Author: Boo Canoe Founder

His twitter https://twitter.com/0x_jem

Abstract

In this paper, we provide an overview of the on-chain market maker business and introduce the on-chain strategy through mathematical and engineering perspectives. In contrast to traditional market makers on centralized finance platforms, the on-chain market maker business significantly differs in terms of fund size, PnL function, volatility modeling, derivative strategy, and arbitrage. Finally, we propose some effective suggestions for new on-chain market makers.

1 Introduction

Enables market makers to seamlessly flow into DeFi liquidity.

The recent collapse of Alamend Research and FTX highlights the power of decentralization philosophy in the DEX and DeFi space. However, it’s worth noting that the liquidity size is still largely controlled by CEX. To shift the balance of price power towards DEX from CEX, we need to focus on building infrastructure for traditional market makers, which would support an “on-chain Alamenda Research” in DEX.

2 Constraints for ETH Arbitrage Strategy.

Running an arbitrage strategy on ETH has become highly competitive due to the existence of MEV. Let’s take a look at two on-chain arbitrage examples.

The first successful arbitrage is within one transaction hash. The red part in the picture shows a profit of 0.8526 ETH ($1,408). It’s a basic arbitrage strategy where the arbitrage space is from the trading router.

To calculate the profit,

$0.8526 = -12.0258( Buy$LOOK ) + 12.8784 ( sell$LOOK ), all in one TX.

Cost of case 1

• Probability (higher nonce by the node means higher probability).

• Profit and cost (flashloan size and its rate)

• MEV cost (optional). MEV bribe ensures the transaction is the first and the profit is maximized.

The second arbitrage, a sandwich, is a bit more complicated with three transactions hash in a same block. MEV cost is necessary in the sandwich as shown in the red part. In this attack, the MEV bot paid 24 ETH for the bribe and sent it to the block builder. Then, we can see a revenue of 362 ETH he can get in the third transaction at this sandwich attack. Revenue subtract principle of the first transaction is profit, where the principle is 313 ETH.

To calculate the profit,

Cost of case 2

• MEV bribe successfully (it’s a high cost which is 24 ETH in case 2)/

• Auto-monitoring and auto-engineering cost on sandwich opportunity

• High principle for influencing the sandwich profit size.

However, the PnL of an arbitrage can’t be modeled. In other words, it’s not a strategy-oriented problem, but an engineer/machine-oriented problem.

Fig1, MEV engineering cost.

It’s not advisable to deploy an arbitrage bot on ETH now. The cost and barrier of ETH arbitrage can be summarized as follows:

1. Engineer and time cost is too high because of gas cost and ETH data structure for most new guys.

2. MEV bots attack the fund on-chain, your fund will be arbitraged by MEV bots.

3. MEV attack is hard to model because it’s based on uptime and MEV-boost bribe which is out of a financial mathematical methodology.

4. Arbitrage profit is highly affected by MEV bribe (~24 ETH in an example below).

3 Comparison of Liquidity Provision Strategies.

To work within the limitations of arbitrage on ETH, it’s best to allocate a significant amount of funds (over $1M) to a professional market maker team focused on DEX liquidity provision. This section will provide an overview of the risk management strategy for DEX LP, including perspectives on IL modeling and options strategies.

3.1 Importance of Risk Hedge for On-Chain Market Makers

Market Makers primarily aim for market neutrality, not market manipulation, as we discussed in Series 2. Hedging risk on LP positions helps them manage significant liquidity, enabling them to flow seamlessly into DeFi liquidity. Once we provide a quantitative framework on risk hedging, market makers can deploy a fund size like CEX, shifting the pricing power from CEX to DEX.

3.2 Risk Source: Mathematical Definition and Figure of IL on UNIv2-v3

Before we discuss risk hedge strategy, let’s analyze the Impermanent Loss math and figure of Uniswap.

V2

Fig2, UNI-V2 IL with a fee still has a positive gain as the k change.

The impermanent loss function IL(k, ρ) is related to price movement, where $k = \frac{P’}{P}$ which means price movement. As shown in the figure above, when the price moves within 2ρ from the original price, liquidity providers will have a positive gain. In other ways, when the market is in high volatility, LP will suffer a loss.

V3

Fig3, UNI-V3 IL as the k change.

Pros: Liquidity Provision’s main risk source is from IL.

Cons: Impermanent Loss is a function of Price Movement(k) in Univ2 / V3.

3.3 IL is a Failed Factor for MM Strategy.

Based on the mathematical function of IL, it is theoretically possible to design a Delta Hedging option strategy or remove liquidity to avoid IL losses.

Strategy I: Delta Hedging Option Strategy

In this section, we construct a Liquidation Position PnL function by introducing a research paper “Delta Hedging Liquidity Positions on Automated Market Makers” [2] by Akhilesh (Adam) Khakhar and Xi Chen. In the paper, PnL is defined by the difference between the final value of the liquidity pool assets and the initial value of the liquidity pool assets, which is highly similar to the IL definition.

Compared with their math functions, they are very similar, in other words, such PnL definition can’t give more signals than IL itself. In Chaos Labs’s LP dashboard solution, we can draw a figure in a real LP case.

Fig4, PnL(blue) and IL(yellow) figure has a high correlation

Following, in the “Delta Hedging Liquidity Positions on Automated Market Makers” paper, they construct the PnL algorithm with options strategy, where the Payoff function part is a combination of the delta-hedge option strategy.

However, this strategy failed to work in practical market-maker hedge scenarios.

Here are three reasons:

1. There is a significant issue with liquidity friction in Options Markets.

2. The key factor is Price movement, as IL(PnL) is a function of K. This factor K is highly dependent on the volatility and is closely related to Delta/Gamma/Vega in Options, influencing Payoff function.

3. From an intuitive perspective, because PnL is similar to IL, the most effective approach to avoid IL is to remove liquidity during periods of high volatility, as seen in many v3 IL hedge products through Automated Liquidity Vault Strategies.

Cons: Reason 3 derives strategy II, removing liquidity when high volatility.

Strategy II: Remove liquidity when high volatility.

A large number of UNIV3 products use Strategy II to help users avoid massive impermanent loss, however, most of them failed.

Let’s take a look at a typical product @dHedgeOrg with Strategy 2, automatically removing the LP when high volatility and rebalancing assets.

Fig5, dHedge remove liquidity in high fluctuation(Volatility)

Through the comparison between the fluctuation(Volatility) region and the log liquidity region, it’s apparent they adopt strategy II frequently during 2022–04 ~ 2023–01, a bear market that ETH dropped -67% during the period.

More analysis on similar products can be seen in a report by Antalpah Labs Zelos team[3], Strategy II products include @GammaStrategies, @ArrakisFinance, @PopsicleFinance, @unipilot_io, @torosfinance.

All of the strategy performance was not satisfactory.

Fig6, strategy performance overview.

3.4 Another Perspective on LP Hedge: DEX LP as Option Itself

In this section, we’ll see two effective strategies from another innovative framework for DEX LP hedge strategy. The framework is summarized as “LPing is like selling options without any upfront premium” by Jason Milionis, the relationship to option strategies math details proposed by an amazing paper, Automated Market Making and Loss-Versus-Rebalancing[4].

In the LvR paper, they apply the risk-neutral pricing equation to evaluate intrinsic value and time value of an LP position. In the paper, the Value of LP can be defined in option equation exactly as follows,

Where,

In simple terms, volatility and premium are the main factors in modeling LP strategies. So, it’s ideal to have a Short Vega option strategy that considers both factors simultaneously in CeFi option market rather than a delta strategy. Therefore, Uniswap LP as an option framework is better than IL-only option strategy.

Strategy III: Spot Hedging — Effective LP Strategy for Billions Dollar Size

Based on the perspective of Uniswap LP as an option, a popular and effective strategy is to buy/sell the risk asset in the opposite way.

In the DeFi summer, an effective LP management strategy works with billions dollar size during a bull market. For example, a fund raised by ETH and USDT, and the rate is following:

• raise ETH(risky asset), 5% rate in ETH principal payment

• raise USDT, 20% rate.

Strategy III is simple:

1. Spot buy/sell at CEX for hedging, trading signal is from CTA, a traditional quant strategy.

2. Remove liquidity at a volatility threshold.

In LvR[4] model, they quantify the cost of LP, which also can guide the strategy III rather than trading based CTA signal. It’s a useful strategy when the TVL boom in a bull market, but as the market goes to bear, it’s impossible to do spot hedge for on-chain LP, every strategy failed in a bear market with few money liquidity.

Strategy IV: LP Short Strategy by Lending

DEX LP is a passive position which typically involves longing the pool assets it provides. For example, in a UNI-USDT pool, when UNI’s price increases, the pool will gradually sell UNI and add more USDT to the LP, resulting in a net positive P&L when denominated in USDT. However, during a bear market like 2022, the LP has to buy low-value UNI and maybe sell all its UNI asset at a low price. This explains why most Uni V3 vault strategy products slightly outperformed or even lost during the period of April 2022 to January 2023, as shown in Strategy III by Fig6.

Strategy IV provides a short strategy or a bearish strategy by borrowing specific assets, as selling the risky asset is not possible without holding such asset on the position. To construct a bearish strategy, the amount of assets to be borrowed can be determined using a formula derived by Guillaume Lambert using the Euler Finance lending protocol.

We can derive the first derivative by calculating the amount H we should borrow for constricting a bearish strategy. The mathematical overview can be seen Guillaume Lamber blog[5].

The Strategy IV is quite straightforward; one should borrow 100% of the risky asset and deposit liquidity in UNI V2 when they wish to provide a UNI-USDT pool but desire to short UNI in a bear market. This will enable them to earn a LP fee on the short strategy. However, the capital utilization is low due to the collateral in the lending protocol.

4. Conclusion

4.1 Suggestions for New On-Chain Market Makers

After discussing arbitrage possibilities and researching four main strategies, we propose three suggestions for new on-chain market makers.

Arbitrage Strategy

• Arbitrage within the same transaction hash costs nothing and there is still opportunity on ETH and other EVM chains like Arbitrum/OP. We can use a flashloan to achieve higher profit margins. If we fail, nothing is lost. In some extreme market conditions, maximum profit can be achieved at $100,000. However, these opportunities are becoming fewer and fewer, 1–2 per month for new market makers.

• Sandwich arbitrage in high-TPS chains like BSC/Aptos. Unlike ETH, sandwich arbitrage works within a few blocks, not in one block, and should model the historical data of pool size, transactions, time intervals, etc.

• Generally speaking, multi-DEX trading router optimization can unlock more profit through arbitrage. If we don’t consider high gas/MEV cost, such problems can be solved in an optimal theory framework. The DEX router algorithm can be easily achieved in Julia/Python by coding examples like Theo Diamandis’s CFMMRouter.jl[6].

LP Management Strategy

Effectiveness Difficulties Suggestions Strategy I: Delta Hedging Option Strategy x Medium Challenging due to complexity and market friction. Strategy II: Liquidity Removal during High Volatility Low Low Simple but somewhat underwhelming. Strategy III: Spot Hedging and Liquidity Removal High Low Migrating to a new chain can be effective. Strategy IV: LP Short Strategy by Lending Medium High Too complex and low capital utilization.

• In summary, Strategy III, which involves spot trading and liquidity removal, is an effective and straightforward approach for any new on-chain market makers. We can sell/buy the risky asset in the LP pool through CTA signals or LvR models, while removing liquidity during specific volatility thresholds is also a straightforward method.

• It is reasonable to create a Profit and Loss (PnL) function based on LvR concept instead of the pool asset value. While monitoring the performance of the strategy, the dashboard should use the PnL function rather than the asset holding value. The latter is not sufficient for managing risk.

• Take advantage of the backtest framework. The team at @Antalpha_Labs has made available an open-sourced backtest framework, Demeter, which evaluates the LP strategy on Univ3. You can check out the coding at zelos-demeter[7]. The performance of Strategy II products is based on the Demeter backtesting framework.

On-Chain Fund Custodian and Strategy Execution

• Approve a predetermined amount to a smart contract in advance, ensuring timely execution of the strategy. Once the withdrawal is complete, the approval will be canceled.

• Use a multi-sig contract to create a shared fund with a whitelist that approves DeFi smart contracts (such as Uniswap router and Aave).

4.2 Future: Shifting Pricing Power from CEX to DEX

As on-chain liquidity grows to exceed that of centralized exchanges (CEX), the pricing power of cryptocurrencies will shift to decentralized exchanges (DEX). This paper introduces an arbitrage and liquidity strategy to attract more CEX market makers to DeFi through profit-driven means, enabling them to seamlessly move liquidity into DeFi.

Fortunately, there are more infrastructure solutions for on-chain market makers, such as RFQ, orderbook DeFi (such as Serum and dYdX), high-TPS chains, and optimal MM incentives in financial engineering.

However, there is a significant gap in solving this problem, which may take decades to resolve. We believe that the gap lies in two parts:

• Engineering: Market makers run high-frequency strategies with uptime that even reaches the millisecond level in CEX. However, on-chain infrastructure cannot support such an environment due to the Blockchain Trilemma. Decentralization and security (with guaranteed gas cost) limit the high-frequency strategy in the micro data structure.

• Automated Market Maker (AMM) model: The current AMM model cannot support proactive market maker strategies apart from low capital utilization, which prevents most projects from considering DEX as a price discovery place.

[1] https://medium.com/@leo-lau

[2] https://arxiv.org/pdf/2208.03318.pdf

[3] https://medium.com/zelos-research/2022-annual-fund-review-of-uniswap-v3-part-1-70ea5d335ff1

[4]https://moallemi.com/ciamac/papers/lvr-2022.pdf

[5]https://lambert-guillaume.medium.com/how-to-deploy-delta-neutral-liquidity-in-uniswap-or-why-euler-finance-is-a-game-changer-for-lps-1d91efe1e8ac

[6]https://bcc-research.github.io/CFMMRouter.jl/dev/

[7]https://pypi.org/project/zelos-demeter/

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