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Momentum on the meta-level.

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The momentum effect has been known for a long time and is still detectable on the markets. This article presents an interesting study that examines the momentum concept on the meta-level - also with a clear result.

A study written by Rob Arnott, Mark Clements, Vitali Kalesnik and Juhani Linnainmaa has the short, concise title "Factor Momentum" [1]. Instead of individual stocks - as is usual with the classic momentum effect - the researchers examine a total of 51 return factors known from the scientific literature. These include beta, value and size, but also the classic momentum factor itself.


The study is particularly interesting because it shows a performance persistence on the meta-level of the return factors. In concrete terms, this means that the most recent best and worst factors tend to continue this development in the short term. Or to put it simply:

once a factor such as the well-known momentum effect gets going, for example, it tends to persist in the short term.

If, on the other hand, the effect such as Value has had a weak momentum in recent years, the underperformance will tend to continue for the time being.

In absolute terms, the researchers examined the US market in the period from 1963 to 2016, demonstrating stable excess returns for factor momentum based on a cross sectional approach, corresponding to an annualized average return of 10.5 percent. In contrast to effects that used to work and then disappear, returns have not visibly declined in recent years. Also interesting: In contrast to the momentum effect, which is afflicted by occasional crashes, the overriding factor momentum in these phases sometimes even shows particularly positive phases (for example, in 2009, see chart).

The following figure shows the cumulative log returns of the factor, industry and classic momentum strategy as well as the market (minus T-Bills as risk-free interest). The factor momentum strategy is based on a universe of 51 factors and selects the top/flop 8 for the long and short portfolio (ranking and holding period 1 month each). The industry momentum strategy is based on 20 portfolios weighted by market capitalization of the individual industries. The classic momentum strategy corresponds to the Carhart momentum factor. For better comparability, all strategies are adjusted for the returns of the 5-factor model and scaled to the volatility of the industry momentum strategy.

factor momentum
Figure 1) Factor-Momentum
Source: Arnott, R. / Clements, M. / Kalesnik, V. / Linnainmaa, J. (2019), Factor Momentum, p. 40

A simple and profitable trading strategy

According to the study, factor momentum is strongest when the ranking and holding period is only one month each.

This results in the possible long strategy of systematically betting only on those factors that were strongest last month. This is in contrast to the often propagated "buy-and-hold" approach of permanently betting on a single factor that historically has delivered the highest premium - but also takes all the drawdowns with it.

Of the 51 factors examined, the study found that those relating to financial distress, illiquidity and volatility provided the largest contribution to returns. It is not absolutely necessary to include the entire universe of all 51 factors. According to the authors' simulations, a set of ten random factors is sufficient for approximately the same results. Even with only the five Fama/French factors - Beta, Size, Value, Investment and Profitability - an average annual return of eight percent could be achieved in the period under consideration, if the strongest (weakest) factor of the last month was bought (shorted).

According to the study, factor momentum differs fundamentally from the classic momentum effect in equities. Factor momentum works best on a one-month basis, whereas classic momentum on this time level tends to reverse in the short term and only develops over six to twelve months. The researchers also point out that factor momentum also fully explains another known effect, industry momentum.

Taking costs into account

From a practical point of view, however, there is a catch: Mapping the individual factors via appropriately large, diversified stock portfolios is comparatively expensive. In addition, the monthly adjustments also result in corresponding transaction costs, so that considerable implementation costs can be expected in the real world.

Nevertheless, the study is a major step forward in the understanding of factor premiums. The very fact that momentum exists at all at the level of large factor portfolios speaks for the universal nature of the phenomenon. After all, one could have assumed that momentum only functions at the level of individual stocks due to idiosyncratic risks and is "diversified away" in factor portfolios.

Further studies

In a recent study, "Factor Momentum Everywhere" [2], authors Tarun Gupta and Bryan Kelly came to similar conclusions based on a total of 65 factors. They show that individual factors regularly exhibit Time Series Momentum and create an overall strategy based on this. They also prove the effect for data from international stock markets. According to the authors, it is particularly interesting to combine factor momentum, classic momentum and value in a portfolio.

The idea of timing other factors using their respective momentum also sounds interesting. This aspect is addressed in the latest paper on this topic: "Factor Momentum and the Momentum Factor" [3] by Sina Ehsani and Juhani Linnainmaa. According to this paper, most return factors are autocorrelated: And since momentum best describes these autocorrelations, it is a superordinate phenomenon that is related to all factors.

Specifically, the studies show that factors achieve an average of high 51 (low 6) basis points per month after positive (negative) years. It is curious that even the momentum factor itself can best be described by factor-momentum.

The following chart shows the returns of the equally weighted winner and loser factor portfolios over time with monthly rebalancing. Time Series Winners (Losers) are factors with positive (negative) returns, Cross Sectional Winners (Losers) are factors with returns above (below) the median, each based on the previous year. The strategies are scaled to the standard deviation of the entire, equally weighted factor portfolio for better comparability.

time series and cross-sectional momentum
Figure 2) Time Series and Cross-Sectional Momentum
Source: Ehsani, S. / Linnainmaa, J. (2020), Factor Momentum and the Momentum Factor, p. 12

One conclusion to be drawn from these findings is that the individual return factors ultimately represent the major mood trends and "stories" that occur in the markets over long periods of time - and which change from time to time depending on the market phase. Momentum can thus be understood as the link between short-term pricing by supply and demand and the emergence of longer-term investment trends that can be quantified by factors.


Factor premiums have a short-term momentum effect that can be used for timing purposes.

[1] Arnott, R. / Clements, M. / Kalesnik, V. / Linnainmaa, J. (2019), Factor Momentum, Research Affiliates & University of Southern California and NBER
[2] Gupta, T. / Kelly, B. (2019), Factor Momentum Everywhere, Yale ICF Working Paper No. 2018-23
[3] Ehsani, S. / Linnainmaa, J. (2020), Factor Momentum and the Momentum Factor, Working Paper

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