Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Leveraged positions on decentralized lending platforms

Bastien Baude, Vincent Danos, Hamza El Khalloufi

TL;DR

This paper addresses optimizing leveraged staking strategies across multiple DeFi lending markets with deterministic, white-box interest-rate models. It introduces a convex reformulation that decomposes each position into an unleveraged and a maximally leveraged component, enabling closed-form solutions under linear, kinked, and adaptive borrow-rate models and accounting for transaction costs. The authors validate the framework via backtests on Morpho wstETH/WETH markets on Ethereum and Base, showing up to 6.2% APY for small budgets versus 3.1% for simple staking, with results highly sensitive to capital size and rebalancing frequency. The work provides a rigorous, transparent basis for automated DeFi portfolio optimization and exposes practical considerations such as liquidity constraints and fee-induced dynamics. Overall, the methodology offers a tractable, mathematically grounded approach to exploiting rate differentials in multi-market DeFi lending.

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.

Leveraged positions on decentralized lending platforms

TL;DR

This paper addresses optimizing leveraged staking strategies across multiple DeFi lending markets with deterministic, white-box interest-rate models. It introduces a convex reformulation that decomposes each position into an unleveraged and a maximally leveraged component, enabling closed-form solutions under linear, kinked, and adaptive borrow-rate models and accounting for transaction costs. The authors validate the framework via backtests on Morpho wstETH/WETH markets on Ethereum and Base, showing up to 6.2% APY for small budgets versus 3.1% for simple staking, with results highly sensitive to capital size and rebalancing frequency. The work provides a rigorous, transparent basis for automated DeFi portfolio optimization and exposes practical considerations such as liquidity constraints and fee-induced dynamics. Overall, the methodology offers a tractable, mathematically grounded approach to exploiting rate differentials in multi-market DeFi lending.

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.
Paper Structure (29 sections, 3 theorems, 60 equations, 11 figures, 3 tables)

This paper contains 29 sections, 3 theorems, 60 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Lending positions
  4. Optimal capital allocation
  5. Unsaturated markets with fully leveraged positions ($\lambda^{\ast} > s$)
  6. Saturated markets with strictly positive unleveraged position ($\lambda^{\ast} = s$)
  7. Algorithm
  8. Interpreting $\lambda^{\ast}$
  9. Linear rate
  10. Kinked rate
  11. Adaptive rate
  12. Dealing with transaction fees
  13. General approach
  14. Algorithm
  15. Numerical results
  16. ...and 14 more sections

Key Result

Proposition 1

Under the linear rate model eq:linear_rate_model, the optimal solution to eq:first_order_condition_i_unsaturated is given by: where, for $i = 1, \ldots, n$ and the optimal Lagrange multiplier reads: Without loss of generality, we assume that the markets are ordered such that: and the index $k \in \{ 1, \ldots, n \}$ is determined by the conditions (with by convention $\varphi_{n+1} = +\infty$)

Figures (11)

  • Figure 1: Borrow rate as a function of utilization under the kinked model (illustrative example).
  • Figure 2: Evolution of WETH reserves (solid line: supplied funds; dashed line: borrowed fund) for the two largest wstETH/WETH markets on Morpho on the Ethereum blockchain from January 1, 2025 to April 1, 2025.
  • Figure 3: Evolution of the interest rate (solid line: effective rate; dashed line: rate at target) for the two largest wstETH/WETH markets on Morpho on the Ethereum blockchain, compared to the staking rate from January 1, 2025 to April 1, 2025.
  • Figure 4: Evolution of the WETH positions of the "loopy" (low cap) strategy on the Ethereum blockchain from January 1, 2025 to April 1, 2025.
  • Figure 5: Evolution of the WETH positions of the "loopy" (high cap) strategy on the Ethereum blockchain from January 1, 2025 to April 1, 2025.
  • ...and 6 more figures

Theorems & Definitions (3)

  • Proposition 1: Linear rate
  • Proposition 2: Kinked rate
  • Corollary 1: Adaptive rate