Fuzzy mixed integer goal programming models for shariah-compliant equities portfolio selection / Mazura Mokhtar @ Mother

Portfolio selection problem is a critical issue in financial decision making and being repeatedly
emphasized by many researchers and practitioners. The success of a portfolio selection
is highly dependent on a reliable prediction of asset future performance and portfolio
optimization. Thus, this study focuses on the development of evaluation and portfolio optimization
models to solve portfolio selection problem for Shariah-compliant equities. This
study consists of four phases. Each phase is designed to achieve the objectives of this study
which are; to identify the most important financial ratios, to develop Adaptive Neuro-Fuzzy
Inference System (ANFIS) models for evaluating Shariah-compliant equities, to formulate
a multi-objective mixed integer programming (MOMIP) model for multi-period portfolio
optimization problem, and to formulate goal programming (GP) models for solving the
MOMIP model. In the first phase, fuzzy Delphi method (FDM) was employed to identify
the most important financial ratios in evaluating Shariah-compliant equities’ performance.
Then, in the second phase, ANFIS was used to develop an evaluation model for classifying
Shariah-compliant equities into classes. Two input space partitioning methods, namely,
Fuzzy C Means clustering (FCM) and Subtractive Clustering (SC) were used to generate
initial fuzzy rules. In the third phase, a multi-period fuzzy portfolio optimization model
was formulated to determine the amount of investment in the selected Shariah-compliant
equities. Four conflicting objectives were considered, namely, maximizing terminal wealth,
portfolio liquidity, cumulative dividend, and minimizing the cumulative risk of portfolios.
Unlike the existing multi-period portfolio optimization models, this study considered zakat
deduction in formulating the portfolio’s net terminal wealth. Several real-world constraints
were also incorporated into the proposed model. In the fourth phase, the resulting MOMIP
model was solved using two GP approaches, namely pre-emptive GP and fuzzy GP (FGP).
Computational experiments and sensitivity analysis using real data from Bursa Malaysia
were performed to verify and validate the models. Result from FDM indicates that the
most important financial ratios in evaluating Shariah-compliant equities’ performance are
return on equity, return on assets, earnings per share, operating profit margin, net profit
margin, and debt to equity ratios. The experimental results from ANFIS show that the subtractive
clustering-based ANFIS model provides better performance with 70.66% of overall
accuracy, 71.43% of sensitivity, 68.38% of specificity, 87.11% of precision, and 78.49% of
F-measure. The FCM based ANFIS model achieved 65.10% of overall accuracy, 64.86%
of sensitivity, 65.81% of specificity, 85.02% of precision and 73.58% of F-measure. Extensive
investigations successfully demonstrate the applicability of the proposed models. The
results of sensitivity analysis also show that reasonable solutions can be achieved through
the GP and FGP approaches. Thus, the models can be used by investors, fund managers,
and investment companies to assist them in planning their investment strategy and building
their portfolio.