The key for measuring the transaction cost of a security is to find the appropriate
 proxy for the underlying market efficient price. The midpoint of the bid and ask
 prices (midquote) are often used as a proxy. However, among midquotes at and after
 the transaction time, which one is the best chioce? The current midquote is the best
 choice in a market without information asymmetry. The choice of miduoqtes is discussed
 for a market with information asymmetry under the criterion of the minimum bias and
 the minimum variance. The focus of this paper was to propose a methodology to find
 the optimal lagged midquotes in the minimum MSE sense in the market with information
 asymmetry. Our method chooses the lagged midquote by optimally balancing variance and
 bias effects over a time period that is easily customized to microstructure characteristics
 of the stock. The empirical analysis were conducted on S&P100 stock. We show that our optimal
 rules imply a much shorter lag interval than the traditional rules of thumb often used
 in the empirical literature. We also showed that using the same waiting period for all
 stocks at any time is not appropriate. Our proposed optimal rules translate into drastic
 increases in the precision of transaction cost estimates.