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 statisticsin 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 .
Cross-sectional "Information Coefficient" (IC) is a widely and deeply accepted measure in portfolio management. The paper gives an insight into IC in view of high-dimensional directional statistics: IC is a linear operator on the components of a centralizing-unitizing standardized random vector of next-period cross-sectional returns. Our primary research first clearly defines IC with the high-dimensional directional statistics, discussing its first two moments. We derive the closed-form expressions of the directional statistics' covariance matrix and IC's variance in a homoscedastic condition. Also, we solve the optimization of IC's maximum expectation and minimum variance. Simulation intuitively characterizes the standardized directional statistics and IC's p.d.f.. The empirical analysis of the Chinese stock market uncovers interesting facts about the standardized vectors of cross-sectional returns and helps obtain the time series of the measure in the real market. The paper discovers a potential application of directional statistics in finance, proves explicit results of the projected normal distribution, and reveals IC's nature .
R
In this paper , we propose that IC
The paper gives an insight into IC in view of high-dimensional directional statistics: IC
A
centralizing-unitizing
R
next period
next-period
R
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
Our primary research first clearly defines IC with the high-dimensional directional statistics, discussing its first two moments. We derive the
R
are given by directional statisticsin a specific condition. Simulation analysis discloses the influence of market information, such as the number of stocks, on IC.
of the directional statistics' covariance matrix and IC's variance in a homoscedastic condition. Also, we solve the optimization of IC's maximum expectation and minimum variance. Simulation intuitively characterizes the standardized directional statistics and IC's p.d.f..
D
a set of
D
to
R
Our research
The paper
R
reveals the nature of the IC measure, and deepens the understanding of active portfolio management
proves explicit results of the projected normal distribution, and reveals IC's nature