📈 economics

Triangular Pricing Consistency and Limits to Arbitrage in Ethereum Markets

This paper analyzes Ethereum's triangular pricing consistency across USD, BTC, and stablecoin numeraires from 2022 to 2023, finding that while price deviations generally remain near zero and non-arbitrageable even during market stress, they represent frictional parity deviations rather than executable profit opportunities.

Original authors: Hongzhe Wen

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hongzhe Wen

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the cryptocurrency market as a giant, 24-hour global bazaar where people trade digital assets like Ethereum (ETH) and Bitcoin (BTC). In this bazaar, you can buy things in three different ways:

Directly: Paying with US Dollars (USD).
Indirectly: Paying with Bitcoin (BTC).
Via a Proxy: Paying with a "digital dollar" called a stablecoin (like USDT).

The paper by Hongzhe Wen asks a simple but crucial question: Do these different ways of pricing the same item actually agree with each other?

The "Three-Point Check" Analogy

Think of the market like a set of three connected scales.

Scale A weighs Ethereum in Dollars.
Scale B weighs Ethereum in Bitcoin.
Scale C weighs Bitcoin in Dollars.

Mathematically, if you take the price of Ethereum in Bitcoin (Scale B) and multiply it by the price of Bitcoin in Dollars (Scale C), you should get the exact same number as the direct price of Ethereum in Dollars (Scale A).

If Scale A says "100 dollars" but the math from Scales B and C says "105 dollars," the scales are out of sync. This difference is called a "wedge."

What the Research Found

The author looked at data from Coinbase (a major exchange) over 18 months to see how often these scales disagreed. Here is what they discovered, using simple terms:

1. The Scales Usually Agree (Most of the Time)
In normal, calm market conditions, the "wedge" is almost non-existent. The direct price and the calculated price match up incredibly well. It's like having three clocks in a room; usually, they all show the exact same time. The average difference is so tiny (less than one-hundredth of a penny) that it's practically zero.

2. The Scales Don't Drift (They Snap Back Fast)
Sometimes, the scales might disagree for a moment. But the paper found that these disagreements don't last. They don't slowly drift apart over days. Instead, they snap back to zero very quickly (in about 12 minutes). This suggests that if a price looks "wrong" for a second, the market fixes it almost immediately.

3. Chaos Makes the Scales Wobble (Stress Events)
The study looked at three specific times when the crypto market was in panic mode:

The collapse of the Terra/Luna coin.
The collapse of the FTX exchange.
The banking crisis involving Silicon Valley Bank (SVB).

During these stressful times, the "wedges" got bigger. The scales disagreed more often and by larger amounts. However, the author argues this isn't because the market is broken or because Ethereum is fundamentally "worth" a different amount. Instead, it's like a busy airport during a storm: flights get delayed, and the schedule looks messy, but it's just friction and panic, not a permanent change in the value of the planes.

The "Arbitrage" Myth (Can You Get Rich Off This?)

A common idea in finance is that if prices don't match, you can make free money by buying low and selling high instantly (called "arbitrage").

The author tested this by looking at the "bid-ask spread" (the difference between the buying and selling price) and the fees you have to pay to trade.

The Finding: Even when the prices looked slightly off during the panic events, the gap was never big enough to cover the fees and the spread.
The Metaphor: Imagine you see a store selling a toy for $9.90 and another selling it for $10.10. It looks like you can make 20 cents. But if it costs you 50 cents in gas and tolls to drive between the stores, you actually lose money. The paper found that in the crypto market, the "gas and tolls" (fees and spreads) are always higher than the "free money" gap.

The "Digital Dollar" Question

The author also checked if using "digital dollars" (stablecoins like USDT) instead of real US Dollars caused more confusion.

The Surprise: The market using digital dollars (on Binance) was actually more consistent (tighter) than the market using real dollars (on Coinbase).
The Lesson: This suggests that the "digital dollar" isn't the main reason for price confusion. Instead, the confusion comes from how busy or calm the specific exchange is at that moment.

The Bottom Line

This paper concludes that the Ethereum market is actually quite efficient.

On average: Prices are consistent across different currencies.
During panic: Prices get messy and disagree more, but this is due to market stress and trading costs, not a fundamental flaw in the value of Ethereum.
For investors: You generally cannot find "free money" by exploiting these tiny price differences because the costs of trading eat up any potential profit.

The study treats the market like a well-oiled machine that occasionally gets a little sticky during a storm, but it doesn't break.

Technical Summary: Triangular Pricing Consistency and Limits to Arbitrage in Ethereum Markets

Problem Statement
Digital asset markets operate continuously across multiple venues and numeraires (e.g., U.S. dollar, Bitcoin, and stablecoins). A central question in market efficiency is whether prices remain internally coherent across these different units of account. Specifically, this paper investigates whether Ethereum (ETH) prices satisfy a triangular pricing identity linking the direct ETH/USD rate, the ETH/BTC rate, and the BTC/USD rate. The core problem is distinguishing between a genuine pricing inefficiency (an executable arbitrage opportunity) and a frictional parity deviation caused by market microstructure, liquidity constraints, or stress events. The paper argues that observed deviations should not be automatically interpreted as intrinsic misvaluation of Ethereum in dollar terms, but rather as relative pricing inconsistencies subject to limits to arbitrage.

Methodology
The study employs a conservative, single-venue empirical design to isolate cross-numeraire consistency from cross-exchange settlement frictions and stablecoin-specific risks.

Baseline Data: The primary analysis uses hourly spot data from Coinbase (January 2022 – June 2023) for three pairs: ETH/USD, ETH/BTC, and BTC/USD. The "true-USD" leg ensures the dollar proxy is fiat, not a stablecoin. Synchronization is performed via intersection-only (no forward filling) to avoid artificial alignment.
The Wedge Metric: The paper defines a triangular pricing wedge, $\epsilon_t$ , as the log-difference between the direct price and the synthetic price:
$\epsilon_t = \log P^{ETH/USD}_t - \log P^{ETH/BTC}_t - \log P^{BTC/USD}_t$
A value of zero indicates perfect consistency.
Statistical Diagnostics: The paper utilizes Augmented Dickey–Fuller (ADF) tests to check for unit roots, AR(1) coefficients to measure persistence, and state-dependent regressions to analyze how the absolute wedge $|\epsilon_t|$ responds to market volatility, trading volume, and specific stress events (Terra/Luna collapse, FTX collapse, USDC–SVB crisis).
Extensions and Robustness:
- Binance Extension: A parallel analysis using USDT (Tether) as the dollar proxy to test if stablecoin denomination inherently creates larger deviations.
- Gate.io Extension: A stress-window analysis using historical order-book snapshots (bid/ask) to construct executable bands. This tests whether observed midquote wedges translate into positive after-fee round-trip profits.
- Methodological Negative: An attempted reconstruction of Coinbase midquotes using OHLC high-low ranges was found invalid due to aliasing and lack of synchronization, serving as a boundary for the study's claims.

Key Results

Near-Zero Mean and Low Persistence: In the Coinbase true-USD baseline, the wedge has a sample mean of approximately $-0.065$ basis points (bp), which is economically indistinguishable from zero. The ADF statistic ($-110.893$) strongly rejects a unit root, and the AR(1) coefficient is low ( $\approx 0.0315$ ), implying a half-life of roughly 0.20 hours. This indicates that deviations are not persistent drifts but rapid, mean-reverting fluctuations.
Stress-State Widening: While the average wedge is tight, the magnitude of deviations increases significantly during market stress. Mean absolute wedges rise from $2.604$ bp in calm periods to $4.472$ bp during the FTX collapse and $4.176$ bp during the USDC–SVB crisis.
Stablecoin Denomination is Not the Dominant Driver: Contrary to the hypothesis that stablecoin proxies introduce mechanical noise, the Binance USDT extension shows a tighter unconditional wedge (mean absolute $0.862$ bp) compared to the Coinbase true-USD baseline ($2.655$ bp). This suggests that venue liquidity and arbitrage efficiency are more critical determinants of wedge magnitude than the specific type of dollar proxy.
Limits to Arbitrage (Executable Bands): The Gate.io order-book analysis reveals that even during stress events, the measured midquote wedges remain well within the bid-ask spread plus transaction fee bands. Across 524 event-hour observations, there were zero instances of a positive after-fee executable triangular breach. The largest observed gap remained inside the executable band by over 23 bp.

Key Contributions

Conceptual Framing: The paper reframes Ethereum pricing from a standalone absolute valuation problem (determining the "true" dollar value of ETH) to a relative asset-pricing problem focused on cross-numeraire consistency. It treats the triangular identity as a no-arbitrage restriction in relative prices rather than a structural valuation model.
Empirical Discipline: By isolating a single venue with true-USD legs, the study provides a "clean" reduced-form measure of cross-numeraire consistency, free from the confounding factors of cross-exchange settlement or stablecoin reserve risks.
Distinction Between Wedge and Arbitrage: The research explicitly demonstrates that a non-zero pricing wedge does not equate to an executable arbitrage profit. The Gate.io extension provides empirical evidence that stress-state widening represents frictional parity deviations rather than costless profit opportunities.

Significance and Claims
The paper makes a modest, bounded claim: Ethereum cross-numeraire prices are tightly consistent on average, and deviations are best interpreted as state-dependent frictional parities rather than evidence of persistent intrinsic mispricing.

The findings support the view that while market stress (e.g., FTX collapse) slows the adjustment of relative prices and widens wedges, these deviations do not constitute exploitable arbitrage opportunities once transaction costs and bid-ask spreads are accounted for. The paper concludes that the triangular pricing restriction holds as a useful first-order constraint in digital asset markets, but its violation during stress reflects limits to arbitrage and liquidity frictions rather than fundamental valuation errors. The study explicitly avoids claiming to identify the specific structural mechanisms (e.g., inventory constraints vs. risk-bearing capacity) driving these frictions, positioning its results as a disciplined baseline for future research into market microstructure and stress dynamics.