Linear-quadratic efficient frontiers for portfolio optimization

Finding portfolios with given mean return and minimal lower partial mean or variance, two risk criteria of interest in the theory of optimal portfolio selection, is a stochastic linear‐quadratic program that can be converted to a large‐scale linear or quadratic program when the asset returns are finitely distributed. These efficient frontiers can be computed on presently available platforms for problems of reasonable size; we discuss our experience with a problem involving one thousand assets. Asymptotic statistics for stochastic programs can be applied to justify sampling as a means to approximate continuous distributions by finite distributions.