An integrated generalized TODIM model for portfolio selection based on financial performance of firms

Highlights

• Develop an integrated generalized TODIM model for portfolio selection.

• A multi-dimensional criteria system is put forward for portfolio selection.

• A multi-stage generalized TODIM decision mechanism is implemented.

• A novel multi-objective MV portfolio selection model is constructed.

Abstract

Multi-criteria decision-making (MCDM) models are well-suited for solving portfolio selection problems. Diversified financial indices and complex subjective preferences are important factors affecting investment decisions within the MCDM framework. Therefore, this study adopts a well-known behavioral MCDM model called generalized TODIM (TOmada de Decisão Iterativa Multicritério) for portfolio selection based on the financial performance of firms. First, a multidimensional financial evaluation index system is proposed for financial performance evaluation, which is the most appropriate approach for stock investment within a long-term horizon. Second, features are selected from the financial ratios using affinity propagation clustering (APC). Through the APC algorithm, financial ratios with a strong influence on stock evaluation can be obtained. Third, a generalized TODIM method with entropy weight is used to calculate the dominance relation between stocks and reflect investors’ bounded rational behaviors. Fourth, an extended mean–variance multi-objective portfolio selection model that considers financial and stock market performance is constructed. The compromise solution is used when solving the multi-objective optimization programming. Finally, a case study on medical stock investment in the Chinese stock market is examined to recommend the optimal portfolio allocation for investors. Sensitivity and comparative analyses are performed to demonstrate the robustness, effectiveness, and superiority of the proposed methodology.

Introduction

The modern portfolio theory was originally instituted by Markowitz [1] in 1952. The classical mean–variance (MV) model is also viewed as a pioneer of portfolio selection. Portfolio selection is a problem in the designing of an optimal allocation of limited funds among several alternatives. It is closely related to our lives and has wide application prospects in project portfolio selection [2], [3], [4], energy research and development [5], [6], and the stock market [7]. Different academic studies, such as behavioral finance [8], operational research [9], and intelligent optimization technology [10], have also been conducted to boost the development of portfolio selection [11]. Among these methods, the multi-criteria decision-making (MCDM) method is a useful tool because investors tend to analyze the characteristics and evaluate alternatives with several objectives or criteria in portfolio selection.

MCDM is an active research field in operational research that aims to address decision-making problems that involve multiple criteria, and it can primarily satisfy the inherent multi-criteria nature of portfolio selection problems [12]. Under the MCDM framework, besides the two basic criteria of return and risk, one can consider several other crucial financial criteria, such as the return on equity and net profit margin. Furthermore, MCDM has the advantage of considering the preferences of any particular investor. Thus, there is potential for more realistic models to be built by exploiting the MCDM for the portfolio selection problem [13]. Portfolio selection in the MCDM framework mainly includes two stages: financial performance evaluation of the firms and portfolio allocation of the stocks. Firms’ financial performance is of great interest to institutional investors, led by funds, social insurance security, and securities. This feature is consistent with the notion of value investment. Financial performance generally refers to the financial ratios of firms [13], [14], [15]. The financial statement offers guiding significance to investors in acquiring information on financial position, operating results, and investment value. The fusion of all pertinent financial factors can well describe the financial performance of firms. This is in accordance with the MCDM paradigm, which greatly facilitates the portfolio allocation process.

Regarding the multi-criteria context of portfolio selection, various MCDM methods have been used such as the TOPSIS and DEA [16], DEMATEL, ANP, and VIKOR [17], and DEA cross-efficiency [18], [19], [20]. However, most of them are based on linear utility measures and thus, do not consider the influence of decision makers’ (DMs’) psychological factors. In practice, DMs’ psychological factors (e.g., subjective cognition, experimental judgment) notably influence the decision-making results. The TODIM (TOmada de Decisão Iterativa Multicritério) method, initiated by Gomes and Lima [21], is a typical behavioral MCDM method. It offers a robust framework for describing a DM’s subjective psychological behaviors, such as reference dependence, loss aversion, and diminishing sensitivity [22]. In recent decades, the TODIM method has drawn much attention and has been extensively applied in various fields [23], [24], [25]. In 2018, Llamazares [26] proposed a generalized TODIM method using a simplified form of dominance function. Compared to the classical TODIM method, the generalized TODIM method can produce more stable and consistent decision results. The investment decision process involves fluctuations in investors’ psychology and behavior. Therefore, it is suitable to employ the generalized TODIM method to model investors’ subjective psychological behaviors in the portfolio selection process.

In this study, we propose an integrated MCDM framework for portfolio selection based on financial analysis (financial indexes), machine learning (affinity propagation clustering, APC), objective weighting method (entropy weight method), behavioral MCDM model (generalized TODIM method), and an extended MV portfolio selection model (multi-objective optimization programming). The COVID-19 pandemic has actively promoted the development of the medical industry, which has received significant attention from global investors. Thus, we document these methods in detail and apply them to medical portfolio selection in the Chinese stock market. The motivations and solutions are summarized as follows.

• First, multidimensional financial data is used in this study. Usually, a single data source obtained from the stock price, such as mean, variance, skewness, and maverick, is employed [27], [28], [29], [30]. However, stock prices are vulnerable to good and bad news, fluctuations in international markets, and economic policies. Using the stock price to assess firm performance is one-sided. The better a firm’s financial performance, the higher is its investment value. Here, data in the financial statements are compiled to assess the firms’ financial performance. The use of a multidimensional dataset enables stock portfolio selection in a broader framework.

• Second, the affinity propagation clustering (APC) algorithm is used for feature reduction. There are 22 financial indices in the dataset, and there is always some relativity between them. The feature reduction technique makes the analysis more concise while retaining a relatively high accuracy in showing the original features. APC is a machine learning technique [31] that transforms high-dimensional data into low-dimensional data through an unsupervised learning process [32], [33], [34], [35]. By employing APC as a feature reduction technique, the number of features is effectively reduced.

• Third, an integrated generalized TODIM method is applied to the MCDM analysis. The objective entropy weighting method is used to calculate the criteria weights. The generalized TODIM method [26] is applied to derive firms’ financial performance, which has simple mathematics, solid decision theory foundation, flexible dominance functions, and considers the DM’s psychological behaviors [36]. Handling financial performance evaluation using the integrated generalized TODIM method can make the decision result more objective and accurate.

• Fourth, a novel multi-objective portfolio selection model considering both financial and stock market performance is designed, which acts as an extension of the classical MV model. The compromise solution is used to solve multi-objective optimization programming. Using generalized TODIM and multi-objective portfolio selection models, we can capture investors’ attitudes in both the evaluation and decision processes, making the results more comprehensive and flexible.

Through the aforementioned analysis, this study develops an integrated portfolio selection model in the MCDM framework and applies it to Chinese medical stock portfolio selection. The main contributions of this study are as follows:

• A multi-source decision framework that includes financial analysis, machine learning, behavioral decision, and portfolio optimization is constructed for portfolio selection. This framework can solve decision and evaluation problems with multi-source data processing, high-dimensional data analysis, and behavioral decision-making modeling, which has strong practicability and expansibility.

• Analyzing the financial performance of a firm is conducive to the long-term investment philosophy. Normalizing these financial indices using different piecewise linear value functions conforms to their characteristics. Feature reduction can reduce computational complexity while retaining a suitably high accuracy in presenting the original criteria.

• The novel MV portfolio selection framework based on the generalized TODIM method provides meaningful lessons for solving portfolio selection problems using many other MCDM methods. The proposed framework is an organic combination of behavioral decision theory and portfolio optimization, and has many potential applications in the field of economic management.

The remainder of the paper is organized as follows. Section 2 offers a literature review. Section 3 describes the basic methods employed in this study. In Section 4, a novel multi-objective portfolio selection model combining generalized TODIM and classical MV models, considering financial and stock market performance, is proposed. Section 5 applies the proposed model to the medical stock portfolio selection in the Chinese stock market. The sensitivity and comparative analyses are presented in this section. Finally, Section 6 concludes the study.