Portfolio management with heavy-tailed distributions in Islamic Finance

In Islamic Finance (IF hereafter), the safety-first rule of investing (hifdh almal) is held to be of utmost importance. According to the honesty principle (amanah), the Islamic portfolio manager (mudharib) is committed to do his best to fulfill this investing rule. This involves the use of the most appropriate management tools. The use of the normal assumption in the financial modeling is growing criticized. This also applies to Islamic Finance which assets' show empirical evidence such as asymmetry, heavy-tail and volatility clustering. For these reasons, we suggest the use of the stable and tempered stable distributions and the Student's t related copulas for portfolio modeling. The optimal portfolios are then selected and their performances are measured employing the STARR and Rachev ratios. We demonstrate, in this paper, that the simulated data based on stable and tempered stable distributions and related Student's t copula methods significantly improve the performance of IF portfolios, which even outperform non-Islamic ones, especially in stressed financial periods.