Solving interval-valued returns mean absolute deviation portfolio selection model under basis stability

Abstract

This work discusses a portfolio selection model with interval linear programming arising from the uncertainty of future rates of return and the disagreement over their estimates. The risk of the overall portfolio is proposed as an objective function to obtain a well-diversified portfolio with a certain threshold rate of return. The optimization problem employs mean absolute deviation as a risk measure for the sake of risk diversification and time complexity. The possible ranges of optimal portfolio returns and associated risks are derived. The duality theory contributes to an enclosure of the optimal portfolios. When the bounds on future rates of return are sufficiently tight, the ambiguity of optimal portfolio compositions can significantly be reduced by basis stability. A theoretical framework for the study of the interval linear programming is also provided. The use of this method is illustrated with the historical returns of S&P 500 stocks, for which the negative correlation condition empirically holds, with a 6-month investment horizon from November 2018 to April 2019. The historical data is collected monthly over the past four years from November 2014 to October 2018. Compared to the bilevel optimization method, our proposed algorithms produce better results in both empirical and theoretical aspects.