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 $\delta t = 100\,\mathrm{ms}$, and the complete calendar year 2025 at $\delta t = 1\,\mathrm{ms}$.

1. Mathematical Preliminaries

Let $A \in \{\mathrm{BTC}, \mathrm{ETH}\}$ and let $W_k$ denote the $k$-th non-overlapping 60-second window of Binance spot trade data. Within each window, construct the per-millisecond signed-volume process

where $s_i$ is trade size in base-asset units and $t \in \{1, \ldots, T\}$ with $T = 60{,}000$. The discrete cross-correlation between BTC and ETH in window $W_k$ is

Notation. $\delta t$ denotes the bin width: the resolution at which $\tau$ is discretised before the argmax is taken. The peak-lag estimator for window $W_k$ is

rounded to the nearest multiple of $\delta t$. A window is classified as BTC-leads if $\widehat{\Delta\tau}^{(k)} > 0$, ETH-leads if $\widehat{\Delta\tau}^{(k)} < 0$, and no-lag if $\widehat{\Delta\tau}^{(k)} = 0$.

Among the $n_d = N_{\mathrm{BTC}} + N_{\mathrm{ETH}}$ 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 $\tau > 0$, define the pointwise asymmetry ratio

$R(\tau) > 1$ means BTC-leads windows outnumber their ETH-leads mirror images at that lag; $R(\tau) < 1$ 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 $\delta t \in \{1000, 100, 10, 1\}\,\mathrm{ms}$. Each day contributes 1,440 non-overlapping 60-second windows, for a total of $N = 43{,}200$ qualifying windows. The search radius is $\tau_{\max} = 200\,\mathrm{ms}$.

Per-window cross-correlations are computed via the FFT using the Cooley-Tukey radix-2 algorithm as implemented in rustfft. At $T = 60{,}000$ samples, the complexity per window is $\mathcal{O}(T \log T)$, and all 31 days are processed in parallel across CPU cores via rayon.

2.2. Multi-Resolution Histograms

At $\delta t = 100\,\mathrm{ms}$, the distribution collapses almost entirely to $\widehat{\Delta\tau} = 0$: 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 $\delta t = 10\,\mathrm{ms}$, a secondary bump emerges at $\widehat{\Delta\tau} = -10\,\mathrm{ms}$, and the ETH-leads bin is approximately $1.7\times$ larger than the BTC-leads bin. At $\delta t = 1\,\mathrm{ms}$, the distribution resolves into a left-skewed unimodal shape with mode $\widehat{\Delta\tau} = -1\,\mathrm{ms}$.

The interquartile range at 1 ms resolution is $[-20, +21]\,\mathrm{ms}$, confirming that the per-window lag estimate is noisy.

2.3. Direction Breakdown by Resolution

The ETH-leads fraction grows monotonically as $\delta t \to 0$:

The direction of dominance reverses as resolution improves. At coarse $\delta t$, BTC holds a marginal advantage at a p-value of $3.5 \times 10^{-8}$; 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 $\delta t = 1\,\mathrm{ms}$ 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 $N = 522{,}719$ qualifying 60-second windows (99.5% data completeness over 365 days), a factor of $\approx 12\times$ more than January alone. All full-year analysis in this section uses a single resolution $\delta t = 100\,\mathrm{ms}$ with $\tau_{\max} = 1{,}000\,\mathrm{ms}$.

The larger sample sharply reduces the standard error of $\hat{p}_{\mathrm{BTC}}$:

compared to $\mathrm{SE}_{\mathrm{Jan}} \approx 0.0032$, enabling detection of directional biases approximately four times smaller in absolute terms.

3.2. Distributional Structure

The full-year distribution at $\delta t = 100\,\mathrm{ms}$ is bimodal. A spike at $\widehat{\Delta\tau} = 0$ 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.

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 $P_{75}$ from $+100\,\mathrm{ms}$ to $+200\,\mathrm{ms}$ and the sample mean from $+19.6\,\mathrm{ms}$ to $+25.9\,\mathrm{ms}$.

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 $R(\tau)$ from [eq:ratio] directly measures the imbalance at each lag magnitude without conflation from the zero spike.

For the full year, $R(\tau) > 1$ at every tested lag magnitude:

The ratio peaks near $\tau = 200\,\mathrm{ms}$, 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 $R < 1$ 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 $\hat{F}_{\mathrm{FY}}$ and $\hat{F}_{\mathrm{Jan}}$ 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 $\widehat{\Delta\tau} > 0$, the full-year distribution assigns more probability mass to larger BTC-leads lags than January does. The third quartile shifts from $+100\,\mathrm{ms}$ (January) to $+200\,\mathrm{ms}$ (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 $N_{\mathrm{BTC}} = 178{,}551$ and $N_{\mathrm{ETH}} = 156{,}461$ for the full year, the directional count is $n_d = 334{,}752$ and the z-statistic is

The full-year z-statistic of 38.17 rejects $H_0$ at any conventional significance level. Both January and the full year show BTC dominance at $\delta t = 100\,\mathrm{ms}$. 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 $\delta t = 1\,\mathrm{ms}$ and $\tau_{\max} = 2{,}000\,\mathrm{ms}$. 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 $\widehat{\Delta\tau} = -1\,\mathrm{ms}$ 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 $h = -0.019$) is substantially diluted relative to January ($h = -0.139$), where the BTC bull-run concentrated a strong ETH-leads regime.

The mean of $+19.1\,\mathrm{ms}$ appears inconsistent with the mode of $-1\,\mathrm{ms}$. The explanation lies in the long positive tail of the full $\pm 2{,}000\,\mathrm{ms}$ distribution: among windows outside the $\pm 10\,\mathrm{ms}$ 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 $-1\,\mathrm{ms}$ mode, but the magnitude of the ETH-leads bias differs substantially. In January the BTC-leads fraction among directional windows is 43.1% ($z = -27.65$), versus 49.0% over the full year ($z = -13.73$). The effect size dilutes by a factor of approximately 7 as the dataset expands from 31 days to 365 days:

The January ETH-leads signal is a small-to-medium effect ($|h| > 0.1$), 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:

The sign of $z$ flips from negative (ETH leads) to positive (BTC leads) as $\delta t$ 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, $R(\tau) < 1$ for every lag magnitude $\tau \in \{1, \ldots, 10\}\,\mathrm{ms}$ in both datasets, the opposite of the $R > 1$ pattern seen at 100 ms. The minimum asymmetry ratio for the full year occurs at $\tau = 1\,\mathrm{ms}$:

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 $H_0: N(+\tau) = N(-\tau)$ 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 $h$, because the chi-squared statistic grows with $n$; 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 $z$ and Cohen's $h$ is determined primarily by $\delta t$, not by the dataset. At $\delta t \in \{1, 10\}\,\mathrm{ms}$, ETH leads; at $\delta t \in \{100, 1000\}\,\mathrm{ms}$, BTC leads. The January 1 ms scenario carries the largest absolute effect size ($|h| = 0.139$), 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 $\pm 10\,\mathrm{ms}$ 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 $\tau > 0$, pulling the cumulative distribution rightward. For comparison, the same KS test at 100 ms gives $D = 0.055$, $p = 6.7 \times 10^{-83}$, 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 $\tau_{\max} = 1\,\mathrm{ms}$, 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 $\tau_{\max} = 100\,\mathrm{ms}$, BTC leads in both datasets (46.7% ETH in the full year, 48.2% in January). By $\tau_{\max} = 2{,}000\,\mathrm{ms}$, the full-year ETH-leads fraction recovers to 50.96%, very slightly ETH, because the large negative-$\tau$ mass in the full $\pm 2{,}000\,\mathrm{ms}$ distribution leans marginally ETH in aggregate.

The crossover, where $p_{\mathrm{ETH}}$ crosses 50% from above as $\tau_{\max}$ 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:

1. 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.

2. ETH leads BTC at 1 ms resolution, both in January and over the full year. The mode is $-1\,\mathrm{ms}$ in both datasets. The directional bias is highly statistically significant in both ($z = -27.65$ in January, $z = -13.73$ in the full year), but the effect size dilutes substantially outside the January bull run (Cohen's $h$: $-0.139$ vs $-0.019$).

3. The full-year 1 ms distribution differs significantly from January. The KS statistic ($D = 0.046$, $p = 3.7 \times 10^{-29}$) 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: $\hat{p}_{\mathrm{BTC}} = 0.533$, $z = 38.17$, with an asymmetry ratio peaking at $R(200\,\mathrm{ms}) = 1.320$.

At millisecond resolution, the direction reverses. Both January and the full year show ETH leading BTC with mode $\widehat{\Delta\tau} = -1\,\mathrm{ms}$. The effect is larger in January (Cohen's $h = -0.139$, a small-to-medium effect) than over the full year ($h = -0.019$, negligible in magnitude but statistically unambiguous given $n_d > 500{,}000$).

The cumulative threshold analysis pins the crossover at 15–20 ms: at lag thresholds below this value, $p_{\mathrm{ETH}} > 50\%$; above it, $p_{\mathrm{BTC}} > 50\%$. 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.

$\widehat{\Delta\tau}$ is a function of $\delta t$, 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.