Understanding Uniswap Returns

Measuring Liquidity Pool Growth

To find a price-independent measure to understand Uniswap pool size, growth, and transaction volume, we need to look at the trading formula at its heart. Uniswap depends on the “constant product” principle to govern trading — that is the product of the two liquidity pools should be the same after a trade as before (excluding fees). The Uniswap price is given by the ratio of the two liquidity pools. The constant product is therefore price-independent.

GM = sqrt(eth_value * token_value)

Calculating Actual Returns

Of course, liquidity providers don’t care about the growth in the geometric mean of their stake. More likely, they are interested in the value of their stake as measured in one of the two tokens on the exchange. Sticking with the ETH-DAI exchange, we’ll look at what happens when we measure the value of a liquidity stake in DAI only (i.e. under the assumption that we can convert the entire ETH side of the stake into DAI at the current price). First, we’ll do this in the same way as in the previous article, where we calculated the “divergence loss” by making a comparison between someone supplying X ETH and PX DAI to the Uniswap ETH-DAI exchange, and someone holding those same amounts. Under these conditions, we get the following formula for liquidity provider returns.

Comparison with Holding a Single Token Type

The above scenario assumes that potential liquidity providers already have quantities of both ETH and DAI which they can choose to supply as liquidity or simply HODL. This analysis makes sense for understanding the results of supplying liquidity in isolation. However, in reality it is more likely that a potential liquidity provider has a quantity of only ETH or the ERC-20 token traded on the exchange.

  1. continue to hold ETH only, in the hope of profiting from an expected future price rise, or
  2. trade half of the ETH for another token such as DAI, in order to supply liquidity on Uniswap.

Reasoning About Future Growth Rates

The models above are based on an assumption of a continued annual growth rate α of close to that observed during the first 3 months of Uniswap’s operation, around 11%. As mentioned previously, this growth rate has been very consistent in those 3 months despite massive changes in liquidity pool size, and this may give us moderate confidence in extrapolating this growth rate into the near future.



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