Portfolio weight optimization, a crucial step in building strong investment portfolios, faces a hurdle in Islamic finance. The traditional method, involving short selling to achieve diversification, clashes with Islamic principles concerning interest, uncertainty, and gambling. This challenges Islamic investors seeking optimal returns while adhering to their faith-based financial guidelines. Optimizing these portfolios becomes complicated as individual ethical preferences and risk tolerance are also taken. The objective function of the model with Sharia constraints is optimized using the Frank-Wolfe optimization. A total of 4 types of stocks from one of the Islamic stock indices in Indonesia, Jakarta Islamic Index (JII), from 2020 to 2025 are used to construct portfolios at various levels of risk aversion. The performance of the portfolio returns at various risk aversion is compared with the condition of the composite stock index in Indonesia. The optimization methods help determine the optimal weight allocation in terms of maximizing returns and minimizing risk on risk aversion taken without ignoring Sharia principles.
Maruddani et al. (Fri,) studied this question.