A New Test for the Detection of the Pricing Role of Aggregate Idiosyncratic Risk in the Predictive Regression

Abstract

The standard test for the pricing role of aggregate idiosyncratic risk in the conventional predictive regression considers aggregate total idiosyncratic risk a reasonable proxy for its undiversified component, which should be priced as theory suggests. However, when the priced component is relatively small, the test has little statistical power to reject the null hypothesis that idiosyncratic risk does not matter, even when the priced component, albeit small, explains an economically large portion of future excess return variation. We propose a simple regression-based method that can, under certain conditions, substantially improve the power of the test when economically important alternative hypotheses are true, but sacrifices little in the size of the test for the improved power. Based on the new test, we strongly reject the proposition that idiosyncratic risk does not matter and uncover a significantly positive relationship between aggregate undiversified idiosyncratic risk and future market excess returns.