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Cross-sectional "Information Coefficient" (IC) is a widely and deeplyaccepted measure in portfolio management. The paper gives an insight into IC inview of high-dimensional directional statistics: IC is a linear operator on thecomponents of a centralizing-unitizing standardized random vector ofnext-period cross-sectional returns. Our primary research first clearly definesIC with the high-dimensional directional statistics, discussing its first twomoments. We derive the closed-form expressions of the directional statistics'covariance matrix and IC's variance in a homoscedastic condition. Also, wesolve the optimization of IC's maximum expectation and minimum variance.Simulation intuitively characterizes the standardized directional statisticsand IC's p.d.f.. The empirical analysis of the Chinese stock market uncoversinteresting facts about the standardized vectors of cross-sectional returns andhelps obtain the time series of the measure in the real market. The paperdiscovers a potential application of directional statistics in finance, provesexplicit results of the projected normal distribution, and reveals IC's nature.

Centralizing-Unitizing Standardized High-Dimensional Directional Statistics and Its Applications in Finance