Ramp 3pool A Parameter to 2000


Proposal to ramp 3pool A parameter to 2000, or to discuss alternative values.


Our recent simulations (A Parameter Research [Demo and Code]) suggest that an A parameter of ~2000 would maximize returns for 3pool by increasing arbitrage volume. This would also substantially reduce slippage (est. ~2.5x more pool depth) relative to the current A value of 600. The primary risk is increasing pool imbalance; however, imbalance risks are largely mitigated by the large size of 3pool, and market-wide liquidity for all coins in 3pool.


  1. Increase expected returns for 3pool LPs. Simulations including arbitrage alone suggest an increase of about 0.1% in annual returns (in USD). Note that this estimate is conservative given that it only includes purely optimal arbitrage trades (i.e., those trades that benefit traders the most).
  2. Decreased slippage. Simulations suggest that pool depth (the cost to shift the pool price by 0.05%) would be increased by ~2.5x. Increased price stability is likely to attract more non-arbitrage trading as well.


  1. Increasing A increases the risk of pool imbalance. However, due to the large amount of capital in 3pool, and high market-wide liquidity for the coins in 3pool, this risk is largely mitigated. Simulations suggest a decrease in average balance of ~0.15 from 0.85 to 0.73, where 1 is optimal balance and 0 is complete imbalance.
  2. Another, slightly lower A value may be preferred if the community is particularly concerns about holdings imbalance.

Additional Details:

We supplemented our previous simulations by (a) including gas fees, and (b) estimating volume-weighted price depth.

The results were unaffected by any reasonable gas price, because gas fees only made up a very small proportion of the typical arbitrage trade size (ranging from the $100,000 to $10,000,000 range).

Using volume-weighted price depth allowed us to emphasize price depth “when it matters most” (i.e., when there is high volume). The results were largely unaffected by using volume-weighting, but showed that price depth is actually slightly improved for higher A when considering volume.


Do we need to understand the effect of this change on the meta-pools that would be indirectly effected; or is it just all goodness assuming the above is true?


This is a good question. My sense is that the only effect on meta-pools is that the 3pool token could accrue value faster (ie, increasing virtual price) which means meta-pool A may have to be lowered to offset IL. That said, this effect really shouldn’t be too drastic. Unfortunately, our meta-pool simulator is not ready yet.

I’d be interested to hear what @michwill and @jiecut think.

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Definitely interested in metapool simulator. But if anything, I think that if pool stays liquid, metapools should only become better with higher A.

So a metapool simulator would be good to find optimal metapool parameters once 3pool parameters are adjusted


Isn’t A still used in a meta-pool swap since you have to calculate a new D for 3pool after withdrawing assets (e.g. USDp->USDC)? I’m not convinced there’s an issue here, just curious in the cascading effect.

Good points. I’ve been looking at this the last few days and will report back soon