Optimum Risk-Adjusted Islamic Stock Portfolio Using the Quadratic Programming Model: An Empirical Study in Indonesia

Risk-adjusted return is believed to be one of the optimal parameters to determine an optimum portfolio. A risk-adjusted return is a calculation of the profit or potential profit from an investment that takes into account the degree of risk that must be accepted to achieve it. This paper presents a new procedure in portfolio selection and utilizes these results to optimize the risk level of risk-adjusted Islamic stock portfolios. It deals with the weekly close price of active issuers listed on Jakarta Islamic Index Indonesia for a certain time interval. Overall, this paper highlights portfolio selection, which includes determining the number of stocks, grouping the issuers via technical analysis, and selecting the best risk-adjusted return of portfolios. The nominated portfolio is modeled using Quadratic Programming (QP). The result of this study shows that the portfolio built using the lowest Value at Risk (VaR) outperforms the market proxy on a risk-adjusted basis of M-squared and was chosen as the best portfolio that can be optimized using QP with a minimum risk of 2.86%. The portfolio with the lowest beta, on the other hand, will produce a minimum risk that is nearly 60% lower than the optimal risk-adjusted return portfolio. The results of QP are well verified by a heuristic optimizer of fmincon.