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

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.