Mean-Variance Portfolio Management with Functional Optimization
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.
Keywords
Cite
@article{arxiv.2005.12774,
title = {Mean-Variance Portfolio Management with Functional Optimization},
author = {Ka Wai Tsang and Zhaoyi He},
journal= {arXiv preprint arXiv:2005.12774},
year = {2020}
}