**The Profitability Of Low Volatility full study via SSRN**

**David Blitz**

Robeco Asset Management – Quantitative Strategies

__Milan Vidojevic __

VU University Amsterdam; Robeco Asset Management

July 4, 2016

**Abstract: **

Low-risk stocks exhibit higher returns than predicted by established asset pricing models, but this anomaly seems to be explained by the new Fama-French five-factor model, which includes a profitability factor. We argue that this conclusion is premature given the lack of empirical evidence for a positive relation between risk and return. We find that exposure to market beta in the cross-section is not rewarded with a positive premium, regardless of whether we control for the new factors in the five-factor model. We also observe stronger mispricing for volatility than for beta, which suggests that the low-volatility anomaly is the dominant phenomenon. We conclude that the low-risk anomaly is not explained by the five-factor model.

### The Profitability Of Low Volatility – Introduction

Vast empirical evidence shows that the unconditional Capital Asset Pricing Model fails to explain cross-sectional differences in average stock returns. The early tests of the model already indicated that the relation between beta and return is flatter than predicted; see, for instance, Black, Jensen and Scholes (1972), Fama and MacBeth (1973), and Haugen and Heins (1975). Two decades later, Fama and French (1992) conclude that, if one controls for size effects, market beta is unpriced in the cross-section of stock returns, implying that firms with higher market sensitivity are not rewarded with higher average returns. Closely related to the low-beta anomaly is the low-volatility effect of Blitz and van Vliet (2007) and Blitz, Pang and van Vliet (2013), who document that the relation between past stock volatilities and subsequent stock returns is not merely flat, but even negative in all major stock markets over recent decades. The low-volatility effect is also related to studies which report superior risk-adjusted returns for minimum-variance portfolios, such as Haugen and Baker (1991) and Clarke, de Silva and Thorley (2010), and to the work of Ang et al (2006, 2009), who find a similar anomaly for very short-term idiosyncratic volatility. More recent studies such as Baker, Bradley, and Wurgler (2011), Baker and Haugen (2012), and Frazzini and Pedersen (2014) confirm the low-volatility and/or low-beta effects.

Various studies show that the three- and four-factor models fail to explain the low-risk anomaly. For instance, Blitz (2016) finds that the three-factor model is unable to explain the anomalous returns of low-volatility stocks, and Frazzini and Pedersen (2014) report that the low-beta anomaly is not subsumed by the three- and four-factor models. However, Novy-Marx (2014) argues that the low-beta and low-volatility anomalies are explained by a three-factor model augmented with a profitability factor. Fama and French (2016) also find that their (2015) five-factor model, which adds profitability and investment factors to their original three-factor model, is able to explain the returns on beta-sorted portfolios. Both papers use time-series regressions to come to these conclusions. This means that they first create beta- or volatility-sorted portfolios, and next regress the resulting time series of portfolio returns on the time series of the factors that comprise their proposed asset pricing models. The absence of economically large and statistically significant alphas in these regressions is interpreted as evidence that the low-beta and low-volatility anomalies are explained.

This paper does not question the empirical results of Fama and French (2016) and Novy-Marx (2014), but argues that direct evidence for a linear, positive relation between market beta and returns, which is assumed in their models, is still lacking. If the Fama and French (2015) and Novy-Marx (2014) asset pricing models were correct, it should be possible to construct portfolios which show that the linear relation between beta and returns holds in practice, provided one controls appropriately for the other factors in their models. This can be tested by conducting Fama-MacBeth (1973) regressions, as the estimated coefficients in these regressions can be interpreted as returns on portfolios which have unit exposure (exante) to factors, controlling for the exposures (ex-ante) to all other factors included in the regression. Fama (2015) also argues for considering not just one, but multiple asset pricing tests, including Fama-MacBeth (1973) cross-section regressions. However, the rejections of the low-beta anomaly by Novy-Marx (2014) and Fama and French (2016) are solely supported by time-series spanning tests.

Using Fama-MacBeth regressions we test whether the factors in the five-factor model are rewarded with significant premia, and find that all factors are, except market beta. In other words, a unit exposure to market beta in the cross-section does not result in significantly higher returns, regardless of whether one controls for the additional factors proposed by Fama and French (2015). At the same time, the constant in the regressions, which ought to be zero according to this asset pricing model (if returns in excess of the risk-free return are used), is large and significant. Taken together, these results imply that the relation between risk and return in the cross-section is flat instead of positive, which is consistent with the asset pricing models of Blitz (2014) and Clarke, de Silva and Thorley (2014). Simply put, we are unable to construct high-beta portfolios with high returns and low-beta portfolios with low returns by controlling for factors such as profitability, while it should be possible to do so if the low-beta anomaly is fully explained by such factors.

We also find more pronounced mispricing for volatility than for beta. This suggests that the low-volatility anomaly is stronger than the low-beta anomaly, and, given that the two are closely related, that the low-volatility anomaly is the dominant phenomenon. These results are consistent with the earlier findings of Blitz and van Vliet (2007), who find higher alpha spreads for volatility-sorted portfolios than for beta-sorted portfolios.