Estimates of the cost of equity are often sensitive to the specification of the linear factor model used in their construction. In this article, we use techniques developed for high-dimensional factor models to consider the identity of systematic risk factors in the Australian equities market. Our results support the use of neither the Capital Asset Pricing Model (CAPM) nor the Fama and French model, although they provide an explanation for the empirical performance of these models. Many other model specifications are also rejected. We find that a single-factor model with an equal-weighted market index is the best model for estimating the cost of equity in the Australian context.