Properties of VaR and CVaR Risk Measures in High-Frequency Domain: Long–Short Asymmetry and Significance of the Power-Law Tail

This study investigates the properties of risk measure, value at (VaR) and conditional VaR (CVaR), using high-frequency Bitcoin data. These data allow us to conduct a high statistical analysis. Our findings reveal disparity in CVaR values between left right tails return probability distributions. We refer this as “long–short asymmetry”. In domain, tail distribution can be accurately described by power-law function. Moreover, ratio is expected determined solely exponent. Through empirical analysis, we confirm that property holds true for confidence levels. Furthermore, investigate relationship measures (VaR CVaR) realized volatility. observe they trace trajectory two-dimensional plane. changes gradually, indicating periods both low risk.