Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
http://www.sciepub.com/author/signin

To unsubscribe from our mailing list, please click on the following link: unsubscribe

I am looking forward to hearing from you.

Kind regards,

David Rain
Email:join@sciepub.com
Science and Education Publishing (http://www.sciepub.com)

A Behavioral Portfolio Model with Interval Return and Investor’s Sentiment

Qiansheng Zhang

School of Mathematics and Statistics, Guangdong University of Foreign Studies, Guangzhou 510006, China

Abstract: This paper proposes a behavioral portfolio decision model with interval returns and investor’s sentiment. A sentiment-adjusted mean model for behavioral portfolio selection is presented by taking into account investor’s sentiment return and multiple mental accounts. The proposed behavioral model maximizes the sentimental mean value of portfolio interval return and ensures the portfolio interval return of each mental account exceeding the given minimum return level with a given possibility degree. Then, multiple programming models are designed to solve the optimal behavioral portfolio strategy. Finally, a numerical example is given to illustrate the validity of the proposed approach.

Keywords: behavioral portfolio decision, interval return, possibility degree, mental account

Received September 14, 2019; Revised October 19, 2019; Accepted November 05, 2019

Citation: Qiansheng Zhang, A Behavioral Portfolio Model with Interval Return and Investor’s Sentiment. Journal of Finance and Economics, 7 (4). 112-117. January 2019. doi:10.12691/jfe-7-4-1

1. Introduction

Portfolio selection as a field of study began with the Markowitz model [1] in which return is quantified as the mean and risk as the variance. Portfolio selection discusses the problem of how to allocate a certain amount of investor’s wealth among different assets and form a satisfying portfolio. In 1952 Markowitz proposed the mean-variance portfolio decision model which provides a fundamental basis for modern portfolio selection theory by maximizing the expected return for a given level of risk or minimizing the expected risk for a given level of expected return. After that, many scholars have studied the portfolio selection models in fuzzy uncertain environment [2,3,4]. Moreover, in real world the portfolio selection problem are usually involved by decision-maker’s pshchology [5,6] and mental accounts, since the investor decision-makers tend to segregate different types of gambles into separate accounts, and then apply the prospect theory [7,8] to each account by ignoring possible interactions. It refers to the tendency for people to separate their money into separate accounts based on a variety of subjective criteria. Mental account proposed by Thaler [9] is a foundation for the way decision-makers set reference points for the accounts that determine profits and losses. Behavioral portfolio theory proposed by Shefrin and Statman [10] is a positive theory of asset choice under uncertainty. They developed a model of multi-layered portfolio construction in which each layer is associated with a particular aspiration level and the covariances between the layers are overlooked. Thus, each portfolio layer resembles a separate mental account. Shefrin and Statman suggest that investors have varied aims and create an investment portfolio that meets a broad range of goals. After that, Ma [11] proposed a practical decision making method for behavioral portfolio choice, Muradoglu Yaz [12] studied a behavioral approach to efficient portfolio formation, Mehlawat [13] and Amelia [14] developed multi-criteria behavioral portfolio decision models. Jin [15] developed multi-period and multi-objective behavioral portfolio approach. Also, Xie [16] studied the behavioral assets portfolio method based on sentiment recognition.

Recently, interval number or interval value fuzzy set have been generally used in handling and describing imprecise and complex phenomena that often rise in business, financial and managerial systems [17,18,19,20]. In uncertain portfolio decision scenario, the return of financial asset is conveniently evaluated by interval. Inspired by the idea of Markowitz’s M-V model, a lot of interval portfolio model extensions have been proposed to deal with portfolio decision with interval return and risk under interval uncertain environment [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36]. For example, Giove [21], Zhang [22], Wu [23], Chen [24] studied on interval portfolio selection problem, and Mohagheghi [25,26] studied the portfolio selection problem under interval fuzzy environment. Rupak Bhattacharyya [27], Li [28], Guo [29], Xu [30], MASAAKI [31], Feng [32] studied the fuzzy portfolio selection models by interval analysis. Also Liu [33] discussed a multi-period portfolio selection optimization model by using interval analysis. Zhao [34], Lu [35], Lai [36] developed the multiple objective interval number linear programming model for the portfolio investment.

However, the above mentioned interval-valued portfolio decision models have not consider the investor’s sentiment and investor’s behavioral interacting factors as well as the socio-psychological nature. Therefore, we will provide a new methodology to build portfolios for behavioral investors that follow ethical, environmental and social considerations in their investment decisions. To do so, we construct interval behavioral portfolio theory with mental accounts, multiple-objective programming models and sentiment factors. In this work, we propose the interval behavioral portfolio models for determining the allocation between the different mental accounts according to the investor’s profile and the expert knowledge provided by the financial manager.

2. Preliminaries

Let us first review some basic concepts and preliminary theory about interval value, which will be utilized in the following sections about interval behavioral portfolio decision model construction.

Definition 1 [17]. is named an interval value, if . And the length of this interval is defined as length(.

Definition 2 [18]. Let , be two interval values, the addition and the scalar multiplication operators between them are defined as

(1) .

(2) .

Definition 3 [19]. Let be any two interval values, the degree of possibility of is defined as

where , denote the length of interval values , respectively.

Theorem 1 [20]. Let be any two interval values, then

(1) .

(2) .

(3) if and only if .

(4) if and only if .

(5) if and only if ;

Especially, if and only if

(6) If then

Definition 4. Let be an interval value, then the mean value of interval value is defined as

Definition 5 [16] Letbe the sentiment of investor on financial asset the sentiment influential function and the sentiment-adjusted return of asset , respectively, are defined as the following forms.

Obviously, and is a increasing function, that is to say, the greater is the investor ’s sentiment, the higher is the estimated return of asset .

(1) If then , i.e., if the investor is optimistic on asset, the return of asset will be over-estimated;

(2) If then , i.e., if the investor is rational on asset, the return of asset is estimated properly;

(3) If then , i.e., if the investor is pessimistic on asset, the return of asset is under-estimated.

3. The Formulation of Interval Behavioral Portfolio Decision Problem

In this section, we discuss the behavioral portfolio selection problem with interval returns and sentiment. We first introduce the problem description and notations used in the following section. Then, we formulate the interval behavioral portfolio model by maximizing the sentimental mean of return of portfolio.

3.1. Problem Description and Notations

Let us consider a behavioral portfolio selection problem with mental accounts. Each mental account consists risky assets. The return rates of risky assets are evaluated by interval values. Assume that the investor intends to allocate his/her wealth among the risky assets for making accounting investment plan in mental accounts. To make it easier to follow our exposition, we put together all the notations that will be used hereafter.

: the investment proportion of risky asset in mental account ;

: the importance degree of the holding mental account ;

: the lower boundary of investment proportion of risky asset at mental account ;

: the upper boundary of investment proportion of risky asset at mental account ;

: the sentiment of investor on asset in mental account ;

: the sentiment function of investor on asset in mental account .

3.2. Sentiment-adjusted Mean of Interval Return for Behavioral Portfolio

Assume that the whole investment process is self-financing, that is, the investor does not invest the additional capital during the portfolio selection process. Let be the interval return of asset at mental account . According to the previous section, the sentimental mean value of the return rate of the portfolio at mental account is determined by

3.3. Construction of Behavioral Portfolio Selection Model with Interval Return and Investor’s Sentiment

Assume that the objective of the investor wants to maximize the expected sentimental return of portfolio over the whole T mental accounts. At the same time, the portfolio return at each mental account must achieve or exceed the given minimum wealth return level. Thus, the multi-mental accounting behavioral portfolio selection problem can be formulated as the following programming model denoted by (P1):

(P1)

s.t.

where is the weight vector of all the mental accounts, is the importance degree of mental account And represents the given minimum aspiration interval return level of the portfolio wealth regarding the -th mental account; is the given possibility degree level assuring that the interval return of -th mental account greater than the given minimum aspiration interval return level . In general, the higher level is the account mental, the greater is the parameter.

If we suppose is the sentiment function of investor on asset at mental account , then the above programming model (P1) can be transformed to the following optimization models (P11-P13) according to Definition 3 of possibility of interval returns and Theorem 1.

(P11)

s.t.

(P12)

s.t.

(P13)

s.t.

Hence, we can get the optimal portfolio solution that achieves the maximum objective function value by solving the above multiple-account programming models (P11-P13) with Lingo or Matlab programming software.

4. Numerical Example

Example 1. In order to express the idea of our model and the effectiveness of the proposed interval behavioral portfolio algorithm, we give an example for simulating the real transaction. For simplicity, in the example we consider two-mental accounting behavioral portfolio decision problem with interval-valued returns. Assume that the financial market has two mental accounts, i.e. T = 2. The lower-level mental account has two alternative financial assets . The high-level mental account has two alternative financial assets All the financial assets in the above mental accounts of this example are selected from Shanghai Stock Exchange. To simulate the transaction, we collect the weekly closing pricing of assets from September 2018 to September 2019, with 1 yearly observations. By analyzing the stock historical data, the corresponding corporations’ financial reports and the future information, we can utilize the simple statistical frequency method to assess the interval return of assets in the above two mental accounts, which are shown in Table 1.

Table 1. The assessed interval return of the selected stock assets

Suppose that the investor’s initial sentiment vector on the selected four financial assets is

If we choose as the sentiment influential function, we can compute the sentiment influential function value vector as

In this example we let the lower boundary and upper boundary of investment proportion of risky asset at mental account is 0 and 1, respectively. Assume , are the given minimum expected interval return of the portfolio for mental account 1 and 2, respectively. And we let be the possibility degree that the interval return of the first mental account is greater than , and is the given possibility degree that the interval return of the second mental account exceeds the minimum return aspiration In order to obtain the corresponding portfolio solution we construct the following sentiment-adjusted interval behavioral portfolio model (P2).

(P2)

s.t.

In fact, the above interval portfolio model is equivalent to the following four linear programming models (P21-24).

(P21)

s.t.

i.e.,

and

i.e.,

and

(P22)

s.t.

The above model (P22) can also be transformed into the following linear programming model.

()

s.t.

i.e.,

and

i.e.,

and

(P23)

s.t.

i.e.,

and

i.e.,

and

(P24)

s.t. ,

i.e., ,

and

i.e.,

and

According to the different importance agree the investor regarding each mental account, we consider three different types of investment importance vectors for the two mental accounts as W1=(0.1,0.9), W2=(0.2,0.8), W3=(0.5,0.5), W4=(0.8,0.2), W5=(0.9,0.1). Then, we apply the optimization software package Lingo to solve the above-mentioned four linear programming models. Finally, we get the optimal behavioral portfolio strategy, which is the solver corresponding to maximum objective function value of portfolio. The optimal behavioral investment portfolio solution corresponding to the maximum objective function value or maximum sentimental mean regarding the different weight of mental accounts are easily computed as listed in the following Table 2.

Table 2. The Optimal behavioral portfolio strategy regarding different weight vector of mental accounts

5. Summary and Conclusion

In this paper, we consider the multi-account behavioral portfolio selection problem in interval uncertain environment. We use the sentiment-adjusted mean value to measure the interval return of the behavioral portfolio. Furthermore, based on the possibility degree of the interval return of each mental account exceeding the given minimum return aspiration we propose a sentiment-adjusted behavioral portfolio model with interval return and investor’s sentiment. In order to solve the proposed model, we transform it into the equivalent linear programming models. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

Acknowledgements

We thank the Editor and the anonymous referees for their good suggestions concerning this paper. This research is supported by the Natural Science Foundation of Guangdong Province, China (Nos. 2018A030313996 and 2017A030313435).

References

[1]   | Markowitz H., Portfolio selection, Journal of Finance, 1952, 7, 71-93.
[2]   | Fang Y., Lai K.K., Wang S.Y., Portfolio rebalancing model with transaction costs based on fuzzy decision theory, European Journal of Operational Research, 2006, 175, 879-893.
[3]   | Gupta P., Mehlawat M.K., Saxena A., Asset portfolio optimization using fuzzy mathematical programming, Information Sciences, 2008, 178, 1734-1755.
[4]   | Yue Wang , A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios, , 2017, 465(1), 124-140.
[5]   | Kahneman D., Tversky A., The framing of decisions and the psychology of choice, Science, 1981, 211, 453-458.
[6]   | Lopes L., Between hope and fear: The psychology of risk, Advance in Experimental Social Psychology, 1987, 20: 255-295.
[7]   | Kahneman D., Tversky A., Prospect theory: An analysis of decision making under risk, Econometrica, 1979, 47, 263-291.
[8]   | Michael J. Besta, , Prospect theory and portfolio selection, , 2016, 11, 13-17.
[9]   | Thaler R., Mental accounting and consumer choice, Marketing Sciences, 1985, 4(3): 199-214.
[10]   | Shefrin Hersh, Meir Statman, Behavioral portfolio theory, Journal of Financial and Quantitative Analysis, 2000, 35(2): 127-151.
[11]   | Ma Y.K., Tang X.W., Decision making method for behavioral portfolio choice, Journal of Systems Engineering, 2003, 18(1), 71-76.
[12]   | Yaz Gulnur Muradoglu, Aslihan Altay-Salih, Muhammet Mercan, A behavioral approach to efficient portfolio formation, The Journal of Behavioral Finance, 2010, 6(4): 202-212.
[13]   | Mukesh Kumar Mehlawat, Behavioral optimization models for multicriteria portfolio selection, Yugoslav Journal on Operations Research, 2013, 23(2), 279-297.
[14]   | Amelia Bilbao-Terol, Mar Arenas-Parra, Veronica Canal-Fernandez, Celia Bilbao-Terol, Multi-criteria decision making for choosing socially responsible investment within a behavioral portfolio theory framework: a new way of investing into a crisis environment, Ann. Oper. Res., 2016,247, 549-580.
[15]   | Jin X., Chen N., Yuan Y., Multi-period and tri-objective uncertain portfolio selection model: A behavioral approach, North American Journal of Economics and Finance, 2019, 47, 492-504.
[16]   | Xie J., Yang C.P., Lack of diversification and investor sentiment-The behavioral assets portfolio based on sentiment recognition, Soft Sciences, 2012, 26, 8, 131-135.
[17]   | Bai C. Z., Zhang R., Shen S., Huang C.F., Fan X., Interval-valued probabilistic linguistic term sets in multi-criteria group decision making, International Journal of Intelligent Systems, 2018, 33(6), 1301-1321.
[18]   | Xu Z.S, Da Q.L., New Method for Interval multi-attribute decision-making, Journal of Southeast University, 2003, 33(4), 498-501.
[19]   | Xu Z.S., Da Q.L., Multi-attribute decision-making based on fuzzy linguistic assessments, Journal of Southeast University, 2002, 32(4), 656-658.
[20]   | Xu Z.S., A practical method for priority of interval number complementary judgment matrix, Operations Research and Management Science, 2001, 10, 16-1.
[21]   | Giove S., Funari S., Nardelli C., An interval portfolio selection problem based on regret function, European Journal of Operational Research 2006, 170, 253-264.
[22]   | Zhang P., An interval mean-average absolute deviation model for multiperiod portfolio selection with risk control and cardinality constraints, Soft Comput, 2015, 1-10.
[23]   | Wu M., Kong D.W., Xu J.P., Huang N.J., On interval portfolio selection problem, Fuzzy Optim Decis Making 2013, 12, 289-304.
[24]   | Chen G.H., Chen S., Wang S.Y., Interval Number fuzzy selection model, Systems Engineering, 2007, 25(8), 34-37.
[25]   | Mohagheghi Vahid , Meysam Mousavi S., Vahdani Behnam, A New Optimization Model for Project Portfolio Selection Under Interval-Valued Fuzzy Environment, Arab J Sci Eng, 2015, 8, 1-11.
[26]   | Mohagheghi V., Mousavi S. M., Vahdani B., Shahriari M. R., R&D project evaluation and project portfolio selection by a new interval type-2 fuzzy optimization approach, Neural Comput & Applic, 2016, 3, 1-20.
[27]   | Rupak Bhattacharyya , Samarjit Kar, Dwijesh Dutta Majumder, Fuzzy mean-variance-skewness portfolio selection models by interval analysis, Computers and Mathematics with Applications , 2011, 61, 126-137.
[28]   | Li J., Xu J.P., A class of possibilistic portfolio selection model with interval coefficients and its application, Fuzzy Optim Decis Making, 2007, 6, 123-137.
[29]   | Guo H.F., Sun B.Q., Karimi Hamid Reza, Ge Y.J., Jin W.Q., Fuzzy Investment Portfolio Selection Models Based on Interval Analysis Approach, Mathematical Problems in Engineering, Volume 2012, Article ID 628295, 1-15.
[30]   | Xu X.N., He F., Chen R., Zhang Q.Z., Solving non-linear portfolio optimization problems with interval analysis, Journal of the Operational Research Society, 2015, 66(6), 885-893.
[31]   | MASAAKI IDA, Solutions for the Portfolio Selection Problem with Interval and Fuzzy Coefficients, Reliable Computing, 2004, 10, 389-400.
[32]   | Feng B.J., Yan D.W., Chi G.T., Assets and liabilities optimization model of the risk control based on nonlinear interval number, Chinese Journal of Management Science, 2012, 20(1), 79-89.
[33]   | Liu Y.J., Zhang W.G., Zhang P., A multi-period portfolio selection optimization model by using interval analysis, Economic Modelling, 2013, 33, 113-119.
[34]   | Zhao Y.M., Chen H.Y., Multiple objective Interval number linear programming model for the portfolio investment, Operations and Managements, 2006, 15(2), 124-127.
[35]   | Lu Y.J., Tang X.W., Zhou Z.F., Interval number linear programming method for the portfolio investment, Journal of Systems Engineering, 2004, 19(1), 33-37.
[36]   | Lai K.K, Fang Y., Wang S.Y., A class of linear interval programming problems and its applications to portfolio selection, IEEE Transaction on Fuzzy Systems, 2002,10(6), 698-704.