Radar Perene / Archive / science

Risk premium and factors: empirical fact, not a buy tip

◦ Index methodology v2.2 (working papers with DOI). See the methodology.

Science

There is a curious journey certain words make: they are born in the table of an academic journal, surrounded by caveats, and reappear twenty years later in a sales brochure, surrounded by promises. "Momentum" and "value" made the full trip. In the article of origin they were anomalies to be explained — empirical discomforts the theory could not accommodate well. In the brochure of arrival they became product attributes. Between departure and destination they lost their luggage: the caveats stayed at the journal.

A risk premium is the return difference a class of assets has delivered, on average and over long horizons, above a lower-risk alternative — the historical compensation for carrying uncertainty. Factors, such as value and momentum, are documented patterns of return differences between groups of assets: empirical regularities identified by the academic literature, with magnitudes that vary, periods in which they vanish, and explanations still in dispute.

The whole definition fits in that register: observed fact, not guaranteed property. It is the part the journey from journal to brochure tends to misplace.

What the literature actually documented

The vocabulary has precise birth certificates. In 1992 and 1993, Eugene Fama and Kenneth French showed that two groups of stocks — those of smaller companies, and those trading cheap relative to their book value — exhibited average returns above what market risk alone explained; the "value factor" came from there. In 1993, Narasimhan Jegadeesh and Sheridan Titman documented that stocks with good recent performance tended to keep doing better for a few months — "momentum". In 1997, Mark Carhart assembled the pieces into a four-factor model that became the standard ruler for evaluating funds.

It is worth recording what those articles are: careful accounting of the past, with hypotheses about the why. And what they are not: none of them promises the pattern will persist, none prescribes a portfolio to any reader, and all of them live alongside rival explanations — the extra return may be compensation for a real risk the usual metric fails to capture, may be a bias of collective behavior, and may be, in part, statistical artifact.

The zoo and the shrinkage

The decade after the factors' consecration produced a new problem: success. With hundreds of researchers combing the same databases for the next publishable pattern, the inventory of discovered "factors" swelled until the discipline itself gave it a mocking nickname — the factor zoo. Review papers counted the species in the hundreds and concluded that a good share does not survive stricter statistical criteria: they are the multiple-testing mirages this trail has already visited in p-hacking.

And even the factors with pedigree face a documented fate: shrinking after publication. The literature measured the performance of dozens of patterns before and after their debut articles and recorded a systematic decline — partly because publication attracts capital that competes for the same pattern, partly because the original result carried a component of sample luck. The premium that survives tends to be smaller, more intermittent and more uncomfortable to hold than the historical table suggested.

That discomfort, in fact, is the most serious defense of the premia that remain: a pattern that crosses years of poor performance without everyone abandoning it probably compensates exactly that capacity to endure. The literature calls it a premium; daily life calls it patience put to the test.

The contrast this article can offer

The house publishing this trail reads that literature from the only place it can be read with neutrality: that of someone with no product tied to it. Radar Perene manages no fund, sells no portfolio and charges no performance fee — its own output is studies published in an open repository with DOIs, and none of them has a factor to defend. When commercial material presents "momentum exposure" as a selling point, there is a structural conflict the reader does well to name: the one describing the pattern is the one who profits from adherence to the pattern.

The distinction requires no bad faith from anyone. It only requires remembering where each sentence comes from: the journal's sentence says "this pattern existed, on average, in this sample, with these caveats"; the brochure's sentence says "this pattern is an attribute of our product". The two use the same word. They do not say the same thing.

Frequently asked questions

Is a risk premium a guaranteed amount?

No. It is a long-run historical average, with entire decades in which it failed to materialize. The word "premium" describes the measured past, not a contract about the future.

Are an investment factor and a management style the same thing?

The factor is the documented statistical regularity; the style is the commercial decision to pursue it. The literature supports the first concept; the second inherits all the costs, frictions and implementation risks the academic table never pays.

Why do factors shrink after publication?

The two main explanations: new capital starts competing for the same pattern, compressing it; and part of the original result was sample luck, which does not repeat. The studies that measured the phenomenon found shrinkage on average — not universal extinction.

Is there a "Brazilian" factor?

The local literature has tested the classic factors on Brazilian data, with mixed results and samples shorter than the American ones — which widens the uncertainty of any conclusion. Short samples are a subject with its own chapter on this trail.

Every historical average arrives with a question that is rarely asked out loud: how precisely was that number measured? The next step on the trail is about the frame missing from almost every headline: Confidence interval: what a number says — and what it withholds →

House readings: today's note, in the Daily · the precedents, in the Atlas.

Confronting a piece of commercial material with the literature it invokes is workbench material — the kind of exercise the house does on request.