Mean-Variance Portfolio Management with Functional Optimization

TL;DR

This paper proposes a novel functional optimization method for mean-variance portfolio management, modeling portfolio weights as functions of past data, leading to improved performance over traditional plug-in methods.

Contribution

It introduces a new functional optimization framework, derives optimality conditions, and develops gradient-ascent algorithms with convergence guarantees for portfolio optimization.

Findings

Functional approach outperforms plug-in methods in simulations

Optimal solutions are generally non-constant functions

Algorithms demonstrate convergence and improved results

Abstract

This paper introduces a new functional optimization approach to portfolio optimization problems by treating the unknown weight vector as a function of past values instead of treating them as fixed unknown coefficients in the majority of studies. We first show that the optimal solution, in general, is not a constant function. We give the optimal conditions for a vector function to be the solution, and hence give the conditions for a plug-in solution (replacing the unknown mean and variance by certain estimates based on past values) to be optimal. After showing that the plug-in solutions are sub-optimal in general, we propose gradient-ascent algorithms to solve the functional optimization for mean-variance portfolio management with theorems for convergence provided. Simulations and empirical studies show that our approach can perform significantly better than the plug-in approach.