The Bias of Simple Bid-Ask Spread Estimators

We study why widely used low-frequency liquidity cost estimators based on high, low, and close prices perform well in some markets and poorly in others, often yield negative or indeterminate estimates, and how to quantify estimation bias empirically. Using the high-low spread estimator as our main setting, we show that the measure is biased due to two common bias factors. These bias sources contribute to performance loss significantly more than idiosyncratic factors, including model assumption violations and specific market microstructure characteristics, and are common to different spread estimators. Estimation bias increases in liquid assets or when price volatility is high. This relationship implies that evaluation studies in US equities inflate performance by almost 25%, as a few illiquid stocks disproportionately drive cross-sectional correlations. We then develop a theory-consistent method to calculate estimation bias bounds in any empirical context. Our bias bounds provide greater credibility to the use of the high-low estimator and address several practical issues introduced by its misbehavior