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[This article originally appeared on our sister website, IndexUniverse.eu.]

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According to economics textbooks, the more risk you take on, the greater the return you can earn. A moment’s thought will show why this has to be the case. If investors didn’t receive any extra compensation for buying riskier stocks, what would be the incentive to hold them in the first place?

And yet the evidence suggests that precisely the opposite occurs in practice:stocks with a recorded history of low volatility end up doing much better than their riskier counterparts.

In a paper published last year in the Financial Analysts Journal, authors Malcolm Baker, Brendan Bradley and Jeffrey Wurgler looked back at over 40 years of US share data. For each month, they sorted the universe of shares into five groups, according to two measures of risk—volatility and beta—as measured over the previous five years (the two risk concepts are closely related, but volatility records the variability of a stock’s return, while beta measures its sensitivity to the overall market).

In what Wurgler describes as a “spectacular anomaly”, it turned out that the least volatile stocks massively outperformed the riskiest stocks over the four decades under review. The less risk you took on, at least on a backward-looking basis, the more you seemed to earn, in other words.

A dollar invested in the lowest-volatility portfolio in 1968 grew to US$58.55 by 2008 (or US$10.12 after adjusting for inflation). But a dollar put into the highest volatility portfolio at the outset was worth only 58 cents four decades later, or merely 10 cents in real terms, a 90 percent loss of purchasing power.

There’s an active debate about the reasons for such a counter-intuitive result.

Investors’ overconfidence in their ability to select high-performing (and therefore volatile) stocks may be one cause of the anomaly, suggest Baker, Bradley and Wurgler. In other words, active fund managers may indulge in a counter-productive chase for “winners” as they seek to outperform their benchmarks. As the performance of such high-momentum stocks has a tendency to go into reverse, the low-volatility, less glamorous stock market “tortoises” end up beating the “hares” in the long run.

Another reason for the low-volatility anomaly may lie in investors’ choice of benchmark itself, and specifically in their preference for capitalisation-weighted indices, say the FAJ paper’s authors. And it is active managers, rather than the passive funds tracking the same indices, which are primarily to blame, they suggest.

“The typical institutional contract for delegated portfolio management could increase the demand for higher-beta investments,” write Baker, Bradley and Wurgler, suggesting that the herd instinct of mutual fund investors could be amplifying such index effects.

“Mutual fund investors tend to chase returns over time and across funds, possibly because of an extrapolation bias,” they continue. “These forces make fund managers care more about outperforming during bull markets than underperforming during bear markets, thus increasing their demand for high-beta stocks and reducing their required returns.”

However, Felix Goltz, head of applied research at France’s EDHEC-Risk institute, has downplayed the low-volatility anomaly. The widespread use of capitalisation-weighted benchmarks may indeed increase the likelihood of short-term reversals in return from high-momentum stocks, Goltz concedes, but the apparent outperformance of low-volatility stocks may be reduced if you look at it on a different timeframe, for example by conducting risk measurements every two years rather than every month.

And, given that volatility is only one measure of risk (and a rather crude one, since it doesn’t tell us about the likelihood of extreme movements), the positive “skewness” of many volatile stocks’ returns may be missed by those talking of a low volatility effect, says Goltz. In other words, investors may gain from an additional, option-like payoff when owning high-performing stocks like Apple or Google, while this inbuilt “optionality” is not measured by standard risk measures, like those for volatility or beta.

Indeed, it is in strongly one-way markets that the low-volatility strategy is most likely to underperform. In an article to be published in the forthcoming March/April issue of the Journal of Indexes Europe , Xiaowei Kang, director of index research and design at Standard and Poor’s, notes that a low-volatility portfolio lost significant ground against a capitalisation-weighted benchmark index during the 1999 technology bubble, and again in 2003 and 2009 during the momentum-driven recoveries from cyclical bear market lows.

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However, Kang’s figures also show that low-volatility strategies can do particularly well in flat or down years for the overall equity market. Since the turn of the millennium, 2000, 2002, 2008 and 2011 have been years of particularly strong relative performance by such portfolios.

Investors should therefore be prepared for such periods of divergent returns between low-risk funds and capitalisation-weighted benchmarks, argues Kang. “Despite the potential of alternative beta strategies (including low volatility) to deliver better risk-adjusted performance than the market over the long term, investors may need to be prepared for periods of significant underperformance,” he writes in the Journal of Indexes Europe .

There is increasing evidence that investors are taking a long-term view and are prepared to devote money to index-tracking funds embedding such strategies.

Invesco PowerShares’ ETF tracking the S'P 500 low volatility index (NYSE Arca:SPLV) has raised over US$1 billion in assets in its first eight months. The firm recently added two more “low-vol” ETFs to track emerging and developed non-US equities, also based on indices from S'P.

In Europe, ETF issuer Ossiam, a subsidiary of Natixis Global Asset Management, is building its ETF range around non-standard, strategy-focused ETFs, and has now launched three funds that aim to minimise fund volatility, the latest being listed on the London Stock Exchange last week. Between them, Ossiam’s iStoxx Europe Minimum Variance (LSE:EUMV), US Minimum Variance ( USMV ) and FTSE 100 Minimum Variance (LSE:UKMV) ETFs have around €200 million under management, representing 80 percent of the firm’s total assets.

There’s a fundamental difference in construction between minimum variance and low-volatility indices, if not, apparently, in the end-results. A minimum variance portfolio is arrived at by a mathematical optimisation, using historical volatilities and correlations between stocks as the inputs. As pure optimisations can lead to imbalanced portfolios, constraints for individual stock and sector weightings and for a minimum number of holdings are often set as well.

As constraints for the FTSE 100 minimum variance ETF, for example, Ossiam and the index provider set a 4.5 percent maximum stock weighting and a 20 percent maximum sector weighting, with 50 shares as the minimum number of holdings.

Low-volatility portfolios are simpler in make-up, typically ranking stocks by their historical volatilities and then weighting them by the inverse of the volatility figure, with the least volatile stocks receiving the highest weightings.

According to Kang at Standard and Poor’s, who compared the returns of his own firm’s S'P 500 low-volatility index and MSCI’s optimised minimum volatility strategy over a 13-year period, both arrived at a similar reduction in volatility from a standard capitalisation-weighted approach, reducing this risk measure by about 20-30 percent. Although optimised, minimum variance approaches should in theory reduce risk by more than non-optimised strategies, the practical constraints applied to such funds may dampen the reduction, says Kang.

There’s an overlap between low-risk index approaches and other non-capitalisation-weighted strategy indices, for example value-weighted portfolios or the fundamental equity indices popularised by Research Affiliates, Alex Matturri, head of S'P’s index business, told IndexUniverse.eu. All these index methods often end up selecting similar stocks, usually those with higher dividend payouts, which produce a less volatile return stream to end investors, Matturri clarified. There’s increasing interest in replicating such market “factors” via systematic, index-based approaches, added Matturri, whose firm is building up its research efforts in this area.

With 2012 off to a flying start for equity markets—the Stoxx Europe 600 basic resources supersector index is already up 18 percent in January—many investors appear to be banking on the idea that this year will be one for momentum-chasing. However, a growing demand for strategy indices, including those promising low volatility, suggests that a longer-term shift in investors’ portfolio allocations is also taking place.

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