The Statistics of Cross-Sectional Information Coefficient

17 Pages Posted: 2 May 2011 Last revised: 21 Sep 2011

Date Written: July 5, 2011

Abstract

Information coefficient (IC) is one of the most commonly used statistics in quantitative financial analysis that is usually defined as the correlation coefficient between a variable's predicted and actual values. In this paper, I derive the asymptotic distribution of the sample average cross-sectional information coefficient (IC) when the true underlying IC is time varying. I show that sample average IC divided by sample IC standard deviation approaches the ex ante expected portfolio IR as derived in Ding (2011). I extend the result to cross-sectional factor return and factor return standard deviation. Simulation result is strikingly close to what theory suggests. I also conduct empirical simulation using actual quantitative factors and the relationships between cross-sectional IC, IC standard deviation and sample size are all as predicted by a linear one factor model with time varying IC.

Keywords: information coefficient (IC), asymptotic distribution, information ratio, the fundamental law of active management

JEL Classification: G1, C2, C5

Suggested Citation

Ding, Zhuanxin, The Statistics of Cross-Sectional Information Coefficient (July 5, 2011). Available at SSRN: https://ssrn.com/abstract=1826303 or http://dx.doi.org/10.2139/ssrn.1826303

Zhuanxin Ding (Contact Author)

Analytic Investors ( email )

555 West Fifth Street
50th Floor
Los Angeles, CA 90017
United States

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