# Variational Bayes Portfolio Construction

arXiv: https://arxiv.org/abs/2411.06192 · HTML: https://mlsanity.com/paper/2411.06192/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 15 of 15)

- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [On the properties of variational approximations of Gibbs posteriors](https://mlsanity.com/paper/1506.04091/) (2015)
- [Concentration of tempered posteriors and of their variational approximations](https://mlsanity.com/paper/1706.09293/) (2017)
- [Frequentist Consistency of Variational Bayes](https://mlsanity.com/paper/1705.03439/) (2017)
- [Variational Bayes for high-dimensional linear regression with sparse priors](https://mlsanity.com/paper/1904.07150/) (2019)
- [Tight Concentrations and Confidence Sequences from the Regret of Universal Portfolio](https://mlsanity.com/paper/2110.14099/) (2021)
- [Efficient Online Portfolio with Logarithmic Regret](https://mlsanity.com/paper/1805.07430/) (2018)
- [Multivariate Gaussian and Student-t Process Regression for Multi-output Prediction](https://mlsanity.com/paper/1703.04455/) (2017)
- [Efficient and Near-Optimal Online Portfolio Selection](https://mlsanity.com/paper/2209.13932/) (2022)
- [Beyond Average Return in Markov Decision Processes](https://mlsanity.com/paper/2310.20266/) (2023)
- [Theoretical Guarantees for Variational Inference with Fixed-Variance Mixture of Gaussians](https://mlsanity.com/paper/2406.04012/) (2024)
- [Covariance Matrix Estimation under Total Positivity for Portfolio Selection](https://mlsanity.com/paper/1909.04222/) (2019)
- [Robust Markowitz mean-variance portfolio selection under ambiguous covariance matrix *](https://mlsanity.com/paper/1610.06805/) (2016)
- [Portfolio Construction with Gaussian Mixture Returns and Exponential Utility via Convex Optimization](https://mlsanity.com/paper/2205.04563/) (2022)
- [Bayesian learning for the Markowitz portfolio selection problem](https://mlsanity.com/paper/1811.06893/) (2018)

## Abstract (arXiv)

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.