Downside deviation quadratic programming and heuristic approaches for shariah stock portfolio optimization

Abstract

Portfolio investment is a passive investment since the investor is not actively involved in the management of the stock corporation. It is the concept of pooling all of one’s assets and managing them in such a way that one earns the highest rate of return with the least risk. One of the most challenging aspects of stock portfolio investment is risk minimization, which can be achieved by addressing portfolio selection and optimization. This study presents a hybrid approach to portfolio selection involving double-layer filtering. Spesifically, a modified mean-variance optimization (MVO) model called the downside deviation quadratic programming (DDQP) is developed. The new model is applied to a secondary dataset consisting of weekly historical prices of all companies listed on the Jakarta Islamic Index (JII) from June 2016 to May 2019, as well as some ancillary financial data. The data was split into four categories for comparative purposes: (1) sectoral, (2) fundamental, (3) technical, and (4) hybrid. All schemes were evaluated using a diversification ratio to create a well-diversified portfolio. The portfolio were then optimized using MVO and DDQP to achieve optimal risk and stock weighting. Two heuristic methods were used to ensure that the results are robust and consistent, namely simulated annealing (SA) and pattern search (PS). The results show that a hybrid analysis of sales growth (SG) and beta ? (risk of an individual stock as compared to composite index) produces a welldiversified portfolio based on actual data. The DDQP is built as an enhancement to MVO, primarily by substituting the standard deviation for the downside deviation in the objective function. Both SA and PS were integrated into portfolio optimization environments. In terms of portfolio optimization, both exact methods of MVO and DDQP can be used to determine the portfolio’s optimal risk and the weight of the shariah stock portfolio. For instance, using the DDQP model, portfolio 6 achieves the lowest risk of 1.18% by investing in TLKM, UNVR, ASII, ICBP, and UNTR with corresponding weights of 26.30%, 20.24%, 23.27%, 29.88%, and 0.31% respectively. The DDQP generated more robust and consistent results in producing lower risk (with an average efficiency rate of 76.99%) than MVO by altering the composition of various portfolios into 12 scenarios. Portfolio 19 was tested as a hybrid study of SGbeta and a well-diversified portfolio by considering six indicators and running the experiment 20 times with different starting points to approach the DDQP optimal solution. The numerical results show that the risk of the portfolio generated by DDQP is similar across all 20 trials. These results also show a linear trend, indicating that the DDQP’s performance is consistent and robust across different initial points. It can be concluded that the SA and PS heuristic methods were successful in reaching the DDQP’s optimal risk threshold. Overall, the PS method was found to be a better approximation of the exact DDQP result than the SA method.