On Information Coefficient and Directional Statistics
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Cross-sectional "Information Coefficient"(IC) is a widely and deeply accepted measure in portfolio management. In this paper, we propose that IC is a linear operator on the components of a standardized random vector of next period cross-sectional returns. From the probability perspective, IC is a linear combination of the components of a directionally projected degenerated random vector. We deduct a solution to its optimization in expectation and obtain the maximum. Their closed-form expressions are given by directional statistics in a specific condition. Simulation analysis discloses the influence of market information, such as the number of stocks, on IC. The empirical analysis of the Chinese stock market uncovers a set of interesting facts about the standardized vectors of cross-sectional returns and helps to obtain the time series of the measure in the real market. Our research discovers a potential application of directional statistics in finance, reveals the nature of the IC measure, and deepens the understanding of active portfolio management.
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