Crude oil starts trending higher on Monday. By Thursday, gasoline futures follow. Two weeks later, heating oil catches up. If you only traded each market based on its own price history, you entered gasoline and heating oil late. The signal was already sitting in crude, days before the lagging markets moved.
This is the problem that network momentum solves. Instead of treating every futures contract as an island, it maps the lead-lag relationships between markets and uses the leaders to generate earlier signals for the laggers. A January 2025 paper on arXiv, “Follow the Leader: Enhancing Systematic Trend-Following Using Network Momentum” (arXiv:2501.07135), formalizes this idea and tests it on commodity futures. The results show statistically significant improvements in Sharpe ratio, return skewness, and downside protection compared to standard time-series momentum.
I run a diversified futures watchlist and have noticed these lead-lag patterns informally for years, especially in energy. Seeing them quantified in a rigorous framework made me want to break down the concept for traders who already use momentum-based indicators but have never considered cross-asset signals.
What Time-Series Momentum Gets Wrong
Standard TSMOM, as documented by Moskowitz, Ooi, and Pedersen in 2012, works like this: look at each asset’s return over the past 12 months, go long if positive, short if negative, and size by inverse volatility. Across 58 futures contracts and 25 years of data, this produced Sharpe ratios around 1.0 with strong crisis-alpha properties.
The approach has a blind spot. It treats every contract independently. Crude oil knows nothing about gasoline. Copper knows nothing about zinc. Each asset waits for its own return to flip before the model acts.
In practice, markets are connected. Supply chains, substitution effects, and macro drivers create persistent lead-lag structures. When the leading asset moves first, the signal is already visible to anyone watching the network. But TSMOM, by design, ignores it.
This is not a minor inefficiency. In choppy markets where TSMOM generates whipsaws, the network signal from a leader can confirm or deny the move before you commit capital to a lagging asset. If crude is flat while gasoline spikes, the network says “caution.” If crude is surging and gasoline has not yet moved, the network says “prepare.”
How Network Momentum Works
The core idea has three steps.
First, detect which assets lead and which lag. The paper uses Granger causality tests and rolling correlation analysis across the futures universe. If past returns in asset A statistically predict future returns in asset B (but not the reverse), A leads B. Run these tests on rolling windows to capture the fact that lead-lag relationships shift over time.
Second, build a directed momentum network. Each asset becomes a node. Each lead-lag relationship becomes a directed edge, weighted by the strength and consistency of the predictive signal. The result is a map showing how momentum propagates across markets.
Third, blend the network signal with the traditional univariate TSMOM signal. For any given asset, the final position incorporates both its own past return and the weighted momentum of its network leaders. The blending weight controls how much influence cross-asset information has versus the asset’s own history.
The formula for the blended signal on asset i at time t looks like this:
S_{i,t} = (1 - \alpha) \cdot \text{TSMOM}_{i,t} + \alpha \cdot \sum_{j \in \text{Leaders}(i)} w_{j \to i} \cdot \text{TSMOM}_{j,t}
Where \alpha is the network blending weight (the paper tests values around 0.2 to 0.3), w_{j \to i} is the lead-lag strength from asset j to asset i, and \text{TSMOM}_{j,t} is the standard momentum signal for the leader.
Where Lead-Lag Relationships Are Strongest
Not all asset pairs have useful lead-lag structure. The paper focuses on commodity futures, where supply chain linkages create natural propagation channels.
Energy is the clearest example. Crude oil, as the upstream input, tends to lead refined products like gasoline and heating oil by days to weeks. When crude trends, the products follow with a lag that reflects refining margins, inventory cycles, and contract roll timing.
Base metals show a similar pattern. Copper, as the most liquid and macro-sensitive metal, often leads zinc, aluminum, and nickel. The mechanism is different (macro sensitivity rather than supply chain), but the statistical result is the same: a persistent directional lead.
Agricultural commodities are noisier. Soybeans sometimes lead soybean meal and soybean oil, but weather events and harvest timing introduce regime-dependent reversals. The lead-lag is real but less stable.
Across asset classes (rates, equities, commodities, FX), the relationships exist but are weaker and more regime-dependent. The paper sticks to commodity futures, where the linkages are most robust. I think that is the right starting point for anyone implementing this. Commodities first, then expand if the out-of-sample results hold.
What the Research Actually Shows
The paper tests network momentum against standard univariate TSMOM on a universe of commodity futures. The key findings:
Sharpe ratio improves. The blended network signal produces higher risk-adjusted returns than the pure TSMOM baseline. The improvement comes from entering lagging assets earlier (capturing more of the move) and avoiding false signals in laggers when leaders are not confirming.
Return skewness improves. Standard TSMOM in choppy markets generates negative skewness through whipsaws. The network filter reduces false entries in laggers, which cuts the left tail. You still take losses, but fewer of the “entered on noise” type.
Downside protection improves. By conditioning lagging-asset entries on leader confirmation, the strategy avoids some of the worst whipsaw losses. The effect is most visible during regime transitions, exactly when TSMOM is most vulnerable.
The results use bootstrapped synthetic data for robustness testing, which addresses the small sample problem inherent in futures backtests. This is a real methodological strength. Too many momentum papers report in-sample Sharpes without addressing the multiple-testing problem.
Practical Implementation for Trend Followers
You do not need a neural network to use this. The core implementation is straightforward if you already run a TSMOM system.
Start with your existing universe. Take 15-20 diversified futures (2-3 energy, 2-3 metals, 2-3 grains, equity indices, rates, FX). Run rolling Granger causality tests with a 60-day window, testing whether the past 5 daily returns of asset A predict the next 5 daily returns of asset B at the 5% significance level. This gives you a directed adjacency matrix that updates weekly.
For each lagging asset, weight the leaders by their Granger F-statistic (normalized to sum to 1). This is your network signal weight vector. Blend it with the univariate TSMOM signal using a 20-30% network weight. Keep the blend conservative at first. More is not better here, because overfitting the lead-lag structure to recent data is a real risk.
The ADX indicator can help filter when to trust the network signal. If the leading asset has ADX above 25, the directional move is established and the lead-lag propagation is more likely to follow through. If ADX is below 20, the leader is range-bound and the network signal carries less conviction.
I would also cross-reference with the rate of change on the leader. A 12-month rate of change that just turned positive is a different signal than one that has been positive for six months and may be decelerating. Network momentum works best when the leader is in the early or middle phase of its trend.
Common Mistakes with Cross-Asset Signals
The biggest risk is treating lead-lag as permanent. It is not. Crude leads gasoline most of the time, but during refinery outages, gasoline can lead crude. The rolling window approach handles this, but you need to respect the signal when it flips. Many traders build a mental model of “crude always leads” and ignore the statistical evidence when the relationship temporarily reverses.
Another mistake is using too short a lookback for Granger tests. With daily data, you need at least 40-60 observations to get stable results. Weekly data is too sparse for most futures pairs. Daily at a 60-day rolling window is a reasonable starting point.
Overfitting the blend weight is tempting. If you optimize \alpha on in-sample data, you will find values that look great historically but degrade out of sample. The paper’s recommendation of 0.2 to 0.3 is a sensible default. I would fix it at 0.25 and not touch it.
Finally, do not apply this to asset pairs without an economic rationale for the lead-lag. Statistical Granger causality can appear between unrelated assets by chance, especially over short windows. If you cannot explain why asset A should lead asset B through a supply chain, macro channel, or substitution effect, treat the statistical result as spurious.
Network Momentum vs. Cross-Sectional Momentum
This is different from traditional cross-sectional relative strength strategies. Cross-sectional momentum ranks assets by recent performance and goes long the winners, short the losers. It does not care about lead-lag structure. It just buys strength and sells weakness.
Network momentum is directional and causal. It asks: “Which specific assets predict which other specific assets, and in which direction?” An asset can be a network leader even if its absolute return ranks in the middle of the cross-section. What matters is predictive power, not relative performance.
The two approaches are complementary. You could run cross-sectional momentum for universe selection (which assets are trending) and network momentum for timing (when to enter the laggers). The drawdown quality filter adds a third dimension by screening which of those trending laggers are pulling back cleanly rather than erratically.
When Network Momentum Fails
Three scenarios reduce the value of this approach.
Synchronized shocks. When all assets in a sector move simultaneously (a macro surprise, a flash crash, a coordinated policy announcement), there is no lead to follow. Everyone moves at once, and the network signal provides no advance warning. March 2020 is a good example. Crude, gasoline, metals, equities, everything gapped together.
Structural breaks in lead-lag relationships. A regulatory change, a new pipeline, or a shift in refining capacity can permanently alter which assets lead. The rolling window adapts, but slowly. You lose signal during the transition period.
Low-volatility environments. When nothing is trending, lead-lag signals are noise. The Granger tests will still produce results, but they are not actionable because the momentum being transmitted is too small to cover transaction costs. ADX filtering on the leaders helps here.
Reading the Network as a Regime Indicator
One underappreciated use of the momentum network is as a regime indicator. When the network becomes highly connected (many significant lead-lag relationships with strong weights), momentum is propagating broadly across markets. This tends to happen during trending regimes where macro themes dominate. Think 2022: rising rates led falling bonds, which led falling equities, which led falling crypto. The network was dense and directional.
When the network becomes sparse (few significant lead-lag relationships), markets are driven by idiosyncratic factors rather than shared momentum. This typically coincides with choppy, range-bound conditions where TSMOM underperforms regardless of whether you add network signals.
Tracking the density of the network over time (count the number of significant edges at each rebalance) gives you a simple regime filter. High density: trust momentum signals, including network signals, and size normally. Low density: reduce overall position sizing and lean more heavily on univariate signals from only the strongest individual trends.
Where This Fits in a Trend-Following System
Network momentum is not a replacement for TSMOM. It is an overlay. The base system remains: 12-month lookback, inverse-volatility sizing, diversified futures universe. The network adds an information source that the univariate system ignores.
The practical improvement is not dramatic. Expect a moderate Sharpe improvement, not a doubling. The real value is in reducing whipsaw losses on lagging assets and slightly better entry timing. Over hundreds of trades per year, that compounds meaningfully. But it is not a silver bullet, and it requires ongoing maintenance of the Granger test pipeline and periodic review of which lead-lag relationships remain economically justified.
For anyone already running systematic trend-following on futures, this is worth testing. Start with energy pairs where the lead-lag is most intuitive, validate out of sample, and expand cautiously.
Educational content only. Not investment advice. Trading involves risk. You are responsible for your decisions.