Bid–ask bias in cumulated returns: an analytical approach

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.