On 7 September 2017, Prof Qing-Guo Wang, Distinguished Professor: Institute for Intelligent Systems in the Faculty of Engineering and the Built Environment (FEBE) at UJ, presented a seminar at JIAS entitled ‘Investment Portfolio Management: Brief Introduction and New Results’.

This was the second in a four-part seminar series on ‘The Challenge of Big Data’, hosted by FEBE and JIAS.

Abstract

Part I is a brief introduction to portfolio management problem, including importance of finance, financial bubbles, key factors of investment, theory and problems.

Part II will deal with a multi-period portfolio management problem over a finite horizon. The objective is to seek the optimal investment policy series which maximizes the weighted sum of a linear combination of the expected return and the variance of portfolio over all the investment periods. This formulation enables the investor to adjust weights for any period and have full freedom and control over their best trade-off between return and risk over each period.

We show that such a problem is a convex quadratic programming problem in terms of the decision variables, regardless of price dynamic nature (either linear or nonlinear cases). By solving the convex quadratic programming problem directly, an optimal solution is developed for its original problem without using dynamic programming. The solution is simplified  for a general linear price model with high-order and coupled asset dynamics and shown to be implementable with historical price data.

Simulation is carried out on USA and China stock markets with real data, which demonstrates feasibility and better performance of the proposed solution than the special case considered in the literature. In particular, the proposed solution with suitable non-zero weights on intermediate time periods offers higher return at the same risk level, compared with one involving the terminal wealth only in the objective function.