Is It the Company, or the Company It Keeps?

This is a subtle paper about a distinction that sounds like philosophy and turns out to be worth a great deal of money.

Fama and French had established that value stocks (cheap, high book-to-market companies) earn higher returns. Their explanation was that value stocks all move together, sharing exposure to a common risk factor, and the premium is compensation for bearing that shared risk.

Kent Daniel and Sheridan Titman asked a devastating question: how do you know it is the shared movement that pays, and not simply the fact of being a cheap company?

The problem: two theories that usually make the same prediction

Lay the two stories side by side.

The covariance story (Fama and French). There exists a risk factor, value. Some stocks load heavily on it, meaning they move with it. Those stocks are risky in a way investors care about, so they earn a premium. The premium is paid for the co-movement, the loading, the beta on the factor. In this world, a stock that happens to be cheap but does not move with other cheap stocks should earn no premium at all, because it carries none of the risk.

The characteristic story (Daniel and Titman). There is no risk factor doing any work. Cheap stocks earn more simply because they are cheap, most likely because the market has mispriced them. The co-movement is real but incidental: value stocks move together because they tend to be in similar industries and situations, not because a priced risk factor is driving them. In this world, any cheap stock earns the premium, whether or not it moves with the pack.

In ordinary data these two theories are almost impossible to tell apart, because cheap stocks generally do move together. The characteristic and the loading come bundled. To distinguish them, you need to break the bundle.

The key idea via analogy: find the cheap stock that doesn't run with the cheap crowd

Here is the elegant test.

Imagine a school where the tall students happen to be good at basketball. Is it height that makes you good, or is it belonging to the tall clique, who practise together?

To find out, you need to locate short students who hang out with the tall clique, and tall students who do not. Then see who can actually play.

Daniel and Titman did the financial equivalent. They sorted stocks twice, independently:

1. By characteristic: is this company actually cheap (high book-to-market)?
2. By factor loading: does this stock actually move together with the other value stocks?

That gives four groups, and the two interesting ones are the mismatches: cheap companies with low value-factor loadings (cheap, but they do not run with the value crowd), and expensive companies with high value-factor loadings (not cheap, but they move like value stocks anyway).

Now the theories make opposite predictions, and the data can adjudicate.

• Fama and French predict that returns follow the loading. The cheap-but-uncorrelated stocks should earn nothing extra, and the expensive-but-correlated stocks should earn the premium.
• Daniel and Titman predict returns follow the characteristic. Cheap is cheap, and it pays regardless of how it moves.

The characteristics won. In their tests, the return premium tracked whether the company was actually cheap and actually small, not whether it co-moved with the factor. A cheap stock that did not load on the value factor still earned the value premium. This is, on its face, a serious problem for the risk-based interpretation of the three-factor model, because it means the thing being rewarded is not the thing that risk theory says should be rewarded.

Why it mattered

• It struck at the heart of the risk-based story. If characteristics pay and loadings do not, then value is not a risk premium. It is a mispricing, and the three-factor model, whatever its practical usefulness, is not the risk model it claims to be.
• It sharpened a distinction the field had blurred. "Value factor" is used to mean two different things: a characteristic of a company, and a source of common movement. Daniel and Titman forced everyone to say which one they meant.
• It has direct portfolio consequences. If characteristics are what pay, you should build portfolios by directly targeting the characteristic (own cheap companies), not by targeting factor loadings. Those two approaches produce genuinely different portfolios, and the argument over which is right is live in practice, not just in journals.
• It is a model of good empirical design. The double-sort that breaks the natural bundling of characteristic and loading is a genuinely clever piece of test construction, and it has been imitated widely.

The honest limitations

• Fama and French fought back, hard. They responded that the result was specific to the sample period and to the way the double-sort was constructed, and that with a longer sample and different portfolio construction, the loadings do the work after all. This exchange has never been fully resolved, and both camps still have adherents.
• The mismatched portfolios are strange. By construction, "cheap stocks that do not move with other cheap stocks" is an unusual, small and possibly unrepresentative group. Sorting stocks into a corner and then measuring their returns invites the worry that you are measuring something idiosyncratic about that corner.
• Estimating loadings is noisy. A stock's factor loading is a statistical estimate with substantial error. If you sort on a noisy variable, you attenuate its apparent effect, which mechanically biases the test in favour of the characteristic. This is a real and serious technical objection.
• It does not tell you why the characteristic pays. Rejecting the risk story leaves you with mispricing, but the paper does not explain what mistake investors are making or why it persists.

The one-line takeaway

Daniel and Titman found the cheap stocks that do not move with other cheap stocks, and discovered they earn the value premium anyway, which suggests you get paid for being a cheap company, not for bearing a common value risk, and that is an argument for mispricing rather than for risk.