Report: Temporary losses are also permanent on Uniswap and other AMMs

Commentary on the runaway: Alexis Direr, a researcher at the University of Orleans in France, released a report stating that compared with the average portfolio of 50:50, the performance of the liquidity pool of the automated market maker (AMM) when there is a large price deviation will be noticeably worse.

Alexis Direr, a researcher at the University of Orléans in France, released a report summarizing the mathematical underpinnings of Uniswap and other automated market makers (AMMs).

Automated market makers are the term used to describe a class of decentralized exchanges that have exploded in popularity in 2020, the standout being Uniswap.

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In simple terms, these exchanges forego traditional order books in favor of liquidity pools managed by mathematical formulas. Traders can strike deals with liquidity pools for even the most illiquid tokens, but each order affects the price of the asset they are trading — a phenomenon known as slippage.

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This mathematical formula defines how the price changes based on the size of a particular trade. For example, the formula defines that exchanging 10 ETH for DAI will generate $3,500, but exchanging 100 ETH will only generate $3,400. This means that in the example of the former order, the price of 1 ETH is 350 USD, while in the latter order its price is only 340 USD. This formula is often referred to as the "bonding curve," and the many possible combinations describe a specific price curve. In the case of Uniswap, this curve is a hyperbola. In order to optimize for different scenarios, the curves of other AMMs may be more complicated.

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AMMs rely on Liquidity Providers (LPs) — individuals and entities that commit capital to liquidity pools to facilitate transactions and low slippage. Correspondingly, LP will get transaction fees paid by users.

While this sounds like a good business, liquidity providers need to deal with "temporary" losses. When prices swing wildly in one direction, LPs may end up getting back less money than they originally put in. For the above assets, compared to the average 50:50 portfolio, the performance of the liquidity pool will be significantly worse when there is a large price deviation.

The researcher explained that the reason for this phenomenon is arbitrage traders. The external market price does not follow the bonding curve, so continuous operations are required to keep the price on Uniswap in balance with the rest of the market. However, when arbitrageurs rebalance the liquidity pool to the correct value, they go to the "suboptimal exchange rate" defined by the bonding curve. This behavior is beneficial to arbitrageurs, but squeezes the profits of liquidity providers.

This loss is commonly referred to as a "temporary loss" because if the price returns to its original value, the liquidity provider is perfectly comparable to a standard 50:50 combination. Leaving aside the case of prices permanently shifting towards a new equilibrium, Direr asks the question:

“The fact that the two strategies actually deliver the same returns can be overwhelming at first. In the liquidity pool strategy, the arbitrage cost is triggered twice... in the holding strategy, the investment The investor avoids the cost of arbitrage, but the final wealth is the same. How is it possible?"

The researchers' answer is that the way benchmarks are often done is misleading. Uniswap constantly rebalances the pool as it moves up or down so that liquidity providers have fewer assets that are rising in price and more assets that are falling in relative price.

In fact, LP has adopted the average cost method in both directions. They lock in a portion of the profits when the price of an asset goes up, and then start buying sequentially as it goes down.

Similar to the principle of cost averaging, a constantly rebalancing 50:50 portfolio generates profits even as prices return to their initial values. In contrast, the value of a liquidity pool simply remains constant. So "temporary loss" seems to be a misleading term. The loss is always permanent, but in an aggressive scenario it only reduces the gains that the 50:50 strategy would have made.

Bancor V2 and Monniswap have adopted techniques to mitigate these types of losses. The former uses oracles to read real market prices and balance liquidity pools accordingly. The latter introduces a gradual time delay to minimize the arbitrageur's profit.

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