Two-Step Multi-Criteria Model for Selecting Optimal Portfolio
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Int. J. Production Economics 134 (2011) 58–66 Contents lists available at ScienceDirect Int. J. Production Economics journal homepage: www.elsevier.com/locate/ijpe Two-step multi-criteria model for selecting optimal portfolio Branka Marasovic´ n, Zoran Babic´ Faculty of Economics, University of Split, Matice hrvatske 31, 21 000 Split, Croatia article info abstract Article history: In spite of a large number of multi-criteria models applied to solve the problem of optimal portfolio Received 31 December 2009 selection and a large number of market criteria and accounting criteria proposed for these models, the Accepted 28 April 2011 problem of portfolio containing securities from different industries has not yet been adequately solved. Available online 8 May 2011 Namely, neither can stocks of companies from different industries be compared using the same criteria Keywords: nor can the weight of a particular criteria be equal for them all. Therefore this paper develops a new Financial risk management two-step model that will overcome the shortcomings of the previously used models. The model is Portfolio selection divided into two different but related pillars: the choice of different industries to form the overall Multi-criteria portfolio and the choice of portfolio for each industry. The multi-criteria model used in this paper is a PROMETHEE modified multi-criteria programming model based on the PROMETHEE II approach. The selected model has been applied at the Zagreb Stock Exchange (ZSE) as a real case. & 2011 Elsevier B.V. All rights reserved. 1. Introduction problem of quadratic programming which consists of minimizing risk while keeping in mind an expected return which should be Several traumatic events (terroristic attacks, natural disasters, guaranteed. business scandals, bank and corporate failures, etc.) over the past The importance of Markowitz’s work is affirmed by the Nobel decade have prompted corporate, government, and non-profit Prize for Economics he won in 1990. However, parallel to organizations to embrace enterprise risk management (ERM). Last introducing the Markowitz model in the common usage its few years, that trend has been recognized by the investment limitations and drawbacks were being noticed. The assumptions industry and now it takes into account a broader, enterprise risk of the Markowitz model for portfolio optimization are the perspective. The development and current status of ERM is following: presented in papers (Wu and Olson, 2010a, b). Although today’s investment industry leaders have accepted the necessity of a utility function which presents the investor’s preferences is a managing different types of risk, financial risk remained the most quadratic function and influential risk in operations in the financial industry. Portfolio the returns have normal distribution. selection models are usually a must in the process of diagnosing risk exposures (Wu and Olson, 2010c). So, that is the reason why These assumptions were the starting point for many critics of we are focused (in this paper) on this important financial risk this model. The majority of the empirical tests on the capital management tool. markets resulted in asymmetrical and (or) leptokurtic distribu- The first model for portfolio optimization has been developed tion (Cloquette et al., 1995). In such distributions, variance is not in 1952 by H.M. Markowitz and with that model he laid the an adequate risk measure. Having recognized the drawbacks of foundation of the modern portfolio theory. His model is based variance as risk measure, new models for the selection of optimal upon only two criteria: return and risk (Markowitz, 1959). The portfolio which use alternative measures, like lover partial risk risk is measured by the variance of returns’ distribution. Marko- measures, Value-at-Risk, and Conditional Value-at-Risk, have witz shows how to calculate portfolio which has the highest been developed (Konno et al., 2002; Rockafaller and Uryasev, expected return for a given level of risk, or the lowest risk for a 2000; Yau et al., in press). Generally it is obvious that over the given level of expected return (the so-called efficient portfolio). past 10 years the field of financial risk management and enter- The problem of portfolio selection, according to this theory, is a prise risk management have experienced a fast and advanced growth at an incredible speed (Wu and Olson, 2008, 2009a, b). However, contrary to the expectations of the modern portfolio n theory, the tests carried out on a number of financial markets Corresponding author. Tel.: þ385 21 430 600; fax: þ385 21 430 701. E-mail addresses: [email protected] (B. Marasovic´), have revealed the existence of other indicators, besides return [email protected] (Z. Babic´). and risk, important in portfolio selection. Considering the 0925-5273/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2011.04.026 B. Marasovic´, Z. Babic´ / Int. J. Production Economics 134 (2011) 58–66 59 importance of variables other than return and risk, selection of the PROMETHEE II method, which has been done in the Section 3. the optimal portfolio becomes a multi-criteria problem which The modification is made for the all preference functions from the should be solved by using the appropriate techniques. The multi- PROMETHEE method and positive and negative flow function. criteria nature of the portfolio selection was well presented in the The selected model has been applied at the Zagreb Stock paper by Khoury et al. (1993), and at present an arsenal of multi- Exchange (ZSE) as a real case. The Zagreb Stock Exchange (ZSE) dimensional and multi-criteria methods such as factor analysis, is a major stock market in Croatia and its market value is more goal programming, AHP, ELECTRE, MINORA, ADELAIS, etc. is than sixty billion dollars. already being applied in portfolio selection (Bouri et al., 2002; This paper is organized as follows: following this introduction, Ogryczak, 2000; Zopounidis, 1999; Shing and Nagasawa, 1999). A in Section 2, we describe the two-step model. Section 3 presents review of MCDA methods applied in portfolio selection and the multi-criteria method which is a modification of the PRO- management is well presented in a paper by Zopoundis and METHEE II method. Section 4 presents its application to the Doumpos (2002). Croatian capital market. Section 5 summarizes the paper and There are a vast number of criteria that can be taken into indicates the possible directions for further research. consideration in portfolio selection and that are usually classified into two groups: accounting criteria and those based on market values. The accounting criteria are obtained analyzing audit 2. Two-step model reports, income statements, quarterly balance sheets, dividend records, sales records, etc. There are a large number of them such In portfolio selection, investors, both individual and institu- as profitability indicators, liquidity and solvency indicators, and tional ones, are governed by a number of criteria that provide an indicators of financial structure of the company. They are used by insight into the current value and an estimation of the future the analysts (or managers) to give a synthesized and clear idea value of stocks making up the portfolio, and thus also the about the firm’s financial situation. The other criteria are market portfolio itself. Such an approach to portfolio selection in which criteria which contain all the information used by the stock we are faced with a number of conflicting criteria requires the use analysts to appreciate a stock’s performance. The criteria used of adequate multi-criteria decision making methods. As we have at this level are the mean return, total risk (variance), systematic already stated in the introduction, a large number of models been risk (beta), the size measured by the stock capitalization, the PER applied in solving this problem (price earning ratio), stock liquidity, and others. The use of one In this paper, the authors present a new multi-criteria model criteria or the other depends on the manager’s attitude and that, unlike the previous models, allows for the specific features of objectives (Albadvi et al., 2007; Bouri et al., 2002). industries (e.g. characteristic multi-annual cycles in shipping, Nevertheless, in spite of a large number of both proposed seasonality in tourism, effect of weather on food industry, etc.) multi-criteria models for optimal portfolio selection and market and the market’s different perceptions of prospects for different and accounting criteria proposed in these models, the problem of industries to be taken into account when choosing the optimal selection of optimal portfolio containing stocks of companies portfolio. These facts result in deviations in the mean value of from different industries has not yet been adequately solved. some criteria in different industries. Also, the criteria which are The problem arises because the evaluation of stocks from very important in one industry can have a significantly lower different industries generally requires different criteria, and even weight in another, and there are some criteria appearing only in a when the same criteria are used they need not have the same certain industry, while in others they will be non-existent (i.e. weight for them all. their weight is zero) (e.g. criterion credits/deposits in banking). Therefore this paper sets out to develop a new two-step model To overcome the stated drawbacks of the previous models we that will overcome