Author: Umberto Natale, [email protected]
Decentralized Finance (DeFi) is a profound paradigm shift, redefining how the world engages with financial services. It is reshaping the world of financial services, with liquidity provision at its core. In traditional finance, centralized intermediaries have controlled access to financial services. DeFi changes this by empowering users and placing liquidity provision as the cornerstone. It's the linchpin that enables seamless trading, lending, and complex financial strategies, making DeFi accessible and efficient.
Automated Market Makers (AMMs) - see e.g. Uniswap - have harnessed the power of liquidity provision, allowing anyone to contribute assets to pools that facilitate trading. A defining characteristic of AMMs is their inclusivity, allowing anyone to create markets for tokens and provide liquidity without needing permission. Both DeFi composability and absence of asset custody by intermediaries push market participants opt for AMMs over centralized exchanges (CEXs). The decentralized nature of AMMs minimizes technical barriers to market making, unlocking a vast reservoir of previously untapped capital. AMMs have the potential to outperform centralized exchanges in terms of liquidity provision (G. Liao and D. Robinson), with a high potential to revolutionize trading.
Conversely, Decentralized Exchanges (DEXs) driven by a Central Limit Order Book (CLOB) - see e.g. dYdX v4 - demand a substantial pool of assets and ample order depth for smooth operation. The CLOB is adept at consolidating liquidity around the market price and has the flexibility to adjust quotes as needed. However, the process of actively matching buy and sell orders to connect traders directly poses a unique challenge. Market makers in CLOB-based DEXs must consistently update their positions to prevent their orders from becoming stagnant. This dynamic nature of CLOBs, while offering powerful tools for price discovery, also renders liquidity provision a more intricate endeavor. This complexity is particularly pronounced for those traders who may not have access to real-time market data, as remaining profitable in such an environment requires a deep understanding of market dynamics and order flow.
AMMs and decentralized CLOBs are the dynamic engines driving the DeFi ecosystem, demonstrating the pivotal role of liquidity provision. Yet, for Liquidity Providers (LPs) navigating the DeFi landscape, a central challenge looms – adverse selection, as extensively explored in J. Milionis et al for AMMs and U. Natale et al for CLOBs. This article delves deep into these intricate mechanisms, unveiling the intricate tapestry of challenges and opportunities that liquidity providers confront. Focusing primarily on Uniswap v3 as our exemplar AMM, we explore the complexities and potential solutions in this dynamic landscape. In the final section, we unveil a beacon of hope for LPs, shedding light on how they can recoup a portion of their losses caused by adverse selection through the powerful strategy of staking.
Among the leading AMMs, Uniswap is a pioneering DEX protocol that has impressively processed over $1.5 trillion in lifetime volume since its 2018 debut (cfr. DefiLlama), with over $1 trillion processed by Uniswap v3 (H. Hadams et al). Central to its operation is the concept of concentrated liquidity (CL), empowering LPs to offer assets within specific price ranges. LPs facilitate the smooth flow of assets and liquidity, making the success of these AMMs critically dependent on LPs participation, who provide liquidity in exchange for trading fees.
For LPs participating in AMMs, the primary challenge is adverse selection, cfr. J. Milionis et al. This issue arises because parties with access to real-time market prices can exploit price discrepancies between AMMs and other platforms. These transactions often involve arbitrage between CEXs and DEXs. To succeed in capitalizing on price disparities, individuals need not only priority access to the first few on-chain transactions in a block (T. Gupta et al) but also the ability to execute high-quality trades on CEX. This intricate dance between different venues clearly forms the backbone of efficient AMM trading, however it might have adverse effect on LPs.
In U. Natale et al, we evaluate how pricing on dYdX v4 could be impacted by the presence of another CLOB with higher liquidity, for a given asset - e.g. a CEX. However, it's important to note that this platform is not live at the moment. This means that making a direct comparison of the profitability of professional Market Makers in a decentralized order book like dYdX v4 is currently unfeasible. Consequently, for the remainder of our analysis, our primary focus will be on Uniswap v3, where Concentrated Liquidity presents intriguing opportunities and challenges worth exploring in the evolving DeFi landscape.
Estimating the effective Profit&Loss (PNL) for a LP has been a subject of extensive study in the literature. One widely debated estimator, discussed fervently in the context of the profitability of ETH/USDC LPs on Uniswap v3, revolves around Markouts, as outlined in a thought-provoking Medium Article by CrocSwap. However, it's crucial to highlight that Markouts, as an estimator, may not present a holistic view of LP profitability on Uniswap v3. This is because Markouts typically overlook the genuine liquidity and the precise price range within the pool. Consequently, they may overlook changes in the value of the numéraire within the pool, focusing solely on the risky asset's fluctuations. The omission of these critical factors can significantly impact the accuracy and comprehensiveness of LP profitability assessments.
In order to avoid possible biases in the analysis, we decided to use an estimator that is dependent from the actual variation in pool value. For this purpose, let’s observe that, for any price range, the pool value in terms of token1 ($T_1$) can be written as
$$ \begin{equation} V(P) = T_0 P + T_1\,. \end{equation} $$
This can be easily expressed in terms of the current price, the price range, and liquidity as (H. Hadams et al)
$$ \begin{equation} V(L,P,P^L,P^H) = L\left(2\sqrt{P}-\frac{P}{\sqrt{P^H}}-\sqrt{P^L}\right)=L\bar{V}(P,P^L,P^H)\,. \end{equation} $$
From Eq. (2), we can define the pool value variation as
$$ \begin{equation} \Delta V(P_i,P_f) = V(P_f) - V(P_i) = V_f - V_i\,, \end{equation} $$
where we removed the dependencies in the notation for the sake of simplicity. We further assumed that the price moves from $P_i$ to $P_f$. It is worth noting that, the price, for a fixed range and liquidity, can be seen as a function of time. This means that, at any given time, we can define the total PNL for the entire pool as