Understanding the Value of Uniswap v3 Liquidity Positions

Looking for guidance in picking a Uniswap v3 liquidity range. Seeking help leads nowhere.

What is the value of a Uniswap v3 LP token?

The Uniswap v3 whitepaper describes how much of each asset has to be added when establishing a new position. The number of token0 and token1 in a new LP position will depend on the range determined by the lower tick tL, the upper tick tH and the price at entry P0.

Token composition of a LP position. Describes how much of token0 and token1 are in a LP position.

Computing Delta, the rate of change in Net Liq Value

How will the value of a LP position be affected by the price of the underlyings? Specifically, we’d like to know how much would the Net Liq change if the value of token0 changes by $1. This quantity is called “delta” and represents the price sensitivity of an option.

Delta of a LP position. How much does the value of a LP position changes when the price of the underlying asset changes by $1?
Delta as a slope. The slope of the red curve represents the value of delta for the normalized LP position 1*sqrtV(P). The slope changes from 100% to 0% as the price changes between the lower tick tL and the upper tick tH. Download GIF version.
Ranged Covered Call. Return of a LP position defined by an ETH price between 2000 and 3000. The LP position’s value will track the price of ETH below the lower tick tL and will remain unchanged when the price of ETH is above the upper tick 3000. Returns from fees are approximately 8%.

Understanding the impact of Net Delta on returns

Why do we care about delta? Understanding a portfolio’s delta can help manage risks and reduce returns volatility. Hedge funds typically need to compute the delta of their financial instruments to create a portfolio containing many assets structured in way that is delta neutral — ie. whose total value will remain constant despite market swings.

LP portfolio. Details of a portfolio consisting of ETH/Dai, ETH/WBTC and ETH/UNI LP positions. The total value and the delta have been converted into ETH to simplify the net delta calculation.
Net delta of a ETH/Dai, ETH/WBTC, and ETH/UNI portfolio. The beta-weighted expected return of the portfolio will change according to the amount of ETH shorted to balancer the delta of the position. Tuning the amount of shorted ETH shifts the position’s break-even points. We assumed an initial 100 Dai in fees were collected to compute the beta-weighted P/L for this position. Download GIF version.

Future work

In this post, we derived an expression for the total value of a Uniswap v3 LP position. We found that the price sensitivity of a Uniswap v3 LP option can help understand future returns, and we described a procedure for calculating the delta of a portfolio composed of many Uniswap v3 LP pairs.

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Guillaume Lambert

Guillaume Lambert

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Asst professor in Applied Physics at Cornell. LambertLab.io PI and proud father. Interests: Biophysics, Math, Crypto, and Options (often all at the same time).