in the short leg, because that is where the mispricing actually is.

The key idea via analogy: optimism is easy to express, pessimism is not

Now add sentiment.

Investor sentiment, the broad wave of optimism and pessimism sloshing across the market, is measurable. When sentiment is high, ordinary investors are excited, speculative stocks are hot, and money is flowing into whatever is most exciting.

Where does all that enthusiasm go? It has to go somewhere. And enthusiasm is easy to express: just buy. So when sentiment is high, the most speculative, most lottery-like, most junk-quality stocks get bid up. Precisely the stocks that every anomaly says you should be short.

Meanwhile, the correction mechanism is broken. The sophisticated investors who can see that these stocks are overpriced are precisely the ones who face the short-selling constraints described above. They cannot lean against the wave with enough force.

The result is a prediction the authors test and confirm:

• Every anomaly is stronger following periods of high sentiment. The long-short profits are larger after the crowd has been euphoric.
• This is driven entirely by the short leg. After high sentiment, the stocks you are supposed to short do especially badly, which is where the extra profit comes from.
• Sentiment has essentially no relationship to the returns on the long leg. The stocks you are supposed to buy behave much the same regardless of the mood.

That is a remarkably clean set of results, and it holds across a broad set of anomalies rather than one cherry-picked example.

Why it mattered

• It changed what an anomaly means. After this paper, "anomaly X earns 8% a year" is an incomplete statement. The right question is: how much of that 8% requires shorting stocks that are hard and expensive to short? For many anomalies, most of it does, which means the tradeable long-only version is far less impressive.
• It explains why anomalies survive. If the profit lives in the short leg, and the short leg is exactly where arbitrage is most constrained, then the mispricing can persist indefinitely. The anomaly is protected by the very difficulty of correcting it.
• It made sentiment a conditioning variable. Anomaly returns are not constant. They are predictably stronger at some times than others, and the times are identifiable in advance. That is genuinely useful, and it opened a large literature on timing factor exposures.
• It reframes overpricing as the natural state. Because optimism can be expressed freely and pessimism cannot, markets should be biased toward overvaluation, particularly in the most speculative names. That is a structural insight, not a behavioural one, and it is hard to argue with.

The honest limitations

• Sentiment is hard to measure. The paper relies on a sentiment index built from market-based proxies, and reasonable people dispute whether such indices capture mood or merely capture past returns. If the sentiment measure is partly mechanical, some of the result may be too.
• The short leg is expensive precisely because it is profitable. The stocks with the biggest short-side profits are the ones with the highest borrow costs and the greatest risk of a squeeze. A large part of the paper's short-leg alpha is likely eaten by the real cost of shorting, which is exactly the point but also a limit on exploiting it.
• It requires timing. Acting on the result means dialling anomaly exposure up and down with sentiment, and timing anything is notoriously unreliable out of sample.
• The evidence is a small number of sentiment cycles. Sentiment moves slowly, so despite decades of data there are only a handful of genuine high-sentiment episodes. The statistical evidence is thinner than the number of monthly observations suggests.

The one-line takeaway

Because anyone can buy a stock but shorting one is hard, overpricing persists while underpricing gets corrected, so almost all anomaly profits come from the stocks you are supposed to sell, and they come especially after periods when investors have been euphoric.