Mean-Variance Portfolio Management with Functional Optimization

Ka Wai Tsang and Zhaoyi He

Papers from arXiv.org

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.

Date: 2020-05, Revised 2020-11
New Economics Papers: this item is included in nep-cmp
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