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.
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