Abstract
The aim of this paper is to develop a mean-entropy-skewness stock portfolio selection model with transaction costs in an uncertain environment. Since entropy is free from reliance on symmetric probability distributions and can be computed from nonmetric data, it is more general than others as a competent measure of risk. In this work, returns of securities are assumed to be uncertain variables, which cannot be estimated by randomness or fuzziness. The model in the uncertain environment is formulated as a nonlinear programming model based on uncertainty theory. Also, some other criteria like short-and long-term returns, dividends, number of assets in the portfolio, and the maximum and minimum allowable capital invested in stocks of any company are considered. Since there is no efficient solution methodology to solve the proposed model, assuming the returns as some special uncertain variables, the original portfolio selection model is transformed into an equivalent deterministic model, which can be solved by any state-of-the-art solution methodology. The feasibility and effectiveness of the proposed model is verified by a numerical example extracted from Bombay Stock Exchange, India. Returns are considered in the form of trapezoidal uncertain variables. A genetic algorithm is used for simulation. The efficiency of the portfolio is evaluated by looking for risk contraction on one hand and expected return and skewness augmentation on the other hand. An empirical application has served to illustrate the computational tractability of the approach and the effectiveness of the proposed algorithm.
Highlights
The Markowitz [1] formulation of modern portfolio theory has been the most impactmaking development in mathematical finance management to date
In the ‘Mean-entropy-skewness model formulation’ section, a tri-objective mean-entropy-skewness portfolio selection model is formulated with constraints on short-term and long-term returns, dividends, number of assets in the portfolio, and the maximum and minimum allowable capital invested in stocks of any company
This paper has introduced a new framework of mean-entropy-skewness portfolio selection problem with transaction cost under the constrains on short-and long-term returns with transaction costs, dividends, number of assets in the portfolio, and the maximum and minimum allowable capital invested in stocks
Summary
The Markowitz [1] formulation of modern portfolio theory has been the most impactmaking development in mathematical finance management to date. Consideration of variance as risk is erroneous as it suggests penalties for up and down deviations from the mean. To face this problem, Markowitz [2] recommended semi-variance, a downside risk measure. Markowitz [2] recommended semi-variance, a downside risk measure Another alternative definition of risk is the probability of an adverse outcome [3]. Different authors like Philippatos and Wilson [6], Philippatos and Gressis [7], Nawrocki and Harding [8], Simonelli [9], Huang [10], Qin et al [11], and Bhattacharyya et al [12] used entropy as an alternative measure of risk to replace the variance proposed by Markowitz [1]. Entropy is more general than others as an efficient measure of risk because entropy is free from reliance on symmetric distributions and can be computed from nonmetric data
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