What Are the Limitations of the Standard Impermanent Loss Formula in Multi-Asset or Weighted Liquidity Pools?

The standard impermanent loss formula is designed for two-asset, 50/50 weighted pools. Its main limitation is that it doesn't apply directly to pools with more than two assets or unequal weightings, like those found on Balancer.

For these more complex pools, the calculation of impermanent loss is not as straightforward. It requires a multi-dimensional analysis that accounts for the individual price movements and weights of each asset, as divergence can occur between multiple pairs of assets simultaneously, making the simple price ratio inadequate.