MEAN–VARIANCE PORTFOLIO MANAGEMENT WITH FUNCTIONAL OPTIMIZATION

Ka Wai Tsang and Zhaoyi He ()
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Ka Wai Tsang: School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, P. R. China
Zhaoyi He: School of Data Science, The Chinese University of Hong Kong, Shenzhen, Guangdong, P. R. China

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 08, 1-24

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: Portfolio management; functional optimization; Sharpe ratio; time-series; resampling (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500557

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