The significant outperformance of apparently ‘low-risk’ stocks over time is a well-known
‘anomaly’ in investment theory. Martin Steward asks, if it is an anomaly, won’t it eventually be corrected?

The capital asset pricing model (CAPM) predicts that investors will be paid the time value of their money, plus an additional return for the extra risk of an investment, where risk is defined as beta. Unfortunately, this doesn’t describe what happens in the real world. As table 1 shows, over the long term low-beta portfolios of both US and global stocks not only deliver lower volatility, as expected - but also significantly higher returns.

“We would describe this as one of the most important and pervasive anomalies in investment,” says Kent Hargis, director of quantitative equity research and low-volatility equities portfolio manager at AllianceBernstein. He observes that it holds as far back as data exists in bonds, commodities and currencies, as well as equities (he describes his firm’s new Short Duration High Yield Bond fund as an attempt to exploit it). “It is unique in its pervasiveness across time, asset classes and countries.”

Note that Hargis calls this an ‘anomaly’ - a genuine break from the predictions of the CAPM induced by biases in markets, rather than a premium paid for some kind of risk that low-beta investments present above that of high-beta investments. But he adds: “Regardless of the reasons for this, it is something that investors can exploit.”

But understanding the source of this mysterious excess return might be important. Bill Smith, UK CEO at Lazard Asset Management, observes that pension funds are taking an interest in any way equities can be made more capital-efficient in a world of multiple regulatory onslaughts on already shrinking risk budgets. “But certainly the question that we are asked is, ‘Why won’t this be arbitraged away?’”

At Danish pension provider PKA, the equity portfolio has been re-engineered to exploit 17 different sources of return - from ‘traditional betas’ like the small-cap risk premium to ‘alternative betas’ like the dividend risk premium and momentum factor. It calls some of these 17 return sources ‘risk premia’, and others ‘effects’ - and PKA puts the low-beta anomaly in the latter group.

“Is this a risk premium or an anomaly?” asks equity portfolio manager Anders Blomgreen Petersen. “Can it be arbitraged away? These are questions we have also asked ourselves, and I wouldn’t say that we have any definitive answers.”

Calling something an ‘effect’ rather than a ‘risk premium’ acknowledges that there is no reason to assume that it will persist - because we cannot identify the risk being compensated by the excess return. If we regard it as an ‘anomaly’ caused by behavioural biases in markets, structural changes in behaviour could erode it away - most obviously, of course, a wholesale move into low-beta investing.

Of course, there is one relevant ‘effect’ that is not a risk premium but which certainly will persist because it is simple mathematics - the effect of compounding. Consider two stocks with an average arithmetic return of zero: the more volatile one goes down 50% and then up 50%, generating a compound return of -25% over the two periods; the other that goes down 10% and then up 10% compounds a loss of just -1%.

A few practitioners consider this sufficient to explain low-beta’s excess returns, but they are in a minority. Paul Bouchey, director of research at Eaton Vance affiliate Parametric Portfolio Associates, says that the volatility drag on compound returns is “not behavioural and not possible to arbitraged away”, and explains “the vast majority” of the low-beta effect.

But it doesn’t explain all of it. He notes that the relationship between volatility and compound returns is linear and “dramatically downward-sloping”, but that the relationship between volatility and arithmetic returns is “basically flat”. That doesn’t make sense under the CAPM model, either, which would assume that the line would be upward-sloping, as higher-volatility stocks generate higher arithmetic returns (with the volatility-drag of compounding stripped out).

“Why is it flat?” he asks. “That is an interesting question which does take you into behavioural theory.”

So, even after taking account of the compounding effect, we still need to identify a way in which low-beta stocks are more risky than high-beta stocks to be persuaded that the excess returns - like those of equities-over-bonds or small-over-large-caps - will be persistent.

“There could be risk - just not risk in terms of volatility - which leads to structural excess demand for high-volatility stocks,” suggests Dimitris Melas, global head of new product research at MSCI, which constructs a minimum variance index.

There is one very clear sense in which this is the case. Much of the investment industry is benchmarked against cap-weighted indices, and low-beta stocks exhibit lower correlation with those benchmarks.

“The second you step away from the cap-weighted index you pick up huge tracking error,” says Bouchey. “That could be a barrier to an investor who’s concerned about their relative performance.”

Your low-beta portfolio may have smashed the benchmark with its long-run, risk-adjusted compound return from 2003 to 2009, but the only calendar year in which it outperformed was 2008. Your risk is getting the boot sometime in 2006 - and you mitigate it by holding higher-beta stocks.

You could borrow money to generate more low-beta exposure, of course. That would reduce your tracking error and the risk of short-term underperfomance. But you might not be able to borrow enough money at a cheap enough rate, and even if you could, you may not want to: buy a beta 2.0 stock and the worst that can happen is a 100% loss; gear-up a beta 0.5 stock four times and you assume a liability much greater than 100% of your capital. In this cap-weighted benchmark context, high-beta stocks look much less risky than low-beta.

But this is, arguably, a risk artificially created by a behavioural bias - equating risk with tracking error - that could be ‘corrected’. And the behavioural aspect feels stronger when we consider that this phenomenon is at least as much about wanting high-beta stocks as rejecting low-beta stocks.

There is a ‘rational’ inclination behind this. As Alexei Jourovski, head of equity at Unigestion observes, plenty of finance professionals get paid bonuses for high performance while being cushioned against the downside by fixed management fees: “In that context, low-volatility stocks would seem higher-risk in terms of the probability of delivering that bonus.” David Blitz, head of quantitative equity research at Robeco, points out that managers recognise that new money flows in following outperformance in up-markets, but outperformance does little to stop outflows in down-markets.

An attempt to identify an even more rational and systematic source of risk has been offered in a recent white paper from GMO’s co-head of quantitative equities, Sam Wilderman, and portfolio manager David Cowan, which argues that this is “not an anomaly at all”. They emphasise the idea that high-beta stocks provide “leverage with protection” - which relates back to our observations about both compound returns and high-beta stocks appealing to investors with leverage aversion. Theoretically, the high-beta stock offers convexity, relative to its reference market: in trending markets it will generate higher returns than its beta suggests on the way up, and smaller losses on the way down.

“The form of leverage offered by high-beta is different in an important way from explicit borrowing,” the authors argue. “Investors should prefer this kind of leverage and, in an efficiently priced market, they will accept a lower return for it.”

High-beta’s convex payoff looks like what you would get from owning the market, plus a call on the market, and by simulating a covered call programme on a high-beta portfolio and showing that this transforms its convex payoff into a more linear one, Wilderman and Cowan claim to demonstrate that “the pricing of high beta is consistent with the asymmetric upside payoff that portfolio offers”. In other words, all the excess returns of low-beta portfolios can be explained as the risk premium that the investor is paid to forego the convexity of high-beta stocks.

However, this is controversial. Most practitioners share Blitz’s scepticism when he says that “you need a magnifying glass” to see the convex slopes in GMO’s charts: “I have a hard time reconciling the apparently tiny convexity in the data with the huge premium paid for low-volatility stocks.” He also draws attention to a flaw in assuming that options pricing is rational and can tell us something about the rationality of high-beta stock pricing. “The option anomaly is merely proof that the low-beta anomaly exists within different markets,” he observes. “It is not an explanation.”

Indeed, what the data suggests is that buyers and holders of high-beta stocks have been paying for a call that hasn’t paid out for 70 years. That does not seem rational. Moreover, while you are paid a premium for holding equities rather than bonds because your subordination introduces greater risk of capital loss, and you are paid for holding undervalued stocks because of the risk that cash flows won’t be realised, there appears to be no systematic risk attached to holding low-beta stocks, except in the event of huge market momentum (of a magnitude that is exceptionally rare and short-lived) or single-stock momentum (less rare, but easily diversified away).

“There might be an unknown risk out there, and whoever discovers it will win a Nobel Prize,” says Kunal Ghosh, portfolio manager and head of the systematic team at Allianz Global Investors Capital. “But, in our analysis, since the 1970s there has only been one short period when that convexity has paid off. The option embedded in high-beta stocks is horribly overpriced.”

If you buy it, you have to make a big call - on either market or single-company momentum. “Our argument is that investors aren’t chasing beta or volatility so much as the third moment, the skew, or lottery-like payoff,” Ghosh explains. “Interestingly, low-volatility stocks that have higher positive skew end up delivering a lower payoff, which demonstrates that not all low-volatility stocks are made equal and that the anomaly has more to do with investors chasing skew.”

This draws us back again to the cap-weighted benchmark - Ghosh suggests that the largest stocks have, by definition, exhibited high positive skew at some point in their lives - but it all begins to feel less like a ‘rational’ response to the way markets work and more like a deep-behavioural explanation as to why markets and the industry work that way in the first place. If you are out on the savannah hunting for protein, will you kill three small, abundant and harmless animals every single day - or attempt to bag the rarer, more dangerous big beast that will feed you for a week? Probably the latter, especially as eventual success will make you look like a hero next to your more cautious co-hunters - even if, for five days in a row, you have had to abandon the big game hunt late in the day and settle for just one small kill next to your colleague’s three.

The evidence seems significantly weighted to the behavioural ‘anomaly’ side, rather than the systematic ‘risk’ side. And where there is a clear premium being paid for risk, that risk has emerged due to peculiarities of industry and market practice with their roots in behavioural biases. So why shouldn’t we expect this ‘anomaly’ to be corrected in the future?

The fact that it has persisted for so long, despite being so well-documented (Wells Fargo launched a strategy called Stagecoach to exploit it as far back as 1972), might be why some practitioners fall back on essentialist notions about ‘human nature’. That would be a poor foundation for an investment strategy. After all, very few of us still waste our energy hunting for game on the savannah. More to the point, most of the practitioners in low-beta portfolios have developed quantitative strategies to strip human biases out of the investment process. If it can be done by some market participants, why wouldn’t it be done by an increasing number?

A better argument for the persistence of the effect is that no one invests in a vacuum. “There is no reason why we should expect the relationship between risk and return to be linear,” as Ciprian Marin, a portfolio manager at Lazard Asset Management, puts it. “Investors will always come to market with different appetites for and definitions of risk. Those are more than just behavioural anomalies because they are real constraints.”

While it is arguably anomalous that such a large part of the market is fixated on cap-weighted benchmarks, the anomaly is that they all seem to think that they share the same appetite for risk in terms of time horizon, momentum, turnover costs and liquidity. Take the cap-weighted index away, and those investors wouldn’t gravitate to the same efficient portfolio - because ‘efficient’ would mean different things to every one of them.

“Our view is that this is not purely a risk premium, but something that is at least partly caused by behavioural effects in the market,” says Petersen at PKA. “But maybe the way markets work is systematic? And what’s the worse that can happen? If the effect goes away, you get the same risk-adjusted return from your low-risk as from your high-risk portfolio. Maybe you used your risk budget inefficiently, but you haven’t made a loss in risk-adjusted terms.”

It just happens that the major bias in markets today - towards the cap-weighted portfolio - pays a particularly high premium to holders of low-beta stocks. If that bias diminishes, the premium may decline; but as long as there is a market, it seems likely that this mysterious excess return will persist.