Barone-Adesi (1985) has formulated a multivariate test (likelihood ratio) of an arbitrage equilibrium model, based on a quadratic specification of the process generating returns, that can be related to a three-moment CAPM. Australian equity returns are used to replicate this approach over the period 1963 to 1987. Furthermore, a generalised method of moments test of the Barone-Adesi model is also conducted. The results are favourable with regard to the arbitrage model. In addition the quadratic market model performs well against its traditional counterpart. This latter conclusion is robust with respect to allowing for monthly seasonal regularities in Australian returns. However, evidence regarding the three-moment CAPM is largely inconclusive.