State-Contingent Optimality: A Principle for Portfolio Selection

This paper explores a normative framework for portfolio selection, the Principle of State-Contingent Optimality (SCO), recasting the classic challenge of finding a single, robust portfolio as a problem in the geometry of distributions. The objective is formulated as minimizing the expected divergence between a portfolio’s realized return distribution and a state-dependent, ideal target across all possible market conditions. By employing a metric like the Wasserstein distance, this approach moves beyond simple moments to compare the full shape and character of outcomes, aiming to identify a strategy that is holistically resilient to an uncertain future. We acknowledge that the principle, in its purest form, rests on profound idealizations: a Platonic target distribution, a knowable state-space, and the validity of ensemble averaging. Rather than treating these as insurmountable barriers, we frame them as explicit signposts for a structured research program. The framework is therefore offered as a theoretical lens, one that cleanly separates the philosophical act of defining investment goals from the mathematical task of achieving them. In doing so, our hope is to provide a more principled way to critique existing methods and guide future inquiry toward truly robust financial solutions.