Title: The downside deviation quadratic programming for stock portfolio optimisation: an empirical study of shariah and conventional indices in Indonesia

Authors: Noor Saif Muhammad Mussafi; Zuhaimy Ismail; Nur Arina Bazilah Aziz

Addresses: Department of Mathematics, Faculty of Science and Technology, UIN Sunan Kalijaga, 55281 Sleman, DIY, Indonesia ' Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia ' Department of Mathematical Sciences, Faculty of Sciences, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

Abstract: The quadratic programming (QP) for portfolio optimisation may yet be improved to generate better results on the risk. This study presents the downside deviation quadratic programming (DDQP) to optimise the risk of portfolio as a refinement of QP. The data deals with the price of stocks listed in Jakarta Islamic Index and IDX30 Indonesia for a definite interval. The selection of portfolio for all the stocks considered the sectoral approach. Upon selection, the DDQP model was constructed and applied to the selected portfolio before benchmarking to QP. The results showed that the portfolio group 1 had the best risk on the shariah platform, while the portfolio group 7 was superior to conventional. Additionally, the empirical analysis revealed that ten scenarios can be inferred based on the DDQP as it is consistently stable in producing a lower risk portfolio than the QP. Lastly, heuristic pattern search also verified the results of DDQP.

Keywords: portfolio selection; portfolio optimisation; risk; quadratic programming; downside deviation quadratic programming; DDQP; pattern search; Indonesia.

DOI: 10.1504/AAJFA.2024.138386

Afro-Asian Journal of Finance and Accounting, 2024 Vol.14 No.3, pp.350 - 371

Received: 29 Apr 2021
Accepted: 07 Mar 2022
Published online: 02 May 2024 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article