We define the outperformance (resp. underperformance) of an investment fund as the percentage of funds in the peer universe for which the true performance of the focal fund is higher (resp. lower). We show that the p–values of the pairwise tests of equal performance can be used to obtain estimates of the out– and underperformance ratio that are robust to false discoveries – estimated alpha differentials for which the significance test has a low p–value while the true alpha is identical. When applied to hedge funds, we find that ranking funds on the outperformance ratio leads to a top quintile portfolio with a higher absolute and risk–adjusted performance than when the estimated alpha is used.

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.