Quantile Spectral Beta: A Tale of Tail Risks, Investment Horizons, and Asset Prices

Abstract This article investigates how two important sources of risk—market tail risk (TR) and extreme market volatility risk—are priced into the cross-section asset returns across various investment horizons. To identify such risks, we propose a quantile spectral (QS) beta representation based on decomposition covariance between indicator functions that capture fluctuations over frequencies. We study asymptotic behavior proposed estimators risk. Empirically, find TR is short-term phenomenon, whereas by investors in long term when pricing individual stocks. In addition, popular industry, size value, profit, investment, or book-to-market portfolios, as well portfolios constructed from classes, sorted cash flow duration, other strategies. These results reveal tail-dependent horizon-specific risks are heterogeneously datasets for investors.