Since the mid-2000s, low-risk investing has become a widely accepted phenomenon. Its increased acceptance, however, has also led to heightened criticism. Initially, the most frequent objection was that the low-risk anomaly is simply a different manifestation of the well-known value anomaly, i.e. low-risk was accused of merely being value in disguise.

In the paper titled “The Value of Low Volatility” (published in the Spring 2016 issue of the Journal of Portfolio Management) we showed that a distinct low-volatility effect exists which cannot be explained by the value effect. On the whole, the evidence even appears to support low-volatility more than value.

## Can the low-risk anomaly be explained by the profitability (quality) factor?

More recently, the low-risk anomaly has been attacked from another angle. Some now argue that it can be explained by another factor, namely profitability (an example of what is known in the industry as a ‘quality’ factor). Novy-Marx (2014) takes the standard Fama-French three-factor model, which consists of the market, size and value factors, but adds profitability factor. This factor reflects the observation that highly profitable stocks tend to yield higher returns than stocks with poor profitability. He proceeds to show that low-beta and low-volatility stocks benefit from that phenomenon because they also tend to have a strong profitability, and that the model which includes a profitability factor can resolve their apparently anomalous returns. Fama and French (2016) also found that with their (2015) five-factor model, which adds profitability and investment factors to their original three-factor model, they could explain the returns on beta-sorted portfolios.

But what do the authors of these latest studies mean when they claim to have ‘explained’ the low-risk anomaly? Both studies reach these conclusions using an approach based on time-series regressions. This means that every month they sort stocks into portfolios based on their risk (e.g. by using beta or volatility), then calculate the returns of these portfolios over the subsequent month, and next regress the return series obtained in this way on the returns of portfolios in which stocks are sorted on other factors, such as size, value, and profitability. They then find that the implicit exposures to these factor portfolios largely explain the superior performance of the low-risk strategies. Based on these results, they conclude that their proposed factors resolve the low-risk anomaly.

In our new paper “The Profitability of Low Volatility” we do not question these results. We acknowledge that high quality stocks do share certain traits with low-risk stocks, and therefore that low-risk portfolios have an embedded quality tilt. However, we do not believe that profitability can fully explain the returns on low-risk stocks.

Suppose we sort stocks such that the resulting portfolios have neutral exposures to size, value, profitability, and investments, and only differ in terms of market beta or volatility. If the asset pricing models of Fama and French (2015) and Novy-Marx (2014) hold true, high-risk portfolios that are neutral in terms of other factors should yield higher average returns than their low-risk counterparts. Unfortunately, as the number of factors increases, the sorting approach becomes practically infeasible. With five factors, you would need to construct 3125 (5x5x5x5x5) portfolios. In the early years of our sample, the number of portfolios was larger than the number of stocks in the universe, so we have to find another way to achieve this goal.

In our paper we describe an approach that can be used to calculate the return on portfolios with pure exposure to one factor (such as market beta), while neutralizing interaction with all other factors (such as value and profitability). We find that as a portfolio’s exposure to factors such as size, value, momentum, profitability and investment increases, so do average returns, while, notably, they do not as market beta increases. Instead, we find that the relationship between market risk and return is flat, regardless of whether we control for new factors, such as profitability.

## The low-risk anomaly exists beyond value and profitability

So what is the key difference between our approach and the time-series approach applied in the previously mentioned studies? For one thing, the time-series regressions reveal that low-risk portfolios have some similarities to high profitability and value portfolios, and that, on average, these two factors can replicate returns on low-risk portfolios rather well. However, our analysis, which is conducted at the single-stock level, reveals that simple averages don’t tell the entire story. The low-risk anomaly exists beyond value and profitability.

We acknowledge that our research represents just one attempt to obtain a positive risk-return relationship by controlling for the factors that allegedly explain the low-risk anomaly. The fact that we were not successful does not necessarily mean that portfolios constructed differently cannot exhibit a clear positive risk-return relationship consistent with the predictions of the Fama and French (2015) and Novy-Marx (2014) models. But as long as the data indicates that portfolios with higher risk do not generate higher returns, it is premature to claim that the low-risk anomaly has been resolved.

This is a summary of the paper ‘The Profitability of Low Volatility’, which can be found at: SSRN

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