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

This paper proposes five new simple moment estimators of the effective spread based on the covariance estimator of Roll (1984) and the High-Low estimator recently developed by Corwin and Schultz (2012). And then the authors theoretically investigate the statistical properties of six simple High-Low 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 study, reveal explicitly the superior performance of newly developed High-Low estimators over Corwin and Schultz's estimator in both ideal and non-ideal conditions. Moreover, this paper also develops GMM estimators constructed by three or more moment conditions and compares with the six simple High-Low estimators. Finally, several example applications on the U.S. and Chinese financial markets are conducted to demonstrate the superior performance of the new High-Low estimators. The results provide alternative choices for identifying the liquidity proxies that well capture different structure of markets