Sizing the Risk: Kelly, VIX, and Hybrid Approaches in Put-Writing on Index Options

ArXiv ID: 2508.16598 “View on arXiv”

Authors: Maciej Wysocki

Abstract

This paper examines systematic put-writing strategies applied to S&P 500 Index options, with a focus on position sizing as a key determinant of long-term performance. Despite the well-documented volatility risk premium, where implied volatility exceeds realized volatility, the practical implementation of short-dated volatility-selling strategies remains underdeveloped in the literature. This study evaluates three position sizing approaches: the Kelly criterion, VIX-based volatility regime scaling, and a novel hybrid method combining both. Using SPXW options with expirations from 0 to 5 days, the analysis explores a broad design space, including moneyness levels, volatility estimators, and memory horizons. Results show that ultra-short-dated, far out-of-the-money options deliver superior risk-adjusted returns. The hybrid sizing method consistently balances return generation with robust drawdown control, particularly under low-volatility conditions such as those seen in 2024. The study offers new insights into volatility harvesting, introducing a dynamic sizing framework that adapts to shifting market regimes. It also contributes practical guidance for constructing short-dated option strategies that are robust across market environments. These findings have direct applications for institutional investors seeking to enhance portfolio efficiency through systematic exposure to volatility premia.

Keywords: Put-Writing Strategy, Volatility Risk Premium, Kelly Criterion, VIX Scaling, Short-Dated Options, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical frameworks including the Kelly criterion, Monte Carlo simulations, and sophisticated volatility regime analysis, demonstrating moderate-to-high mathematical density. It achieves high empirical rigor through comprehensive backtesting using real S&P 500 options data, extensive parameter sweeps, and focus on implementation details like transaction costs and margin requirements.

  flowchart TD
    A["Research Goal<br>Optimize systematic put-writing<br>position sizing for SPX options"] --> B["Key Methodology<br>Evaluate 3 Sizing Approaches"]
    
    B --> B1["Kelly Criterion<br>Fractional Kelly versions"]
    B --> B2["VIX-Based Scaling<br>Regime-dependent sizing"]
    B --> B3["Hybrid Method<br>Combined Kelly & VIX scaling"]
    
    C["Data & Inputs<br>SPXW Options 0-5 DTE<br>2010-2024, multiple moneynesses"] --> D["Computational Process<br>Exhaustive Grid Search<br>over design space"]
    
    B1 & B2 & B3 --> D
    
    D --> E{"Key Findings & Outcomes"}
    
    E --> F1["FAR OTM + Ultra-Short DTE<br>Best risk-adjusted returns"]
    E --> F2["Hybrid Method Dominates<br>Superior drawdown control<br>Optimal in 2024 low-vol"]
    E --> F3["Dynamic Sizing Framework<br>Adapts to market regimes<br>Enhances portfolio efficiency"]
    
    F1 & F2 & F3 --> G["Practical Application<br>Institutional volatility<br>premium harvesting"]