The Statistics of Cross-Sectional Information Coefficient

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, we derive the asymptotic distribution of the sample average cross-sectional information coefficient (IC) when the true underlying IC between risk-adjusted return and risk-adjusted factor exposure is time varying. We show that sample average IC divided by sample IC standard deviation approaches the ex ante expected portfolio IR as derived in Ding and Martin (2017). Simulation result is strikingly close to what theory suggests. We 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 factor model with time varying IC