Price Momentum or Factor Momentum: What Leads What?

Continuing our research of different factor allocations and models, we will look at evergreen momentum effect closer. Price momentum is one of the most popular equity anomalies—their past returns predict future performance. But the main question that’s still unresolved is where it comes from. While many academics advocate that this comes purely from the momentum factor, others believe it is merely the right timing of other factors and its right combination, be it value, quality (minus junk), or (low) volatility, and the momentum factor itself does not exist. They claim that price momentum is already included in various other factors.

Looks like another interesting point of view is being cast by the recent paper we present. Cakici, Fieberg, Metko, and Zaremba’s (January 2023) paper contributes to the never-ending debate of the chicken-or-egg problem of what comes first: Does the stock price momentum originate from the factor momentum? This study reexamined the relationship between the factor and price momentum on an extensive sample of 95 years of data from 51 countries. Various momentum strategies were formed using up to 145 anomalies per country, which provided a much-needed battery of robustness tests to provide significant findings free of errors and biases. While other also recent research, for example, Ehsani and Linnainmaa (2022), argue that the stock momentum does not represent a distinct risk factor, and all its profit may be captured by timing other factors: other factors returns are transmitted into those on individual securities; the authors of our reviewed paper corrected some findings and put light on the clarification.

Summary of the evidence from the U.S. market challenges Ehsani and Linnainmaa (2022) findings in a way that couldn’t be replicated as they mark that ability to subsume the classical price momentum effect depends on the research design. The evidence for the principal components (PC) factor momentum in US is more robust but volatile than previously prevalent and generally accepted by academia. In global markets, factor momentum remains significant after controlling for the price momentum. Simplistically, following momentum indicators, such as RoC or Mom, often brings better results for momentum-focused traders than searching for the right opportunities in factor investing focusing on momentum factor. This observation holds for various methodological approaches—such as different factor momentum implementations, anomaly samples, and study periods.

Conversely, the stock price momentum better explains the factor momentum than vice versa. It captures a large portion of the average momentum profits, rendering the momentum factor a distinct risk factor that cannot be captured simply by timing other factors. On average, various variants of the principal components (PC) factor momentum capture only between 8% and 20% of the profits on the price momentum anomaly. The problem here is, obviously, controlling them and adjusting long-short portfolios of those momentum strategies to capture that price momentum based on regime changes.

Video summary:

Authors: Nusret Cakici, Christian Fieberg, Daniel Metko, Adam Zaremba

Title: Factor Momentum Versus Stock Price Momentum: A Revisit



Does factor momentum drive the stock price momentum? Motivated by the recent findings from the United States, we revisit this relationship across 51 countries. The evidence on factor momentum’s ability to capture the stock momentum profits depends fundamentally on methodological and dataset choices. Consequently, the factor momentum cannot robustly subsume the stock momentum in global markets. On the contrary, the latter explains the former better than vice versa. Our conclusions challenge the view that momentum only times other factors rather than constituting a distinct anomaly.

As always, we present several interesting figures and tables:

Notable quotations from the academic research paper:

“Ehsani and Linnainmaa (2022) argue that these stock- and anomaly-level effects are closely related: the factor momentum returns transmit into the cross-section of stocks. Consequently, it explains most—if not all—of the price momentum profits. In this framework, the stock price momentum does not represent a distinct risk factor; instead, it only times other factors.
The central hypothesis in Ehsani and Linnainmaa (2022, p. 3-5) is whether “individual stock returns display momentum beyond that due to factor returns?”; the main contribution, in turn, is showing that investors “can capture all of momentum profits by timing other factors.” In this study, we comprehensively revisit this relationship. Rather than examining one type of factor momentum in a single country, we take a holistic approach and explore various empirical designs in broad international markets. We scrutinize up to 95 years of returns on 145 anomalies across 51 countries. We consider two principal versions of factor momentum: in empirical anomalies and in their principal components (PC). We implement them in multiple ways to reach a simple, yet unambiguous conclusion: one cannot capture all the stock momentum profits by timing other factors.
Our findings contribute in four fundamental ways. First, we demonstrate the material sensitivity of the factor momentum performance to methodological choices. To this end, we begin by reproducing the U.S. tests from Ehsani and Linnainmaa (2022). We confirm a powerful factor momentum effect in the U.S. market. Nonetheless, its ability to price the stock momentum profits depends substantially on the testing framework.

[T]he empirical factor momentum can no longer capture the profits on long-short stock price momentum portfolios. On the other hand, although the explanatory power of momentum in principal components is more robust, its effectiveness varies considerably across research designs; the unexplained monthly alphas on stock momentum portfolios range from 0.08% to 0.62%. […] The “winner” factors outperform their “loser” factors counterparts in multiple countries, regardless of the implementation details. For example, the PC time-series factor momentum—advocated by Ehsani and Linnainmaa (2022)—generates a cross-country average monthly return of 0.10% and is significant at the 5% level in 23 out of the 51 markets. […] Third, we document that the factor momentum fails to capture the stock momentum profits. In order to explore the association between the patterns in individual securities and factors, we regress the long-short stock momentum strategy payoffs on the factor momentum returns and vice versa. […] Fourth, we find that stock price momentum better explains the factor momentum than vice versa.

To sum up, our findings challenge the conclusions of Ehsani and Linnainmaa (2022). While the factor momentum exists within international markets, it fails to explain the price momentum profits. Any alleged earlier evidence is specific to the U.S. market and materially depends on the methodological choices. The momentum effect remains an essential and distinct anomaly, which cannot be captured by simply timing other factors.

Table 1, Panel A summarizes the performance of the factor momentum strategies. The results confirm the existence of a significant factor momentum effect. Our outcomes closely match those in Ehsani and Linnainmaaa (2022), corroborating their findings. For the empirical factor momentum (Table 1, Panel A.1), the average returns on the time series Winner-Loser portfolio is 4.06% versus 3.92% in Ehsani and Linnainmaa (2022). The cross-sectional version of the momentum generates the average return of 2.51% versus 2.40% in the referred study. The results for the PC factor momentum are also qualitatively consistent. The mean return on the time-series Winner-Loser strategy amounts to 2.50%; this closely resembles the value of 2.28% seen in Ehsani and Linnainmaa (2022).5 The minor differences may stem from small retroactive changes in popular data sources, such as the Kenneth R. French database (Akey et al., 2021). Indeed, the summary statistics for factor returns in Table A3 in the Internet Appendix depart slightly from the values reported by Ehsani and Linnainmaaa (2022).

The results in Table 2, Panel A indicate that the ability of the empirical factor momentum to explain the returns on long-short price momentum portfolios strongly hinges on the research designs. Departing from the original methodology leads to qualitatively different conclusions on whether empirical factor momentum can explain stock price momentum. The original specification results in the lowest alpha (and t-statistic) among each of the 48 variants we test—even the minor modifications matter. For example, excluding the global factors from the anomaly set increases the alpha to 0.44% (t-stat = 1.92). Similarly, extending the factor set to 145 anomalies from Jensen et al. (2022)— ceteris paribus—raises the average abnormal returns to 0.52% (t-stat = 2.17). Overall, the mean abnormal returns on price momentum portfolios remain positive and significant at the 10% (5%) level in 46 (44) out of the 48 specifications we consider.

Table 3 summarizes the performance of factor momentum portfolios. For each country, we consider both empirical and PC factor momentum strategies; for each of these, we report the two canonical construction methods employed by Ehsani and Linnainmaa (2022): cross-sectional (FMOMCS) and time-series (FMOMTS) factor momentum. Furthermore, we use all 145 anomaly portfolios from Jensen et al. (2022).”

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