Regen token AMM boost

[robert-zaremba]

Summary

Increase the Regen token collateral power by sharing REGEN between different AMMs.

Context

At Regen we are planning to run eco-finance AMM pools. Each AMM pool requires to stake liquidity, which partially looks the underlying assets. The size of the liquidity pool matters because it defines the slippage in the mostly adopted AMM pools - constructed by a Constant Function. The liquidity the smaller slippage.
Slippage is the difference between the expected price of a trade and the executed price of that trade. It is more likely to happen when there is a higher level of volatility, such as breaking news that forces unexpected trends in the market.

In the most basic sense (Uniswap v1), an AMM is represented by a pool of 2 tokens with equal power, and the Constant Function formula is k = x*y where, k is constant, x and y is respectively the amount of X and Y tokens in the pool. Buying dx of X out of the pool requires sending dy of Y to the pool such that the CF formula is preserved: k = (x-dx)*(y+dy).
There are many CF formula and many mechanisms to define AMM. Most of them share a problem of providing lot of liquidity to reduce slippage and unused long tails. Uniswap V3 approach greatly reduces both problems. Let's look at the MKR-ETH pool at Uniswap. Selling 10 MKR (40,000 USD at the time of writing) will induce:

• 0.05% slippage on UniswapV3 - with $15.54m total value locked.
• 0.14% slippage on UniswapV2 - with $27m total value locked.

However - it still requires lot of liquidity, even though most of it is not used.

Solution

If we take REGEN token as a reserve currency for the eco finance AMM, then we can pool it together. Depending on the pool activity and risk, we can increase the REGEN token power.

With the assumption above, for a CFMM f(x, r) for X-REGEN pair, we can boost the REGEN token power and create CFMM-bo0sted using f(x, boost(X)*r) market function. The boost function will determine the pool risk based on the token X. For example, if boost(X) = 1.33 then only 75% (1/1.33) of REGEN is required in the pool to provide the same behavior as with the original

Consequences

• Less REGEN is required to back AMMs.
• We unlock more value of the REGEN by sharing it among pools.

Open Questions

1. Who will define boots function? We can have a small default, eg: 105% for all tokens, and governance can increase it for particular pools or token classes.