Balance Ratio

  1. The balance ratio is "forgiving near the center", which means that if a pool is "fairly balanced" then its balance ratio will be very close to 1. For example, a two-token pool with value split 60:40 among the two tokens will have a balance ratio of 0.96.

These features of the balance ratio offer the follow uses for measuring risk:

  1. A low balance ratio for a pool indicates that there is a heavy overweight of value in one token, which means more market participants are providing this token as liquidity to the pool. In the event that there is a run to sell the overweighted token, the imbalance in the pool describes how many tokens will be unable to be swapped.

  2. For stablecoins, this sell-pressure could be an indicator for potential depegging. In cases where a stable coin has depegged, it can be telling to monitor the balance ratio as the token price moves (toward or away from its peg). For example, if the token regains its peg but the balance ratio continues to drop, this may indicate some underlying market dynamics have not yet recovered even though the price of the token has.

For Two-Token Pools

Definition

To define the balance ratio, we fix some notation for some of the quantities associated with a two-token liquidity pool.

Some examples

Abstract examples

The balance ratio is 1 exactly when the value of the pool is evenly split between both tokens.

The balance ratio is 0 exactly when one of the pool tokens represents all the value in the pool.

The following table displays balance ratio values based on a few different value ratios.

FRAX-3CRV

MIM-3CRV

A metaphor from commercial real estate

Another consideration would be that although expense ratios are normalized (take values between 0 and 1), it doesn't mean you should compare across categories. For example, multi-family homes have an average expense ratio of 0.4, but this "better number" doesn't mean every multi-family investment is better than every SNF investment. Context matters.

Similarly, the balance ratio offers a quick look at one feature of a liquidity pool. A ratio very close to 1 does not mean everything is okay with the tokens in that pool, but it does indicate a fairly balanced liquidity pool. Similarly, a balance ratio closer to 0.3 doesn't mean "RUN", but it does mean that if you're concerned about short-term liquidity, one token in this one pool may not be sufficiently liquid in the short-term. There may, for example, be other places that provide liquidity for the illiquid token, and the imbalance may be specific to this pool. Or not. Context matters.

For example, every constant-product AMM defines the price of its tokens so that the balance ratio of its pools is always equal to 1. For these pools, the balance ratio being 1 does not tell you very much about the tokens. Context matters.

Modeling Question: what is the average balance ratio for two-token stablecoin pools on Curve?

Modeling Question: is there a strong correlation between volatility/depeg of a stablecoin TKN and the balance ratio of the corresponding TKN-3CRV pool?

For Three-Token Pools

Modeling Question: What is the average balance ratio for three-token pools on Curve?

The general picture

Geometry of the balance ratio

Contributors

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