New general dependence measures: construction, estimation and application to high-frequency stock returns

ArXiv ID: 2309.00025 “View on arXiv”

Authors: Unknown

Abstract

We propose a set of dependence measures that are non-linear, local, invariant to a wide range of transformations on the marginals, can show tail and risk asymmetries, are always well-defined, are easy to estimate and can be used on any dataset. We propose a nonparametric estimator and prove its consistency and asymptotic normality. Thereby we significantly improve on existing (extreme) dependence measures used in asset pricing and statistics. To show practical utility, we use these measures on high-frequency stock return data around market distress events such as the 2010 Flash Crash and during the GFC. Contrary to ubiquitously used correlations we find that our measures clearly show tail asymmetry, non-linearity, lack of diversification and endogenous buildup of risks present during these distress events. Additionally, our measures anticipate large (joint) losses during the Flash Crash while also anticipating the bounce back and flagging the subsequent market fragility. Our findings have implications for risk management, portfolio construction and hedging at any frequency.

Keywords: dependence measures, risk asymmetries, extreme dependence, tail asymmetry, high-frequency data, Equities

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper introduces advanced mathematical constructs involving copulas and theoretical proofs of consistency and asymptotic normality, indicating high mathematical complexity, and applies these measures to real high-frequency data with practical implications for risk management, showing strong empirical rigor.

  flowchart TD
    A["Research Goal:<br>New Dependence Measures"] --> B["Methodology:<br>Non-linear, Local, Invariant Construction"]
    B --> C["Estimator:<br>Nonparametric, Consistent, Asymptotic Normal"]
    C --> D["Data Input:<br>High-Frequency Stock Returns"]
    D --> E["Computational Process:<br>Measures around Flash Crash & GFC"]
    E --> F["Outcome:<br>Quantified Tail Asymmetry & Risk Buildup"]
    F --> G["Outcome:<br>Anticipated Joint Losses & Fragility"]