Uniswap v3 and Implied Volatility
Introduction
This post aims to demonstrate an example of how one might derive Implied Volatility (IV) from Uniswap v3’s liquidity distribution and use it to identify pools with relatively small liquidity and volatility yet high fee returns. In other words, we seek a systematic approach to pinpoint “profitable pools” by comparing fees, liquidity, and volatility.
What Is IV?
Implied Volatility (IV) is generally understood as “the anticipated future volatility of the underlying asset.” In traditional finance, this figure is often derived from options pricing, where a higher implied volatility suggests a greater expected range of price movement.
Below is an illustration from the options exchange Deribit, comparing Implied Volatility (IV) with Realized Volatility (RV). Notice that IV tends to be reasonably close to RV over time.
(Source: Deribit)
IV in the Context of Uniswap v3
Guillaume’s IV Definition
This post highlights one specific definition of Uniswap v3 implied volatility proposed by Guillaume Lambert. Uniswap v3 allows liquidity providers (LPs) to specify a custom price range for their liquidity. If we assume LPs act rationally, then the expected fee earnings should roughly offset the expected impermanent loss (IL). Based on this equilibrium assumption, Guillaume derives a formula that relates daily trading volume, the distribution of liquidity (by tick), and the implied volatility.
(Source: Medium (Guillaume Lambert))
Visualizing Profitability
In Guillaume’s formula, daily volume is divided by “tick liquidity,” but the Dune dashboard referenced below takes the more granular approach of calculating volume/tick liquidity\text{volume}/\text{tick liquidity}volume/tick liquidity per swap (rather than on a daily basis) and then aggregates it via a weighted average. This swap-based approach arguably provides a more precise measure.
Comparing IV and RV Across Chains
Below is an example dashboard showing ETH/USDC (0.05% fee tier) on multiple chains. It also compares Realized Volatility (the actual price movement, approximating impermanent loss) over a 20-day average so you can quickly see the difference between IV and RV.
(Source: Dune: kyoronut)
We also have a custom dashboard that filters by chain and currency, directly visualizing IV minus RV. An area above zero indicates the fee earned surpasses impermanent loss, while an area below zero indicates fees have not compensated for IL. The cumulative area above or below zero over time effectively illustrates an LP’s profitability.
Important note: the liquidity provision or rebalancing period is assumed to be 20 days. Pairs like BTC/ETH, which can be more correlated over a longer horizon, might look unprofitable over a 20-day window. For longer holding periods, the results could differ.
(Source: Dune: satoshicoin)
Identifying Profitable Pools
A major takeaway is that large pools (with substantial TVL) have often yielded negative returns for LPs over the past few months. This suggests that standard LP strategies—such as supplying liquidity in a reasonably wide range and occasionally rebalancing—may fail to outpace IL under current market conditions. Furthermore, in 2023, the relatively low yields in DeFi lending protocols (e.g., ~2% on Curve, Aave) indicate that achieving higher yields may require a distinct competitive edge or a more specialized approach.
In the IV-RV comparison, smaller altcoin pools or less liquid pools periodically show short bursts of higher profitability. This creates an opportunity for LPs who can time these “profitable windows.” Since IV is predicated on a balance of fee income and impermanent loss, any short-term inefficiency in the market (a “mispricing” in terms of liquidity distribution) can be exploited before new entrants add liquidity and reduce the yield.
Potential Approaches
Short-Term Exploitation: Jump into pools during temporary imbalances, where fees exceed the anticipated IL.
Non-Standard LP Positions: Rather than simply providing a wide range of liquidity, consider more dynamic or specialized strategies.
Under-the-Radar Pools: Explore less prominent pairs that exhibit occasional spikes in trading volume relative to their liquidity.
Future Challenges and Considerations
Risk-Free Rate
Current IV calculations do not factor in the risk-free rate. Similar to the Black-Scholes model, incorporating the risk-free rate could produce a more accurate measure of fair implied volatility.
Event-Driven Volatility
Single events like the Shanghai upgrade for ETH or the temporary USDC de-peg can cause significant short-term distortions. Measuring long-term profitability may require normalizing or filtering out these event-driven spikes.
Benchmarking Against “Base” Pools
Comparing a target pool’s performance to an established benchmark pool (e.g., WETH/USDC 0.05% on Ethereum) could help identify true outliers. You might track IV-RV or overall LP returns relative to an “average” or “reference” pool to see if a particular pool is consistently outperforming the market.
References
Panoptic Paper – Calculating IV from Uniswap v3 Liquidity Distribution
Guillaume Lambert’s Blog – On-chain Volatility and Uniswap v3
Note: GammaSwap’s approach aligns with the “fee vs. IL” equilibrium concept but derives IV from historical data to find an aggregated breakeven, whereas Guillaume Lambert’s method calculates volume/tick liquidity\text{volume}/\text{tick liquidity}volume/tick liquidity on a per-swap basis.
Final Thoughts
Uniswap v3’s Implied Volatility can provide a unique lens for evaluating the profitability of a particular liquidity position. By comparing IV to Realized Volatility (RV), LPs can identify when fees are sufficiently high to offset expected impermanent loss. However, market conditions, specific events, and the dynamics of liquidity provision (e.g., rebalancing intervals) play significant roles.
Ultimately, strategies that rely on identifying short-term dislocations in IV-RV, or adopting an unconventional method of supplying liquidity, may hold the best chance for outperformance in the current DeFi environment.
