Mathematical modelling of a shariah-compliant capital asset pricing model

The Capital Asset Pricing Model (CAPM) is the most widely used asset pricing model that measures the risk-return relationship. The CAPM is based on Markowitz’s Mean-Variance Analysis. The advancement of Islamic finance leads to the question whether or not the practice of modern investment theories and analyses like the Markowitz’s Mean-Variance Analysis and CAPM are in accordance to shariah and could be used in pricing Islamic financial assets. Therefore, this paper presents a review of the CAPM and to discourse the set of assumptions underlying the model in terms of shariah compliance. Although most of the assumptions are not contradictory to shariah principles, there are Islamic variables such as prohibition of short selling, purification and zakat that should be taken into consideration when pricing Islamic financial assets. We then develop a mathematical model which is a modification of the traditional CAPM that incorporates principles of Islamic finance and integrating zakat, purification of return and exclusion of short sales. As a proof-of-concept, this paper presents the results of an empirical study on the proposed shariah-compliant CAPM in comparison to the traditional CAPM. The results show that the proposed Islamic CAPM is appropriate and applicable in examining the relationship between risk and return in the Islamic stock market. This study contributes to existing body of knowledge by presenting an algorithm and mathematical derivation of the shariah-compliant CAPM which has been lacking in the literature of Islamic finance. The paper offers a novel approach in pricing Islamic financial assets in accordance to shariah, advocated by modern investment theories of Markowitz’s Mean Variance Analysis and CAPM.