Many studies have investigated the issue of time stationarity of an asset's systematic risk. While there is considerable evidence to suggest that an asset's systematic risk is best described by some stochastic parameter model, little work has been conducted in determining the most appropriate stochastic parameter model. This paper addresses this issue. We extend the study conducted by Faff et al. to investigate which varyingcoefficient model best describes the systematic risk of assets in the Australian equity market for those assets for which a constant-coefficient model is found to be inadequate. The testing strategy is point-optimal (see King, M. L. (1987a)) given that this approach to testing is designed to have good small-sample properties. Our results suggest that, generally, in cases where a stochastic parameter is appropriate, a Hildreth-Houck random-coefficient model is the preferred model.