Abstract
A stochastic bound is a portfolio that stochastically dominates all alternatives in a reference portfolio set instead of a single alternative portfolio. An approximate bound is a portfolio that comes as close as possible to this ideal. To identify and analyze exact or approximate bounds, feasible approaches to numerical optimization and statistical inference are developed based on linear programming and subsampling. The use of reference sets and stochastic bounds is shown to improve investment performance in representative applications to enhanced benchmarking using equity industry rotation and equity index options combinations. This paper was accepted by Kay Giesecke, finance.