Why Nobody Fixes the Low-Volatility Anomaly

The low-volatility anomaly is old news by now: high-beta, high-volatility stocks have long underperformed their calm, boring counterparts on a risk-adjusted basis, which is the reverse of what every textbook promises.

The obvious question is not whether it is true. It is why on earth it survives. Anomalies are supposed to be destroyed by professional investors, who are numerous, sophisticated and highly motivated. There are trillions of dollars managed by people whose entire job is to find exactly this sort of thing.

Malcolm Baker, Brendan Bradley and Jeffrey Wurgler gave the best answer anyone has: the professionals are not going to fix it, because the way they are paid and judged makes fixing it irrational for them.

The problem: an anomaly that money managers cannot trade

Start with the standard argument. If low-volatility stocks offer better risk-adjusted returns, an institutional investor should overweight them heavily. Everybody piles in, the prices adjust, the anomaly dies. That is how markets are supposed to work.

Now look at how an institutional investor is actually evaluated.

They are not judged on absolute returns. They are not judged on risk-adjusted returns in the sense a textbook would use. They are judged relative to a benchmark, typically a market index. Their performance metric is the return they earn above the index, and their risk metric is tracking error: how far their portfolio wanders from the index.

That single fact changes everything.

The key idea via analogy: the sailor who is graded on staying near the fleet

Imagine a fleet of ships crossing an ocean, and each captain is graded not on how fast they get there but on how closely they stay to the fleet's position. Wander too far from the pack, even in a better direction, and you get fired for recklessness.

Now suppose one captain notices a faster current, a few miles off the fleet's course. Should they take it?

If they do, and it works, they arrive slightly early and are mildly praised. If they do, and it takes a few years to pay off, they spend that time visibly far from the fleet, which is exactly what their evaluators have defined as risk. They will very likely be relieved of command before the current pays off.

So the rational choice for the captain is to stay with the fleet, even though they can see a better route.

Institutional investors are in exactly this position, and it has two specific consequences that the paper spells out.

One: they will not buy low-beta stocks, even though they should. A portfolio of calm, low-beta stocks has a huge tracking error against the market index. In a rip-roaring bull market it will lag badly, and the manager will spend that period explaining themselves to clients who are watching the index outperform. Even if the low-beta portfolio has a better long-run risk-adjusted return, the manager who owns it is taking on enormous career risk. Almost nobody will do it.

Two: it is worse than mere neglect, because the benchmark actively pushes them the other way. A manager who wants to beat the index has an easy lever: hold high-beta stocks. In a rising market, high-beta stocks outperform mechanically, and the manager looks like a genius without having to be one. So there is a standing incentive to lean into exactly the overpriced high-beta stocks that ought to be sold.

Put these together and the picture is grim for market efficiency. The class of investors who could correct the anomaly, the large, sophisticated, well-capitalised institutions, are the very class whose incentives forbid them from doing so, and in fact push them to make it worse. The benchmark is not a neutral measuring stick. It is a limit to arbitrage.

Why it mattered

• It explained persistence, which is the hard part. Documenting an anomaly is easy. Explaining why it has not been arbitraged away for decades is much harder, and this paper's answer is both simple and hard to argue with.
• It indicted a universal industry practice. Benchmarking is everywhere and is generally regarded as prudent, sensible governance. The paper argues it has a large, unintended cost: it institutionalises a mispricing.
• It legitimised low-volatility products. The rise of minimum-volatility and defensive equity funds owes a lot to this argument, which gave allocators a story for why the free lunch had not already been eaten.
• It generalises well beyond volatility. Any mispricing whose correction requires a manager to look very different from the index for a long time is protected by the same mechanism. This is a general theory of which anomalies survive, and it predicts that the durable ones will be those that are most painful to track-error.

The honest limitations

• It does not explain everyone. Plenty of investors, hedge funds, family offices, endowments with long horizons, are not benchmark-constrained in this way. Why has their money not corrected the anomaly? The paper's answer, that such capital is limited relative to the size of the market and often itself leverage-constrained, is reasonable but not airtight.
• It complements rather than replaces the leverage story. Frazzini and Pedersen explain the same anomaly with borrowing constraints. Both mechanisms are plausible and probably both operate, which means neither is cleanly identified.
• Low volatility can get expensive. Ironically, the popularity of low-volatility investing since this paper means those stocks have sometimes traded at high valuations, which is exactly the condition under which the premium should disappear. The cure erodes itself.
• The prediction has a sting. If the anomaly persists because benchmarked money cannot touch it, then the arrival of large benchmarked low-volatility funds should destroy it. The evidence on whether that has happened is mixed and still being argued.

The one-line takeaway

Boring stocks beat exciting ones, and the anomaly survives because professional investors are graded on how closely they hug a benchmark, which makes owning calm stocks a career risk and owning high-beta stocks a cheap way to look clever, so the people best placed to fix the mispricing are paid to sustain it.