---
# System prepended metadata

title: How bad is impermanent loss in Uniswap V3?
tags: [AMM]

---

---
title: How bad is impermanent loss in Uniswap V3?
author: "Prevert"
date: "02/12/2023"
description: post
tags: AMM
---

# How to manage impermanent loss in Uniswap V3?

As a long time liquidity provider in Uniswap V2 pools, you learned about impermanent loss (or [divergence loss](https://pintail.medium.com/uniswap-a-good-deal-for-liquidity-providers-104c0b6816f2), oh well) and how it can affect the return to providing liquidity when the price diverges from the one at which you deposited the assets. Then Uniswap V3 came out, and you got familiar with the concept of liquidity concentration and understood how large impermanent loss (IL) can grow compared to Uniswap V2. You read excellent [blog posts](https://crypto-defiworld.medium.com/impermanent-loss-in-uniswap-v3-222d01668d6e) and [twitter threads](https://twitter.com/korpi87/status/1400963750425989121) explaining how IL is amplified by concentrating liquidity starting with a 50/50 asset allocation. But as you know well, a feature that makes Uniswap V3 a great product is the possibility to start with a non 50/50 allocation. How IL is changed in this case is an important practical questions as liquidity providers (LPs) start most of the time with a ratio different from 50/50. So, let's find out! 

## 50/50 initial allocation

Let's start with a balanced allocation as a benchmark. Suppose you decide to provide liquidity in a ETH/DAI Uniswap V3 pool. The current price is 1634 and you spread your assets over the range 1000/2660. For this interval, your initial wealth is allocated 50/50 between the two assets. The Figure shows the amount of IL you can expect from this strategy.

![](https://i.imgur.com/LOXbcAA.png =450x275)

The two dotted vertical lines indicate the lower and upper bounds of the range. IL is the difference of wealth between someone just holding the asset and someone LPing. To compare IL across various price ranges, we first need a way to quantify potential losses. We estimate IL as the return rate of the pool needed to compensate the loss when the price reaches one of the two boundaries of the range. In the Figure, the return rate which equalizes the two wealths at the two boundaries of the range is 15.5%. IL, as measured by the compensating return rate, is identical at both ends of the range for a 50/50 allocation.
<!-- Or, more precisely, the return rate from earning transaction fees minus the return rate obtained by staking the two assets in a safe Notice that despite a 50/50 asset ratio, the allocation is slightly skewed toward the upside. For this reason, IL will be a bit higher on the upside than on the downside. -->

![](https://i.imgur.com/Iwvfdfz.png =450x275)


## Asymmetric initial allocation

### Leaning toward selling a covered call

Now, suppose you are optimistic about the ETH price and willing to extend your price range on the upside and limit your downside. Instead of a balanced price range 1000/2660, you choose a range  1300/3120. The amount of IL you can expect is shown in the Figure.

![](https://i.imgur.com/Msbx4RB.png =450x275)

Your new strategy has a lot more IL on the upside than the downside. The return rates to LPing needed to compensate a price reaching the lower and upper bounds are 3.5% and 30% respectively.

In the extreme case you expect the price only to increase, you could choose a range 1634/2660 which starts at current price. Upward IL is maximum and compensated for a return rate of 38%. The form of IL resembles the loss profile you would expect by selling a covered call.

![](https://i.imgur.com/QkFuGdb.png =450x275)

### Leaning toward selling a put

Alternatvely, if you are pessimistic about the ETH price and willing to give more room to the downside than the upside, you could choose a price range 700/2180 with the corresponding amount of IL shown in the Figure.

![](https://i.imgur.com/WoWKvb4.png =450x275)

This time IL is a much bigger risk on the downside than on the upside. The return rates to LPing needed to compensate a price reaching the lower and upper bounds are 42% and 5% respectively.

You could even choose a range 700/1634 if you expect the price to decrease. Downward IL is maximized and compensated for a return rate of 52%. The form of IL resembles the loss profile of selling a put.

![](https://i.imgur.com/fsIzH7O.png =450x275)

## Conclusion

The main takeaway from this analysis is that if your market expectations are strongly skewed toward one particular direction, you should probably just hold the asset you expect its price to increase. The extent of IL you are facing is so large that only an extremely high return rate to LPing might compensate for it. Your prospect is different if you hold a neutral view of the market. IL is better distributed between the two ends of your price range and your chances of overperforming holding are better.


<!--
The definition was initially applied to Uniswap V2 but naturally extends to Uniswap V3 with one major difference. While LPs in Uniswap V2 are required to deposit the two assets in equal value, in Uniswap V3, they can choose in which proportion the assets are deposited. This means that in V2, the holding portfolio against which the strategy is compared is composed of the two assets in equal value, in V3, the benchmark portfolio has the same asset composition which was initially deposited in the pool.

This brings the question of whether some initial proportions are better than others to mitigate the effects of impermanent loss. To take an illustration, suppose that you consider providing liquidity in the ETH/DAI Amm pool over the price range 1000-2000 and that the current price of ETH is 1200. Should you wait 

Currently, the most widely used metric is “EV in USD terms compared to HODL”. 