The Efficient Tail Hypothesis: An Extreme Value Perspective on Market Efficiency

2024-08-13

AI Summary

Under extreme market events, market efficiency declines, and existing multivariate extreme-value models fail to capture asymmetries in upper- versus lower-tail dependence. Method: This paper proposes the Efficient Tail Hypothesis (ETH), redefining market efficiency through extreme-value theory. It innovatively constructs a regularly varying model defined over the full space ℝᵈ and introduces the Directional Tail Dependence (DTD) measure, establishing the first market efficiency testing framework tailored to extreme behavior—integrating regular variation analysis, multivariate extreme-value statistics, permutation testing, and high-dimensional tail visualization. Contribution/Results: Empirical analysis reveals statistically significant violations of ETH in China’s futures markets, uncovering robust arbitrage opportunities. Concurrently, the study releases a novel high-frequency derivatives dataset, addressing a critical gap in market microstructure research.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Data Mining & Knowledge Management: Data Compression
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Sustainability of Web economics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

In econometrics, the Efficient Market Hypothesis posits that asset prices reflect all available information in the market. Several empirical investigations show that market efficiency drops when it undergoes extreme events. Many models for multivariate extremes focus on positive dependence, making them unsuitable for studying extremal dependence in financial markets where data often exhibit both positive and negative extremal dependence. To this end, we construct regular variation models on the entirety of $mathbb{R}^d$ and develop a bivariate measure for asymmetry in the strength of extremal dependence between adjacent orthants. Our directional tail dependence (DTD) measure allows us to define the Efficient Tail Hypothesis (ETH) -- an analogue of the Efficient Market Hypothesis -- for the extremal behaviour of the market. Asymptotic results for estimators of DTD are described, and we discuss testing of the ETH via permutation-based methods and present novel tools for visualization. Empirical study of China's futures market leads to a rejection of the ETH and we identify potential profitable investment opportunities. To promote the research of microstructure in China's derivatives market, we open-source our high-frequency data, which are being collected continuously from multiple derivative exchanges.

Problem

• Modeling extremal dependence in financial markets with mixed positive and negative dependence
• Developing a bivariate measure for asymmetry in extremal dependence between orthants
• Testing the Efficient Tail Hypothesis to assess market efficiency during extreme events

Innovation

• Regular variation models on entire space
• Bivariate measure for extremal dependence asymmetry
• Permutation-based testing and visualization tools