Article1990

Statistical Properties of the Roll Serial Covariance Bid/Ask Spread Estimator

195 citations0/0 files storedThe Journal of Finance

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Financial Markets and Investment Strategies Stochastic processes and financial applications Financial Risk and Volatility Modeling

Abstract

ABSTRACT Exact small sample population moments of the standard serial covariance and variance estimators are derived under the assumptions of the Roll bid/ask spread model. Noise explains why serial covariance estimates are often positive in annual samples of daily and weekly returns. Small sample estimator bias partially explains why weekly estimates are more negative than daily estimates. Noise causes the Roll spread estimator to be severely biased by Jensen's inequality. The French‐Roll adjusted variance estimator is unbiased but noisy. Empirical tests confirm the major implications.

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References

1984A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market 1986Stock return variances 1987Trading Mechanisms and Stock Returns: An Empirical Investigation 1987Components of the Bid-Ask Spread and the Statistical Properties of Transaction Prices 1985Volatility increases subsequent to stock splits: An empirical aberration 1988On the Estimation of Bid-Ask Spreads: Theory and Evidence 1989A Day-End Transaction Price Anomaly

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