arXiv2026
Auto-deleveraging (ADL) mechanisms are a critical yet understudied component of risk management on cryptocurrency futures exchanges. When available margin and other loss-absorbing resources are insufficient to cover losses following large price moves, exchanges reduce positions and socialize losses among solvent participants via rule-based ADL protocols. We formulate ADL as an optimization problem that minimizes the exchange's risk of loss arising from future equity shortfalls. In a single-asset, isolated-margin setting, the \emph{minimax leverage} policy -- minimizing the maximum leverage among participants -- is optimal for all monotone risk measures. This policy has a transparent structure: positions are reduced first for the most highly levered accounts, and leverage is progressively equalized via a water-filling (or ``leverage-draining'') rule. The policy is distribution-free, wash-trade resistant, Sybil resistant, and path-independent. It provides a canonical and implementable benchmark for ADL design and clarifies the economic logic underlying queue-based mechanisms used in practice. We further study the multi-asset, cross-margin setting, where the ADL problem becomes genuinely multi-dimensional: the exchange must allocate reductions across accounts with portfolios exposed to correlated price moves. Under the expected loss objective, asset-level shadow prices separate the problem across accounts, yielding a scalable numerical method. Naive gross leverage misleads here, ignoring within-portfolio hedging. When prices are driven by a single risk factor, the optimal policy is again water-filling, but in a factor-adjusted leverage, so better-hedged portfolios are deleveraged less. We apply the framework to the October~10, 2025 Hyperliquid ADL event. Relative to the exchange's realized allocation, our risk-minimizing allocations achieve lower expected shortfall.