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An interval mean–average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints

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Abstract

Interval number is a kind of special fuzzy number and the interval approach is a good method to deal with some uncertainty. An interval mean–average absolute deviation model for multiperiod portfolio selection is presented by taking risk control, transaction costs, borrowing constraints, threshold constraints and cardinality constraints into account, which an optimal investment policy can be generated to help investors not only achieve an optimal return, but also have a good risk control. In the proposed model, the return and risk are characterized by the interval mean and interval average absolute deviation of return, respectively. Cardinality constraints limit the number of assets to be held in an efficient portfolio. Threshold constraints limit the amount of capital to be invested in each stock and prevent very small investments in any stock. Based on interval theories, the model is converted to a dynamic optimization problem. Because of the transaction costs, the model is a dynamic optimization problem with path dependence. A forward dynamic programming method is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis of the different desired number is provided by a numerical example to illustrate the efficiency of the proposed approach and the designed algorithm.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (nos. 71271161).

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Authors and Affiliations

  1. School of Management, Wuhan University of Science and Technology, Wuhan, 430081, People’s Republic of China

    Peng Zhang

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  1. Peng Zhang
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Correspondence to Peng Zhang.

Additional information

Communicated by V. Loia.

Appendix

Appendix

The codes of thirty stocks are, respectively, S\(_{1}\) (600000), S\(_{2}\) (600005), S\(_{3}\) (600015), S\(_{4}\) (600016), S\(_{5}\) (600019), S\(_{6}\) (600028), S\(_{7}\) (600030), S\(_{8}\) (600036), S\(_{9}\) (600048), S\(_{10}\) (600050), S\(_{11}\) (600104), S\(_{12}\) (600362), S\(_{13}\) (600519), S\(_{14}\) (600900), S\(_{15}\) (601088), S\(_{16}\) (601111), S\(_{17}\) (601166), S\(_{18}\) (601168), S\(_{19}\) (601318), S\(_{20}\) (601328), S\(_{21}\) (601390), S\(_{22}\) (601398), S\(_{23}\) (601600), S\(_{24}\) (601601), S\(_{25}\) (601628), S\(_{26}\) (601857), S\(_{27}\) (601919), S\(_{28}\) (601939), S\(_{29}\) (601988), S\(_{30}\) (601998). The trapezoidal possibility distributions of the return rates of assets at each period can be obtained as shown in Tables 4, 5, 6, 7, 8.

Table 4 The fuzzy return rates on assets of five periods investment
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Table 5 The fuzzy return rates on assets of five periods investment
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Table 6 The fuzzy return rates on assets of five periods investment
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Table 7 The fuzzy return rates on assets of five periods investment
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Table 8 The fuzzy return rates on assets of five periods investment
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Zhang, P. An interval mean–average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints. Soft Comput 20, 1203–1212 (2016). https://doi.org/10.1007/s00500-014-1583-3

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