Bid-Ask Bias in Cumulated Returns: An Analytical Approach

Abstract

Several studies in Finance and Accounting literature have measured security returns subsequent to some economic events over long-horizons by cumulating the returns over time. It is well known that when single period returns are cumulated over long-horizons, the bid-ask error in the measured returns could be very high. One way of estimating the bid-ask error is by simulation. This paper offers an alternative to the simulation approach and provides a closed form expression for the bid-ask error in cumulated returns. Our analytical approach has two main advantages over the traditional simulation method: first it quantifies the bias precisely and second, it is computationally simpler by several orders of magnitude.

JEL Classification: G12, G14