Regardless of whether the CAPM is rejected for valid reasons or by mistake, a single long-short portfolio will always … “Low-Minus-High (LMH) portfolio,” need not proxy for fundamental risk. We show theoretically how factors based on valuation …

various frequencies, we define a \textit{quantile spectral} beta representation that characterizes asset's risk generally … market risk that captures dependence between extremely low market and asset returns. Second, extreme market volatility risk … as daily data. These results suggest that both frequency-specific tail market risk and extreme volatility risk are priced …