Paradigm Research: How to use rebalancing strategies to profit from Uniswap?

problem

On October 14, Charlie Noyes posted on Twitter a question he had been arguing with Dan Robinson:

background

Automated market maker (AMM) is a type of decentralized exchange that allows customers to trade between on-chain assets like USDC and ETH. Uniswap is the most popular AMM on Ethereum. Like most asset management systems, Uniswap facilitates transactions between specific asset pairs by holding reserves of two assets. It determines the transaction price between them based on the size of its reserves, so that the price is consistent with the broader market.

Set up problem

The asset pool provides liquidity between stablecoins and risky assets with random price changes. We also made a particularly cruel assumption that all transactions entering the pool are informed (arbitrage transactions are only between AMM prices and normal It only occurs when there is a deviation between transaction prices).

Traditional thinking

At first glance, in this situation, becoming a Uniswap LP may seem like a costly mistake.

challenge

However, Dan and Charlie believe that the story does not end here.

solution

If the volatility of an asset is sufficiently high relative to its average rate of return, then over time, the LP on Uniswap will perform better than the HODLer, even if all transactions are arbitrage transactions Case.

Control standard

We evaluate different strategies by comparing their progressive wealth growth rates, which measure how quickly they compound (or lose) value over the long term.

Volatility Drag

Wait, what happened?

If you are trained to analyze gambling from the perspective of expected value, the previous section may look very strange or even completely incorrect.

Rebalancing value

In the face of volatility resistance, even when the expected value is positive, some funds should be reserved. In this way, when things go wrong, your losses will be reduced, which will increase your compound wealth in the long run.

Resources

Chances are you are not satisfied with these explanations and want to learn more.

Cost alchemy

mathematics

Having said that, we can now accurately answer the questions raised in Charlie’s initial problem statement.

LP wealth growth rate

Optimal fees and excess returns

If and only under the following circumstances, as an LP holding half of the stable currency and half of the risky assets, the return is more than simply holding the currency:

Explanation

Since geometric Brownian motion simulates compound growth, they are also affected by volatility resistance, which is expressed mathematically as

  1. If the volatility resistance makes the asset loss more than 200% of its average log return, then rebalancing on Uniswap will not eliminate enough resistance, then you’d better hold stablecoins.
  2. If volatility resistance makes the asset loss less than 66% of its average log return, then rebalancing on Uniswap is not worthwhile, and you’d better simply hold the asset.
  3. Within this range, becoming a Uniswap LP will eventually make you rich, in fact, richer than any unbalanced portfolio of stablecoins and volatile assets you hold. This includes assets that will eventually become worthless, as well as assets that will exhibit parabolic growth.

prove

You can find a preprinted paper with full proof here. Its working principle is to establish a dynamic model for discrete random walks, and then adopt behavior restrictions when the step size is reduced to zero.

How much should we trust in the results of these studies?

In my personal opinion, this is very credible.

future job

Although we hope you agree that these research results are theoretically interesting (or crazy), there is still a lot of work to be done to determine their relevance to the real world.

  1. How to turn these results into a multi-asset case, or when can LP choose a ratio other than 50/50 like Balancer to rebalance?
  2. What happens when we no longer allow unlimited transactions per unit of time?
  3. What happens when we introduce transaction costs that can even be changed to reflect the dynamics of priority gas auctions?
  1. Can we estimate these parameters for securities transactions on the market today?
  2. How many actively traded tokens can benefit from the rebalancing strategy we describe?
  3. Can we determine what percentage of Uniswap LP returns are realized in reality due to volatility returns?

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