A Model of Instantaneous Price Impact and Implied True Price∗

We show that the S-shaped hyperbolic tangent function of signed volume is appropriate to model the price impact of a trade. This model enables an implied true price to be obtained without relying on the quotes. We compare this implied true price with the quotes’ midpoint. For the 1,748 common stocks traded on the NYSE in 1997, we find that the implied true price is superior than the midpoint in proxying for the unobservable true price. The difference between these two proxies is statistically and economically significant. In addition, there is evidence that the price impact function changes over time and relates to the information environment of the company. In light of our trade-based approach to estimating transaction costs, the quote-based effective spread is found to have an upward bias. In sum, this article reveals that both the midpoint and the effective spread are not as reliable as most researchers have implicitly predicated. ∗We would like to thank Liuren Wu for comments on the initial draft. We are also indebted to Joel Hasbrouck for his insights and suggestions for improvement. A partial funding from the Wharton-SMU Research Center is gratefully acknowledged. †Corresponding author. Email: [email protected].