Cross-Chain Arbitrage and the Leader-Follower Problem

1. The default assumption

When you deploy a cross-chain arbitrage strategy, one of the first decisions you make is how to split capital across chains. Most people default to 50/50. It feels symmetric, neutral, and safe.

It is none of those things.

A 50/50 split is not a neutral choice. It is an implicit assumption: that both chains are equally likely to present exploitable spreads, that those spreads last the same amount of time, and that each unit of capital generates the same expected return regardless of where it sits. In a real market, none of these assumptions hold.

This article is about why, and what the right allocation looks like instead.

This builds on the SIA/SDA framework from https://alessiogiannini.dev/reasoning-under-uncertainty-the-decision-layer-of-a-cross-chain-mev-bot.

The capital allocation principle discussed here applies to both: in SIA it determines how much inventory to pre-position on each chain, in SDA it determines which direction to originate trades from most of the time.

2. Price discovery is not symmetric

In any two-venue market, price discovery is never perfectly symmetric. One venue moves first. The other follows.

The asymmetry is informational. Markets are continuously processing signals: a large trade on a CEX, a shift in the order book, a macro event, an oracle update. Each carries new information about what the asset is worth. The venue that processes this first and reflects it in its prices is the leader. The venue that adjusts later, once arbitrageurs or its own participants notice the discrepancy, is the follower.

This is not random. It is structural. The leader tends to be the venue with faster block times, deeper liquidity, and direct exposure to external price flows. Its prices are more current. The follower's prices are older, sometimes by one block, sometimes by several.

The gap between the current price and the price on the follower chain is exactly the spread a cross-chain arbitrageur is trying to capture.

This dynamic exists between any two markets that trade the same asset. But it becomes most pronounced and most exploitable when the venues differ significantly in speed. A CEX updating its order book in milliseconds versus a DEX that settles in blocks.

Two chains with different block times, different liquidity depth, different exposure to informed order flow. The greater the speed differential, the longer the follower takes to catch up, and the wider and more durable the spread.

3. The asymmetry of time

Knowing that a leader-follower relationship exists is not enough. The more important question is: how long does the spread last?

It is not symmetric. And this is the part most capital allocation models ignore.

When price moves upward, it tends to do so gradually. The leader adjusts in increments as new information arrives. The follower lags. Each block on the follower chain still reflects a price that is one or two adjustments behind. The leader reaches the new price and holds it.

The follower converges block by block. The spread is wide, it persists across multiple blocks, and there is time to observe it, size a position, and execute.

Upper line: leader (3s blocks, price fluctuates around the new level as liquidity adjusts). Lower line: follower (converging at each 10s block but never fully closing the gap). Between t=0 and t=40s the leader has produced 13 blocks. The follower has produced 5.

The gap between the two lines is the spread available to the arbitrageur at each moment. It starts at $500 and narrows, but never reaches zero. Fees, slippage, and execution latency create a floor below which arbitrage becomes unprofitable. The residual gap is not an opportunity: it is the cost of the market.

The spread narrows but never closes completely. The final residual (~$50) sits below the cost threshold (gas, bridge fees, slippage) and is no longer actionable. This floor is structural, not accidental.

When price moves downward, the dynamic changes. Downward moves tend to be more impulsive: sharp drops concentrated in a few blocks, driven by liquidations, panic selling, or large directional trades.

Arbitrageurs react immediately. The follower is realigned quickly, often within a single block or two. The spread exists, but it closes before most participants can act on it.

The implication is direct: not all spreads have the same expected value. Spreads aligned with upward price discovery (where the leader is expensive and the follower is cheap) last longer, are easier to execute, and generate more robust EV. Spreads in the opposite direction exist but are shorter, noisier, and profitable only when wide enough to compensate for the shorter window.

EV does not come from the direction of the spread. It comes from the duration during which the spread remains exploitable.

4. Capital follows the leader

The implication for capital allocation is direct: if one direction generates more durable and more frequent spreads, your strategy will execute it more often.

You need the right asset, in the right place, when the opportunity appears.

A 50/50 split ignores this. Equal capital on both sides means regularly exhausting inventory on the high-frequency side while carrying idle capital on the other. Idle capital has zero EV.

The correct allocation skews toward the dominant direction. The exact split is not fixed: it depends on measured EV, how often each spread appears, how long it lasts, and what the fill rate is under real conditions.

One constraint matters: the allocation does not react to price. It reacts to structure. It changes only when the underlying relationship changes: relative liquidity, block times, access to external price flows.

Price moving is not a signal to reallocate. Structure changing is.

5. When there's no leader

Not every pair of venues has a clear leader. When two chains are similar in block time, liquidity depth, and access to external price flows, neither systematically discovers price before the other. Price discovery is more balanced, though rarely perfectly equal.

In this case, a rigid asymmetric allocation is not justified upfront. But 50/50 is still not the answer.

Even without a structural leader, the two directions of arbitrage are not equivalent. They differ in average spread duration, fill rate, slippage, and competitive pressure. These differences may be smaller than in a clear leader-follower regime, but they exist, and they show up in EV.

The correct approach is not to assume a split, but to measure one. Start with a near-symmetric allocation as an exploratory state. Run simulations across both directions. Measure EV per direction, fill rate, spread duration, and variance. Then break the symmetry based on what the data shows, not on prior assumptions.

6. How to identify the leader

Identifying the leader requires structural signals first, empirical measurement second.

Block time is the most direct proxy: a faster chain updates prices more often and processes arbitrage corrections before the slower one catches up.

Liquidity depth and volume point in the same direction: deeper, busier markets attract more informed order flow, and informed flow is what drives price discovery.

These signals are hypotheses. The confirmation comes from data.

7. Conclusion

The 50/50 default is not neutral. It is a claim: that both directions are equally valuable, in a market with a leader and a follower, none of this is true.

Price discovery is asymmetric. The venue that processes information first holds the current price. The other holds an older one. The gap between them is the opportunity, and how long that gap persists determines its value.

Capital should follow that structure: not the trend, not the price, not intuition about which chain is faster. Put capital where spreads are most durable, where EV per unit is highest, as confirmed by real data.