Leveraged positions on decentralized lending platforms

We develop a mathematical framework to optimize leveraged staking ("loopy") strategies in Decentralized Finance (DeFi), in which a staked asset is supplied as collateral, the underlying is borrowed and re-staked, and the loop can be repeated across multiple lending markets. Exploiting the fact that DeFi borrow rates are deterministic functions of pool utilization, we reduce the multi-market problem to a convex allocation over market exposures and obtain closed-form solutions under three interest-rate models: linear, kinked, and adaptive (Morpho's AdaptiveCurveIRM). The framework incorporates market-specific leverage limits, utilization-dependent borrowing costs, and transaction fees. Backtests on the Ethereum and Base blockchains using the largest Morpho wstETH/WETH markets (from January 1 to April 1, 2025) show that rebalanced leveraged positions can reach up to 6.2% APY versus 3.1% for unleveraged staking, with strong dependence on position size and rebalancing frequency. Our results provide a mathematical basis for transparent, automated DeFi portfolio optimization.