Portfolio Optimisation Using Genetic Algorithms and Copula Financial Models
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Portfolio optimisation aims to efficiently find optimal proportions of portfolio assets, given certain constraints, and has been well-studied (Jin et al. 2016). While portfolio optimisation ascertains asset combinations most suited to investor requirements, numerous real-world problems impact its simplicity, e.g., investor preferences. Trading restrictions are also commonly faced, and must be met. However, in adding constraints to Markowitz’s basic mean-variance model, problem complexity increases, causing difficulties for exact optimisation approaches to find large problem solutions inside reasonable timeframes. The concern of this study concern is portfolio optimisation under three real-world constraints, using Markowitz’s mean-variance portfolio optimisation problem to obtain optimal risk-return trade-off (the efficient frontier). A genetic algorithm (GA) is formulated, efficiently solving cardinality-constrained portfolio optimisation problems and generating the same quality of results as the literature. It is then applied to minimum proportion cardinality-constrained problems, and experimental results are presented based on historical daily financial markets of five benchmark datasets from five recognised indices of the OR-library. Results show that increasing cardinality (K) from 2 to 10 gives higher solution quality while computational time increases significantly with K. Additionally, applying a high minimum proportion leads to shape differences in efficient frontier curves. Also, solutions tend to be restricted to smaller portions of efficient frontiers, producing lower convergence and spread. The high-dimensional problem of constructing optimal risky portfolios concerns investors looking for maximum reward to variability ratios. Thus, we consider a GA operating on portfolio optimisation problems subject to class constraints, rather than cardinality and minimum proportion constraints. GA usage in constructing optimal portfolios in Gulf Cooperation Council (GCC) stock markets, incorporating precious metals and oil, is investigated. Results show that combining stock assets, oil and precious metals reduces risk, creating further investment and diversification opportunities. Shifting yearly frontiers arising from the GCC dataset are also investigated, showing that inward/upward shifts denote higher expected returns for the same risk levels, though economic events may affect frontiers. Finally, Worst-Case Value-at-Risk is considered as an alternative risk measure using copulas on the GCC dataset, allowing a more accurate investment risk assessment to be applied, compared with traditional methods such as Value-at-Risk. To ameliorate the large computation times required to find solutions to these problems under the required quantities of assets, the researcher utilised the University of Plymouth High Performance Computer cluster.
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