Underperformance due to Divergence

Digital Assets Institute (DASI)
4 min readJan 31, 2021

There is a lot of confusion around one of the most important terms of the Automated Market Makers, IMPERMANENT LOSS. Balancer`s blog offers an really excelente article about that.

This term defines the impact of offering liquidity in the market. This operation continuously produces a change in the assets that are initially provided, by providing counterpart to the market. These changes produce a different result in terms of profitability with respect to the profitability that we would have with initial assets.

This difference in returns is what is known as IMPERMANENT LOSS.

However, it is a name that does not really reflect the essence of this effect. We could even say that it really misleads with respect to reality, which leads to not being understood.

Let us explain exactly what the problem is and why we propose a new definition that is Underperformance due to Divergence.

— — LOSS — — —

The term defines the effect with a loss, which we associate with a loss in capital. The reality is that the effect is not really a loss every time. When assets go up we will not have a loss of our capital. The reality is that the effect will make us earn something less. In other words, we will have a worse result than what we would have with the initial assets. So we UNDERPERFORMANCE the returns of the original assets.

Which means that being in a Pool offer a worse performance than having the original assets as a result of providing liquidity to the market.

By offering counterpart to the market, the pool increases its position of the worst asset and lowers the exposure to the best asset.

This implies that we will almost always have a worse result than our original assets. But if the two assets have risen, our capital will always have a profit, because even if we have less than the most profitable, as both have risen we will always win.

It is not a problem if it is compensated with the profitability of commissions obtained by the pool.

For that reason our suggestion is to call it UNDERPERFORMANCE.

Because it is the reality of the effect. It doesn’t have to be a LOSS. Only if we see it compared to what we could have won. But calling it LOSS calls for confusion. We think UNDERPERFORMANCE is more accurate.


The reason for the loss is that the assets diverge in their returns. In fact, if the pool is made up of two tokens that have the same underlaying asset even though they are different tokens, that divergence does not really exist.

As we explain before by offering counterpart to the market the pool increases its position of the worst asset and lowers the exposure to the best asset according the DIVERGENCE in returns

The greater the divergence, the greater the change in these weights. That is, the more difference in profitability that occurs between the two assets, the more weight of the one with the worst performance will have the pool.

In the extreme case that one of asset is worth zero, any trader will always try to exchange that asset for any amount of the other asset of the pool. Whenever you return some amount of the asset with value to us it will be more than zero. This is one of the risk of the Pools and the risk of doing market making. In that case the DIVERGENCE will be extreme.

When we speak of divergence, the result of the two assets is different. Even raising, the two won’t raise the same.

But in the definition of the term we speak of IMPERMANENT, assuming that the two assets will at some point have the same return. This is false. It does not necessarily have to occur. Because for that UNDERPERFORMANCE to be canceled that should happen

If the Pool is created with 1 Ethereum equal to 100 Dollars. Is it really expected that ethereum returns to that level? Is it reasonable to call it IMPERMANENT? It doesn’t seem right.

For that reason we call the term DIVERGENCE, because it explains that not something IMPERMANENT, but that it will depend on the type of divergence. There may be divergences that tend to converge, but it doesn’t have to be that way for all the assets. In fact, we generally believe that if we have two different assets we should talk about the level of correlation that historically presents and how that correlation behaves. If there really is a certain regression when these assets are separated.

— — CONCLUSION — — —

For this reason, the term Underperformance due to Divergence we think is much more accurate, and represent better the effect. We think that definition will help to understand better that concept.



Digital Assets Institute (DASI)

Digital Assets Institute is specialized on teaching and research across the full range of crypto economic science.