Time Series Momentum
Source: Moskowitz, T. J., Ooi, Y. H. & Pedersen, L. H. (2012). Journal of Financial Economics
104(2), 228–250.
TL;DR
An asset's own past 12-month excess return predicts its future return. A strategy that goes long
instruments with positive trailing-year returns and short those with negative returns, each scaled
to a constant volatility, earns a large, diversified Sharpe ratio across 58 futures and forwards —
and crucially delivers positive returns during equity market crises ("crisis alpha").
What anomaly it documents
Time-series (absolute) momentum is distinct from cross-sectional momentum: it depends only on an
asset's own past return, not its rank against peers. Past 12-month returns positively predict the
next ~1–12 months, after which returns partially reverse — the signature of initial underreaction
followed by delayed overreaction. The effect is remarkably consistent across equity indices, bonds,
commodities, and currencies.
How to construct it
negative). Some implementations scale by the return's magnitude or use multiple lookbacks.
estimate, so no single instrument dominates.
when its trailing 12-month excess return is positive and short when negative, rebalanced monthly.
This is a deliberately minimal proxy for the diversified, vol-scaled factor in the paper.
Evidence and replication
| Period | Sharpe | Source |
|---|---|---|
| IS (1985–2009, diversified TSMOM factor) | ~1.4 gross, strongly positive in 2008 | this paper |
| OOS (post-2012, ConvexPi single-asset market version) | 0.48 (vs 0.17 pre-2012) | ConvexPi benchmark |
The diversified factor's Sharpe is far higher than the single-asset replication because most of
TSMOM's strength comes from diversification across dozens of trends; our minimal market-only version
nonetheless remains positive out of sample. Note the OOS estimate is flattered by the short
post-2012 window and the strong 2020 and 2022 trends.
Why it might work
extrapolate, producing trends that persist before reversing.
profits when equities fall — a diversification benefit, not just a return source.
Limitations and risks
the effect is statistically fragile once the near-always-long tilt and time-varying means are
accounted for — a useful caution that the headline result is sensitive to specification.
Key references
Reference replication on ConvexPi
An open, verified replication of this strategy is maintained at convexpi/replications. It recomputes the strategy from underlying building blocks and scores it out of sample (the McLean & Pontiff test):
| Period | Annualized Sharpe |
|---|---|
| In-sample (pre-2012) | +0.09 |
| Out-of-sample (≥ 2012) | +0.41 |
| Last 10 years | +0.39 |
Verdict: alive. Run it on live data in Colab · view the code