Optimal Portfolio Allocation with Gromov-Wasserstein Barycenter

This paper develops a technique for an optimal portfolio allocation that explicitly accounts for different market phases. The basic idea is to distinguish market phases with respect to the dynamics of a sentiment index and to accordingly interpolate among bull, bear, and neutral input portfolios. The algorithm we design is based on optimal transport theory and exploits the notion of Entropic Gromov-Wasserstein discrepancy to generate optimal asset allocation. The resulting optimal portfolio is obtained as the barycenter of the input portfolios with barycentric coordinates that vary according to the different market conditions. Through simulation studies and empirical applications, we demonstrate the effectiveness of this approach. Comparative analysis against alternative portfolios indicates that our proposed technique delivers superior risk-adjusted performance over the full evaluation window, while its year-by-year performance varies, as expected from a dynamic strategy.