Introduction
Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from impermanent loss by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liquidity concentration around the market price, using the entry of a blockchain scaling solution, Polygon, as our instrument. Polygon's lower gas fees allow LPs to update more frequently than on Ethereum. Our results demonstrate that higher repositioning intensity and precision lead to higher liquidity concentration, which benefits small trades by reducing their slippage.
Centralized exchanges
One of major cryptocurrency exchanges, FTX, filed for bankruptcy on November 11, 2022 (Reuters: “At least $1B of customer funds have vanished”).
FTX was a centralized exchange (CEX), like Binance and Coinbase. CEXs keep custody of clients tokens (i.e.they and they alone control the reserves of tokens which are used to back the balances of their clients).
On CEXs, price discovery and trading is done through a limit order book (LOB), which is composed of makers’ limit orders and consumed by takers’ market orders. The CEXs ensure order matching.
Decentralized exchanges
On the other hand, decentralized exchanges operate directly on the blockchain, using “smart contracts”. Most of them are automated market makers (AMMs), which use liquidity pools for price discovery and trading. Since the AMM is takers’ unique counterparty, there is no need for matching takers and makers.
More importantly, with DEXs, clients trade directly from their own wallet and keep custody of their tokens, which provides a higher level of security for clients' funds.
The costs of higher security
However, since all the transactions on DEXs have to be validated and recorded on a blockchain, which requires the consensus of all the validators, transactions on DEXs are slower than on CEXs, which operate off-chain.
Moreover, any wallet that carries out a transaction on a blockchain must pay the “gas fees” to the validators, which are deducted directly from the wallet’s “gas token” reserve (e.g. ETH on Ethereum blockchain). Importantly, these gas fees represent a fixed cost, which makes them a greater concern for small transactions.
Largest DEX: Uniswap v3
Uniswap v3 is the largest DEX in terms of volume. It is a concentrated liquidity AMM, where LPs (which are equivalent to makers on CEXs) can choose the price range [plower,pupper] on which their position is active in a given liquidity pool. The rewards from taker fees are only distributed to positions active on the market elementary price range, which contains the market price.
Subsequently, and as the name suggests, LPs will naturally concentrate their liquidity as much as possible around the market price to maximize their rewards, which improves capital efficiency and reduces takers’ slippage, compared to uniform liquidity (Uniswap v2).
How do LPs make money on Uniswap v3?
LPs are remunerated with the exchange fees that takers pay when they trade tokens on a liquidity pool. These fees are taken from the tokens they buy, in a proportion which depends on the fee tier of the pool (e.g. 0.05%), and distributed to the LPs who have a position active on the market elementary price range (the elementary price range that contains the market price) when the trade occurs.
In the example below, a taker buys $10K worth of ETH with USDC, which makes ETH market price increase. Another one sells $10K worth of ETH, which brings the market price back to its initial value. One LP has a position containing all the liquidity involved during these two swaps, thus getting all the corresponding rewards ($10).
But LPs are subject to adverse selection
When the index price changes, an arbitrage opportunity appears. In the example below, ETH index price goes from 1000 USDC to 2000 USDC, which leaves an opportunity for arbitrageurs to buy ETH at a discount on the pool and sell it at the index price on another exchange (inter-exchange arbitrage), until the market price reaches the index price of 2000 USDC.
For the LP who has a position around the initial index price, it means selling ETH at a discount to arbitrageurs, creating impermanent loss (IL), i.e. loss compared to the “hold strategy” which consists in holding the two tokens in position’s initial proportion. It is impermanent since if the index price gets back to its initial value, the loss is zero. However, in the event of a large and sudden change in the index price, the rewards are not enough to compensate for IL and losses actually become “permanent”, i.e. an LP is adversely selected by arbitrageurs.
Solution 1: wide price range
One possible solution for LPs to protect themselves from adverse selection is to set a wider price range. With a wider position price range, the LP still sells ETH to arbitrageurs at a discount in case of a large and sudden increase in ETH price, but at a higher average price, which reduces IL.
Solution 2: frequent updating
Another solution is to update the position before arbitrageurs start trading. By updating the position around the new index price before the arrival of arbitrageurs, the LP arbitrates before them and therefore protects from IL.
But frequent updating is costly, since LPs have to pay gas fees for each update.
Research question
How does repositioning intensity, i.e. position updating frequency by LPs, affect liquidity concentration on DEXs?
In presence of high gas fees, we expect infrequent updating by LPs. To protect themselves from adverse selection, we rather expect them to set wider price ranges. Therefore, we expect low concentration of liquidity around the market price in this setting.
In contrast, if gas fees are low, LPs can update more frequently at a cheaper cost. They are now able to protect themselves from adverse selection through more frequent updating, which we refer to as repositioning. In this setting, it is optimal for LPs to set narrow price ranges, concentrating their positions around the market price to maximize their rewards. Therefore, we expect that greater repositioning intensity should increase concentration of liquidity around the market price.
Identification strategy: launch of Uniswap v3 on Polygon
Whereas Ethereum is currently the most secure blockchain with a number of validators exceeding 500,000 as of December 2022, its main disadvantage is low scalability. Specifically, Ethereum can only handle up to 30 transactions per second (TPS), which results in high gas fees. For example, an estimated average of gas fees for a trade on Uniswap v3 amounts to $14 in 2022.
To address the scalability issue, there exist overlays of Ethereum that offer higher speed and, consequently, lower gas fees. Polygon PoS (proof of stake), often simply referred to as Polygon, is one of the most adopted Ethereum scaling solutions. It can handle around 700 TPS, up to 70 times Ethereum's TPS. Polygon's gas fees are around $0.01 per transaction.
Whereas Polygon allows for faster transaction processing and lower gas fees, it requires its own security and decentralization efforts that are not as robust as Ethereum's. Specifically, Polygon PoS is a sidechain secured by a proof-of-stake consensus mechanism. It is a sidechain, because all the staking management is defined on Ethereum, i.e. Polygon depends on Ethereum. The overall number of validators on Polygon is lower, but it still has a decent level of decentralization with over 100 unique validators. Fewer validators can achieve consensus more quickly, hence leading to a shorter time between blocks and higher overall throughput.
Uniswap v3 was launched on Ethereum in May 2021, and on Polygon in December 2021.
Polygon allows LPs to update their positions more frequently, so we use the launch of Uniswap v3 on Polygon as an instrument for an exogenous increase in repositioning intensity.
Main findings
We document that Ethereum has a larger liquidity (TVL) due to its higher security, but that Polygon offers lower slippage for small trades (up to $10K), due to higher liquidity concentration around the market price.
Our instrumental variable regressions show that Polygon’s higher liquidity concentration is due to higher repositioning intensity and precision by LPs.
Data
For our analysis, we used the historical events logs (mints, burns, swaps) of the 3 most liquid ETH/$ pools on Uniswap v3 that exist both on Ethereum and Polygon:
- USDC/(W)ETH 0.05%
- USDC/(W)ETH 0.3%
- (W)ETH/USDT 0.3%
Our study period is the year 2022 (01/01/2022-12/31/2022).
Summary statistics
Ethereum has more volume and TVL:
Polygon is used for smaller trades:
Explanation: security vs gas fees tradeoff
Polygon has fewer validators than Ethereum, lowering the gas fees but also the security. Large traders and LPs prefer Ethereum’s security, and care less about gas fees because they do not depend on transaction size. Small traders and LPs prefer Polygon’s gas fees, and care less about security because the amounts involved are small. Thus, Ethereum has larger liquidity and trades than Polygon. In contrast, Polygon is attractive for smaller traders and LPs.
Slippage
Liquidity characteristics (size and distribution) have a direct effect on traders, through “slippage”, which is the relative difference between the average execution price and the pre-execution market price. Slippage is higher for larger trades and inversely related to liquidity size and concentration. Our regression analysis shows that slippage of small trades is significantly lower on Polygon.
Let’s explain why…
Repositioning intensity and liquidity concentration
We define liquidity concentration as the value of liquidity around x% of the market price, divided by TVL. We first observe that liquidity concentration is significantly higher on Polygon.
We also define repositioning intensity as:
Minted and Burned being the value of liquidity minted and burned within the 5min interval for which Intensity is measured.
And we observe that repositioning intensity is also significantly higher on Polygon.
We finally test the causality between repositioning intensity and liquidity concentration, with the following instrumental variable regressions:
We show that liquidity concentration is significantly increasing in repositioning intensity, and repositioning intensity is significantly higher on Polygon.
Repositioning precision and liquidity concentration
In addition to repositioning intensity (time related), we define three metrics to measure the repositioning precision of LPs:
- Position gap is the relative difference between the mid price of the position and the market price. It is inversely related to repositioning precision.
- Position length is the price range length of the position. It is inversely related to repositioning precision.
- Position concentration is the concentration of the position around the market price. It is positively related to repositioning precision.
We observe that repositioning precision is, again, significantly higher on Polygon, through its three metrics.
As for repositioning intensity, we test the causality between repositioning precision and liquidity concentration, with the following instrumental variable regressions:
We show that liquidity concentration is significantly increasing in repositioning precision, and repositioning precision is significantly higher on Polygon.
Conclusion
Blockchain scaling solutions allow for more frequent position updating by LPs. As a result, LPs can better protect themselves from impermanent loss by updating their positions more frequently in response to index price changes (repositioning intensity), and maximize their rewards by concentrating their positions around the market price (repositioning precision). Higher repositioning intensity and precision by LPs lead to higher liquidity concentration, which reduces slippage, especially for small trades. Blockchain scaling solutions are attractive for small traders and LPs, with low gas fees and slippage, but are less secure. In contrast, Ethereum pools are deeper and provide better execution terms for large traders and LPs.
Looking ahead
In June 2023, Uniswap Labs announced the upcoming launch of Uniswap v4, which will base on v3's concentrated liquidity but will introduce "hooks", offering pool launchers a very high degree of customization, opening up the field of possibilities. Uniswap v4 will also feature other structural changes that will notably reduce gas fees, both for traders and LPs. Our research can in particular help and guide these launchers in the design and architecture of their hooks.
We plan to extend our study to other blockchain scaling solutions such as Arbitrum or Optimism for example.
Read our full paper here.
