How Effective are Realized Effective Spreads?
Federico M. Bandi, Lei Lian*, Jeffrey R. Russell (University of Chicago)
Measures of financial asset transaction costs often are constructed as the average difference between transaction prices and a notional efficient price. The efficient price is inherently unobserved and is often proxied in empirical work by the midpoint of the bid and ask prices. In a rational expectation setting with asymmetric information and learning on the part of market participants trades carry information about the efficient price. Since it may take several transactions before the ultimate price impact is realized it is natural to use a value of the midquote at some point after the trade takes place as the efficient price proxy. In this way, the information contained in the trade being considered can be incorporated in the efficient price proxy. But how much lag should be used? Too short of a lag and the midquotes may not accurately reflect the current information. Too long of a lag and the variance of the proxy can become excessively large. This paper shows how to optimally balance these two competing effects by optimally choosing a lag period that is easily customized to microstructure characteristics of the stock. Our methodology is applied to the S&P 100 stocks. 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 show 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.