A Note On Borrowing Constant Function Market Maker Shares

Constant function market makers (CFMMs) such as Uniswap, Balancer, and Curve, among many others, make up some of the largest decentralized exchanges on smart contract platforms like Ethereum. As the amount of capital deposited in these protocols has grown, improving capital efficiency for liquidity providers (LPs) has become an increasingly important challenge. One way to improve efficiency is to allow LPs to borrow Ether or USD against their shares in a CFMM protocol. In this note, we investigate the security and capital efficiency of allowing such lending. We provide sufficient conditions for LP borrowing to be at least as secure and capital efficient as direct borrowing in Aave/Compound. Furthermore, we show that the exposure taken by CFMM lenders can be replicated via barrier options, allowing for risks to be hedged. Finally, we show that the payoff of borrowed CFMM LP shares replicates bounded convex payoffs. Combined, these results suggest that CFMM lending is a safe mechanism for improving capital efficiency.