Discussion

Optimal portfolios do not just happen: they must be calculated, and there is a constant interplay between models and solvability. Linear programming models provide great modeling power with a great limit: the handling of risk must be done in a linear fashion (like our Risk factors here). Other models you will see in finance will look at the co-variance of returns between investments, a fundamentally nonlinear effect. This can give rise to nonlinear models like those that try to minimize variance subject to return requirements. It is very difficult to embed idiosyncratic constraints (like (c) and (d) here) in such models.