Portfolio Optimization with a Mean–Absolute Deviation–Entropy Multi-Objective Model

Abstract

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.

Stock Portfolio Optimization on JII Index using Multi-Objective Mean-Absolute Deviation-Entropy

“…The MAD portfolio is a portfolio with a weight that gives the maximum value to the MAD function (2). During period a portfolio using the MAD model is the solution to the optimization problem that can be solved by using linear programming [3]…”

“…Let 𝑅 * and 𝑊 * be the maximum average return and minimum absolute deviation for every objective, respectively. Rewriting the optimization problem into (11)-( 16) [3], [9], [11], the MAD-Entropy portfolio weight is calculated by using nonlinear programming approach.…”

“…Stock portfolio optimization allocates stock assets from investors to manage returns and risks. Managing the portfolio problem leads to the optimization model, and various approaches have been proposed, as discussed by [1], [2].The basic theory of portfolio optimization was first introduced by Markowitz using the Mean-Variance (MV) model that selects a portfolio by minimizing risk at the level of return targeted by investors [3]. The variance of portfolio returns represents the risk of the MV portfolio.…”

“…Lu et al [7] investigated portfolio optimization using the entropy principle. Lam et al [3] proposed including entropy in the MAD portfolio to keep portfolio diversity since the greater the entropy value of the portfolio, the greater the diversification of the portfolio. Using stocks in the Dow Jones Industrial Average, Lam et al show that the proposed MAD-Entropy model outperforms the MAD and Equal Weight portfolio.…”

“…Weng Siew Lam et al [3] investigated portfolio optimization by combining MAD and entropy. This study aimed to find a portfolio by minimizing risks as in the MAD method and maximizing entropy.…”