Factor momentum versus price momentum: Insights from international markets

The momentum effect is one of the most pervasive anomalies ever documenteddriving prices across various asset classes: stocksbondscommoditiesand many others (Asness et al.2013; Baltussen et al.2021). Notablyit also shows up in equity anomalies—their past returns predict future performance (Avramov et al.2017; Gupta & Kelly2019). 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. Consequentlyit explains most—if not all—of the price momentum profits. In this frameworkthe stock price momentum does not represent a distinct risk factor; insteadit only times other factors.

In this studywe comprehensively revisit this relationship. Rather than examining one type of factor momentum in a single countrywe take a holistic approach and explore various empirical designs in a broad global context. We scrutinize the performance of 145 anomalies across 51 markets. We consider two principal versions of factor momentum: in empirical anomalies and their principal components (PC). We implement them in multiple ways to reach a simple yet unambiguous conclusion: one cannot capture all the stock or industry momentum profits just by timing other factors.

Our results contribute in five fundamental ways. Firstwe extend the prior factor momentum evidence to 51 global markets. We find that “winner” factors outperform their “loser” factors counterparts in multiple—though not all—countriesregardless of the implementation details. For examplethe 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. The effect works well in both cross-sectional and time-series momentum implementationsbut it is neither ubiquitous nor always significant. For exampleour baseline specification of time-series (cross-sectional) empirical factor momentum generates significant gains in only 16 (12) out of 51 countriesand cannot be confirmed in many large markets such as FranceGermanyor Japan. It does show uphoweverin broad international portfolios.

Secondwhile our international evidence confirms the existence of factor momentumit calls into question its ability to explain stock price momentum. While Ehsani and Linnainmaa (2022p. 1881) argue that investors can “capture all momentum gains by timing other factors,” our findings reveal a more complex picture. Empirical factor momentumin particularfails to fully explain stock momentum gains inter-nationallycapturingat bestonly a fraction of price momentum profits across countries. Principal component factor momentumin turnproves more effectiveexplaining a large part of price momentum profits in global developed and emerging market portfolios and entirely subsuming them in prominentlarge capitalization markets like the United StatesUnited Kingdomand France. Howevereven this more robust approach does not generalize universally. As Fig. 1 showsneither form of factor momentum fully captures price momentum gains in numerous countries.

The long-short equity momentum strategy earns an average return of 0.58% per month across the 51 markets tested. Applying local Fama and French's (2015) five-factor models extended with the factor momentum portfolio leaves an unexplained return of between 0.19% and 0.57% (depending on the specific implementation). The remaining alpha ison averagehighly significant—regardless of the specific test design. Overallthe five-factor model of Fama and French (2015) extended by factor momentum captures between 2% to 67% of the price momentum gains across countries. A large fraction of returns remains frequently unexplained. Looking at individual marketsstock momentum continues to generate significant alpha in between 8 and 32 of the analyzed markets. Our results hold for both classical and alternative forms of momentumsuch as residual momentumintermediate momentumor Sharpe ratio momentum.

Thirdwe find that stock price momentum explains factor momentum frequently better than vice versa. When regressed against each otherstock price momentum accounts for a significant fraction of factor momentum gains worldwide. This effect is particularly pronounced in the case of empirical factor momentumwhere the average alphas across countries shrink to a range between -0.01% and 0.10%remaining statistically significant only in a handful of markets. Additionallynewer factor modelssuch as those proposed by Daniel et al. (2020) or Stambaugh and Yuan (2017)effectively capture the empirical factor momentum gains. PC factor momentum proves to be more robust. It may generate Sharpe ratios exceeding those of stock price momentumand its alphas often retain statistical significance after controlling for one another. Neverthelessthe price momentum still captures a notable part of PC factor momentum profits.

Fourthwe take advantage of international data to reexamine the findings of Arnott et al. (2023) that cross-sectional factor momentum explains industry momentum. We find no convincing support for this claim. While particular forms of factor momentum may capture the gains from industry momentum in specific marketsthis pattern does not extend globally. As a resultindustry momentum alphas remain typically positive and significant in many markets. These conclusions are qualitatively unaffected by different definitions of factor momentumstudy periodsor factor sets. Againwhat works for U.S. stocks under a particular specification does not necessarily translate into a global pattern.

Fifthwe look closer at the international variation in the factor momentum effect. Analyzing a wide range of country characteristicswe find that factor momentum returns are unrelated to factors that typically influence return predictabilitysuch as market developmentmarket-level arbitrage constraintsdistress riskcultural traitsor market conditions and structure. In particularit does not depend on features typically associated with the magnitude of stock price momentumsuch as firm sizeindividualismor past market returns and volatility. In essencecross-country differences in factor momentum exhibit a distinct behavior that distinguishes them from popular drivers of return predictability.

To sum upour findings challenge the conclusions from the previous literaturee.g.of Ehsani and Linnainmaa (2022) and Arnott et al. (2023). While factor momentum exists in international marketsit fails to explain the price or industry momentum profits entirely. Any alleged evidence is mainly limited to PC factor momentum and concerns specific markets—including the United States. The momentum effect remains an essential and distinct anomaly that cannot be captured by simply timing other factors.

Our study relates to three major strains of asset pricing literature. Firstwe add to the discussion of the factor momentum effect in equity markets. This phenomenoninitially documented in the United States by Avramov et al. (2017)has been later examined using different estimation windows and anomaly sets (e.g.Leippold & Yang2021; Fan et al.2022; Arnott et al.2023). Several smaller studies extended the tests to individual foreign marketssuch as China or South Africa (Ma et al.2024; Page et al.2022). FurthermoreGupta and Kelly (2019) and Leippold and Yang (2021) test factor momentum in pooled global samples. Against this backdropour article is most closely linked to Ehsani and Linnainmaa (2022) and Arnott et al. (2023)—who argue that factor momentum subsumes most forms of the stock momentum effect.

Secondour work connects to the long-standing debate on the replication crisis in finance and verifying external validity with international data (Jensen et al.2023). Karolyi (2016p. 2075) highlights a persistent U.S. (home) bias in academic researchwith only a small fraction of studies in top-tier journals scrutinizing non-U.S. markets. This presents two risks: firstthe findings from the United States may not necessarily hold elsewhere (e.g.Goyal & Wahal2015; Jacobs & Müller2020; Cakici & Zaremba2022); secondrelying heavily on data from the U.S. carries the risk of widespread p-hacking. Harvey et al. (2016) and Harvey (2017) recommend out-of-sample validation as one of the key ways to mitigate multiple testing problems. International out-of-sample tests provide a broader perspective on the robustness of various asset pricing phenomena.

Finallyour analysis may be relevant to the ongoing debate about the role of discretion in research design choices in financial studies. Menkveld et al. (2024) document how so-called “non-standard errors” can affect results in asset pricing research. Coqueret (2023)Walter et al. (2024)and Soehbag et al. (2023) extend this discussion to illustrate the impact of different methodological decisions on portfolio sorts. Our results suggest that the nature of factor momentum also leaves room for a substantial variety of research designswhich can critically shape the overall conclusions.

The remainder of the study proceeds as follows. Section 2 presents the data and methods. Section 3 revisits the evidence from the United States. Section 4 presents the results for international markets. Section 5 provides further insights into the properties of factor momentumalternative factor modelsmomentum types—including the industry momentum—portfolio turnoverand the cross-country variation in the factor momentum effect. FinallySection 6 concludes the study.