All Curve users should take some time to digest this in-depth research by @nagaking on optimizing the A parameter. Weโll take a stab at adding some background on this research for the casual ape.
Curve became the dom site in DeFi largely due to its impressive architecture. Mostly the pools just run on their own, with the Egorov Stableswap Invariant doing the heavy lifting of keeping the price stable while avoiding slippage. Here we present the classic illustration of the Curve curves:
The only parameter that occasionally gets tweaked by community vote is the amplification parameter, A, which affects the shape of the blue line. When the value of A approaches zero, the line approaches the purple dotted line. Larger values of A and it approaches the dotted red line.
The research by @nagaking creates a robust simulation of Curve pools under market conditions over the past two months. They use this simulation to optimize the value of A across a wide range.
The existence of such a simulator is quite exciting, as the code is open sourced so you can run it yourself for any variety of practical applications. However, it currently leans on a paid API, so the sorts of paupers who complain about gas will probably bellyache on this point.
The results are shown here for 3pool, with the x-axis demonstrating the effects of cranking up the dial on A to extremely high values on several factors.
The research concludes that for 3pool, a higher A value is generally optimal.
โRaising A generally increases profits with few directly observable negative side effects. Raising A to even quite high values (>1000) did not radically reduce the poolโs balance or generate additional susceptibility to slippage.โ
This also holds for bUSD, but the more naturally unbalanced sETH pool requires lower values of A and trades at a bit of a loss in simulations due to this discrepancy.
Now, most Curve pools are currently using much smaller values of A. We track this as an available column on CurveMarketCap. Most pools have a value between 100-200. 3pool is indeed on the higher end at 600. Y and USDT the only pools with a value of A currently in the thousands.
Why not jack up A to higher values? Thereโs a few caveats in the paper. A big proviso is simply that with few Curve pools actually carrying an amplification factor above 1000, itโs tougher to accurately model the tail-end risks these could carry in a real life setting. Larger A values could push the pools to be heavily imbalanced, but in reality this is assiduously avoided.
The paper indeed observes that the behavior of the simulation is already a bit more nuanced than actual behavior:
โNotably, results tend to be in a similar range, but slightly lower, than actual returns, which makes sense given that the simulations donโt include โrandomโ non-arbitrage trades.โ
In real life, random whales splash the pools for reasons we can only imagine, and such effects are difficult to accurately simulate. We also wonder if it would be useful to model the effect of pools naturally growing in size over longer time horizons as Curve gains adoption, which is not heavily relevant in the two month window considered.
At any rate, the research all reinforces that Curve v1 was exceptionally designed. In slightly different research study, among a [presumably biased] sample, we found the expectation is that Curve v1 is robust enough to survive indefinitely.
Although we acknowledge the question was poorly phrased.
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