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This study aims to utilize the optimization framework of Markowitz and Random Immigration Non-dominated Sorting Genetic Algorithm-II (RINSGA-II) to trace portfolio with extreme values, which are Pareto optimal. Using dataset from OR-library, this study tested the efficacy of the modified algorithm against NSGA-II. The results indicate that random immigration NSGA-II is efficient to trace the extreme values. The suggested optimization algorithm of random immigration NSGA-II replicates the efficient frontier of OR-library and gives better spread compared to NSGA-II. Finally, to our best of knowledge this is the first study to adopt random immigration NSGA-II to construct an optimized portfolio with additional constraints.
Key Words: Genetic Algorithm, Heuristics, NSGA-II, Portfolio optimization, Random Immigration
(ProQuest: ... denotes formulae omitted.)
INTRODUCTION
Maximizing return and minimizing risk with appropriate selection of investable assets is a prima-facie challenge for both the investors and the portfolio managers. In connection with this context, Markowitz's (1952) laid the foundation of the MeanVariance (henceforth MV) framework to achieve this objective. However, the major drawback of this model was that one of the objectives was constrained into a single objective problem to obtain an optimal solution using a quadratic optimization technique. However, the literature supports otherwise; this problem was formulated more as a bi-objective problem (Arone, Loraschi and Tettamanzi, 1993; Loraschi, Tettamanzi, Tomassini and Verda, 1995; and Fieldsend, Matatko and Peng, 2004). This rationale was attributed mainly for two reasons: (a) the efficient frontier could be generated with desired multiple solutions with a single run of the algorithm; and (b) the user need not have sufficient knowledge about the expected return to define the optimization process.
Even though the original MV model uses only two constraints, researchers criticize this extensively for its distance from reality. The model's assumptions of zero transaction cost or taxes and the infinite divisibility of market instruments do not reflect market reality. Consequently, several researchers have tried to extend this model by incorporating multiple constraints for better portfolio allocation. Some of them are: (a) Cardinality constraints, i.e., limiting the number of portfolio assets (Busetti, 2000; Chang, Meade, Beasley and Sharaiha, 2000; Schaerf, 2002; Crama and Schyns, 2003; Skolpadungket, Dahal and Harnpornchai, 2007; Chiam, Tan and Mamum, 2008; Soleimani, Golmakani and Salimi, 2009; and Anagnostopoulos and Mamanis, 2010); (b) Floor and...