Hedging Impermanent Loss (part 1) (2024)

This article is the first part in aseries of articles on hedging and insuring Impermanent Loss (IL). The series starts with very simple way to hedge IL and will move through more complex possibilities, such as almost perfect IL hedge with custom options, up to insurance.

LPs earn a profit only when the fees LPs earn from the traded volumes outstrip the losses from impermanent loss due to price changes.

Impermanent loss can be hedged with call and put options, not perfectly but well enough.

In this example imagine a user that measures value of his/hers portfolio in USDC. Imagine an extreme scenario when price moves, between the start and end of the move no trade happens and the price of the AMM is arbitraged after the move. For simplicity

• price of ETH/USD is 1500
• pools contain 1000 ETH and 1 500 000 USD
• user owns 0.1% of the pool — 1ETH and 1500USD at the start
• value of user’s stake is 1500USD + 1ETH * 1500 = 3000USD

now price moves to 1000 and arbitrager trades

• arbitrager sells circa 225 ETH for 275k USD
• this trade moves price to efficient level of 1000
• now the pools contain 1225 ETH and 1.225mil USD
• user owns 0.1% of the ETH and USD which makes it 1.225 ETH and 1 225USD
• value of user’s stake is 1 225 USD + 1.225 ETH * 1000 = 2450USD

As it can be seen, the user suffered a loss of roughly 550USD due to impermanent loss.

Now lets have a look how the impermanent loss looks like with different prices. Assuming current price is 1500.

As can be seen the impermanent loss does not behave linearly but in a “near” range to the current price, the behaviour is similar to linear.

To hedge the impermanent loss, based on this simplified example, user can buy put option at strike 1500 (equal to current price) and size 1.1. The put strike 1500 best reflects the (almost) linearity of the impermanent loss and the size 1.1 “just” scales the option. Note that this assumes user initially staked 3 000 USD that got split between USD and ETH pool segments, for different amounts the user should increase/decrease the option size. For details go to here.

• The put option was selected because it covers the loss in case of price drops. In another words, buying put option brings profit if price goes down.
• The strike price of 1500 was selected because it corresponds to a current price of 1500. If the price was 1700, the hedge would work better with a strike price of 1700.
• The 1.1 size was calculated just by looking at the expected loss at an ETH price of 1000, which was circa 550 and since the difference between strike and the 1000 price was 500. Ratio 550/500 = 1.1.
• If the user has different staked capital, for example 10 000 USD (in total value between the USDC and ETH part of the pool). Simple take the $10k divide by $3k of the capital we used for modeling and multiply by 1.1. So 10 000 / 3 000 * 1.1 = 3.67 which means the above described hedge for this volume should be done with long PUT at strike 1500 with size 3.67.

Because our user values its portfolio in USD, he/she doesn’t have to hedge the “price growing” side, since in that case the stake becomes more valuable (in terms of USD). If the user calculated the value of its portfolio in ETH, it would be vice versa, the hedge would have to be done against growing value with CALL option.

Conclusion

The topic of impermanent loss is much more complex than the use case described above. This simplification was done so that anyone can easily understand this topic and that anyone can hedge against impermanent loss. The simplification is not only in terms of volumes being traded on the AMM but also in terms of the opportunity cost that is part the Impermanent loss definition. In this article we used 0 (ie USDC only portfolio), but the opportunity cost is actually “how much would a user made by holding theinitial ETH”.

We will continue this series with making assumptions that are much more closer to the real world. By providing manual to have better hedges both in terms of covering the impermanent loss and decreasing the cost of the hedge (for example with buying put option at a lower strike price).

Stay safe and DYOR!

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Carmine Options — AMM enabling anyone to buy and sell options at a fair price.

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