Before revision:  Based on the decomposition of covariance between indicator functions capturing fluctuations of different parts of return distributions over various frequencies, we define aquantile spectral beta representation that characterizes asset's risk generally. Nesting the traditional frameworks, the new representation explainstail -specific as well as horizon-, or frequency-specificspectral risks.
After revision:  Based on the decomposition of covariance between indicator functions capturing fluctuations of different parts of return distributions over various frequencies, we define aquantile spectral tail -specific as well as horizon-, or frequency-specificspectral risks.