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A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market

Authors

  • RICHARD ROLL

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    • Graduate School of Management, University of California at Los Angeles. I am grateful for the thoughtful and constructive comments of Gordon Alexander, Eugene Fama, Dan Galai, Jon Ingersoll, Eduardo Lemgruber, Ron Masulis, Mark Rubinstein, and the referee.


ABSTRACT

In an efficient market, the fundamental value of a security fluctuates randomly. However, trading costs induce negative serial dependence in successive observed market price changes. In fact, given market efficiency, the effective bid-ask spread can be measured by

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where “cov” is the first-order serial covariance of price changes. This implicit measure of the bid-ask spread is derived formally and is shown empirically to be closely related to firm size.

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