Mathematical modelling of a shariah-compliant capital asset pricing model

Abstract

Purpose The capital asset pricing model (CAPM) is the most widely used asset pricing model that measures 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 such as 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 aims to present a review of the CAPM and to discourse the set of assumptions underlying the model in terms of shariah compliance. Design/methodology/approach 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. Findings 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. Originality/value 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.

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

“…Several explanations for the term purification exist. Based on the study by Hazny et al (2017), this purification is defined separately from zakat because it is calculated as a follow-up step to avoid accepting non-halal actions. In Indonesia, the purification process is included in selecting Shariah-compliant stocks.…”

“…Shariah-compliant stock portfolio modeling is done by adding the expected return on assets exceeding the zakat rate and using goal programming to accommodate several goals simultaneously (Masri, 2018). Consistent with developing MV by considering reducing zakat and purification, the SCAPM return was used to construct a portfolio with Shariah-compliant stock in Malaysia (Hazny et al, 2017). (Allaj, 2020;Bessler et al, 2017;Duqi et al, 2014).…”

Shariah Compliance in Islamic Economics: A Bibliometric Analysis

“…In this case, Alkhan and Hassan (2020) affirmed it was the foundation of how ideally takaful operates. Hazny et al (2020) offered a mathematical concept of shariah compliance in the capital asset pricing model (CAPM). Prior to that, Hazny et al (2012) successfully introduced a model based on Markowitz's mean-variance analysis using the shariah compliance framework.…”

“…Second is shariah compliance in the non-bank financial industry. Several issues were discussed, such as (1) it is the foundation of the assumption, (2) it is the measurement for Islamic values, and (3) it is the co-factor that affects the performance of non-bank financial institutions (Ahmed & Farooq, 2018;Hazny et al, 2020;Kasim, 2012;Mustapha et al, 2019). Third is shariah compliance in the industry in general, which includes sets of issues as follows:…”

Modern portfolio theory with sharia: a comparative analysis

“…As pointed out by Hazny et al (2017), "…the traditional CAPM is a relevant model in Islamic finance. Most of the assumptions underlying the Markowitz's Mean-Variance Portfolio Theory are not contradictory to shariah principles."…”