The volatility of asset class returns is not constant over time. Similarly, traditional strategies aiming to capture factor premia also show variable volatility over time. Volatility tends to form two distinct regimes: a high-volatility regime with poor returns and a low-volatility regime with higher returns. Typically, in a high volatility regime, volatility tends to remain high and in a low volatility regime, volatility tends to remain low. That persistence makes volatility predictable. Constant volatility approaches can be successful ways to exploit these anomalies, also when applied to factor investing.

We have long said that smart-beta strategies could be much smarter. In a 2012 paper, we showed that traditional smart-beta strategies such as minimum variance, maximum diversification and risk parity can be explained well by very few key exposures to well-known factor premia such as small capitalisation, low volatility and value. The risk allocation to those factor premia is however not controlled and left to the mercy of the markets.

In another paper, published earlier this year, we introduced a superior and flexible portfolio construction framework which allows for proper diversification in terms of factor premium exposures and focuses on the risk budgeting allocation to factor premia, the allocation of active risk relative to the market portfolio and the efficient handling of portfolio constraints.

**SURPRISING RESULTS**

In this 2014 paper, essentially about the construction of optimal portfolios with factor premium exposures, we presented a back-test of how a risk parity allocation to the four main factor premia – value, momentum, low volatility and small capitalisation – would have performed in recent years. The results were astounding for several reasons.

• First, because a simple equal allocation of active risk to each factor premium has worked so well for investors in the past.

• Second, because attempts to derive more refined ways of allocating risk to different factors added no additional value.

• Astonishing was also that in this framework, we targeted an ex-ante constant allocation to active risk over time and this was very successfully delivered in ex-post. Not only for the total active risk budget, but also for the risk allocation to each factor. In ex-post, each factor generated an equal and constant contribution to total active risk as sought in ex-ante.

In a new paper, which will appear in the Journal of Investment Strategies this December, we explain these results in more depth. Our goal was i) to understand why a risk allocation based on ex-ante risk is so successful, i.e. the ex-post risk allocation comes out so perfectly in line with the ex-ante targets, and ii) to find out if the re-balancing of the weights allocated to each factor premium required to keep their risk contribution constant over time in ex-ante added anything to performance.

**CAPTURING PREMIA WITH LONG AND SHORT POSITIONS**

Traditional strategies designed to capture factor premia are relatively simple. For the value premium, for example, you build a portfolio that sells short expensive stocks, e.g. stocks with high price-to-book ratios, and you use the proceeds to buy cheap stocks, e.g. stocks with a low price-to book ratio. For the momentum premium, you build a portfolio of long positions in stocks with the largest returns over the past year and shorts in stocks with the weakest returns. Value and momentum premia can also be captured in fixed-income and foreign-exchange markets with equivalent long-short strategies. In these traditional approaches, the leverage of the long-short is usually kept constant relative to the assets under management.

**LOW-VOLATILITY ANOMALIES ALSO IN THE TIME SERIES OF FACTOR PREMIA**

That approach, however, fails to take advantage of the fact that factor premia seems to exhibit a low-volatility anomaly in the time series of their returns. Much like asset class premia, the factor premia, when captured via constant leverage long-short portfolios, do not have a constant volatility over time. Moreover, much like asset class premia, over time, the volatility of factor premia forms two distinct regimes, one with low volatility and positive and high returns and one with high volatility and low or even negative returns.

Much like for asset class premia, constant volatility approaches that reduce exposure in high-volatility regimes and increase exposure in low-volatility regimes can significantly improve the factor premium per unit of risk. Results appear stronger for momentum than for value, which can be explained by the large differences in volatility and returns in both high and low-volatility regimes as well as the higher probability of staying in a given regime. The reason why constant volatility strategies are so successful in ex-post at delivering constant volatility is this persistence of volatility in each regime. This makes volatility predictable.

In line with what was found in the cross-section of equities and fixed income, low-volatility anomalies seem to be everywhere, even in the time series of asset class premia and that of factor premia. Constant volatility approaches can be an effective way for investors to profit from these low-volatility anomalies in the time series of returns.