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Time Series Momentum (2012)

Academic Research Review Momentum Cross-Asset

Robert Stowe, AAMS® Investment Advisor

This page reviews "Time Series Momentum," a 2012 paper by Tobias Moskowitz, Yao Hua Ooi, and Lasse Heje Pedersen. The researchers found strong evidence that an asset's own past returns predict its future returns: investments that have gone up over the past 12 months tend to keep going up, and investments that have gone down tend to keep going down. This "time series momentum" showed up across 58 different futures markets spanning stocks, bonds, currencies, and commodities.

Published in the Journal of Financial Economics, the paper draws an important distinction from the cross-sectional momentum documented by Jegadeesh and Titman (1993), which compares stocks against each other. Time series momentum compares each asset against its own past, asking simply "has this gone up or down?" This makes it the academic foundation for the trend-following strategies used by managed futures funds and commodity trading advisors (CTAs).

Key Findings

The paper's central contribution is demonstrating that a simple, systematic rule based on an asset's own past returns produces consistent profits across a remarkably wide range of markets. The breadth of the evidence is what sets this paper apart from earlier trend-following research.

The Core Result

The researchers tested a straightforward rule: go long (buy) assets whose returns over the past 12 months were positive, and go short (bet against) assets whose returns over the past 12 months were negative. This simple approach produced statistically significant profits across nearly all 58 markets tested. The signal was strongest at the 12-month lookback period, meaning that looking at the past year of returns gave the clearest indication of where an asset was heading next.

Shorter lookback periods (1 and 3 months) also produced positive results, but the effect was weaker. Very long lookbacks (beyond 12 months) showed weakening returns or outright reversals, suggesting that trends eventually exhaust themselves and prices correct.

Pervasive Across Asset Classes

The time series momentum effect showed up in equity index futures (24 markets), currency forwards (12 markets), commodity futures (27 markets), and government bond futures (10 markets). The consistency across such different types of investments is the paper's strongest evidence. A pattern that appears in only one market could be a statistical accident. A pattern that appears in stocks, bonds, currencies, and commodities simultaneously is far harder to dismiss.

Each asset class contributed positively to the overall strategy. No single market or asset type was driving the results. This broad base of evidence distinguishes the paper from earlier studies that focused on narrower samples.

Diversified Time Series Momentum Portfolio

Combining the strategy across all 58 markets produced a portfolio with a Sharpe ratio (return per unit of risk) of about 1.0, which is historically high within the study's framework. For context, the long-run Sharpe ratio of the U.S. stock market is roughly 0.4. Individual market strategies had Sharpe ratios around 0.3 to 0.5, but the diversification benefit of combining them was substantial.

The high combined Sharpe ratio comes from the fact that time series momentum returns in different markets are not perfectly correlated. When the strategy loses money in one market, it tends to make money in others. This diversification effect is a key practical finding: trend-following works best when applied broadly across many markets, not concentrated in a single one.

Time Horizon and Lookback Periods

The researchers tested three lookback windows: 1 month, 3 months, and 12 months. All three produced positive average returns, but the 12-month lookback was the most profitable and statistically robust. The 1-month lookback captured short-term continuation effects, while the 12-month lookback captured the medium-term trend that is most commonly associated with momentum.

Beyond 12 months, the researchers found that the momentum effect weakened and eventually reversed. This pattern is consistent with the broader momentum literature: trends persist for roughly a year, then prices tend to partially revert. This reversal at longer horizons suggests that momentum profits come from an initial underreaction to information that eventually corrects.

Time Series vs. Cross-Sectional Momentum

Understanding the difference between time series and cross-sectional momentum is central to this paper. Cross-sectional momentum, documented by Jegadeesh and Titman in 1993, asks "which stocks are doing better than others?" It ranks assets relative to their peers, buying the top performers and selling the bottom performers. Time series momentum asks a different question: "is this individual investment going up or down?" It compares each asset only against its own history.

The paper shows that these are distinct phenomena, even though they are related. Time series momentum can exist even when cross-sectional momentum is zero. If all assets are moving in the same direction (all going up, or all going down), there is no cross-sectional spread to exploit, but time series momentum can still profit by going long everything (when all are rising) or short everything (when all are falling).

This leads to a critical practical difference: time series momentum can be net long or net short the market as a whole. In a broad downturn, the strategy goes short most assets and effectively bets against the market. Cross-sectional momentum, by contrast, is typically dollar-neutral, holding equal long and short positions regardless of the market's overall direction.

Practical Implications

Foundation for Trend Following

This paper provides the academic evidence base for the trend-following approach used by many CTAs and managed futures funds. Before this research, trend following was widely practiced by professional traders but lacked a comprehensive academic study documenting its effectiveness across a broad set of markets and time periods. The paper bridges the gap between practitioner intuition and rigorous statistical evidence.

The results validate the core idea behind trend following: prices tend to move in sustained directions, and a systematic approach that follows those trends can capture profits. The fact that a simple 12-month lookback rule works across dozens of markets suggests that the phenomenon is driven by fundamental forces, not by the specifics of any one market's structure.

Portfolio Diversification

Time series momentum returns showed low correlation with traditional stock and bond returns. The low historical correlation suggests that time series momentum may serve as a diversifier for conventional portfolios. The diversification benefit comes from the strategy's ability to go both long and short: it is not inherently tied to the direction of any single market. When stocks are falling, a time series momentum strategy may be short equities, generating returns that offset losses in a traditional portfolio.

The researchers found that adding a diversified time series momentum portfolio to a traditional stock-bond allocation historically improved risk-adjusted returns in their sample. This finding is consistent with the broader case for managed futures as a portfolio diversifier, a topic that has received significant attention from institutional investors.

Crisis Performance

The strategy tended to perform well during extended market downturns because it goes short assets that are in downtrends. During the 2008 financial crisis, for example, equity markets declined over many months, giving the 12-month signal ample time to shift to a short position. This offered a form of crisis protection, as the strategy profited from the sustained decline.

This crisis-hedging property is one of the most appealing features for institutional investors. However, it depends on the crisis unfolding as a trend rather than a sudden shock. A market that drops sharply in a single day and then recovers would not give the signal time to adapt. The protection works best for slow, sustained drawdowns.

Implementation Considerations

The strategy uses futures markets, which means leverage is involved. Futures contracts require only a fraction of the contract's value as collateral (margin), so a portfolio can hold positions whose total notional value exceeds the cash invested. This leverage amplifies both gains and losses. The researchers utilized volatility-targeting to manage position sizing, an approach common among systematic funds, to control the overall level of portfolio risk.

The researchers scaled each position to target equal volatility (price variability) across instruments. This means that a calm, low-volatility market like short-term bonds receives a larger position than a volatile market like crude oil, so that each position contributes roughly the same amount of risk to the portfolio. This volatility-targeting approach is standard practice among managed futures funds.

How the Researchers Tested This

Data and Time Period

The study uses data from 58 liquid futures contracts and currency forwards spanning 1965 to 2009. This 44-year sample covers a wide range of market environments: the inflation of the 1970s, the 1987 stock market crash, the dot-com bubble, and the 2008 financial crisis. Testing across such different conditions gives the findings more credibility than a study confined to a single era.

The 58 instruments include 24 equity index futures, 12 currency forwards, 27 commodity futures, and 10 government bond futures. The researchers selected contracts based on liquidity, ensuring that the results are relevant to practical implementation. Illiquid markets, where trading costs could erase the strategy's profits, were excluded.

Signal Construction and Portfolio Rules

Each month, the researchers calculated the excess return (return above the risk-free rate) for each instrument over the past 1, 3, and 12 months. If the excess return was positive, the strategy went long that instrument. If negative, it went short. Positions were sized to target a constant level of volatility for each instrument, based on a rolling estimate of recent price variability.

The strategy was rebalanced monthly. Returns were reported after accounting for the cost of rolling futures contracts (the price difference when replacing an expiring contract with the next one) but before explicit trading commissions. The researchers also decomposed the overall portfolio's returns into contributions from each asset class to show that no single group was responsible for the result.

Why Does It Exist?

If past returns predict future returns, it challenges the efficient market hypothesis, which holds that prices already reflect all available information. The paper discusses several explanations for why time series momentum might persist.

Initial Underreaction

The most widely cited explanation is that information incorporates into prices slowly. When good news arrives for an asset, the price does not immediately jump to its new fair value. Instead, it drifts upward over weeks or months as more investors become aware of the news and adjust their positions. This slow adjustment creates trends that a momentum strategy can exploit.

The researchers note that the partial reversal of momentum profits after about one year is consistent with this story. Prices initially underreact (creating the trend), then eventually overshoot (creating the reversal). The momentum strategy captures the underreaction phase but is exposed to losses during the overreaction and correction phase.

Herding and Feedback Trading

A second explanation involves investor behavior. When prices start rising, more investors buy in, pushing prices higher still. This herding effect amplifies price moves beyond what fundamental information alone would justify. Trend-following strategies themselves can contribute to this dynamic: as more capital flows into momentum strategies, the buying pressure from these strategies reinforces existing trends.

Central Bank and Institutional Behavior

Large institutional investors, including central banks, pension funds, and sovereign wealth funds, often adjust their portfolios slowly due to bureaucratic processes, investment committee approvals, and risk management constraints. These slow-moving capital flows create sustained buying or selling pressure that can last for months. Central bank interventions in currency and bond markets, which tend to be gradual and predictable, are a particularly clear example of how institutional behavior can create exploitable trends.

Limitations and Caveats

Limitations to Consider

Leverage required: Futures-based implementation involves leverage and margin management. Losses can exceed the initial capital committed, and margin calls during volatile periods can force liquidation at the worst times.
Conservative transaction cost estimates: The paper accounts for trading costs but uses estimates that may understate the true cost of frequent rebalancing, especially in less liquid commodity markets.
Crowding risk: As more capital chases trend-following strategies, the profits from these strategies may erode. The growth of managed futures and systematic trend-following funds since the paper's publication raises questions about whether the effect remains as strong.
Momentum crashes: Sudden market reversals (like March 2009) can produce severe losses before the signal adapts. A sharp V-shaped recovery is the worst-case scenario for a trend-following strategy, as the signal remains short while the market snaps back.
Favorable bond environment: The study period (1965–2009) includes a roughly 30-year stretch of generally declining interest rates (from the early 1980s onward), which provided a persistent tailwind for long positions in government bonds. Whether the strategy performs equally well in a rising-rate environment is an open question.