New Moment Estimators of the Effective Spread Based on Daily High and Low Prices

Abstract

In the paper we propose five new moment estimators for effective spread based on the covariance estimator of Roll (1984) and the High-Low estimator recently developed by Corwin and Schultz (2012, \textit{J. Finance}, Vol.67, 719-760), and further investigate theoretically the statistical properties of six bid-ask spread estimators including Corwin and Schultz's estimator. The biases and mean squared errors (MSE) of these six estimators have been derived and compared with each other asymptotically, which, together with the subsequent simulation studies and empirical examples, reveal explicitly the superior performance of new developed High-Low estimators over Corwin and Schultz's estimator. Furthermore this paper also puts forward GMM estimators constructed by three or more moment conditions, which also perform well compared with the six High-Low estimators. The method discussed here is different to the existing literatures which usually resort to the correlation between the bid-ask spread estimators with a benchmark calculated from high-frequency data as they compare the performance of different estimators.