Information Coefficient : From a New Perspective

IC (Information Coefficient) is a widely and deeply accepted measure in active portfolio management.This paper investigates its probability properties that requires basic and in-depth research. First, this paper brings a new perspective on IC: a linear operator of a random unit vector generated by projecting returns onto a unit sphere. The new definition distinguishes IC from correlation coefficients or common statistics like t-statistics. Second, we theoretically solve the maximization of IC in expectation, and specify its almost closed-form solution with directional statistics. Third, simulation analysis reveals the influence of market condition like the stock number on IC, and emphasizes the difference between the optimal solutions and the population mean of returns. Last, empirical studies on Chinese stock market present a set of facts emerging from the unit transformed vectors of cross-sectional returns, and obtain the time series of IC in the real market with rolling windows. Our research profoundly reveals the nature of IC and sharply deepens the understanding of active portfolio management. Both the methodology and empirical study on IC suggest great potential in its further research