Real Risk or Paper Risk? Mis-Measured Factors, Granular Measurement Errors, and Empirical Asset Pricing Tests

We study implications of unpriced "granular measurement errors" -- idiosyncratic shocks to large firms that aren't well-diversified in market indices -- for asset pricing tests and propose alternative tests insensitive to them. We find stronger evidence of an intertemporal relation between the expected return and variance of the market after these corrections. Cross-sectionally, estimated market betas -- especially for small/high beta stocks -- are biased, the size anomaly disappears, and the price of risk for the market portfolio is consistent with theory. The granular residual is volatile and less informative about real activity than our adjusted index, potentially rationalizing lower/zero risk compensation