Time series momentum (also known as trend following)—the tendency for an asset’s own past returns to predict its future returns—has become one of the most well-documented and widely exploited anomalies in finance. Moskowitz, Ooi, and Pedersen’s seminal 2012 paper “Time Series Momentum“ showed that trend-following strategies have produced strong, diversifying returns across equity, bond, currency, and commodity markets for decades, and the strategy remains a staple among managed futures funds and CTAs.
But momentum strategies aren’t immune to failure. They are well known to suffer periodic crashes, and academics have long searched for the conditions under which trends are more or less likely to persist. Matti Suominen and Erik Hjalmarsson, authors of the June 2026 paper “Boundaries of Time Series Momentum,” make an important contribution to this literature by identifying exactly where—not just when—momentum tends to break down.
What the Authors Examined
Suominen and Hjalmarsson set out to test the hypothesis that equity time series momentum works well when valuation measures are in “normal” or mid-range territory but breaks down—and can even reverse—when valuations reach historical extremes, which they define as the 10th and the 90th percentiles of the past valuation ratios.
To test this, they built a dataset spanning nearly a century of U.S. equity and bond data (July 1927 to December 2024) along with a 20-country international sample running from January 1989 to December 2024. They used three well-established valuation and business-cycle indicators:
Shiller’s CAPE ratio (cyclically adjusted price-to-earnings), used only in the U.S. sample due to limited international data availability
Dividend yield, used in both the U.S. and international samples
The term spread (the difference between long- and short-maturity Treasury yields), used as a bond-market valuation gauge in both samples
A key methodological choice was to use 12-month moving averages of these ratios rather than their raw, point-in-time values. In their 2005 paper “Bond Risk Premium,” John Cochrane and Monika Piazzesi had previously shown that taking moving averages of return predictors improves predictive power. Suominen and Hjalmarsson build on this, noting that the smoothing also helps separate the valuation signal from the momentum signal itself, since moving averages reduce the mechanical correlation between past 12-month returns and the level of the valuation ratio.
From there, the authors constructed a new variable they call “Boundaries.” Each valuation measure is first normalized relative to its trailing 10-year or 20-year historical range, scaled to fall between -1 and +1. Boundaries is then defined as the sum of the squared normalized term spread and the squared normalized CAPE or dividend yield. This means Boundaries reaches its theoretical maximum of 2 when both the equity and bond market valuation measures are simultaneously at historical extremes, and falls to zero when both sit at their historical mid-points.
The diversified time series momentum strategy itself follows the standard Moskowitz-Ooi-Pedersen construction: long the market (financed at the risk-free rate) when trailing returns are positive, short otherwise, using cash market positions rather than futures. The authors build 25 separate momentum strategies using lookback periods of 1, 3, 6, 9, and 12 months crossed with equal holding periods, then equally weight them into a single diversified index.
Key Findings
The central finding is that momentum’s effectiveness is highly regime-dependent, and Boundaries is a powerful way to identify the regime.
Momentum works in the middle, but fails at the edges. Sorting returns into deciles by term spread and CAPE (or dividend yield), the authors show that momentum returns are strongest in the mid-valuation cells and deteriorate—often turning negative—in the corner cells where both bond and equity valuations are simultaneously extreme. This pattern holds regardless of whether valuations are extremely high or extremely low, and regardless of whether the prevailing momentum signal is positive or negative. That symmetry is part of what makes the finding compelling: it isn’t simply that “expensive markets crash,” it’s that extremes in either direction coincide with trend reversals.
Reversals replace momentum near the boundaries. Using a more formal regression framework, the authors show that when Boundaries is high, the interaction between past 12-month equity returns and Boundaries becomes significantly negative—returns tend to revert rather than continue. In the U.S. sample, this interaction term is significant at the 1% or 5% level in every specification tested. In the 20-country international sample, the effect is even stronger.
Controlling for this reversal effect dramatically improves return forecasts. In the international sample, past 12-month return is statistically insignificant as a standalone predictor of future 12-month return once dividend yield, term spread, and past bond returns are controlled for (adjusted R² of about 8%). Once the Boundaries variable and its interaction term are added, past return becomes a significant positive predictor in normal regimes, and the regression’s adjusted R² rises to roughly 15%. Similar improvement shows up in the U.S. sample.
Momentum returns themselves are predictable using Boundaries. Without the Boundaries variable, a regression of time series momentum returns on valuation levels, market volatility, and past absolute returns explains only about 2% of variation (adjusted R²) in the U.S. sample. Adding Boundaries alone lifts that to roughly 10%; adding the interaction terms pushes it to about 12%. The authors describe this as up to a 550% increase in R² relative to the base case—the paper’s headline statistic. The Boundaries coefficient is negative and significant at the 1% level in nearly every specification: high Boundaries reliably forecasts weak subsequent momentum returns, and the effect is concentrated in states following large absolute equity market moves.
A Plausible Economic Mechanism: Monetary Policy Sensitivity
Rather than leaving the finding as a pure statistical curiosity, the authors offer a structural explanation. They show that industrial production, unemployment, and short- and long-term interest rates all become more sensitive to past equity returns when Boundaries is high than when it is low. In other words, at valuation extremes, the economy and the Federal Reserve appear to respond more forcefully to recent market moves—raising or cutting rates, or seeing growth accelerate or decelerate—in ways that plausibly trigger the very reversals the data shows. The authors liken the market to an elevator moving between high and low valuation, with momentum working in the middle but reversing once the elevator “hits” a boundary, possibly because central bank actions or unsustainable valuations change its direction.
The results hold up out of sample and under more rigorous econometrics. Using the CUMSUM methodology of Ivo Welch and Amit Goyal from their 2008 paper “A Comprehensive Look at The Empirical Performance of Equity Premium Prediction,” the authors show that simple one-factor models using the Average Boundaries variable produce positive out-of-sample predictive power for both momentum returns and the equity risk premium in data beginning in the year 2000—true out-of-sample validation rather than an in-sample artifact. The core findings also survive when the authors apply Hodrick (“Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement”) standard errors and the IVX procedure of Kostakis, Magdalinos, and Stamatogiannis (“Robust Econometric Inference for Stock Return Predictability”), both of which are designed to correct for the Stambaugh (“Predictive Regressions”) bias (statistically significant predictive relationships that may be spurious due to this bias rather than genuine predictability) and overlapping-observation problems that plague long-horizon return-predictability regressions.
Taken together, Suominen and Hjalmarsson conclude that accounting for these reversal states is what unlocks the bulk of the forecasting improvement documented throughout the paper.
Key Investor Takeaways
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