Common misconceptions about impermanent loss
Usual explanations make misunderstanding easier than properly understanding
I assume you are already familiar with the concept of impermanent loss, if you are not, check it out, I will wait. Sorry, pointing you to some explanation to then explain where it fails would not be classy, you will have to find it yourself.
The misconceptions are usually two:
- If you remove the liquidity before the token ratio is restored, you make the loss permanent.
- Liquidity pools work like smart algorithmic investment funds, maximizing your earnings.
1. About the “impermanence” of the loss
Some explanations mention “divergence” loss, as when the price diverges you lose, and when it gets back to the original ratio you get it back. This is not exactly wrong, but it is two fallacies: sunk cost, and opportunity cost. Let us consider an example with a calculator, and let us use the advanced settings, I will help1:
- Initial: A is 1 at $100, B is 0.5 at $200
- Change: $100 for A, $0 for B.
The final situation is that you have approximately 0.7 of each, and a total value of $282.84, while if you had kept the A and B tokens from the start, you would have $300: $200 for 1A, and $100 for 0.5B. Where $300 — $282.84 = $17.16 (your loss).
After this happens, some people consider that keeping the liquidity is the best option, especially if the values return to the original ratio 2A = 1B. However, that second change in the ratio has the same result as the first change in the ratio: more “impermanent” loss.
Consider the third scenario where B rises to $400, after the previous movements. We have three possible scenarios:
- Holding from the start: 200$/A * 1A + 400$/B * 0.5B = $400
- Providing liquidity from the start: same result.
- Providing liquidity until the first movement, then removing it: 200$/A * 0.7A + 400$/B * 0.7B = $420
$420 — $400 = $20, your loss. Arguably, this should not be “divergence” loss, but “convergence” loss. This is confusing for some people because we have a point of reference from where we consider the gain and the loss, but for a liquidity pool any time is just the same as any other time. The point of reference only leads us to fallacious reasoning.
The loss is “impermanent” because the expectation for the long term is accumulating interests (fees) and yields, which over time will compensate for the divergence and price movement. If you would rather benefit from the price movement and the divergence, you should look into trading and arbitrage; beware that both are quite competitive and the losses caused by any mistake may be more significant as a consequence.
2. About the “self-balancing” of the pools
After understanding impermanent loss, the “self-balancing” misconception is simple, at least in comparison.
Investment funds keep a portfolio of assets with different allocations for each. Liquidity pools keep several assets (usually 2, but sometimes more) with some fixed allocation for each2. Considering that a liquidity pool may work as an investment fund is a big mistake, the way it works is in fact contrary to investment funds.
When participating in a market with assets that change value over time, we can find ourselves in several positions in this scenario, with respect to alpha (α):
- Zero α: performing similarly to the market, e.g. just holding several tokens. This is the normal expectation for FIRE people, seeking future average returns similar to past returns, in the 10%+ range.
- Negative α: performing worse than the market is normal for liquidity pools, as they are arbitraged and incur in “impermanent loss”. This negative performance is then offsetted by the fees and the yield.
- Positive α: this is the aspirational goal of investment funds and any trader, not just winning3, but winning more than the average market participant. Investment funds normally hire the best people they can find to achieve this.
In summary, liquidity pools are not in the positive α, but in the negative α, because they are the object (and not the subject) of arbitrage, therefore they do not “maximize your earnings”, and without fees and yield they would in fact “minimize” your earnings, by “impermanent loss”.
Cross-posted from the Sigmoid newsletter
