Atomic Arbitrage and the Current and Future Impact of CeFi-DeFi Arbitrage

Original title: A Tale of Two Arbitrages

Original author: Ellipsis Labs: Eugene Chen, Jump Crypto: Alex Toberoff and Suraj Srinivasan, Frontier Research: Ankit Chiplunkar

Original source: notion

Translation: Lynn, MarsBit

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TL;DR

• For the same opportunity, arbitrage through CeFi-DeFi (EV_signal) extracts more value than atomic (EV_ordering) arbitrage. Whether an EV_signal or EV_ordering style strategy is executed depends on the cost of bearing risk.

• In Q1 2023, 60% of arbitrage opportunities are captured by CeFi-DeFi strategies.

• EV_signal dominates for high liquidity tokens (i.e., low cost of bearing risk) while EV_ordering dominates for low liquidity tokens.

• In many cases, atomicity is less important than liquidity. The future of cross-chain arbitrage will not be risk-free atomic execution (e.g., chain <> chain), but economically-efficient statistical execution (e.g., chain <> CEX).

Introduction

This work is an extension of “The New Game in Town” where we introduced EV_signal and EV_ordering. The difference between these two extractable values (EVs) is information (also known as alpha). EV_signal requires an information advantage to extract value, while EV_ordering does not. In this article, we introduce the concept of risk into the MEV equation. Theoretically, a trader who bears risk can extract more value from an opportunity than a risk-free trader.

We studied the theory and market structure behind arbitrage opportunities for EV_signal and EV_ordering. Specifically, we studied atomic arbitrage and CeFi-DeFi arbitrage – subsets of EV_ordering and EV_signal, respectively – and proved that atomic arbitrage is risk-free while CeFi-DeFi arbitrage requires bearing risk. We compared them in the theoretical framework and in execution, and used these findings to predict the future of on-chain trading.

This article is divided into four main parts:

• First, we define atomic arbitrage and CeFi-DeFi arbitrage and discuss their conditions for execution on-chain.

• Second, we compare them theoretically and study under which conditions one may have an advantage over the other.

• Third, we measure on-chain arbitrage activity and compare their market sizes empirically.

• Finally, we use these empirical findings to make predictions about the future.

Arbitrage Types

Arbitrage refers to trading price discrepancies between different trading venues in order to bring prices into balance and realize profits. In simplest terms, it involves buying assets on an exchange where the price is lower and selling on an exchange where the price is higher, or vice versa. In cryptocurrency, there are thousands of tokens and hundreds of exchanges (both on-chain and off-chain). Any price discrepancies between them can create an arbitrage opportunity.

Atomic Arbitrage

Atomic arbitrage is one of the earliest MEV opportunities we saw in the wild. The simplest example of atomic arbitrage is when a trading pair is listed on multiple DEXs at different prices. The following image describes how atomic arbitrage strategy trades on two chain-based DEXs until the price is in equilibrium.

(Left) Prices of Binance, Uniswap, and SushiSwap are in equilibrium. (Middle) One user order significantly moves Uniswap’s price. (Right) An atomic arbitrage (back-run) brings the DEX’s price back to equilibrium.

Executing Atomic Arbitrage

Atomic arbitrage is executed in a single, isolated event – hence the name. Either all parts of the trade are executed or none are. Arbitrage happens instantly, and the trader holds no inventory between the two parts of the trade, making this strategy risk-free in terms of inventory hedging. Additionally, off-chain searchers infrastructure (PoW Flashbots auction and PoS block builders private RPCs) guarantees back-run protection; that is, failed trades don’t land on-chain, costing the trader nothing. Because of the above two reasons, this strategy is theoretically risk-free and has a low entry barrier.

Because these trades are risk-free (on the mainnet) and have a low entry barrier, they are highly competitive to execute. Under MEV-Boost, searchers providing the most tips to block builders are included in the block builder’s submission, and block builders providing the most tips to validators win the block. Currently, 91-99% of extractable value goes to the winning searcher to be sent to the validator.

As we add more DEXs and tokens to the picture, atomic arbitrage opportunities become more complex. For example, the route may involve two or more trading pairs or two tokens. But the core idea remains the same: price discrepancies on multiple DEX venues provide arbitrageurs with an atomic, profitable trading opportunity until prices converge.

CeFi-DeFi Arbitrage

When the price of an on-chain asset deviates from its fair value , there is an opportunity for CeFi-DeFi arbitrage. Fair value is simply the best estimate of the valuation of an asset at a given time. The marketplace with the price closest to fair value is referred to as the price discovery venue (this venue changes regularly). In crypto, the price of the strongest liquidity or largest volume exchange can be used to estimate fair value; these are centralized exchanges (CeFi); hence, this strategy is known as CeFi-DeFi. The following figure shows how CeFi-DeFi arbitrage leads to the equilibrium between on-chain prices and fair value (i.e., Binance mid-price).

(Left) The prices of Binance, Uniswap, and SushiSwap are balanced. (Middle) A user’s order causes the price of Uniswap to rise sharply. (Right) CeFi-DeFi arbitrage returns the price to the CeFi price.

CeFi-DeFi arbitrage is possible when on-chain prices move due to large trades or when on-chain prices remain stagnant while off-chain prices move (e.g., off-chain prices move between blocks).

Executing CeFi-DeFi Arbitrage

The simplest form of CeFi-DeFi arbitrage involves two separate trades on two different venues. A leg of the trade is executed until the on-chain price reaches fair value. If this trade is successful, the second leg hedges the accumulated position in another (usually) off-chain trading venue. CeFi-DeFi arbitrage is not atomic and thus involves several risks and significant barriers to entry:

1. Risks:

2. **Inventory risk:** The inventory generated by the first leg of the trade must be warehoused until it is hedged by the second leg of the trade. A mature hedger may exit a position over time, causing the trader to hold the inventory for a longer time. There is inherent risk in holding illiquid tokens because their volatility is higher. CEX liquidity providers may also see that DEX trading has landed and move their quotes in anticipation of this flow.

3. **Inclusion risk:** If multiple traders compete for the same opportunity, it is possible that a trader’s on-chain leg is not included. Thus, the off-chain hedging strategy of the trader needs to consider the on-chain portion not being included. This problem becomes more complex because on-chain reorganizations may restore trades that were confirmed historically.

4. **Adverse selection:** If a CeFi-DeFi arbitrageur trades on-chain, they will bid up the trade over all other arbitrageurs, indicating that they may be overestimating the size of the opportunity (i.e., they are cursed with adverse selection/winners’ curse). Conversely, an atomic arbitrageur is always happy to land their trade because the profit is risk-free.

5. Barriers to entry:

6. **Inventory management:** Having inventory of tokens in both on-chain and off-chain venues is important for statistical arbitrageurs. When dealing with illiquid tokens, the cost of obtaining the tokens and the risk of holding the tokens may outweigh the total opportunity size. Inventory across venues also needs to be rebalanced in preparation for upcoming trades and managed according to the accumulation position of the revenue leg, which incurs additional operational costs.

7. **Latency:** Latency is critical because traders need to know fair value immediately before proposing blocks. This means the entire path—from CEX to the trading system to the bundled relay to the block builder to the block relay to the validator—needs to be optimized.

8. **High capital requirements:** A successful CeFi-DeFi arbitrage trader requires high capital and low fees in off-chain venues. Conversely, to land a successful atomic arbitrage, a trader only needs a valid smart contract and a good bidding strategy (since actual trading capital can usually be obtained through flash loans).

As CeFi-DeFi arbitrage is risky and has high entry barriers, currently 35-77% of the expected extractable value is sent to validators by winning searchers.

Atomic Arbitrage vs. CeFi-DeFi Arbitrage

The key difference between atomic arbitrage and CeFi-DeFi arbitrage is the concept of fair value. This means that in theory, CeFi-DeFi arbitrage has a higher market share, for the following reasons:

1. If the fair value of an asset changes but the on-chain price does not (for example, between two blocks), such opportunities can only be captured by CeFi-DeFi arbitrage.

2. If the price changes on-chain (for example, through user trades), due to lower hedging costs, CeFi-DeFi arbitrage has higher EV than atomic arbitrage.

The left figure shows the price state after atomic arbitrage; note the difference in on-chain and off-chain prices. The right figure shows the price state after CeFi-DeFi arbitrage; note all three prices have returned to equilibrium.

Let us expand the second claim by considering two trading venues where prices are already misaligned. An arbitrage trade hoping to exploit such a discrepancy can be fundamentally decomposed into: (1) an income leg, which is held until the prices realign (while taking into account some profit margin and trading fees); (2) a hedging leg, which unwinds the position accumulated in the income leg. This framework describing the arbitrage legs can be extended to trades with two or more legs, while maintaining the same attributes.

Atomic arbitrage involves the trader unwinding the entire position accumulated in the income part in one execution, without considering slippage or other execution costs; this approach leads to a significantly negative expected PnL for the hedging part. In contrast, in CeFi-DeFi arbitrage and broader EV_signal execution, each leg of the arbitrage is evaluated and executed independently of fair value, allowing the arbitrageur to fully unwind the hedging leg over time. However, this strategy introduces the risks and costs discussed above – namely, inventory acquisition and management risks associated with low-liquidity tokens. As a result, we empirically observe that the cost of this risk, CeFi-DeFi arbitrageurs bid around 35-77% of the income part to validators, while atomic arbitrageurs bid 90-99% of the income.

Although holding post-trade risks and maintaining trading inventory add complexity to trading, CeFi-DeFi arbitrage allows people to realize more income because they can trade precisely out of balance and hedge income portions inexpensively.

Empirical Evidence

To prove the above conclusion, we studied some examples of atomic arbitrage and evaluated their performance in the context of CeFi-DeFi arbitrage. For this, we simulated the expected income of the arbitrageur hedging in centralized venues.

1. High Liquidity Token Arbitrage

At block 16820372, a user submitted a large amount of SNX transactions through FlashWallet, causing the price on SushiSwap to deviate from $531.285 to $545.292. The fair value of SNX on Binance is $533.488.

1. An atomic arbitrageur takes advantage of this difference to trade, earning $21.55 in income and paying a hedging cost of $5.76.

2. If we simulate the same opportunity through CeFi-DeFi, the trader extracts more value by income portion – $22.49 – and then hedges at almost zero effective cost. For high liquidity tokens such as SNX, the hedging cost is almost zero at a trading volume of 1.4WETH.

The result of atomic arbitrage is $15.79 in income (excluding gas), while the result of EV_signal is $22.49 in income (excluding gas) for this transaction. Since the arbitrageur bid 91-99% of this transaction to the builder, and the bidding behavior of EV_signal transaction was 35-77%, EV_signal transaction has a large profit buffer.

1. Low Liquidity Token Arbitrage

We next analyze a two-legged arbitrage involving low liquidity tokens (DSLA token ranked 758th by market value).

1. For atomic arbitrageurs, the first leg here is not only the hedging leg, but also responsible for acquiring inventory. This is a common pattern where the arbitrageur cannot hold long-tail assets and must acquire inventory to execute the income leg – usually at an expensive price. This transaction involves a $5.39 hedging portion, followed by a $10.58 income portion. The hedging portion here is expensive, costing over 50% of the income, making this transaction a primary candidate for EV_signal-style execution.

2. If we simulate the same opportunity in the EV_signal framework, the arbitrageur’s income increases to $14.66. However, the arbitrageur must hold DSLA inventory on-chain before executing the transaction, adding inventory risk to the transaction; therefore, they have higher profit margins for the transaction and bid lower than the EV_ordering transaction.

Nonetheless, this still makes for a convincing EV_signal execution case, given the relatively small nominal amounts of DSLA transactions.

Today’s Arbitrage Situation

In theory, CeFi-DeFi arbitrage can extract more value than atomic arbitrage. From experience, we find that 60% of opportunities (measured by revenue) are executed through CeFi-DeFi arbitrage. Furthermore, data shows that atomic arbitrage dominates in the following cases:

1. The main (liquidity, price discovery) trading venue is on-chain, or

2. The hedging cost (risk carrying) is significantly higher off-chain.

Comparison of atomic and CeFi-DeFi arbitrage in Q1 2023. CeFi-DeFi generated $37.8 million in revenue in Q1 2023, while atomic strategies generated $25 million in revenue. 91-99% of the revenue from atomic trades is paid to validators for inclusion, while only 37-77% of the revenue from CeFi-DeFi is paid to validators for inclusion. The source of atomic trades is EigenPhi.

While there has been good research on the market size of atomic arbitrage, and it is easy to estimate, the same cannot be said for CeFi-DeFi arbitrage. First, a dataset containing all exchanges with `to_addr’ corresponding to known searchers is collected. Thereafter, EigenPhi’s data is used to filter out exchanges determined to be atomic arbitrage (or related to sandwich attacks). Finally, the revenue for each trade is determined by calculating the instantaneous spot price relative to the mid-price in centralized exchanges (the mid-price used comes from the most liquid venue for a given token). We note that our coverage of swaps is not exhaustive (about 80% coverage), so our estimates are a conservative lower bound .

95% of atomic arbitrage opportunities are executed on low liquidity tokens, i.e. arbitrage includes at least one low liquidity token. 91% of CeFi-DeFi opportunities are executed on high liquidity tokens, i.e. all tokens in the arbitrage are high liquidity.

We see a clear relationship between the liquidity of the traded tokens and the type of arbitrage. Specifically, we find that the majority of CeFi-DeFi arbitrage involves trades with high liquidity tokens (we define high liquidity tokens as the top 100 tokens by market capitalization), and vice versa. This relationship suggests that the price discovery venue for low liquidity tokens is indeed on-chain, and that off-chain hedging costs are significantly higher.

In this analysis, we excluded the days of the USDC strike, as it was an abnormal event. During this period, atomic arbitrage revenue was slightly close to $10 million, while CeFi-DeFi revenue was around $2.8 million. This divergence indicates that the cost of hedging (risk-taking) increased significantly during this time, leading to a reduction in opportunities. In other words, CeFi-DeFi arbitrageurs were forced to consider inventory risks related to USDC during the de-stocking period and accordingly reduced their business.

Conclusion and Future Impact

In this article, we describe and analyze arbitrage opportunities in the EV_ordering and EV_signal frameworks. We dissect and separate the concept of risk and show how, in general, executing EV_ordering trades in an EV_signal manner increases expected PnL. However, inventory acquisition and management risks limit the EV_signal-style execution of low-liquidity tokens. This conclusion is empirically supported, and we observe that low-liquidity tokens are extremely common in atomic arbitrage, while CeFi-DeFi arbitrage dominates high-liquidity tokens. Based on these results, we propose the following impacts on the industry’s future:

The Future of Cryptocurrency Arbitrage

As searchers continue to gain complexity off-chain and off-chain liquidity continues to dominate on-chain liquidity, more arbitrage will be captured through CeFi-DeFi. While temporary short-term shocks (such as CEX solvency and liquidity uncertainty) will temporarily increase the cost of risk-taking, thus benefiting atomic arbitrage, we believe the long-term trend will be EV_signal > EV_ordering. In addition, we note that this analysis does not consider sandwich attacks. With the rise of OFA and intent-based trading, the proportion of on-chain sandwich and other cutting-edge strategies will decrease and convert into reverse arbitrage opportunities, increasing the overall revenue share of atomic and CeFi-DeFi strategies.

The Future of Block Building and Search

Block builders will optimize low-latency connections with exchanges and block relays to obtain more accurate off-chain states before block proposals. As EV_signal style trading becomes more competitive, search will need to develop predictive models that go beyond the midpoint prices in liquidity exchanges to fair value (alpha). We have observed this, with some searchers bidding for block space based on predicted fair value.

The Future of Cross-Chain Arbitrage

This analysis has similarities in the context of cross-chain transactions. Specifically, we believe that concerns about validators proposing blocks on multiple chains are exaggerated because cross-chain MEV can be atomically extracted. In many cases, atomicity is less important than liquidity.

In a world where cross-chain transaction bundling is guaranteed atomicity, arbitrage of high liquidity tokens will continue to be executed in an economically efficient EV_signal style. Even for tokens traded entirely on-chain, well-capitalized actors are willing to hold capital across multiple chains and execute arbitrage in a statistical way rather than paying for guaranteed multi-chain atomicity.

Special thanks to Stephane Gosselin, Mike Setrin, Lev Livnev, and Alex Nezlobin for their valuable insights.

References

1. New game in town

2. MEV Markets Blockingrt 1: Proof of Work

3. MEV Markets Blockingrt 2: Proof of Stake

4. The Orderflow Auction Design SBlockingce

5. Unity is Strength: A Formalization of Cross-Domain Maximal Extractable Value

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