Assessing Liquidity Pool Fee Recommendation through a Benchmark Market Fee

Objective

We look at building a benchmark market fee to assess the performance of Almanak fee recommendation system for liquidity pools against the maximum profit possible that the protocol would retain without Almanak recommendations. The benchmark is built from the estimation of the cost of risk, based on liquidity and volatility on the open market, as well as on the arbitrage volume and the price delta, i.e. impermanent loss.

Background

Since a large portion of liquidity pool protocol volume comes from Arbitrage, it is pertinent to tackle the recommendations performance from the Arbitrage perspective. More specifically, a test focusing on the parameter “Swapping Fees” should be sufficient to estimate the performance. The other parameter “Trading Liquidity” would be indirectly taken into account by such a test through volume effects, but is more relevantly tested through a test on Protocol Deficit.

Overarching requirements

1. The test should encompass all relevant dimensions at stake in the optimization recommendations, i.e. (i) swapping fees/SF (ii) trading liquidity/TL (iii) arbitrage volume/AV (iv) market prices/P (v) transaction costs/TC (vi) slippage/S
2. The test should be sensitive to the relationship between TL and SF with AV, i.e. a change in TL or SF parameters is expected to be reflected in AV
3. The test metric variation (first order derivative) should be normalized with regard to market risk, i.e. the metric of quantification is not sensitive to positive or negative effects coming from market prices.
4. The test should have as little model risk as possible, therefore a benchmark approach where the latter is theoretically robust and practically legible is recommended.

Approach for designing a benchmark

When an arbitrageur interacts with the pool, we assume they maximize their immediate profit by exploiting any deviation from the external market price. In other words, they transfer the pool to a point that allows them to extract maximum value assuming that they can unwind their trade at the external market price P.

If we assume arbitrageurs could do so by interacting frictionlessly with other DEX and CEX, we can build a “strategy” whereby the pool is continuously maintained by the arbitrageurs rebalancing the risky asset between the pool and the external market.

This value of the rebalancing portfolio is equivalent to a best-case scenario, i.e. the “best” trading fee that the protocol would be able to charge in order for the pool to remain sustainable, as in properly balanced, without consideration of trading liquidity levels.

• We can infer the conditions of maintaining a sustainable pool for a particular asset by looking at the trading activity on the open market
• It amounts to estimating the required liquidity and the asset volatility on the open market
• That volatility provides a measure of the “cost of risk” that the protocol is facing to access the required liquidity
• Applying this cost of risk to the volume necessary to cover the price imbalance provides a “fair” value of the trading fee to apply to arbitrageurs: fee that breaks even the protocol’s cost and arbitrageurs’ cost
• Doing so, we can assess the capacity of Almanak fee to adapt to the market cost of liquidity.

Rationale: If the Almanak fee is diverging too much from Benchmark over a given period of time, then a performance breach could be triggered.

Conceptual Workflow

Conceptual Workflow of a Benchmark Market fee (ex. for Bancor one-sided pools)

AMM Math Framework and Test Rationale

We leverage existing relevant AMMs research like Jason Milionis [2022] who lays out foundation for a Loan-Versus-Rebalancing (LVR) approach.

See litepaper.