Expected Price Range Strategies in Uniswap v3
Breaking down recent academic research in liquidity provision on DeFi
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Uniswap v3 was released less than two months ago, which brought a major innovation to liquidity provision on DeFi: concentrated liquidity. Rather than offering the assets you staked in a liquidity pool over all possible prices, you are free to offer your liquidity over a specific range of prices. This innovation is expected to improve capital efficiency, while at the same time adding significant complexity to liquidity provision, requiring active monitoring in order to effectively earn fees.
In this first post, we will be discussing recent research from Harvard researchers who analyze a set of liquidity provision strategies on Uniswap v3, evaluating which strategy offers the most attractive risk-reward proposition for liquidity providers (“LPs”).
The paper is titled “Strategic Liquidity Provision in Uniswap v3”, and it develops a framework for analyzing expected price range strategies¹, which are an intuitive decision rule used to decide at which prices and with which intensity to provide liquidity on automated market makers that allow concentrated liquidity.
In the expected price range strategies proposed by the authors, liquidity is provided over a range around the current price, drawn from historical data on where the price is likely to move in the next 10 minutes (“expected price range”). Thus, the strategy uses prior experience in order to provide liquidity only in the range where the price is expected to be in the near future. This liquidity is provided within the expected price range until the price moves outside a second price range called the “move strategy range”, as indicates when to move the strategy.
A figure from the paper provides an illustration of the strategies that they propose:
Imagine that we are providing liquidity in an ETH/USD stablecoin pool, and that prices are divided into bins, represented as circles in the chart above. The strategy indicates that liquidity should be offered in a three bin range, the green colored circles labelled “allocation 1”, with an identical indicator range. The price begins in the center green ball with a darker overlay, which represents the current price.
The price begins to increase (shown as dark circle shifting to the right), and by t = 2 has left the range over which liquidity is being provided. This implies that the strategy must be moved, with the current price as the new center of the expected price range to be established. In t = 3 the strategy has moved the expected price and move strategy ranges, as can be seen from the change in color to yellow (“allocation 2”) and a movement of the colored bins to the right. In this same time period the price began to drop, and by t = 4 the strategy dictates another movement, with a shift of the strategy visible in t = 5 (“allocation 3”) to cover the downwards moving price.
To calibrate the expected price and move strategy ranges, the authors collected 10-minute ETH price data from March 2018 to April 2020, and estimated how likely the price is to move within this time interval, which varies within the [-3%, 3%] range. The authors consider setting the width of the expected price and move strategy ranges as a percentage of the probability that the price will be within the range in the next 10 minutes. The paper provides visual representation of this distribution of percentage price changes, which is used to derive the strategy’s ranges when a movement for the strategy is triggered:
Having described the general strategy, I will introduce an additional innovation the authors consider that goes beyond the flexibility currently provided by Uniswap v3. In the concentrated liquidity framework, you provide liquidity in the indicated range uniformly, that is, with a similar willingness to trade your assets as long as the price remains in your range.
The authors suggest that offering liquidity differentially within the expected price range can offer a better risk-reward tradeoff than the uniform distribution that is the default. This would require creating several consecutive liquidity provision positions with different deposited amounts, to approximate the distribution in Figure 6.
The three strategies considered are:
- Uniform strategy: liquidity is provided uniformly within the expected price range, as is the default in Uniswap v3.
- Proportional strategy: liquidity within the expected price range is allocated in sub-bins within the range, with the intensity of a bin proportional to how likely the price is likely to be there according to Figure 6.
- Optimal strategy: using tools from decision theory, the authors develop a model to estimate the “optimal” range to provide liquidity over, having as a parameter the degree of “risk aversion” of the liquidity provider.
In the following figure, the authors provide an illustration of the proportional strategy, where the expected price range Bα, is wider than the move strategy range Bτ. The probability distribution from from which the allocations are derived is illustrated in blue, implemented as small bins:
The authors find that providing liquidity with the Uniswap v3 default of a uniform strategy is suboptimal for all but the most risk-averse investors, and for risk-loving types very much so. Providing liquidity proportional to the predicted future prices as in Figure 6, the proportional strategy, is close to optimal for most ranges of risk aversion, with only the most risk averse benefitting from providing liquidity uniformly.
To perform a backtest of their theoretical analysis, they run their strategy over the March 2018 — April 2020 period, and compare the fees that would have been earned with their optimal strategy, and compare this with what would have been earned with a Uniswap v2 uniform strategy over the full range. They find that their optimal strategy generates 230x more utility (unit-less measure of wellbeing that takes into account risk and reward) than providing liquidity over the full range.²
This staggering gap should be a signal to liquidity providers that a passively managed position may not suffice in Uniswap v3 to earn fees with capital efficiency and balanced risk. Active liquidity provision presents both a challenge and an opportunity to the DeFi space.
Gamma is an organization that funds the research and implementation of “Active Liquidity Provider” strategies, that seeks to develop best of class strategies for the new challenge that modern DEXes like Uniswap v3 present. Grants are available for those who want to participate in the research effort, see here to learn more.
[1] The authors call these “reset strategies”.
[2] An important caveat is that the authors do not seem to address the impermanent loss consequences of their strategy, which could have a significant impact on the fees earned.
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