Guided by stylised facts and inspired by Robert Fernholz' stochastic portfolio theory, we present a parsimonious stationary diffusion model for the entire stock market. Its ultimate purpose is to decide whether there is a simple more efficient alternative to the market portfolio. At this stage we discuss the qualitative implications of the model. A crucial role is played by the speed measure and by the local time at the boundary of the support of the diffusion process under consideration.