Low-beta and low-volatility securities can produce superior risk-adjusted returns. Thus, portfolios of calibrated low- versus high-vol stock positions have historically generated significant alpha. Other asset classes display similar ‘low risk effects’. Their plausible cause is many investors’ limited access to leverage and willingness to pay a premium for securities with greater exposure to market performance. Some investors may also pay a premium for lottery-like payoffs with large upside potential. For leveraged portfolio managers this creates relative value opportunities in form of ‘betting against market correlation’ or ‘betting against volatility’.

Asness, Clifford, Andrea Fazzini, Niels Joachim Gormsen and Lasse Heje Pedersen (2017), “Betting Against Correlation: Testing Theories of the Low-Risk Effect”.
and some quotes from
Blitz, David and Pim van Vliet (2007), “The Volatility Effect: Lower Risk without Lower Return”, Journal of Portfolio Management, pp. 102-113, Fall 2007.
Martinelli, Lionel (2013), “Understanding the low volatility anomaly”, EDHEC-Risk Institute Post, May 2013.
Swedroe, Larry (2015), “Explaining the low vol anomaly”, etf.com, February 2015.

The post ties in with this sites’ lecture on implicit subsidies.
The below are excerpts from the paper and the articles. Emphasis and cursive text have been added.

The evidence for the low-risk effect

“One of the major stylized facts on the risk-return relation…is the observation that assets with low risk have high alpha, the so-called ‘low-risk effect’…We use the standard term ‘low-risk effect’ to refer to the (risk-adjusted) return spread between low- and high risk stocks…It does not just refer to low-risk stocks…The systematic low-risk effect is based on a rigorous economic theory and has survived more than 40 years of out of sample evidence.” [Asness et al.]

“Asset pricing theory, as well as common sense, suggest…a strictly positive relationship between systematic risk and expected return, and a positive or zero relationship between specific risk and expected return. Standard asset pricing models first suggest that…systematic volatility should be positively rewarded, and that specific volatility may be positively rewarded, or earn no reward…Empirical analysis, however, has unveiled evidence of a negative risk-return relationship in equity markets…Portfolios formed by sorting stocks by past volatility display higher returns for the low-volatility quintile over the subsequent month than for the high-volatility quintile…The relationship between systematic risk as measured by a stock beta and return is much flatter than predicted by the Capital Asset Pricing Model…High idiosyncratic volatility stocks have had ‘abysmally low returns'” [Martinelli]

“Firstly, we document a clear volatility effect: low risk stocks exhibit significantly higher risk-adjusted returns than the market portfolio, while high risk stocks significantly underperform on a risk-adjusted basis. Secondly, our findings are not restricted to the US stock market, but apply to both the global and regional stock markets. The alpha spread of the top versus bottom decile portfolio amounts to 12% per annum for our universe of global large-cap stocks over the 1986-2006 period. Thirdly, we compare the volatility effect with the classic size, value and momentum strategies and control for these effects. In order to disentangle the volatility effect from those other effects we use global and local Fama and French regressions and apply a double sorting methodology. We find that the volatility effect is in fact a separate effect, and of comparable magnitude.” [Blitz and van Vliet]

The likely causes of the low-risk effect

“The debate is whether (a) the low-risk effect is driven by leverage constraints and risk should be measured using systematic risk versus (b) the low-risk effect is driven by behavioral effects and risk should be measured using idiosyncratic risk…Evidence is consistent with both of the alternative theories playing a role and that the alternative factors may, to some extent, capture different effects…our results suggest that both leverage constraints and lottery demand play a role for the low-risk effect. The results are stronger for leverage constraints, especially outside the US, consistent with the underlying equilibrium theory and the fact that these constraints are observable for many investors.” [Asness et al.]

“One of the assumptions of the CAPM is that there are no constraints on leverage and short-selling. In the real world, many investors actually are either constrained against the use of leverage (by their charters) or have an aversion to its use…Limits to arbitrage (constraints) and an aversion to shorting, as well as the high cost of shorting such stocks, can prevent arbitrageurs from correcting the pricing mistake…Evidence shows the stocks that are most mispriced are the ones with the highest shorting costs.” [Swedroe]

A number of papers document evidence consistent with…leverage constraints…Exogenous changes in margin rates influence the slope of the security market line…Funding constraints…predict [the performance of] ‘betting against beta’ strategies…International illiquidity predict ‘betting against beta’ strategies, and…[there is] a strong link between the return to ‘betting against beta’ strategies and financial intermediary leverage.” [Asness et al.]

“In the real world, there are investors who have a preference, for lottery-like investments…that exhibit positive skewness and excess kurtosis [fat return distribution tails]. This leads such investors to…pay a premium to gamble. Among the stocks that fall into this category of ‘lottery tickets’ are IPOs; small growth stocks that aren’t profitable; penny stocks; and stocks in bankruptcy. Limits to arbitrage and the costs or fear of shorting prevent rational investors from correcting the mispricings.” [Swedroe]

“The alternative view is that the low-risk effect stems from behavioral biases leading to a preference for lottery-like returns…Indeed [academic research papers]…find that stocks with low idiosyncratic volatility have high risk-adjusted returns in the U.S. and internationally. In a similar vein…low maximum return over the past month, a measure related to idiosyncratic skewness…is associated with high risk-adjusted returns.” [Asness et al.]

Investment strategies based on the low risk effect

We decompose ‘betting against beta’ strategies into two factors: ‘betting against correlation’ and ‘betting against volatility’. ‘Betting against correlation’ goes long stocks that have low correlation to the market and shorts those with high correlation, while seeking to match the volatility of the stocks that are bought and sold. Likewise, ‘betting against volatility’ goes long and short based on volatility, while seeking to match correlation. This decomposition…creates a component that is [related to leverage constraints] (‘betting against correlation’) and a component…closely related … to the behavioral factors (‘betting against volatility’).” [Asness et al.]

“Since stocks with low market correlation have low market betas, the theory of leverage constraints implies that ‘betting against correlation’ has positive risk-adjusted returns. Empirically, we find that ‘betting against correlation’ is about as profitable as the ‘betting against beta’ factor and ‘betting against correlation’ has a highly significant CAPM alpha as predicted by the theory of leverage constraints…We find significant alpha…for a variety of combinations of control factors in the US and globally.” [Asness et al.]

‘Betting against beta’ strategies and ‘betting against correlation’ strategies  are robust to controlling for a host of other factors, have survived significant out–of-sample evidence – both through time and across asset classes and geographies – have lower turnover than many of the well-known idiosyncratic risk measures making them more implementable and realistic, and are supported by rigorous theory of leverage constraints with consistent evidence for this economic driver.” [Asness et al.]

“We find that ‘betting against beta’ strategies and ‘betting against correlation’ strategies are predicted by measures of leverage constraints.” [Asness et al.]

We construct a scaled-MAX (SMAX) factor that goes long stocks with low maximum of last month’s return divided by ex ante volatility and shorts stocks with the opposite characteristic. This factor captures lottery demand in a way that is not as mechanically related to volatility as it is more purely about the shape of the return distribution. Behavioral theories imply that these idiosyncratic risk factors should have positive alphas, which we confirm in the data…SMAX performs stronger than both…factors that go long stocks with low MAX return or low idiosyncratic volatility.” [Asness et al.]

“Factors based on idiosyncratic risk…are more often defined based on a relatively short time period…making them susceptible to microstructure noise and making it harder to believe that they capture the idea underlying the behavioral theory. They are less robust to controlling for other factors and to using a lower turnover, and they are weaker globally.” [Asness et al.]