Abstract
The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio’s performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.
Highlights
Investors may apply different strategies to allocate their wealth in the stock markets
A number of downside risk measures have been proposed: semivariance (Markowitz, 1959), lower partial moment (Bawa, 1975; Fishburn, 1977), semi-absolute deviation (Speranza, 1993), value at risk (VaR) (Morgan, 1996), and conditional value at risk (CVaR) (Rockafellar & Uryasev, 2000, 2002)
The portfolio selection problem has been addressed under conditions of certainty and considering solely return and risk as decision criteria
Summary
Investors may apply different strategies to allocate their wealth in the stock markets. The variance penalizes extreme deviations from the expected return, regardless the sign (positive or negative) of the deviations (Gupta et al, 2013b) To approach this issue, a number of downside risk measures (i.e. measures that only take into account undesirable low returns compared to the expected return level) have been proposed: semivariance (Markowitz, 1959), lower partial moment (Bawa, 1975; Fishburn, 1977), semi-absolute deviation (Speranza, 1993), value at risk (VaR) (Morgan, 1996), and conditional value at risk (CVaR) (Rockafellar & Uryasev, 2000, 2002). Due to the above considerations, in this study we model the uncertainty of both the future returns and the liquidity of the potential stocks to be included in the portfolio by means of trapezoidal fuzzy numbers. The main conclusions of the paper are presented in last Section
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