What is Impermanent Loss (IL) and how is it calculated?

What Is Impermanent Loss (IL)?

Impermanent Loss (IL) is a measure of the value lost due to the expected behaviors of all market making systems. All market makers buy when the price falls and sell when the price rises. If the price reverts to the original price then this behavior is profitable. However if the market price does not revert it means that your portfolio will be worth less than if you had not traded. A successful market maker must generate more income from individual price movements than they lose to the overall market movement.

From the point in time when your AMM Instruction was submitted many of the individual market price movements since then will have likely generated some income, depending on the exact parameters you chose. Our AMM is designed so that if the market price later returns to the same price it was at the start, you end up with the same amount of assets as when you started (plus income).

That is why the industry term for the change in portfolio value due to the change in price is impermanent loss; price-related losses are reduced back to zero if the market reverts (meaning, if price returns to the initial price).

How do you measure IL?

Impermanent loss is the difference in value between “what are my current assets currently worth?” versus “what would the original assets I invested now be worth?” For your convenience we use the magnitude loss in USD.

The formula we use is:

IL = Hold Value - Current Value

Where

  • Hold Value = value of your initial asset allocation(s) at the current USD price(s)
  • Current Value = value of your current asset allocation(s) at the current USD price(s)

Example

Suppose that BTC/USD = US$20,000 and you lock 1 BTC and US$20,000 into an AMM Instruction with price bounds of US$16,000 and US$25,000.

Now suppose that the price has moved up and down, generating incomes, but currently stands at US$22,000 per BTC. Since overall the price has increased, we would expect to have sold BTC for USD, so we should have less BTC assets and more USD assets than when we started. Indeed we do:

Updated price: US$22,000 BTC/USD

Updated assets: 0.55919 BTC and US$29,246

Thus

  • Hold Value = 1 * US$22,000 + US$20,000 = US$42,000
  • Current Value = 0.55919 * US$22,000 + US$29,246 = US$41,548.18
  • IL = US$42,000 - US$41548.18 = US$451.82

Finding IL

To find IL:

  1. Go to the left-hand navigation and choose Portfolio.
    Portfolio tab in left-hand navigation.png
  2. Choose the AMM Instructions tab.
    AMM Instructions tab in History screen.png
  3. Choose between Spot AMM Instructions and Perpetual AMM Instructions.
  4. Navigate to the IL (USD) column.
    Impermanent_Loss_column
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