Integrating Zakat and Purification in a Modified Black–Litterman Model for Shariah-Compliant Stock Portfolios

Abstract

Many articles demonstrate the advantages of applying Shariah principles in economic and financial activities, which motivates model development for Shariah investment. The development of the capital asset pricing model (CAPM) and mean-variance (MV) for Shariah portfolios shows various efforts within a Shariah framework. But the MV model has diversification weaknesses, and the Black–Litterman (BL) model solves this problem. According to Islamic principles, the CAPM’s use in the BL model is problematic due to the risk-free rate. This study aims to introduce a modified BL model adapted to Islamic principles. We propose a modified BL model with a Shariah-compliant asset pricing model (SCAPM) that considers the zakat obligation and purification rate to develop the model with Islamic principles. The proposed model was implemented in the Indonesian stock market. A portfolio’s Sharpe ratio using the BL-SCAPM outperforms BL-CAPM. This finding supports the idea that the modified BL model can be applied as a new alternative for a Sharia portfolio model.