We resolve these issues as follows. We show that a nonincreasing returns to scale (nrs) model is usually appropriate when modeling rational choice among investors. We show when multiple risk and return measures can justifiably be combined and identify some suitable measures. We show we need a nonlinear model to justify the assumption of convexity and to model diversification. We develop a method to approximate a solution to this model as accurately as needed using a sequence of linear models. Coherent measures of risk come up again and again in our discussion. They relate to investor preference because they help model stochastic dominance. They allow us to.
