After my last post discussing impermanent loss I wondered whether there was a more rigorous approach to calculating it and if there was an easier way. As it turns out there really wasn’t an easier way to approach it but the end result was a formula which made calculating impermanent losses much quicker.
I know most people don’t care about the derivation and really only care about the formula so I will post the formula and explanation of it here and will leave a link to the full treatment at the end if anybody wants to see the full derivation. Below is a screenshot of the “Summary” from my derivation explaining the formula and the relevant variables.
Below is the link to the full derivation. Most of it is mindless math but all you really need to use the formula is in the above screenshot. It also includes a few examples to show how it can be used.
Hopefully this is helpful or interesting to someone, if not it was interesting to me and the end result was quite mathematically satisfying. I’m sure someone could make a calculator which uses this in order to simplify things for the average person since it only requires 4 prices and the value of the initial investment (if you want more than just the ROI needed).
Edit: Since I’m seeing a lot of people not being able to understand the math (which is perfectly fine , math isn’t everybodys strong point), I’m adding a quick example here. Suppose a pool has two coins in it. One of the coins doubles in USD price (i.e. goes from something like $2 to $4) and the other halves in price (goes from like $10 to $5). This means that our variables gamma and beta are 2 (doubles) and 0.5 (halves) respectively, which allows us to plug them into the formula which spits out a value of 0.25. This means that our impermanent loss is 25% and we would need to make 25% ROI in order to compensate for this.
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