Leveraged positions on decentralized lending platforms

Paper: arXiv 2601.14005

Authors: Bastien Baude, Vincent Danos, Hamza El Khalloufi

Abstract

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.0/10 (capped from 6.5: no out-of-sample test; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an elegant reduction of a non-convex leverage optimization problem in DeFi to a convex formulation with closed-form solutions across common interest rate models. The theoretical framework is complemented by real-world backtests on Ethereum and Base lending markets (Morpho), offering strong practical relevance and clarity.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimize Leveraged Staking<br>('Loopy Strategies') in DeFi"] --> B["Data Inputs: Morpho wstETH/WETH Markets<br>Ethereum & Base (Jan-Apr 2025)"]
    B --> C["Mathematical Modeling:<br>Interest Rates & Constraints<br>(Linear, Kinked, Adaptive IRMs)"]
    C --> D["Convex Optimization & Allocation:<br>Maximize APY Across Multiple Markets"]
    D --> E["Backtesting Engine:<br>Position Sizing & Rebalancing Dynamics"]
    E --> F["Key Outcome: Leveraged APY up to 6.2%<br>vs. 3.1% Unleveraged Staking"]

Cited References (12)

1. C onvex optimization (2004)
2. A survey on the continuous nonlinear resource allocation problem (2008)
3. A ave v1 (2020)
4. A ave v2 (2020)
5. A ave v3 (2022)
6. C ompound: T he money market protocol (2019)
7. M orpho B lue (2023)
8. A daptive C urve I R M (2023)

0 of 12 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.