Summary

• We have performed a study on the following GammaSwap pools against the underlying spot assets: weETH/USDC (Arbitrum), WETH/USDC (Arbitrum) and PENDLE/USDC (Arbitrum).
• In the study, each pool analyzed outperformed holding the underlying assets in a 50:50 ratio outside of the pool even without incentives
• The longer one provides liquidity in GammaSwap, the greater the outperformance due to the effects of compounding

Introduction

It is well known that many AMM liquidity providers in DeFi, particulary in concentrated liquidity AMMs (CLAMMs) like Uniswap V3 are unprofitable due to Impermanent Loss (IL): https://hackernoon.com/half-of-uniswap-v3-users-lose-money-heres-why

Although they are an older product, constant function market makers (CFMMs) like Uniswap V2 tend to provide higher returns for retail LPs. With relatively few studies on CFMM returns, is this actually true? What are the returns like in GammaSwap where in theory LPs should be compensated better for their IL risk?

Let’s dive in 👇

Methodology

We used the following formulas to calculate LP returns vs spot:

TotalInvariant = LPInvariant + LPBorrowedInvariant

LP Return (%) = (TotalInvariant ₜ₂ / TotalInvariant ₜ₁) / (TotalLPSupply ₜ₂ / TotalLPSupply ₜ₁ ) * sqrt( price ₜ₂ / price ₜ₁) — 1

Spot Return (%) = ((( Price ₜ₂ / Price ₜ₁ ) * 0.5 + 0.5) / 1) — 1

Total Invariant is k in the x*y=k

It represents the constant product value, which remains the same regardless of price and increases with the growth of the fees in the pool. We take is as a sum of the LPInvariant which is the liquidity in the pool and LPBorrowedInvariant which is the liquidity borrowed as open interest.

The LP Return is measured by taking the growth of the invariant and discounting the growth in LP supply from deposits (that way we are only measuring fee growth). We then multiply by the sqrt of the price change from t2 to t1 which is the difference between time at any two blocks and subtract by 1 to convert it into percentage terms. For this study, we took snapshots of the returns weekly.

Similarly, for spot returns, we took the price at t2 and divided by the price at t1. We then accounted for the 50:50 LP ratio and converted it into percentage terms.

We used the subgraph to query these values on a weekly basis. Links to the scripts are available in Github here so you can verify the results yourself: https://github.com/0xDeFiDevin/GammaLPvsSpot

Evaluating LP Performance vs Spot

We evaluated performance in the following pools vs spot: weETH/USDC (Arbitrum), WETH/USDC (Arbitrum) and PENDLE/USDC (Arbitrum).

weETH/USDC (Arbitrum)

For this study, we compare the performance of a weETH/USDC LP vs holding the portfolio in spot (50% weETH, 50% USDC) outside of the pool. The returns for the LP are excluding esGS rewards, EtherFi points and EigenLayer points.

The results from the study show that at any point in time the weETH/USDC LP outperformed spot regardless of price and excluding incentives. By the end of the chart at November 15th, the LP had a return of 4.21% vs a spot performance of -2.98%, a massive 7.19% outperformance!

Assuming the average esGS reward APY is 20% with an additional 3% yield from points, the outperformance would be 24.21% as an LP vs -2.98% in spot, a 27.19% difference!

WETH/USDC (Arbitrum)

In this study, we compare the performance of WETH/USDC vs holding the same spot portfolio with 50% in WETH and 50% in USDC outside of the pool. The returns for the LP are excluding esGS rewards.

The results show that at any point in time the WETH/USDC LP either matched or outperformed spot (especially as time in the pool increased). By the end at November 15th, the LP had a return of -0.12% vs -4.09% in spot, a 3.97% outperformance excluding incentives!

Assuming the average esGS reward is 20%, the outperformance would be 12.38% vs -4.09% in spot, a 16.47% difference!

PENDLE/USDC (Arbitrum)

For the final study, we compare the performance of a PENDLE/USDC LP vs holding the same spot portfolio with 50% in PENDLE and 50% in USDC outside of the pool.

The results show that the majority of time the PENDLE/USDC LP outperformed spot returns excluding incentives, the exception is when price dramatically decreased beyond -30% where the IL outweighed the compounding of fees. This is when $PENDLEprice decreased 68% from $6.85 to $2.20. This implies an IL of 14% but the loss was only 5.14% compared to spot.

As price returned to its original level, the PENDLE/USDC LP significantly outperformed spot and by the end of the study the LP had a return of -1.60% with the spot return being -9.65%, an outperformance of 8.05% — the highest in the study!

Analysis

Here are some key highlights and learnings from the study:

• Liquidity concentrates in pools with high returns and minimal risk. This will inform our strategy moving forward: focus on large caps, use yield tokens to increase the APY, partner with new protocols that are experiencing flows.
• Every pool outperformed spot. The longer the liquidity provider participates in the pool, the greater chance that they will be profitable due to compounding.
• Fees from compounding often outweigh IL. The only loss compared to spot was in the PENDLE/USDC pool after the price of the 50:50 pair went down 34% ($PENDLE went down 68%).
• There was never a loss greater than IL at any point in time. This is unlike products where you provide liquidity for perpetual future traders since all borrowing is fully collateralized. Liquidity providers never experience additional losses (beyond IL) when traders are profitable.

Conclusion

In this study, we demonstrated that LPs in all analyzed pools outpeformed spot. Stay tuned for our next article on our upcoming product launch, yield tokens, and the backtesting done for those strategies!