You Can Profit From Reversals Without Anyone Overreacting

By 1990, one of the most reliable-looking findings in finance was the short-horizon reversal: buy last week's losers, short last week's winners, and you make money. It was documented, it was robust, and everyone had the same explanation ready.

The explanation was overreaction. Investors panic and overshoot. They sell too hard on bad news, so the stock falls further than it should and then bounces back. They buy too eagerly on good news, so the stock overshoots and then settles. Contrarian profits, therefore, are the market correcting its own emotional excess. It was a satisfying story, it fit the behavioural finance mood of the era, and it was accepted almost without argument.

Andrew Lo and Craig MacKinlay showed that the story could be completely false and the profits would still be there.

The problem: everyone jumped to the same conclusion

Here is the logical mistake, and it is subtle enough that a generation of researchers walked straight into it.

The claim "stocks overreact" is a statement about an individual stock over time: this stock goes up too much today, so it comes back down tomorrow. In statistical terms, that means each stock's returns are negatively autocorrelated, they reverse against themselves.

The evidence, however, was about a portfolio: a long-short basket of past losers and winners makes money. Everyone assumed that portfolio profit could only come from individual-stock reversal.

Lo and MacKinlay decided to actually do the algebra. They wrote out, precisely, where the expected profit of a contrarian portfolio strategy comes from. And when they decomposed it, they found it had more than one source. Individual-stock reversal was one. But there was another term entirely, and nobody had been paying attention to it.

The key idea via analogy: the crowd that follows a leader

Imagine a school of fish. The big fish at the front turn left. A moment later, the small fish behind them turn left too. Each individual fish is swimming perfectly sensibly, no fish is jerking back and forth erratically, no fish is "overreacting" to anything. Yet if you look at the school, there is a predictable pattern: whatever the big fish did, the small fish will do shortly after.

Now run a contrarian strategy on this school. You buy the fish that are "behind" (the small fish, who have not turned yet, and therefore look like they underperformed) and short the fish that are "ahead." A moment later, the small fish catch up, and you make money. You just profited from reversal without a single fish ever reversing. You profited from the lead-lag relationship between them.

This is what Lo and MacKinlay found in stock data, and the fish analogy is remarkably close to the truth. The technical term for the effect is cross-autocorrelation: the correlation between one stock's return today and a different stock's return tomorrow.

They documented it directly. The returns of large stocks lead those of smaller stocks. When big companies move, small companies tend to follow, with a lag. That is not overreaction. It is information spreading unevenly through the market, arriving in large, closely-watched stocks first and reaching the neglected corners later.

And here is the beautiful part of their evidence, the fact that makes the whole argument bite. Individual stock returns showed negative autocorrelation, consistent with reversal. But weekly portfolio returns were strongly positively autocorrelated. A portfolio of stocks trends, week over week, even though its constituent stocks reverse.

That combination is impossible if the only thing going on is individual stock reversal. If every stock reverses against itself, a basket of them should reverse too. The fact that the basket trends while its members reverse proves there is a second, powerful force at work: the lead-lag links between stocks. And once you measure the size of that force, it turns out to account for a substantial chunk of contrarian profits.

So the honest conclusion is that contrarian profits are a mixture. Some is genuine overreaction. A large part is the mechanical consequence of information flowing from big stocks to small ones with a delay. Making money from a contrarian strategy is not proof that the market is irrational.

Why it mattered

• It stopped a whole field from asserting the conclusion it wanted. The behavioural interpretation of reversal profits was becoming an article of faith. This paper showed that the evidence did not support it, without denying that overreaction exists. It is a model of how to push back on a popular idea: not by arguing about interpretation, but by decomposing the arithmetic and showing there is a second term.
• It gave stat-arb a second engine. If lead-lag relationships between stocks are real and predictable, that is a directly tradeable signal in its own right, separate from reversal. Cross-sectional lead-lag effects, information diffusion from big to small, from suppliers to customers, from one country to another, became a whole research programme and a real family of strategies.
• It sharpened what "market efficiency" tests actually test. A profitable trading rule is not automatically evidence of irrationality. The profit could come from a structural feature of how information propagates, from compensation for providing liquidity, or from a risk premium. Lo and MacKinlay made everyone more careful about that inference, permanently.
• It anticipated the microstructure explanation. Some of the lead-lag effect comes from the plumbing: small stocks trade less often, so their prices are stale, and stale prices look like they lag. Distinguishing genuine slow information diffusion from mere non-synchronous trading became an important sub-literature that this paper set up.

The honest limitations

• It does not prove overreaction is absent. The paper decomposes the profit and shows that lead-lag effects contribute substantially. It does not, and does not claim to, show that overreaction contributes nothing. Both are present. The paper's contribution is to demolish the assumption that only one exists.
• Lead-lag may be partly an illusion of measurement. If small stocks simply trade less frequently, their recorded closing price is older, and they will mechanically appear to follow larger stocks even if no real information delay exists. Untangling the real economic effect from this artefact is genuinely hard.
• The tradeable version is fragile. Weekly reversal and lead-lag strategies operate on small edges, in small stocks, at high turnover. Transaction costs and short-borrow constraints eat much of the paper profit, and the effects have weakened considerably as markets have got faster and more electronic.
• The lead-lag structure is not stable. Which stocks lead and which lag changes over time and across regimes. A strategy fitted on one decade's lead-lag map may be trading yesterday's map.

The one-line takeaway

Lo and MacKinlay showed that the profits from buying losers and shorting winners come substantially from the fact that big stocks lead small ones, not from investors overreacting, which means a working contrarian strategy is not proof that the market is irrational, and which opened up lead-lag effects as a signal in their own right.