We introduce the realized co-range, a novel estimator of the daily covariance between asset returns based on intraday high-low price ranges. In an ideal world, the co-range is five times more efficient than the realized covariance, which uses cross-products of intraday returns, when sampling at...

This note demonstrates that in applied regression analysis, the variance of a coefficient of interest may decrease from the inclusion of a control variable, contrasting with Clarke's assertion (2005, 2009) that the variance can only increase or stay the same. Practitioners may thus be...