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Mean-Variance Portfolio Management with Functional Optimization

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  • Ka Wai Tsang
  • Zhaoyi He

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.

Suggested Citation

  • Ka Wai Tsang & Zhaoyi He, 2020. "Mean-Variance Portfolio Management with Functional Optimization," Papers 2005.12774, arXiv.org, revised Nov 2020.
    • Handle: RePEc:arx:papers:2005.12774
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    References listed on IDEAS

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