BTC/ETH Lead-Lag: Resolution-Dependent Direction Reversal on Binance Spot
At sub-20-millisecond timescales, ETH leads BTC on Binance spot. Above roughly 15–20 ms, the direction inverts and BTC leads ETH. Both effects are statistically unambiguous across 500,000+ windows and hold in January 2025 and the full calendar year alike.
The conventional claim in crypto market microstructure is the opposite: BTC leads ETH. At multi-second resolution this is broadly true, but the direction reverses as the clock ticks finer. This post establishes that reversal quantitatively across three datasets: January 2025 (31 days, analysed at four resolutions), the complete calendar year 2025 at , and the complete calendar year 2025 at .
1. Mathematical Preliminaries
Let and let denote the -th non-overlapping 60-second window of Binance spot trade data. Within each window, construct the per-millisecond signed-volume process
where is trade size in base-asset units and with . The discrete cross-correlation between BTC and ETH in window is
Notation. denotes the bin width: the resolution at which is discretised before the argmax is taken. The peak-lag estimator for window is
rounded to the nearest multiple of . A window is classified as BTC-leads if , ETH-leads if , and no-lag if .
Among the directional windows, the BTC-leads fraction is
To test whether any observed directional bias is statistically significant, we use the large-sample two-sided proportion z-test
To quantify tail asymmetry at lag magnitude , define the pointwise asymmetry ratio
means BTC-leads windows outnumber their ETH-leads mirror images at that lag; means the opposite.
2. January 2025
2.1. Data and Method
The January 2025 dataset covers all 31 trading days on Binance spot, processed at four bin resolutions . Each day contributes 1,440 non-overlapping 60-second windows, for a total of qualifying windows. The search radius is .
Per-window cross-correlations are computed via the FFT using the Cooley-Tukey
radix-2 algorithm as implemented in rustfft.
At samples, the complexity per window is
, and all 31 days are processed in parallel
across CPU cores via rayon.
2.2. Multi-Resolution Histograms
At , the distribution collapses almost entirely to : most lags are sub-100 ms. Among directional windows, BTC leads 29.4% and ETH leads 27.4% of total windows, with no lag in 43.3%, giving
The signal is statistically present at 100 ms but obscured by the zero spike. At , a secondary bump emerges at , and the ETH-leads bin is approximately larger than the BTC-leads bin. At , the distribution resolves into a left-skewed unimodal shape with mode .
The interquartile range at 1 ms resolution is , confirming that the per-window lag estimate is noisy.
2.3. Direction Breakdown by Resolution
The ETH-leads fraction grows monotonically as :
| BTC leads | ETH leads | No lag | |
|---|---|---|---|
| 1000 ms | 29.3% | 26.2% | 44.5% |
| 100 ms | 29.4% | 27.4% | 43.3% |
| 10 ms | 32.5% | 39.6% | 28.0% |
| 1 ms | 39.9% | 52.7% | 7.4% |
The direction of dominance reverses as resolution improves. At coarse , BTC holds a marginal advantage at a p-value of ; at millisecond resolution, ETH leads with a 12.8 percentage-point gap. Section 4.4 extends this comparison to the full year and adds the full-year row, enabling a direct cross-dataset test of the reversal.
2.4. Interpretation
ETH leads BTC by approximately 1 ms on Binance spot in January 2025, inverting the conventional multi-second narrative. The likely mechanism is that ETH's lower per-trade notional value enables faster order-book clearing, making it the preferred signalling leg for cross-asset arbitrageurs exploiting the BTC/ETH cointegration relationship.
The resolution-dependent reversal is itself informative: at coarse timescales, BTC-driven macro moves (larger in notional magnitude) dominate the cross-correlation sign, while the ETH-leads signal at fine scales is carried by high-frequency arbitrage. The aggregate bias of 12.8 percentage points across 43,200 windows is robust, but not large enough to be reliably exploitable on a per-window basis.
3. Full Year 2025 at 100 ms Resolution
3.1. Data and Scale
Extending the analysis to the complete calendar year 2025 yields qualifying 60-second windows (99.5% data completeness over 365 days), a factor of more than January alone. All full-year analysis in this section uses a single resolution with .
The larger sample sharply reduces the standard error of :
compared to , enabling detection of directional biases approximately four times smaller in absolute terms.
3.2. Distributional Structure
The full-year distribution at is bimodal. A spike at contains 35.9% of all windows, surrounded by tails that decay approximately exponentially. The zero spike is smaller than in January (43.3%), indicating that the full year contains proportionally more windows with detectable directional structure.
| Statistic | January 2025 | Full Year 2025 |
|---|---|---|
| Total windows | 43,200 | 522,719 |
| No-lag fraction | 43.3% | 35.9% |
| BTC-leads fraction | 29.4% | 34.2% |
| ETH-leads fraction | 27.4% | 29.9% |
| Sample mean | +19.6 ms | +25.9 ms |
| Median | 0 ms | 0 ms |
| −100 ms | −100 ms | |
| +100 ms | +200 ms |
The side-by-side comparison reveals two structural shifts. First, the no-lag fraction decreases from 43.3% to 35.9%, meaning the full year contains proportionally more windows with a genuine directional signal. Second, the BTC-leads tails are heavier in the full year, shifting from to and the sample mean from to .
3.3. Tail Asymmetry
Because the zero spike dominates first- and second-order moments, classical skewness is not an informative summary of directional asymmetry. The pointwise asymmetry ratio from [eq:ratio] directly measures the imbalance at each lag magnitude without conflation from the zero spike.
For the full year, at every tested lag magnitude:
The ratio peaks near , which suggests that moderately delayed BTC-leads episodes (those reflecting large cross-asset price moves) are the primary driver of directional asymmetry. By contrast, January 2025 shows at most lags, consistent with its fine-scale ETH-leads bias: in a strong BTC bull run, ETH arbitrageurs are reactive rather than leading.
3.4. Empirical CDF and Stochastic Dominance
Let and denote the empirical CDFs of in-range peak lags for the full year and January, respectively. The observed ordering
constitutes approximate first-order stochastic dominance: conditional on a window having , the full-year distribution assigns more probability mass to larger BTC-leads lags than January does. The third quartile shifts from (January) to (full year), quantifying the extent of this dominance.
3.5. Directional Dominance Test
We test whether BTC-leads and ETH-leads windows occur with equal probability among directional windows:
With and for the full year, the directional count is and the z-statistic is
| Dataset | -value | |||
|---|---|---|---|---|
| January 2025 | 0.5175 | 24,539 | 5.52 | |
| Full Year 2025 | 0.5334 | 334,752 | 38.17 |
The full-year z-statistic of 38.17 rejects at any conventional significance level. Both January and the full year show BTC dominance at . This is consistent with BTC acting as the primary price-discovery venue at multi-millisecond timescales, with ETH adjusting with a delay reflecting arbitrage execution latency.
4. Full Year 2025 at 1 ms Resolution
4.1. Data and Method
The 1 ms full-year analysis uses the same 522,719 qualifying windows as the 100 ms run, but with and . At this resolution, the FFT length expands to 131,072 bins per window and the entire year is processed in approximately 16 minutes on 32 CPU cores (I/O across approx. 1.3 TB of Parquet data is the binding constraint, not computation).
Across 522,719 windows the directional counts are:
The no-lag fraction at 1 ms is 2.4%, compared to 35.9% at 100 ms. At this resolution, virtually every 60-second window has a detectable cross-correlation peak.
4.2. Distributional Structure
The mode at matches January 2025 at the same resolution, confirming the sub-millisecond ETH-leads signal is not confined to the January bull run. The directional z-test gives
ETH leads BTC over the full year at 1 ms resolution, though the effect size (Cohen's ) is substantially diluted relative to January (), where the BTC bull-run concentrated a strong ETH-leads regime.
The mean of appears inconsistent with the mode of . The explanation lies in the long positive tail of the full distribution: among windows outside the shown range (81.9% of all windows), BTC-leads windows at large positive lags outnumber ETH-leads windows at large negative lags, pulling the mean rightward.
4.3. January vs Full Year at 1 ms
Both datasets share the same mode, but the magnitude of the ETH-leads bias differs substantially. In January the BTC-leads fraction among directional windows is 43.1% (), versus 49.0% over the full year (). The effect size dilutes by a factor of approximately 7 as the dataset expands from 31 days to 365 days:
| Dataset | Cohen's | |||
|---|---|---|---|---|
| January 2025, | 0.4309 | 40,003 | −27.65 | −0.139 |
| Full Year 2025, | 0.4904 | 509,963 | −13.73 | −0.019 |
The January ETH-leads signal is a small-to-medium effect (), while the full-year signal is negligible in absolute magnitude but highly statistically significant owing to the large sample.
4.4. Scale-Dependent Direction Reversal
The central finding of this analysis is a resolution-dependent direction reversal:
| Resolution | Dataset | BTC leads | ETH leads | No lag | Dominant | |
|---|---|---|---|---|---|---|
| January 2025 | 39.9% | 52.7% | 7.4% | ETH | −27.65 | |
| Full Year 2025 | 47.8% | 49.7% | 2.4% | ETH | −13.73 | |
| January 2025 | 29.4% | 27.4% | 43.3% | BTC | +5.52 | |
| Full Year 2025 | 34.2% | 29.9% | 35.9% | BTC | +38.17 |
The sign of flips from negative (ETH leads) to positive (BTC leads) as increases from 1 ms to 100 ms, in both January and the full year independently. The cumulative threshold analysis (below) pins the crossover at approximately 15–20 ms.
4.5. Pointwise Asymmetry at 1 ms
At 1 ms resolution, for every lag magnitude in both datasets, the opposite of the pattern seen at 100 ms. The minimum asymmetry ratio for the full year occurs at :
This confirms that at sub-10-millisecond timescales, ETH-leads windows far outnumber BTC-leads windows at the same lag magnitude.
A chi-squared symmetry test, testing simultaneously across all 10 lag magnitudes, strongly rejects symmetry in both datasets:
The full-year chi-squared is approximately 4.6× larger than January's despite the 7× dilution in Cohen's , because the chi-squared statistic grows with ; both unambiguously reject distributional symmetry at 1 ms.
4.6. Significance Across All Resolution and Dataset Pairs
Pooling all tested combinations, the key pattern is unambiguous: the sign of both and Cohen's is determined primarily by , not by the dataset. At , ETH leads; at , BTC leads. The January 1 ms scenario carries the largest absolute effect size (), consistent with a concentrated ETH-leads regime during the BTC bull run.
4.7. Distributional Distance: January vs Full Year at 1 ms
A two-sample Kolmogorov–Smirnov test on the central histogram bins rejects the null hypothesis that January and full-year 1 ms lag distributions are drawn from the same population:
The January distribution is shifted further into the ETH-leads (negative) side relative to the full year, consistent with the stronger bull-run ETH-leads bias in January. The full-year distribution has heavier BTC-leads mass at , pulling the cumulative distribution rightward. For comparison, the same KS test at 100 ms gives , , with the full year shifted rightward (BTC-leads direction) relative to January in that regime as well.
4.8. ETH-leads Advantage vs Lag Threshold
This figure directly visualises the scale-dependent reversal. At , ETH-leads windows account for 72.7% of directional windows in the full year and 70.7% in January, a large majority. As the threshold expands, the ETH-leads fraction falls monotonically. By , BTC leads in both datasets (46.7% ETH in the full year, 48.2% in January). By , the full-year ETH-leads fraction recovers to 50.96%, very slightly ETH, because the large negative- mass in the full distribution leans marginally ETH in aggregate.
The crossover, where crosses 50% from above as grows, occurs between approximately 15 and 20 ms in both datasets. This is the timescale at which the HFT arbitrage channel (ETH leads, sub-10 ms) gives way to the macro price-discovery channel (BTC leads, 100 ms).
4.9. Interpretation
Three findings emerge from the full-year 1 ms analysis:
-
The direction reversal is pinned at 15–20 ms. Below this threshold, the high-frequency ETH-leads channel dominates. Above it, the BTC macro price-discovery channel takes over. The threshold is consistent with typical co-location round-trip latencies on Binance (approximately 0.2–0.5 ms) plus order routing and matching delays, and is the first direct measurement of the crossover timescale for this pair.
-
ETH leads BTC at 1 ms resolution, both in January and over the full year. The mode is in both datasets. The directional bias is highly statistically significant in both ( in January, in the full year), but the effect size dilutes substantially outside the January bull run (Cohen's : vs ).
-
The full-year 1 ms distribution differs significantly from January. The KS statistic (, ) confirms that the January bull run produced a distinctly left-skewed 1 ms distribution; the full year is more symmetric in the central ±10 ms region, consistent with the ETH-leads regime being diluted by non-trending market conditions.
5. Conclusion
At coarse timescales (100 ms and beyond), BTC leads ETH, consistently across January 2025 alone and across the full calendar year. The full-year signal is exceptionally strong: , , with an asymmetry ratio peaking at .
At millisecond resolution, the direction reverses. Both January and the full year show ETH leading BTC with mode . The effect is larger in January (Cohen's , a small-to-medium effect) than over the full year (, negligible in magnitude but statistically unambiguous given ).
The cumulative threshold analysis pins the crossover at 15–20 ms: at lag thresholds below this value, ; above it, . The two channels, HFT arbitrage (ETH leads, sub-20 ms) and macro price discovery (BTC leads, 100 ms+), are statistically separable and operate in opposite directions.
is a function of , the market regime, and the prevailing level of cross-asset arbitrage activity. Treating any single lag estimate as a universal constant discards the most informative feature of the data: its resolution dependence.