Abstract
We examine how extreme market risks are priced in the cross-section of asset returns at various horizons. Based on the frequency decomposition of covariance between indicator functions, we define the quantile cross-spectral beta of an asset capturing tail-specific as well as horizon-, or frequency-specific risks.
Further, we work with two notions of frequency-specific extreme market risks. First, we define tail market risk that captures dependence between extremely low market as well as asset returns.
Second, extreme market volatility risk is characterized by dependence between extremely high increments of market volatility and extremely low asset return. Empirical findings based on the datasets with long enough history, 30 Fama-French Industry portfolios, and 25 Fama-French portfolios sorted on size and book-to-market support our intuition.
Results suggest that both frequency-specific tail market risk and extreme volatility risks are significantly priced and our five-factor model provides improvement over specifications considered by previous literature.