Two-Stage Fuzzy Portfolio Selection Problem with Transaction Costs

This paper studies a two-period portfolio selection problem. The problem is formulated as a two-stage fuzzy portfolio selection model with transaction costs, in which the future returns of risky security are characterized by possibility distributions. The objective of the proposed model is to achieve the maximum utility in terms of the expected value and variance of the final wealth. Given the first-stage decision vector and a realization of fuzzy return, the optimal value expression of the second-stage programming problem is derived. As a result, the proposed two-stage model is equivalent to a single-stage model, and the analytical optimal solution of the two-stage model is obtained, which helps us to discuss the properties of the optimal solution. Finally, some numerical experiments are performed to demonstrate the new modeling idea and the effectiveness. The computational results provided by the proposed model show that the more risk-averse investor will invest more wealth in the risk-free security. They also show that the optimal invested amount in risky security increases as the risk-free return decreases and the optimal utility increases as the risk-free return increases, whereas the optimal utility increases as the transaction costs decrease. In most instances the utilities provided by the proposed two-stage model are larger than those provided by the single-stage model

Dynamic changes and multi-dimensional evolution of portfolio optimization

Although there has been an increasing number of studies investigate portfolio optimization from different perspectives, few attempts could be found that focus on the development trend and hotspots of this research area. Therefore, it motivates us to comprehensively investigate the development of portfolio optimization research and give some deep insights into this knowledge domain. In this paper, some bibliometric methods are utilized to analyse the status quo and emerging trends of portfolio optimization research on various aspects such as authors, countries and journals. Besides, ‘theories’, ‘models’ and ‘algorithms’, especially heuristic algorithms are identified as the hotspots in the given periods. Furthermore, the evolutionary analysis tends to presents the dynamic changes of the cutting-edge concepts of this research area in the time dimension. It is found that more portfolio optimization studies were at an exploration stage from mean-variance analysis to consideration of multiple constraints. However, heuristic algorithms have become the driving force of portfolio optimization research in recent years. Multidisciplinary analyses and applications are also the main trends of portfolio optimization research. By analysing the dynamic changes and multi-dimensional evolution in recent decades, we contribute to presenting some deep insights of the portfolio optimization research directly, which assists researchers especially beginners to comprehensively learn this research field

Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

[EN] 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.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). 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INVESTMENT PORTFOLIO REBALANCING DECISION MAKING

Nowadays financial markets’ volatility and significant stock prices’ fluctuations allow improving investment return actively managing investment portfolio, rather than choosing long term investment strategy. Active portfolio management also allows personal investor’s development and gives opportunity to avoid losses in terms of market instability. However active portfolio management is more risky. Rebalancing the investment portfolio investor incurs real costs for expected return, so actively managing the investment portfolio it is crucial to use a good, investor needs meeting portfolio rebalancing method. Dealing with mentioned problem scientific information sources analysis is made and a new portfolio rebalancing method is suggested in the article

PEMILIHAN PORTOFOLIO FUZZY MEAN-SEMI VARIANCE MULTI-PERIODE DENGAN BIAYA TRANSAKSI DAN JUMLAH TRANSAKSI MINIMUM MENGGUNAKAN ALGORITMA GENETIKA

Pembentukan portofolio saham optimal berhubungan dengan penentuan bobot optimal untuk masing-masing saham pada portofolio. Dalam penelitian ini akan dibahas bagaimana mencari bobot optimal yang meminimalkan resiko dan memaksimumkan return dengan mempertimbangkan parameter biaya transaksi dan minimal jumlah transaksi menggunakan algoritma genetika. Hasil akhir dari penelitian Porotofolio yang dibentuk dengan biaya transaksi dan jumlah transaksi memiliki kinerja yang yang lebih baik dibandingkan, portofolio yang tanpa mempertimbangkan kedua parameter tersebut , sehingga parameter biaya transaksi dan minimal jumlah transaksi dapat digunakan pada penelitian selanjutnya. Kata kunci : Portofolio, Algoritma Genetika, fuzzy ,semi-variance,biaya transaksi, jumlah transaksi minimu

An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts’ evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm

A Comparative Study of Multi-Objective Multi-Period Portfolio Optimization Models in a Fuzzy Credibility Environment Using Different Risk Measures

The purpose of the present research is to compare portfolio optimization models in a fuzzy credibility environment, aimed for end-of-period wealth maximization and risk minimization. The investor’s risk was measured using the Value at Risk (VaR), Average Value at Risk (AVaR) and semi Entropy. In order to get closer to the real world investment model, while allowing for transaction costs and investing part of wealth in risk-free assets, in addition to the cardinal constraints, other constraints including the minimum and maximum amount of wealth assigned to each asset, and the minimum and maximum number of stocks present in portfolio were applied. The results of the multi-period models running by MOPSO algorithm indicated for the models Mean-AVaR, Mean-Semi Entropy, and Mean-VaR, respectively, performed better, in terms of Sharp and Treynor measures

The possibilities and consequences of investment decisions by stepwise optimization

The paper deals with the application of stochastic optimization principles for investment decision making. The authors present the investment management system based on an adequate portfolio model. For optimal portfolio construction and stock selection, the method of stochastically informative expertise and ranging is used. Investment portfolios in equity and currency markets are formed considering investor risk tolerance and risk preference level, as well as an individual utility function. Investment portfolios are constructed according to three criteria: return, risk, and reliability. The markets of Germany, the USA, and China, as well as foreign exchange markets, are analysed. The results reveal the efficient investment possibilities in the mentioned markets, allowing to reach investment return substantially exceeding market index return. Along with that, an innovative stochastic clustering methodology for investment assets is proposed. The obtained results are of great value for individual as well as institutional investors and are a suitable means to form efficient investment strategies in financial markets

AN EVALUATION OF ALTERNATİVE METHODS FOR FINANCIAL PERFORMANCE: EVIDENCE FROM TURKEY (ISTANBUL STOCK EXCHANGE)

This study aims to determine which financial performance ranking methods accurately predict the actual rankings by using multiple criteria decision techniques, and it compares the accuracy of the rankings based on the financial performance indicators and the market based approach which involves market value and average return. Companies listed in BIST50 index (Borsa Istanbul) were investigated, as a result, when considering average return, Promethee and Copras produced similar and consistent rankings. Besides, since it places emphasize on the functional structures of variables, Promethee method was noted to produce the most accurate rankings, thus deemed most effective method helping investors give rational decisions