Testing for the Asymmetric Optimal Hedge Ratios: With an Application to Bitcoin

Paper: arXiv 2407.19932

Authors: Abdulnasser Hatemi-J

Abstract

Reducing financial risk is of paramount importance to investors, financial institutions, and corporations. Since the pioneering contribution of Johnson (1960), the optimal hedge ratio based on futures is regularly utilized. The current paper suggests an explicit and efficient method for testing the null hypothesis of a symmetric optimal hedge ratio against an asymmetric alternative one within a multivariate setting. If the null is rejected, the position dependent optimal hedge ratios can be estimated via the suggested model. This approach is expected to enhance the accuracy of the implemented hedging strategies compared to the standard methods since it accounts for the fact that the source of risk depends on whether the investor is a buyer or a seller of the risky asset. An application is provided using spot and futures prices of Bitcoin. The results strongly support the view that the optimal hedge ratio for this cryptocurrency is position dependent. The investor that is long in Bitcoin has a much higher conditional optimal hedge ratio compared to the one that is short in the asset. The difference between the two conditional optimal hedge ratios is statistically significant, which has important repercussions for implementing risk management strategies.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 5.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a straightforward econometric formulation for testing asymmetry in optimal hedge ratios using partial cumulative sum decompositions within a multivariate GARCH framework. While mathematically accessible, the methodological contribution is clear and applied directly to Bitcoin spot and futures markets.

Research Flowchart

  flowchart TD
    A[Research Goal: Test & Estimate Asymmetric Optimal Hedge Ratios OHR] --> B[Data Inputs: Bitcoin Spot & Futures Prices]
    B --> C[Methodology: Multivariate GARCH Modeling]
    C --> D[Hypothesis Testing: Symmetric OHR Null vs. Asymmetric Alternative]
    D --> E{Null Rejected?}
    E -- Yes --> F[Estimate Position-Dependent Conditional OHRs]
    F --> G[Key Outcome: Long position requires significantly higher OHR than Short position]