A new class of Shariah-compliant portfolio optimization model: diversification analysis

This study proposes a novel Shariah-compliant portfolio optimization model tested on the daily historical return of 154 Shariah-compliant securities reported by the Shariah Advisory Council of Securities Commission Malaysia from 2011 to 2020. The mathematical model employs an annual rebalancing strategy subject to a Conditional Value-at-Risk (CVaR) constraint while considering practical and Islamic trading concerns, including transaction costs, holding limits, and zakat payment. To validate the model, the optimal portfolios are compared against an Islamic benchmark index, a market index, and portfolios generated by the mean-variance model, as well as a forecast accuracy test by the Mean Absolute Percentage Error and Mean Absolute Arctangent Percentage Error. Furthermore, this study examines the inter-stock relationship within the generated portfolios using correlation and Granger causality tests to identify the diversification performance. Results show an outperformance of the model in offering portfolios with higher risk-adjusted returns under a comparably short computational time and an indication of generally well-diversified portfolios by the weak correlations between securities. The study further noted that the model is adept at risk management in addition to higher forecast accuracy during financial crises by showing remarkably fewer causal relationships during bear markets in 2011, 2014, and 2020. The findings of an inversed relationship between portfolio risk and the number of causalities between securities offer new insights into the effect of dynamic relationships between securities on portfolio diversification. In conclusion, the proposed model carries higher moral and social values than the conventional models while portraying high potential in enhancing the efficiency of asset allocation, contributing to economic diversification and the scarce literature on Islamic portfolio optimization modelling. The study also supports the substantially increasing demand for Shariah-compliant strategies following globalization and the changing demographic of the real financial world with growing priorities of social and sustainability values.