Asymptotic Comparison of Different Spread Estimators

• Activity Number: 337
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yang Gao*+ and Mingjin Wang
• Companies: and Peking University
• Keywords: liquidity ; bid-ask spread ; price range ; asymptotic property ; bootstrap

Abstract

In the paper we investigate theoretically the statistical properties of two bid-ask spread estimators, i.e., the covariance estimator of Roll (1984) and the estimator based on daily high and low prices recently developed by Corwin and Schultz (2012, J. Finance, Vol.67, 719-760). The biases and mean squared errors (MSE) of these two estimators have been derived and compared with each other asymptotically, which, together with the subsequent simulation studies and bootstrap analysis on empirical examples, reveal explicitly the superior performance of high-low estimator over the Roll's estimator. 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.