Return-based and Range-Based (Co)Variance Estimation - With an Application to Foreign Exchange Markets

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Abstract
This paper analyzes and compares range-based and return-based variance/covariance estimates. We provide new results on the relative efficiency of the range. We show that the use of the range is compatible with time varying volatilities and we extend the range to a multivariate setup. A new estimator for the covariance, termed co-range, which is based on high and low prices, is proposed. The main properties of the new estimator are derived. Empirically, we find that range-based measures of variance, standard deviation, co-variance and correlation possess a much higher degree of persistence compared to conventional measures based on open/close prices.