Slippage-at-Risk (SaR): A Forward-Looking Liquidity Risk Framework for Perpetual Futures Exchanges

Abstract

We introduce $\textbf{Slippage-at-Risk (SaR)}$, a quantitative framework for measuring liquidity risk in perpetual futures exchanges. Unlike backward-looking metrics such as Value-at-Risk computed on historical returns or realized deficit distributions, SaR provides a \emph{forward-looking} assessment of liquidation execution risk derived from current order book microstructure. The framework comprises three complementary metrics: $SaR(α)$, the cross-sectional slippage quantile; $ESaR(α)$, the expected slippage in the distributional tail; and $TSaR(α)$, the aggregate dollar-denominated tail slippage. We extend the base framework with a \emph{concentration adjustment} that penalizes fragile liquidity structures where a small number of market makers dominate quote provision. Drawing on recent work by Chitra et al. (2025) on autodeleveraging mechanisms and insurance fund optimization, we establish a direct mapping from SaR metrics to optimal capital requirements. Empirical analysis using Hyperliquid order book data, including the October 10, 2025 liquidation cascade, demonstrates SaR's predictive validity as a leading indicator of systemic stress. We conclude with practical implementation guidance and discuss philosophical implications for risk management in decentralized financial systems.

Figures (8)

• Figure 1: Cross-sectional distribution of concentration-adjusted slippage across 184 tokens. The vertical line indicates $\mathrm{SaR}^{\mathrm{adj}}(0.95) = 3.47\%$. The 9 tokens to the right (5% tail) exhibit elevated liquidity risk.
• Figure 2: Evolution of SaR and ESaR over the sample period. The spike during October 10-11 corresponds to the liquidation cascade event. Note that SaR began rising 6-12 hours before the cascade peak, demonstrating its leading indicator properties.
• Figure 3: Relationship between effective number of providers ($N_{\mathrm{eff}}$) and raw slippage. Tokens in the lower-left quadrant (low $N_{\mathrm{eff}}$, moderate raw slippage) receive the largest concentration haircuts. The horizontal line indicates $N_{\mathrm{target}} = 15$.
• Figure 4: Lead-lag correlation heatmap between SaR metrics and realized deficits. The gradient from left to right shows that SaR metrics lead deficit events by 6-24 hours.
• Figure 5: Order book depth collapse during the October 10 cascade. Total exchange depth at 100bps fell from $1.12B to $284M - a 75% decline - in the 36 hours preceding the event.

Theorems & Definitions (23)

• Definition 3.1: Slippage Function
• Example 3.2
• Remark 3.3: Directional Slippage
• Remark 3.4: Choosing $\beta$
• Definition 3.5: Slippage-at-Risk
• Definition 3.6: Expected Slippage at Risk
• Definition 3.7: Total Dollar Slippage at Risk
• Definition 3.8: Open Interest-Weighted SaR
• Example 4.1
• Definition 4.2: Herfindahl-Hirschman Index