Variational Bayes Portfolio Construction

TL;DR

This paper introduces a variational Bayes approach to portfolio construction, providing an efficient, scalable, and theoretically sound method for optimal decision-making in finance.

Contribution

It develops a novel variational Bayes methodology for Bayesian portfolio optimization, offering a convergent algorithm with proven statistical consistency.

Findings

Significantly improves speed and scalability in portfolio selection

Achieves competitive performance against state-of-the-art algorithms

Provides theoretical guarantees on decision optimality and convergence

Abstract

Portfolio construction is the science of balancing reward and risk; it is at the core of modern finance. In this paper, we tackle the question of optimal decision-making within a Bayesian paradigm, starting from a decision-theoretic formulation. Despite the inherent intractability of the optimal decision in any interesting scenarios, we manage to rewrite it as a saddle-point problem. Leveraging the literature on variational Bayes (VB), we propose a relaxation of the original problem. This novel methodology results in an efficient algorithm that not only performs well but is also provably convergent. Furthermore, we provide theoretical results on the statistical consistency of the resulting decision with the optimal Bayesian decision. Using real data, our proposal significantly enhances the speed and scalability of portfolio selection problems. We benchmark our results against state-of-the-art algorithms, as well as a Monte Carlo algorithm targeting the optimal decision.