A Note on Modifying the Mean-Absolute Deviation Portfolio Optimization Model to Account for Nonstationarity Biases

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.

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Pivoting Algorithm for Mean Lower Semi-Absolute Deviation Portfolio Optimization Model

2010 Second International Conference on Multimedia and Information Technology ◽

10.1109/mmit.2010.83 ◽

2010 ◽

Cited By ~ 1

Author(s):

Yanwu Liu ◽

Zhongzhen Zhang

Keyword(s):

Portfolio Optimization ◽

Optimization Model ◽

Absolute Deviation ◽

Pivoting Algorithm ◽

Lower Semi ◽

Portfolio Optimization Model

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Portfolio Optimization of the Mean-Absolute Deviation Model of Some Stocks using the Singular Covariance Matrix

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.c6363.098319 ◽

2019 ◽

Vol 8 (3) ◽

pp. 7818-7822

Keyword(s):

Portfolio Optimization ◽

Covariance Matrix ◽

Stock Exchange ◽

Optimal Portfolio ◽

Risk Level ◽

Mean Absolute Deviation ◽

Investment Portfolio ◽

Absolute Deviation ◽

Singular Covariance Matrix ◽

The Mean

Investing in the stock sector, investors often face risk problems. Usually, forming an investment portfolio is done to minimize risk. In this research, investment portfolio optimization is discussed. The data analyzed are 8 shares traded on the capital market in Indonesia through the Indonesia Stock Exchange (IDX). Optimization is performed using the Mean-Absolute Deviation model with the singular covariance matrix to determine the optimal weights. The results of portfolio optimization Mean-Absolute Deviation model with singular covariance matrix method, was obtained optimal portfolio weights that is of 17.22% for BBCA shares; 26.64% for TKIM shares; 9.96% for BBRI shares; 9.96% for BBNI shares; 8.70% for BMRI shares; 3.75% for ADRO shares; 6.52% for GGRM shares; and 17.25% for UNTR shares. Where the optimal portfolio composition is obtained the expected rate of return (expected return) of 0.18% with a portfolio risk level (standard deviation) of 0.07%.

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Portfolio Optimization Model with and without Options under Additional Constraints

Mathematical Problems in Engineering ◽

10.1155/2020/8862435 ◽

2020 ◽

Vol 2020 ◽

pp. 1-10

Author(s):

T. Khodamoradi ◽

M. Salahi ◽

Ali Reza Najafi

Keyword(s):

Portfolio Optimization ◽

Optimization Model ◽

Financial Models ◽

Short Selling ◽

Cardinality Constraints ◽

Absolute Deviation ◽

Data Set ◽

Sharpe Ratios ◽

Portfolio Optimization Model ◽

Additional Constraints

In this paper, first, we study mean-absolute deviation (MAD) portfolio optimization model with cardinality constraints, short selling, and risk-neutral interest rate. Then, in order to insure the investment against unfavorable outcomes, an extension of MAD model that includes options is considered. Moreover, since the data in financial models usually involve uncertainties, we apply robust optimization to the MAD model with options. Finally, a data set of S&P index is used to compare the effectiveness of options in the models in terms of returns and Sharpe ratios.

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