Equal or Value Weighting? Implications for Asset-Pricing Tests

Abstract

Does the choice of weighting scheme used to form test portfolios influence inferences drawn from empirical tests of asset pricing? To answer this question we first show that, with monthly rebalancing, an equal-weighted portfolio outperforms a value-weighted portfolio in terms of total mean return, four-factor alpha, and Sharpe ratio. We then explain that this outperformance is partly because the equal-weighted portfolio has higher exposure to systematic risk factors; but, a considerable part (42%) of the outperformance comes from the difference in alphas, which is a consequence of the rebalancing to maintain constant weights in the equal-weighted portfolio. Finally, we demonstrate that the inferences drawn from tests of asset-pricing models are substantially different depending on whether one uses equal- or value-weighted test portfolios. We illustrate this by considering four applications: (1) a test of the CAPM, using the methodology of Gibbons, Ross, and Shanken (1989); (2) a test of the spanning properties of the stochastic discount factor, using the approach of Hansen and Jagannathan (1991); (3) a test of the relation between characteristics and returns, using the multivariate weighted two-stage procedure of Fama and MacBeth (1973); and (4) a test of whether expected idiosyncratic volatility is priced or not, using the non-parametric methodology of Patton and Timmermann (2010). For all four tests, we explain how the weighting scheme influences our inferences.

Keywords: empirical asset pricing, factor models, systematic risk, alpha, idiosyncratic volatility

JEL Classification: G11, G12