Popular bid–ask spread estimators are downward biased when trading is infrequent. Moreover, they consider only a subset of open, high, low, and close prices and neglect potentially useful information to improve the spread estimate. By accounting for discretely observed prices, this paper derives asymptotically unbiased estimators of the effective bid–ask spread. Moreover, we combine them optimally to minimize the estimation variance and obtain an efficient estimator. Through theoretical analyses, numerical simulations, and empirical evaluations, we show that our efficient estimator dominates other estimators from transaction prices, yields novel insights for measuring bid–ask spreads, and has broad applicability in empirical finance.

We develop a novel approach to separate alpha and beta under model misspecification. It comes with formal tests to identify less misspecified models and sharpen the return decomposition of individual funds. Our hedge fund analysis reveals that: (i) prominent models are as misspecified as the CAPM, (ii) several factors (time-series momentum, variance, carry) capture alternative strategies and lower performance in all investment categories, (iii) fund heterogeneity in alpha and beta is large—an important result for fund selection and models of active management, (iv) performance is increasingly similar to mutual funds, (v) fund valuation is sensitive to investor sophistication.