Lam Weng Siew, Lam Weng Hoe, Jaaman Saiful Hafizah
Department of Physical and Mathematical Science, Faculty of Science, Kampar Campus, Universiti Tunku Abdul Rahman, Jalan Universiti, Bandar Barat, Kampar 31900, Perak, Malaysia.
Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia UKM, Bangi 43600, Selangor, Malaysia.
Entropy (Basel). 2021 Sep 28;23(10):1266. doi: 10.3390/e23101266.
Investors wish to obtain the best trade-off between the return and risk. In portfolio optimization, the mean-absolute deviation model has been used to achieve the target rate of return and minimize the risk. However, the maximization of entropy is not considered in the mean-absolute deviation model according to past studies. In fact, higher entropy values give higher portfolio diversifications, which can reduce portfolio risk. Therefore, this paper aims to propose a multi-objective optimization model, namely a mean-absolute deviation-entropy model for portfolio optimization by incorporating the maximization of entropy. In addition, the proposed model incorporates the optimal value of each objective function using a goal-programming approach. The objective functions of the proposed model are to maximize the mean return, minimize the absolute deviation and maximize the entropy of the portfolio. The proposed model is illustrated using returns of stocks of the Dow Jones Industrial Average that are listed in the New York Stock Exchange. This study will be of significant impact to investors because the results show that the proposed model outperforms the mean-absolute deviation model and the naive diversification strategy by giving higher a performance ratio. Furthermore, the proposed model generates higher portfolio mean returns than the MAD model and the naive diversification strategy. Investors will be able to generate a well-diversified portfolio in order to minimize unsystematic risk with the proposed model.
投资者希望在回报与风险之间获得最佳权衡。在投资组合优化中，均值绝对偏差模型已被用于实现目标回报率并将风险降至最低。然而，根据以往的研究，均值绝对偏差模型并未考虑熵的最大化。事实上，较高的熵值会带来更高的投资组合分散化程度，这可以降低投资组合风险。因此，本文旨在提出一种多目标优化模型，即通过纳入熵的最大化来构建用于投资组合优化的均值绝对偏差 - 熵模型。此外，所提出的模型使用目标规划方法纳入每个目标函数的最优值。所提出模型的目标函数是最大化平均回报率、最小化绝对偏差以及最大化投资组合的熵。使用在纽约证券交易所上市的道琼斯工业平均指数成分股的回报对所提出的模型进行了说明。这项研究对投资者将产生重大影响，因为结果表明所提出的模型通过给出更高的绩效比率优于均值绝对偏差模型和简单分散化策略。此外，所提出的模型比均值绝对偏差模型和简单分散化策略产生更高的投资组合平均回报率。投资者能够使用所提出的模型生成一个充分分散的投资组合，以最小化非系统性风险。
