Risk-Based Auto-Deleveraging

Abstract

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, we show that under a risk-neutral expected loss objective the unique optimal policy minimizes the maximum leverage among participants. The resulting design 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. This 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 a vector of required reductions across accounts with portfolios exposed to correlated price moves. We show that under an expected-loss objective the problem remains separable across accounts after introducing asset-level shadow prices, yielding a scalable numerical method. We observe that naive gross leverage can be misleading in this context as it ignores hedging within portfolios. When asset prices are driven by a single dominant risk factor, the optimal policy again takes a water-filling form, but now in a factor-adjusted notion of leverage, so that more effectively hedged portfolios are deleveraged less aggressively.

Figures (5)

• Figure 1: The minimax leverage policy equalizes leverage by water-filling ("leverage-draining") from the initial leverage $\ell_i(0)$ down to the threshold $t^\star$. A larger total buyback quantity $Q$ leads to a lower threshold $t^\star$ and more accounts being affected (right).
• Figure 2: CVaR-optimal deleveraging under the water-filling rule. Gray curves correspond to individual post-ADL leverage levels $\ell_i(x_i)$, the solid blue curve shows the mean leverage among at-risk accounts, and the dashed horizontal line indicates the stress threshold $\ell_\beta$. The inset displays the CVaR objective value as a function of the total deleveraging budget $Q$, where the gray dotted line is a linear fit and the orange dashed line illustrates the deleverage volume $Q_\beta$ necessary to reach $\ell_\beta$.
• Figure 3: Water-filling with clipping. The target threshold $t^\star$ equalizes post-ADL factor leverage for interior accounts, but account-specific bounds can bind. In the right panel, account $1$ cannot be reduced below $\underline{\ell}_1$, so its post-ADL factor leverage is clipped at $\underline{\ell}_1$ rather than being reduced to $t^\star$.
• Figure 4: Optimal BTC deleveraging paths under the full bivariate model (left panel) and the one-factor approximation (right panel). The main panels plot post-ADL factor leverage $\ell_i^{(v)}(x_i^\star)$ against the BTC deleveraging budget $Q^{\mathrm{BTC}}$; the insets report gross leverage $\ell_i(x_i^\star)$ for the same optimal allocations.
• Figure 5: Samples of price increments under the bivariate GBM model (blue) and the one-factor approximation collapsing the bivariate distribution onto the dominant covariance direction (red).

Theorems & Definitions (75)

• theorem 2.4: Minimax leverage policy
• remark 2.5
• definition 2.6: Sybil split
• definition 2.7: Sybil resistance
• theorem 2.8
• remark 2.9
• definition 2.10: Path-independence
• definition 2.11: Leverage-priority
• theorem 2.12: Characterization by path-independence and leverage-priority
• remark 2.13