Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

Uncertain Portfolio Optimization based on Dempster-Shafer Theory

Nowadays, the selection and management of the optimal portfolio are the most primary fields of financial decision-making. Thereby, selecting a portfolio capable of providing the highest efficiency and, at the same time, the lowest investment risk has been turned into one of the most critical concerns among financial activists. However, in this selection, the two factors above are not the only determining ones. Various factors are affecting financial markets' behavior under different possible scenarios, which should be identified. In this paper, we examine the high sensitivity of the Iranian capital market to the exchange rate fluctuations in the different scenarios due to the lack of a unified view of the value of that rate among experts as one of the mentioned factors and obtain its value using Dempster–Shafer theory (DST). Then, a portfolio selection model that prefers stocks with higher ranks is proposed. Representative results of the real-life case study reveal that the submitted approach is productive and practically applicable.

Fuzzy Portfolio Selection with Sugeno Type Fuzzy Neural Network: Investing in the Mexican Stock Market

The objective of this research is to compare the returns of the portfolios developed by the proposed methodology called Fuzzy Portfolio Selection with Sugeno Type Fuzzy Neural Network against Markowitz’s portfolio theory; to identify the best investment model. For this purpose, we used ten stock time series of the Mexican market in daily format from January 2, 2015, to May 15, 2020, to get the portfolios every week from May 15 to June 12, 2020. The principal result is that our methodology recognized the behavior of each share, generates better risk management, and higher returns in comparison with the traditional techniques. The recommendation is to evaluate other stocks and markets to verify the efficiency of our model, the limitation is that a fundamental analysis must precede the tool, and the originality is the new technique proposed. The main conclusion is that the portfolio selection model based on fuzzy neural networks generated two models that do not have negative returns in any week, the cumulative return obtained was up to 15.68%.

A Portfolio Selection Model Based on the Interval Number

Traditional portfolio theory uses probability theory to analyze the uncertainty of financial market. The assets’ return in a portfolio is regarded as a random variable which follows a certain probability distribution. However, it is difficult to estimate the assets return in the real financial market, so the interval distribution of asset return can be estimated according to the relevant suggestions of experts and decision makers, that is, the interval number is used to describe the distribution of asset return. Therefore, this paper establishes a portfolio selection model based on the interval number. In this model, the semiabsolute deviation risk function is used to measure the portfolio’s risk, and the solution of the model is obtained by using the order relation of the interval number. At the same time, a satisfactory solution of the model is obtained by using the concept of acceptability of the interval number. Finally, an example is given to illustrate the practicability of the model.