Distributed Portfolio Optimization & Decentralized Pricing

Abstract

We present a distributed portfolio construction framework based in network structures and combinatorial optimization. Unlike traditional centralized methods, our approach decomposes the portfolio under consideration into overlapping sub-portfolios, each reflecting a thematic strategy or mandate. This decomposition is guided by the powerset of the available set of assets, capturing all meaningful groupings and inducing a hypergraph structure where assets appear in multiple sub-portfolios. We solve the resulting distributed portfolio optimization problem using a primal-dual algorithm: primal variables represent subportfolio allocations, while dual variables emerge as shadow prices on coupling assets, offering a natural pricing interpretation and a link to microeconomic theory (general equilibrium). The framework integrates both internal portfolio signals and external models such as CAPM. We illustrate the methodology using GICS sector ETFs, constructing sub-portfolios aligned with macroeconomic themes.