Time Series Momentum Explained: Signal Construction, Volatility Scaling and the Evidence

Time series momentum (TSMOM) is a trading rule that goes long a futures market whose own return over a recent lookback period (classically the past 12 months) was positive, and short one whose return was negative, with each position sized so that it carries a fixed amount of volatility. It is the formal, academic version of trend following, and it explains much of what commodity trading advisors (CTAs) do.

In short: the canonical recipe, from Moskowitz, Ooi and Pedersen’s 2012 paper in the Journal of Financial Economics, is: position = sign of the past 12-month excess return x (40% / the market’s estimated annualized volatility), rebalanced monthly, averaged across many futures markets. Simulations back to 1880 show positive average returns in every decade and good performance in most deep stock market declines. Real CTA indexes show the same features with smaller numbers: strong years like 2008 and 2022, long flat or losing stretches like 2010-2016 and early 2025, sharp losses when trends reverse, and big differences between managers. Some researchers argue that much of the measured benefit comes from volatility scaling rather than from trend prediction.

The fund-industry view of trend following is in managed futures and trend following. This article is about the machinery: how the signal is built, how volatility scaling works with real contract sizes, what the evidence says, and where it breaks.

The misconception: “momentum means buying what went up the most”

There are two different momentum strategies, and they are often confused.

Cross-sectional momentum ranks assets against each other and buys the relative winners while shorting the relative losers. It can be long a market that fell, as long as it fell less than others.
Time series momentum looks only at each market’s own past. If crude oil’s 12-month excess return is positive, the rule is long crude, whatever other markets did. If every market fell, the rule is short everything.

Moskowitz, Ooi and Pedersen introduced the term to describe the second. They found that time series momentum and cross-sectional momentum are related (a beta of 0.66 of TSMOM on cross-sectional momentum), but that TSMOM had a significant alpha of 76 basis points a month after controlling for it, and that TSMOM explained the cross-sectional momentum premiums in their asset classes rather than the other way round.

The original paper

Tobias Moskowitz, Yao Hua Ooi and Lasse Heje Pedersen, “Time Series Momentum,” Journal of Financial Economics 104 (2012), pages 228-250. Their data covered 58 liquid instruments: 24 commodities, 12 cross-currency pairs, 9 developed equity indexes and 13 government bond futures, from January 1965 through December 2009, with the main tests from 1985.

Key findings, as stated in the paper:

The past 12-month excess return of each instrument is a positive predictor of its next-month return. The effect “persists for about a year and then partially reverses over longer horizons.”
“All 58 futures contracts exhibit positive time series momentum returns and 52 are statistically different from zero at the 5% significance level.”
A diversified portfolio produced “a Sharpe ratio greater than one on an annual basis, or roughly 2.5 times the Sharpe ratio for the equity market portfolio,” with little correlation to standard factors.
Returns were largest in extreme stock markets, up or down, giving payoffs “similar to an option straddle on the market.” The authors call this the time series momentum “smile.”
Using CFTC positioning data, they found that “speculators profit from time series momentum at the expense of hedgers” (the data is described in the commitments of traders report).
An out-of-sample check on the TSMOM factor from 1966 to 1985, requested by the referee, gave an annualized Sharpe ratio of 1.1, despite the limited number of instruments then available.

The paper is also candid about failure modes. It shows TSMOM losing in the third quarter of 2008, profiting heavily in October to December 2008 as markets kept falling, and suffering “sharp losses when the crisis ends in March, April, and May of 2009.” In its words, “the ending of a crisis constitutes a sharp trend reversal that generates losses on a trend following strategy.”

Building the signal

Step 1: excess returns from rolled futures

TSMOM is defined on excess returns: the return of holding a fully collateralized futures position, which is the futures price change, ignoring the interest on the collateral. The paper builds a daily return series from the most liquid contract (usually the nearest or next nearest) and compounds it. Rolling matters: the return of a futures position includes the roll yield from moving between contracts, which can differ sharply from the spot price change (see rolling futures contracts). Moskowitz, Ooi and Pedersen decompose TSMOM into spot price predictability and roll yield and find that both contribute.

Step 2: the trend signal

The basic signal is the sign of the past 12-month excess return: +1 if positive, minus 1 if negative. Later work uses blends. Brian Hurst, Yao Hua Ooi and Lasse Pedersen’s 2017 study combines 1-month, 3-month and 12-month signals equally. Levine and Pedersen (Financial Analysts Journal, 2016) show that time series momentum in its general form captures moving-average crossovers and other linear trend filters, which is why a CTA’s moving averages and an academic’s lookback returns behave similarly.

Step 3: volatility estimate

The paper estimates each market’s ex ante annualized variance as an exponentially weighted average of past squared daily returns:

sigma squared = 261 x sum over i of (1 minus delta) x delta^i x (r(t-1-i) minus average return) squared

The weight parameter delta is set so the center of mass of the weights is 60 days: delta / (1 minus delta) = 60, so delta = 60/61 = 0.9836. The 261 annualizes daily variance. Crucially, the estimate at the end of month t minus 1 is used for returns in month t, so there is no look-ahead.

Step 4: position size

Each position is scaled to an ex ante volatility of 40%:

TSMOM return = sign(past 12-month return) x (40% / sigma) x next-month return

The 40% is arbitrary (similar to an average single stock). Averaged across markets, the paper’s portfolio had about 12% annualized volatility from 1985 to 2009, and the authors note the construction implies “a use of margin capital of about 5-20%.”

Worked example 1: what volatility scaling does

We generated an illustrative daily return path in Python: 250 days with daily volatility around 1.2%, then 60 days at about 2.4%. Running the paper’s estimator (delta = 60/61, 261-day annualization):

After the calm period, estimated volatility is 18.4%, so the position is 40 / 18.4 = 2.17 times capital in notional exposure.
After 60 turbulent days, estimated volatility rises to 31.2%, and the position shrinks to 40 / 31.2 = 1.28 times capital.

The rule cuts exposure by about 40% as risk rises, without any judgment call. It also means the strategy is slow to re-lever after volatility falls, because the 60-day center of mass forgets slowly.

Worked example 2: sizing a four-market book with real contracts

Take $10 million of capital, four markets and a portfolio-level target of 10% volatility (the target Hurst, Ooi and Pedersen use). If the four strategies were uncorrelated, each would get 10% / sqrt(4) = 5% of volatility. Prices, trends and volatilities below are illustrative; the contract multipliers are the exchanges’ actual sizes.

Market	Notional per contract	12-month return	Volatility	Signal	Target exposure	Contracts
E-mini S&P 500 (ES at 6,800 x $50)	$340,000	+12%	16%	Long	$3.13m	9
10-Year T-Note (TY at 112.85 x $1,000)	$112,850	-3%	6.5%	Short	$7.69m	68
WTI crude (CL at $75 x 1,000 bbl)	$75,000	+18%	35%	Long	$1.43m	19
Gold (GC at $4,000 x 100 oz)	$400,000	+25%	20%	Long	$2.50m	6

Target exposure = 5% / volatility x $10 million. For ES: 0.05 / 0.16 x $10m = $3.125m, divided by $340,000 = 9.19, rounded to 9 contracts. Notice what volatility scaling does: the least volatile market (the note) gets by far the biggest notional position, short $7.7 million, and the most volatile (crude) the smallest. Gross notional, after rounding to whole contracts, is about $14.6 million on $10 million of capital.

Correlation changes the answer. If all four signals pointed the same way and the markets had a 0.5 correlation with each other, the same positions would produce 15.8% portfolio volatility, not 10%, and the portfolio scaler would cut every position by 37% (to 0.632 of its size). Hurst, Ooi and Pedersen use a rolling 3-year covariance matrix for this step. Every position must also be margined, and margin changes with volatility (see how futures margin works).

Worked example 3: a single-market check on EIA data

To see what one market looks like on its own, we ran the paper’s 12-month signal on two energy markets using EIA’s NYMEX futures data (single-contract monthly returns, so no roll is mixed in), with simple monthly returns, a compounded 12-month signal, volatility from the trailing 36-month standard deviation, a 40% target and no costs, through March 2024:

	WTI crude, 1988-2024	Natural gas, 1997-2024
TSMOM Sharpe ratio	0.31	0.27
Volatility-scaled long-only Sharpe ratio	0.21	-0.26
Share of months positive	53%	53%

By decade for crude, the TSMOM Sharpe ratio was 0.41 in the 1990s, 0.44 in the 2000s, 0.07 in the 2010s and 0.05 in 2020-2024. For gas it was the reverse: weak early, stronger later. The results are also fragile to specification: rerun with log returns, crude’s volatility-scaled long-only Sharpe ratio falls from 0.21 to about zero. This is the core statistical fact about the strategy: in any single market, the edge is small and unstable, roughly a coin flip with a slight tilt. The research case rests on diversification across dozens of markets whose trends are imperfectly correlated. Hurst, Ooi and Pedersen report an average single-market Sharpe ratio of about 0.4 across their 67 markets, gross of costs.

A century of evidence

Hurst, Ooi and Pedersen, “A Century of Evidence on Trend-Following Investing” (Journal of Portfolio Management, 2017), extended the test to 67 markets (29 commodities, 11 equity indexes, 15 bond markets, 12 currency pairs) from 1880 to 2016, hand-collecting early commodity futures prices from the annual reports of the Chicago Board of Trade. All three authors were at AQR Capital Management, which runs trend-following funds, a point worth weighing. They caution that before modern futures existed, financing and equity and bond futures are simulated.

Their Exhibit 1, annualized excess returns:

Period	Gross	Net of costs	Net of costs and 2/20 fees	Volatility	Net Sharpe
1880-2016	18.0%	11.0%	7.3%	9.7%	0.76
1910s (weakest)	12.5%	4.1%	1.6%	12.6%	0.13
1970s (strongest)	27.4%	20.5%	15.1%	8.9%	1.70
2000-2009	11.6%	9.9%	6.3%	10.3%	0.61
2010-2016	7.6%	6.2%	3.3%	8.1%	0.41

Correlation to US equities over the full sample was minus 0.01, and to US 10-year bonds minus 0.03. Every decade was positive after costs and fees, but the gap between gross and net is large: fees and costs take almost 60% of the gross return over the full sample, more in the weak decades.

Crisis performance

The paper defines crises as the 10 largest drawdowns of a 60/40 US stock and bond portfolio since 1880. Time series momentum had positive returns in 8 of those 10. The authors’ explanation: most bear markets unfold over months (the 10 largest averaged about 15 months peak to trough), giving the strategy time to turn short. They note it “may not perform as consistently in bear markets that occur very rapidly, such as the 1987 stock market crash.”

In their regime analysis, average excess returns (net of costs, before fees) were 15.5% in bear markets versus 10.2% in bull markets, a difference with a t-statistic of 1.9, which they call “only marginally significant.” They suggest the more robust result is the smile shape. Their simulated 80/20 mix of 60/40 and TSMOM had a maximum drawdown of minus 50.2% versus minus 62.3% for 60/40 alone.

Drawdowns

The strategy’s own worst periods were severe and long. From Exhibit 8 (gross of fees, net of costs):

Rank	Peak	Trough	Size	Months to trough	Months to recover
1	Aug 1947	Dec 1948	-24.7%	16	26
2	Apr 1912	Jan 1913	-22.8%	9	19
3	Feb 1937	Jun 1940	-21.2%	40	14
7	Mar 2015	May 2016	-16.1%	14	not recovered by end of 2016

They also find the strategy did worst when markets were highly correlated, since volatility targeting then forces smaller positions and “there are fewer truly different trends to bet on.” Average correlations rose meaningfully from late 2008 to mid-2014, the risk-on, risk-off period.

The critiques

Two peer-reviewed papers challenge how the evidence is read.

Is the predictability there? Dashan Huang, Jiangyuan Li, Liyao Wang and Guofu Zhou, “Time Series Momentum: Is It There?” (Journal of Financial Economics, 2020), find that “asset-by-asset time series regressions reveal little evidence of TSM, both in- and out-of-sample,” that the pooled t-statistic “is not statistically reliable” against bootstrapped critical values, and that the strategy’s performance “is virtually the same as that of a similar strategy that is based on historical sample mean and does not require predictability.”
Is it the volatility scaling? Abby Kim, Yiuman Tse and John Wald, “Time Series Momentum and Volatility Scaling” (Journal of Financial Markets, 2016), conclude that the Moskowitz, Ooi and Pedersen results “are largely driven by volatility-scaling returns (or the so-called risk parity approach to asset allocation) rather than by time series momentum,” and that “without scaling by volatility, time series momentum and a buy-and-hold strategy offer similar cumulative returns.”

Neither paper says trend-following funds have no value; both say the source of returns may be less about forecasting than the headline studies suggest. Our single-market check above is consistent with the first critique: the edge in any one market is hard to distinguish from noise.

What real CTA indexes show

Simulations are not fund returns. The SG CTA Index, run by Societe Generale’s prime services business, tracks a pool of large CTAs open to new investment, is equally weighted and is reconstituted each January 1. The SG Trend Index is its trend-following subset.

2022: Societe Generale reported the SG CTA Index up 20.1%, its best year since calculation began in 2000, and the SG Trend Index up 27.3%, a year in which stocks and bonds fell together (figures from SG’s 2022 review, as reported by AlphaWeek).
Early 2025: SG’s own “CTA Industry Update” (May 2025) reports that the SG Trend Index lost 4.9% in April 2025, leaving it down 9.3% year to date, in what SG describes as a period when “market trends reverse suddenly and volatility increases”. Over the same months, the SG Short-Term Traders Index was down only 0.9%, which SG uses to illustrate how much model speed matters. The same report notes an average pairwise correlation of 0.78 among SG Trend Index constituents in 2024, yet a range of returns of nearly 15%, and an industry size of about $340 billion (BarclayHedge estimate, Q4 2024).
Model speed: SG’s Trend Indicator, a deliberately simple 20-day/120-day moving average crossover model, has a lifetime correlation of 0.75 to the SG Trend Index. SG found that since 2007 the index has behaved more like slower models, suggesting CTAs have lengthened their signals.
Now: BarclayHedge, which publishes the SG indices, showed estimated performance as of November 10, 2026 of +8.99% year to date and minus 4.28% month to date for the SG CTA Index, and +8.58% year to date and minus 5.09% month to date for the SG Trend Index. Daily estimates are revised, and a sharp loss in the first days of a month is exactly the reversal risk described above.

What can go wrong

Trend reversals. The strategy is built to lose when long trends end abruptly: March to May 2009, the 1987 crash, April 2025.
Trendless markets. Choppy markets generate repeated false signals and transaction costs, as in 2010-2016 and the 2015-2016 drawdown.
High correlation. When markets move together, volatility targeting cuts positions and there are fewer independent bets.
Costs and fees. In Hurst, Ooi and Pedersen’s simulation, costs and fees took roughly 60% of the gross return.
Leverage and margin. Volatility scaling puts the biggest notional positions in the calmest markets, often short-term rates and bonds. A sudden volatility shock in a “calm” market can produce outsized losses and margin calls before the volatility estimate catches up.
Model speed and dispersion. Managers using similar ideas can still differ by 15 percentage points in a year, so an index is not a manager.
Crowding. When many funds hold similar positions, exits can coincide and amplify reversals.

The short version

Time series momentum goes long markets whose own past 12-month return is positive and short those whose return is negative, with each position sized to a volatility target. Moskowitz, Ooi and Pedersen found it in all 58 markets they studied, and Hurst, Ooi and Pedersen found positive returns in every decade since 1880, with gains in 8 of the 10 worst 60/40 drawdowns. The same studies document drawdowns of up to about 25%, multi-year recoveries, weak results in the 2010s and losses when crises end. Critics argue the predictability is statistically fragile and that volatility scaling does much of the work. Real index data confirms both sides: a record 2022, a 9.3% loss by April 2025, and a sharp start to November 2026. This explains how the strategy works and what the evidence shows; it is not a recommendation.