The No-Action Survival Kelly Fraction: A General Equation for Margin Survival with Applications to Three Asset Classes

We derive a closed-form expression for (fₘₐₓ), the maximum Kelly fraction consistent with no-action margin survival—the highest leverage ratio that survives all observed historical market paths without forced liquidation, assuming no intermediate action by the investor. The expression depends on five parameters: collateral haircut, maintenance margin ratio, collateral drawdown, margin position drawdown, and Kelly-optimal leverage ((f^*)). The framework provides an intuitive analytical description of regulated margin trading by relating margin requirements, collateral quality, and leverage limits through a single equation. We apply the model to three representative equity ETF categories: Japanese equity ETFs (1306 TOPIX ETF and 1330 Nikkei 225 ETF), U.S. equity ETFs (SPY and QQQ), and leveraged equity ETFs (including TQQQ and other 3x leveraged equity products). Under historical stress scenarios, we find (fₘₐₓ) values of 23% for Japanese equities, 40% for U.S. equities, and 29% for leveraged equity ETFs. Across all cases, variation in (f^*) explains most of the observed differences in no-action margin survival. The results suggest that sustainable leverage capacity is determined not only by market drawdowns but also by the interaction between collateral quality and Kelly-optimal leverage. The proposed framework provides a practical tool for evaluating sustainable leverage limits in regulated margin environments and offers a unified analytical perspective on margin survival under historical stress conditions.