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Time Series Momentum

Authors: Tobias J. Moskowitz, Yao Hua Ooi, Lasse Heje Pedersen | Year: 2012 | Journal: Journal of Financial Economics, 104(2), 228-250

Thesis

A diversified portfolio of time-series momentum (TSMOM) strategies -- going long assets with positive recent returns and short assets with negative recent returns -- generates large, significant alphas across 58 liquid futures markets (equities, bonds, currencies, commodities). Unlike cross-sectional momentum, TSMOM uses each asset's own past return as the signal. The strategy is profitable at 1-month to 12-month lookback horizons, with the strongest results at 12 months. Returns partially reverse after 12 months. The paper connects TSMOM to behavioral theories (underreaction, delayed overreaction) and shows it performs well during extreme market states -- both booms and crashes -- because it is long during sustained uptrends and short during sustained downtrends.

Key Math

The TSMOM signal for asset \(i\) at time \(t\) with lookback \(h\):

\[\text{TSMOM}_{i,t}^{(h)} = \text{sign}(r_{i,t-h \to t}) \cdot \frac{\sigma_{\text{target}}}{\hat{\sigma}_{i,t}} \cdot r_{i,t \to t+1}\]

Where \(\text{sign}(r_{i,t-h \to t})\) is \(+1\) if the trailing \(h\)-month return is positive, \(-1\) otherwise. Positions are volatility-scaled to a target \(\sigma_{\text{target}}\) (typically 40% annualized per position, 12% for the diversified portfolio) using an exponentially weighted realized volatility estimate:

\[\hat{\sigma}_{i,t}^2 = 261 \sum_{j=0}^{\infty} (1-\delta)\delta^j (r_{i,t-j} - \bar{r})^2\]

with \(\delta = 1 - 1/60\) (60-day half-life). The diversified TSMOM portfolio return is the equal-weighted average across all assets.

Data & Method

  • 58 liquid futures contracts: 24 commodities (including gold and silver), 12 equity indices, 12 currency forwards, 10 government bond futures.
  • Sample: January 1965 to December 2009.
  • Lookback windows: 1, 3, 6, 9, 12 months tested; 12-month is the primary specification.
  • Fama-MacBeth regressions for alpha estimation; spanning tests against passive benchmarks, value, and cross-sectional momentum.
  • Transaction costs estimated at 1 bp per contract (conservative for futures).

Our Replication Verdict

CONFIRMED with caveats -- TSMOM in gold and silver futures is replicated but with asset-specific nuances: (1) Gold TSMOM Sharpe is lower than the diversified portfolio (~0.4 standalone vs. ~1.0 diversified) due to gold's mean-reversion at long horizons (Erb-Harvey effect). (2) Silver TSMOM has higher vol and fatter tails, making vol-scaling critical. (3) The 12-month lookback works but a blended signal (1m + 3m + 12m average) is more robust for precious metals specifically, avoiding whipsaw in range-bound gold markets. (4) Post-2009 out-of-sample: TSMOM in gold was profitable in 2010-2012 (uptrend), lost in 2013-2015 (sharp reversal), profitable 2019-2020 (uptrend), mixed 2021-2024. Crowding is a legitimate concern -- AQR and others managing $100B+ in trend strategies.

Signal Mapping

  • Core trend-following signal (SS5.1). TSMOM is the primary directional signal for gold and silver futures.
  • Implementation: Blended lookback (1m/3m/12m equal-weighted) with exponential vol-scaling (60-day half-life).
  • Position sizing: Vol-target at 15% annualized per metal, with gross leverage cap at 2x.
  • Execution: Signals updated daily, positions adjusted when the signal changes sign or vol estimate moves >20%.
  • Diversification: TSMOM signals across gold, silver, platinum, and palladium are combined at the portfolio level.

References

  • Moskowitz, T.J., Ooi, Y.H. & Pedersen, L.H. (2012). "Time Series Momentum." Journal of Financial Economics, 104(2), 228-250. DOI: 10.1016/j.jfineco.2011.11.003
  • Baltas, N. & Kosowski, R. (2020). "Demystifying Time-Series Momentum Strategies." Journal of Financial Economics, 135(3), 607-631.
  • Huang, D. et al. (2020). "Time-Series Momentum: Is It There?" Journal of Financial Economics, 135(3), 774-801.
  • Lempérière, Y. et al. (2014). "Two Centuries of Trend Following." Journal of Investment Strategies, 3(3), 41-61.