A credibilistic decision support system for portfolio optimization

Fuzzy Portfolio Selection Using Stochastic Correlation

Here we have proposed fuzzy portfolio selection model using stochastic correlation (FPSMSC) to overcome limitations both in fuzzy and stochastic world. The newly proposed model not only gets harmonious efficient frontier, but also considers the future movement of stock prices based on fuzzy expertise knowledge. The investment weights of the model have been optimized based on the monthly return data of 18 stocks listed in S&P500 from October 2011 to September 2015. The proposed model has provided higher returns in the whole regime of risk for the period from October 2014 to September 2015, whose monthly return data are used as training data than other available portfolio selection models, i.e., fuzzy portfolio selection models with credibility and possibility and statistic model. Also, the present model has shown the better smoothness of the variations of returns with respect to risk aversion parameter, λ, from the monthly data from October 2015 to September 2016, which is not included to training database. Especially, our model is superior to other models in the regime of 0-0.3 for the risk aversion level. It is demonstrating that the FPSMSC is efficient for the investors who tend to seek the high return in portfolio management.

Supplementary Information

The online version contains supplementary material available at 10.1007/s10614-023-10371-w.

An integrated fuzzy-grey relational analysis approach to portfolio optimization

This paper combines two approaches (Fuzzy set theory and Grey Relational Analysis) for modelling an investor's imprecise linguistic expectations and the uncertain returns of assets. We propose a novel maximization-type risk measure capable of incorporating the investor's individual preferences. The investor provides the expectations of what is considered the "ideal" return from the portfolio. We use Credibility theory to capture the investors' subjective and imprecise expectations in a precise mathematical form. We construct a portfolio return sequence using the assets' actual return data and an ideal sequence based on investors' preferences. Subsequently, we calculate the Grey similitude and the closeness incidence degree between the two sequences. The closer the portfolio return is to the ideal return, the better. In this manner, we develop a new risk measure that can quantify an investor's perception of risk. This measure is intuitive and easy to calculate. It does not involve estimating many parameters, something which would increase the estimation risk. We use a genetic algorithm to solve the resulting portfolio optimization model. We illustrate this method with two case studies: (i) a case study of 100 assets of the U.S. stock market's NASDAQ-100 index and (ii) a case study of 50 assets of the Indian stock market's NIFTY-50 index. We comprehensively analyze the model's out-of-sample performance and discuss its implications. The portfolios obtained using the proposed approach exhibit healthy growth outside the in-sample period. We also compare the out-of-sample performance of the proposed model with several approaches in the literature to establish its superiority.