Finite sample multivariate tests of asset pricing models with coskewness

Abstract

Exact inference methods are proposed for asset pricing models with unobservable risk-free rates and coskewness; specifically, the Quadratic Market Model (QMM) which incorporates the effect of asymmetry of return distribution on asset valuation. In this context, exact tests are appealing given (i) the increasing popularity of such models in finance, (ii) the fact that traditional market models (which assume that asset returns move proportionally to the market) have not fared well in empirical tests, (iii) finite sample QMM tests are unavailable even with Gaussian errors. Empirical models are considered where the procedure to assess the significance of coskewness preference is LR-based, and relates to the statistical and econometric literature on dimensionality tests which are interesting in their own right. Exact versions of these tests are obtained, allowing for non-normality of fundamentals. A simulation study documents the size and power properties of asymptotic and finite sample tests. Empirical results with well-known data sets reveal temporal instabilities over the full sampling period, namely 1961–2000, though tests fail to reject the QMM restrictions over 5-year sub-periods.