Impermanent Loss Series: Liquidity Provision as a Short Gamma Option Position
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Introduction
The risks of liquidity provision can be analyzed from several different lenses, and in this article we going to be focused on the “options” view of liquidity provision. In particular we will be looking at how the risk profile of LPing is similar to that of being short gamma. After establishing this framework, we will look at what has been used in traditional finance to hedge this risk.
An LP position earns fees from traders undertaking swaps in the pool against the assets that are provisioned, by charging a fixed percentage of the input asset, which varies with the pool. When a pool conducts many swaps of the same asset (for example, swapping out asset A and receiving asset B), this pushes the pool price in one direction, rendering asset B less valuable (the asset you have more of) relative to asset A (the asset you have less of). This is called impermanent loss, and we have discussed this much here.
Uniswap v3 allows concentrated liquidity, which amplifies this impermanent loss. Therefore, having an analytical framework to understand the risks and benefits you are exposed to is key to active management of LP positions.
Note: This analysis excludes income from trading fees, which is the revenue that compensates for this risk exposure, but we will focus on hedging alternatives.
Options Greeks and Liquidity Provision
In the options world, a position’s value is exposed to several risks, which receive have been assigned greek letter names that you may have encountered before, and to get to short gamma we first have to think about delta. Delta is the change in value of your position with a change in price of the underlying asset (in a WETH/USDC pool, we would look at ETH’s price). For example, if instead of LPing you just hold ETH, your delta is 1. if the price of ETH goes up by $1, your position goes up by $1 in value.
If you are LP’ing, the value of your position changes as the asset prices go up and down, as can be seen from the following figure (thanks to JNP777 for providing helpful tools for Uniswap v3 math)¹. The chart tracks the position’s impermanent loss as a function of price, and we can see that both upwards and downwards movements can lead to losses, as on either end you are either selling the appreciating asset or buying the depreciating asset. What’s relevant to our discussion is that this Profit and Loss profile is similar to the exposure an options trader experiences when his portfolio is short gamma.
This position’s delta tells you how much value your position loses as the price moves (see recent analysis of the delta of the full position, not just IL here), and is the first derivative of the previous chart. When the price is low and it increases back to your original price, your position gains value, as can be seen from the positive value of delta when price is around $1600. The reverse happens when the price is above your starting price.
Crucially, your position’s delta changes as the price goes up and down. Gamma is the measurement of how your delta changes as the price of the underlying changes.² Given that gamma for this position is always negative, your position is short gamma and therefore you are effectively selling volatility:
For an LP position gamma is always negative, as any movement from the current price makes your exposure to further price changes higher: the loss from starting at $2,000 and moving to $1,900 is smaller than the loss from $1,900 to $1,800. Your exposure becomes bigger as the price moves against you. This exposure has profound implications on liquidity provision strategies, and how to mitigate this risk.
Hedging Alternatives
Hedging implies combining your original position with another, in order to render the value of your combined portfolio less sensitive (or completely insensitive) to the risk you are analyzing. For example, delta risk is typically hedged by taking a position in the underlying asset in the direction that you need. In the case of gamma this is not possible, as the underlying asset has zero gamma (delta is always 1), and thus combining with an LP position does not change your overall gamma exposure.
Therefore, let’s explore the current options available in DeFi (happy to discuss further in the Gamma Strategies Discord channel of Visor Finance)
- Delta Hedging: You can attempt to dynamically hedge your position to make it delta neutral, by buying/selling the underlying (or perpetual futures for more capital efficiency). However, this protects you from small price changes in the underlying, and would require further protection from large price changes, which are common in crypto markets.³
- Options Hedging: You can attempt to dynamically hedge to make your position both delta and gamma neutral, by in addition to buying/selling the underlying, you trade options that have the opposite risk exposure to your LP positions. This can be costly, particularly in the DeFi space where liquid traded options with many maturities are still not a reality.
- Impermanent Loss Insurance Markets: We have previously discussed here a proposal for a market where you can buy exposure to the inverse of the Profit and Loss chart we presented above, allowing you to eliminate this risk from your position. This market is still to be implemented in DeFi.
- Diversification: Portfolios of LP positions could incur lower impermanent loss, as the gamma risk is more spread out among positions. However, in a high correlation environment like crypto, if all of the positions have an the same pair, diversification can provide little help in mitigating losses.
Closing Thoughts
In this article we have provided a framework for thinking about Impermanent Loss through the lens of options greeks, and discussed potential avenues for mitigating impermanent loss.
An important consideration is that this short gamma risk is precisely what you are being compensated for as an LP, therefore the pricing of this hedge in an efficient market shouldn’t be too different from the return of LPing.
An additional point that this framework shows you is that this loss is indeed impermanent, if the price goes back to your initial price your loss is reduced towards zero. On the other hand, if you rebalance and reset the zero point of your position, you will have taken the loss and made it permanent.
Given the scarce options to fully hedge your risk available, maximizing your fee income to make sure you are appropriately compensated for the incurred risk is key. Active management of these positions requires carefully setting ranges and thinking hard about rebalances. This is what we research at Gamma Strategies.
Every week Gamma Strategies publishes analysis and metrics of active asset management within DeFi:
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[1] https://github.com/JNP777/UNI_V3-Liquitidy-amounts-calcs.
[2] With respect to the square of the asset’s price.
[3] See here for a recent experiment with delta-hedging of liquidity provision positions.
