A new estimator of bid-ask spreads is presented. When the trade direction is known, any estimate of the spread is associated with a unique series of conjectural mid-prices derived by adjusting the observed transaction price by half the estimated spread. It is shown that the covariance of successive conjectural midprice returns is maximised (or least negative) when the estimated spread is equal to the true spread. A search procedure to maximise this covariance may therefore be used to estimate the true spread. The performance of this estimator under various conditions is examined both theoretically and with Monte Carlo simulations. The simulations confirm the theoretical results. The performance of the estimator is good. The final publication (Review of Quantitative Finance and Accounting, 2015) is available at Springer via http://dx.doi.org/10.1007/s11156-015-0499-z
