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

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.

• The paper’s main contribution is evaluating three position sizing methods in put-writing, revealing the hybrid Kelly-VIX approach’s superior risk control.
• The analysis demonstrates that ultra-short-dated, far OTM options deliver enhanced risk-adjusted returns through dynamic sizing validated by Monte Carlo simulations.
• The paper offers actionable insights for institutional investors, emphasizing portfolio diversification and drawdown management amid variable market volatility.

Overview

"Sizing the Risk: Kelly, VIX, and Hybrid Approaches in Put-Writing on Index Options" (2508.16598) explores systematic put-writing strategies for the S&P 500 Index, emphasizing position sizing as a determinant of long-term performance. Despite the recognized volatility risk premium, the practical application of short-dated put-writing strategies lacks clarity in prior literature. This paper evaluates three position sizing techniques: the Kelly criterion, VIX-based volatility regime scaling, and a novel hybrid strategy blending both. The findings show that ultra-short-dated, far out-of-the-money (OTM) options yield superior risk-adjusted returns. The hybrid sizing consistently manages return generation and drawdown control, particularly under low-volatility conditions. This research offers actionable insights for institutional investors aiming to integrate systematic volatility harvesting into diversified portfolios.

Methodology

Position Sizing Strategies

1. Kelly Criterion: Based on maximizing logarithmic wealth growth, applied using a Monte Carlo simulation to estimate probabilities and outcomes.
2. VIX-Rank Sizing: Dynamically adjusts position size based on the VIX's percentile rank over a historical window, with the rank indicating market sentiment.
3. Hybrid Kelly-VIX Approach: Combines the Kelly criterion with VIX-Rank as a scaling factor, adapting bet sizes according to volatility conditions.

Strategy Configurations

• Days-to-Expiration (DTE): Strategies evaluated for 0, 1, 3, and 5 DTE.
• Moneyness: Put options evaluated from at-the-money (ATM) to 10% OTM.
• Volatility Estimators: Historical volatility, Garman-Klass, and Yang-Zhang estimators calculated across multiple time horizons.

  Figure 1: The graphical representation of information ratios for hybrid Kelly-VIX sizing strategies demonstrates the diverse performance outcomes across DTE and moneyness levels.

Results

Kelly Criterion Sizing

• Performance: The best results were observed with 5-10% OTM options and 0-1 DTE.
• Volatility Estimators: The Garman-Klass estimator was most effective with longer windows (63 days), while shorter windows (5-10 days) favored Yang-Zhang.
• Risk-Adjusted Returns: Kelly sizing excelled in risk control but with modest absolute returns.

VIX-Rank Sizing

• DTE Impact: Longer DTE resulted in higher absolute returns, whereas shorter DTE provided better information ratios.
• VIX Tenor Variety: Shorter VIX tenors (e.g., VIX9D) yielded better risk-adjusted results due to more relevant short-term volatility insights.

Kelly-VIX Sizing

• Dynamic Sizing: Effectively reduced volatility and adapted to changing market conditions.
• Risk and Return Balance: Provided a compromise between maximizing returns and controlling risk, demonstrating robustness across various configurations.

  Figure 2: The comparison of annualized returns of hybrid Kelly-VIX strategies with VIX9D, emphasizing superior performance with varying DTE.

Implementation and Considerations

Computational Requirements

• Monte Carlo Simulations: Essential for estimating Kelly fractions, demanding significant computational resources depending on scenario complexity.
• Historical Volatility Calculations: Require high-frequency market data for effective implementation.

Practical Applications

• Institutional Investors: These strategies provide avenues for enhancing portfolio efficiency through systematic volatility premia exposure.
• Market Regime Adaptation: The hybrid method is particularly adaptable to shifting market environments, seamlessly adjusting position sizes.

Implications for Portfolio Management

• Diversification: The put-writing techniques discussed offer an opportunity for diversification within portfolios, emphasizing controlled risk.
• Drawdown Management: Hybrid approaches deliver consistent control over potential losses, crucial during market downturns.

Conclusion

The insights from "Sizing the Risk: Kelly, VIX, and Hybrid Approaches in Put-Writing on Index Options" contribute valuable strategies for institutional investors focusing on volatility risk premiums through systematic put-writing. The combination of dynamic sizing methods adapts efficiently to market conditions, enhancing risk-adjusted returns across various scenarios. Future work should explore parameter sensitivity, alternative underlyings, and international markets to further bolster the robustness of these findings.