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Computational Economics 11: 189–204, 1998. c 1998 Kluwer Academic Publishers. Printed in the Netherlands.

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Portfolio Selection Using the ADELAIS Multiobjective Linear Programming System C. ZOPOUNIDIS1 , D.K. DESPOTIS2 and I. KAMARATOU3 1

Technical University of Crete, DSS Laboratory, 73100 Chania, Greece University of Piraeus, Dept. of Informatics, 80 Karaoli and Dimitriou Street, 18534 Piraeus, Greece 3 Mediterranean Agronomic Institute of Chania, P.O. Box 85, 73100 Chania, Greece 2

(Accepted 21 January 1997) Abstract. The ADELAIS (Aide a` la DEcision pour syst`emes Lin´eaires multicrit`eres par AIde a` la Structuration des pr´ef´erences), multiobjective linear programming system is proposed as a decision tool for the selection of stock portfolios. A portfolio selection model is developed and applied to a set of fifty-two stocks from the Athens Stock Exchange for the two years period of 1989–1990. On the basis of this model, ADELAIS is used to design and evaluate alternative portfolios by considering a set of well-known criteria such as return, price earnings ratio, volume of transactions and dividend yield. A final portfolio of maximal utility is obtained as an outcome of an interactive process of individual inter-alternative preference modelling. Key words: ADELAIS, portfolio analysis, portfolio selection.

1. Introduction and Review Portfolio selection is concerned with the problem of finding the most desirable categories of stocks to hold, given the characteristics of each of the stocks. The determination of an efficient way to split the investor’s wealth amongst stocks is another important aspect of the portfolio selection problem. Since the pioneering article of Markowitz (1952) in the theory of portfolio analysis, based on the mean-variance formulation, several portfolio selection models have been proposed. According to this formulation, an investor regards expected return as desirable and variation of return (variance) as undesirable. Elton and Gruber (1987) provide a complete overview of different portfolio selection models. Apart from the meanvariance model, they cite the single index models, the multi-index models, the average correlation models, the mixed models, the utility models in which the preference function of the investor play a key role in the construction of an optimum risky portfolio, and the models which employ different criteria such as the geometric mean return, safety first, stochastic dominance and skewness. Pardalos et al. (1994), also, provide a review and some computational results of the use of optimization models for portfolio selection. In recent years, the development of new techniques in operations research and management science as well as the progress in computer and information tech-

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nologies gave rise to new approaches to modelling the portfolio selection problem: the expert systems approach and the multicriteria analysis approach. The expert systems approach is discussed in Lee et al. (1989); Lee and Stohr (1985); Shane et al. (1987); Suret et al. (1991). Multicriteria analysis provides the methodological basis to resolve the inherent multicriteria nature of the portfolio selection problem and builds realistic models and processes by taking into consideration besides the two basic criteria of return and risk (mean-variance model), a number of important criteria, such as marketability, price/earnings ratio, growth of the dividends and others (cf. Hurson and Zopounidis, 1993; Zopounidis, 1993). The studies concerning the use of multicriteria analysis in portfolio selection can be classified according to their special methodological background (cf. Pardalos et al., 1995; Siskos and Zopounidis, 1993) as follows:  multiobjective mathematical programming: Colson and De Bruyn (1989); Lee and Chesser (1980); Muhlemann et al. (1978); Spronk (1981).  multiattribute utility theory: Evrard and Zisswiller (1983); Rios-Garcia and Rios-Insua (1983); Saaty et al. (1980).  outranking relations (ELECTRE methods): Martel et al. (1988), Szala (1990), Hurson and Zopounidis (1995).  preference disaggregation approach (MINORA system): Zopounidis (1993), Zopounidis et al. (1995). In relation to the above studies, one can add Zeleny’s work on the multidimensional measure of risk connected with the return in the portfolio analysis (Prospect Ranking Vector, see Colson and Zeleny, 1979; Zeleny, 1977). In this paper interactive multiobjective programming is used as a decision tool for portfolio evaluation and selection. The study concerns the application of the ADELAIS multiobjective linear programming system to the evaluation and selection of stock portfolios in the Athens Stock Exchange (ASE). Section 2 presents a multiobjective linear programming portfolio selection model applied to the case of 52 securities in ASE. The ADELAIS system is outlined in Section 3. Section 4 summarizes the decision process which was carried out by an expert by using ADELAIS for designing a satisfactory portfolio. The results and the advantages of the use of the ADELAIS system in portfolio selection and management are also discussed. 2. The Portfolio Selection Model 2.1. SECURITIES AND EVALUATION CRITERIA The sample considered in the study consists of 52 securities of the ASE covering a broad spectrum of business activities (sectors). The study period includes the years 1989 and 1990 and the closing prices were recorded on a weakly basis. The different sectors with the number of companies (securities) in each of them are presented in Table I. The classification of the securities is made by the statistical department of the ASE.

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Table I. Number of securities selected for each sector of the ASE Banks (X1–X15) Insurance – Investment (X16–X22) Leasing Companies (X23) Textiles (X24–X26) Chemical Products (X27) Building Materials Cement Co (X28–X30) Mines – Metallurgical (X31–X37) Food – Spirits (X38–X41) Flour Mills (X42) Tobacco (X43–X44) Miscellaneous Corporations (X45–X52)

15 7 1 3 1 3 7 4 1 2 8

The criteria used in the study for stock evaluation are well established and widely used indices, both in theory and practice: (1) Increase in profits per share (P ) = Profits per share in period(t)-Profits per share in period (t , 1)/Profits per share in period (t , 1); (2) Price Earnings Ratio (P/E) = Share price in the stock market (t)/Earnings per share (t , 1); (3) Dividend yield (D ) = Dividend (t)/Share price closed (t); (4) Marketability (M ) = Number of transactions of shares of a company during period (t)/Total number of shares of a company during period (t); (5) Beta coefficient (B ) = COV (Ri,Rm)/VAR(Rm), Ri = the return of the share i and Rm = the return of the market portfolio (6) Return per share (R) = Pt ,PPtt,,11+Dt

where Rt is the return on a share in period t, Pt is the share price in period t, Pt,1 is the share price in period t , 1, and Dt is the dividend that the share gives to the investor in period t. Extended theoretical presentation of these criteria can be found in Alexander and Sharpe (1989); Copeland and Weston (1983); Huang and Randall (1987); and Jones (1985). Table II presents the securities included in the sample, their coding variables and their scores on the criteria, estimated on an average basis for the years 1989 and 1990. 2.2. THE MULTIOBJECTIVE PORTFOLIO SELECTION MODEL Decision variables Xi: percentage of capital to be invested in security i; i = 1; : : : ; n, where n is the number of securities under consideration (n = 52 for the current application).

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Objectives

n

Maximize dividend yield: max f1

i=1

= Di Xi , n i=1

Maximize increase in profits per share: max f2

n i=1

Maximize marketability: max f3

= Mi Xi ,

n

Maximize return per share: max f4

n i=1

i=1

Minimize the P/E ratio: min f5

n i=1

Minimize risk: min f6

= Pi Xi ,

= RiXi ,

= (Pi =Ei )Xi ,

= Bi Xi .

Concerning the fifth objective, the P/E ratio is to be minimized as the lower the ratio is the bigger are the margins that the security has to increase its price. The last objective (beta coefficient) reflects the portfolio manager’s attitude towards risk. A risky portfolio manager for example, could have asked for maximization of portfolio risk. Constraints Capital Availability All the available capital must be invested:

X1 + X2 +


+ X52 = 1: Upper Limit Concerning the Amount of Capital Allocated to Different Stocks The portfolio theory does not permit the allocation of the investor’s capital only in one stock primary because it is required the portfolio to be of low risk. Therefore the available capital must be split to the stocks in the portfolio (diversification) and this is possible only with the determination of some upper bounds concerning the amount invested in each stock, as follows:

X1 6 U1;

X2 6 U2; : : : ; X52 6 U52 ;

where Ui is the upper limit of the capital to be invested in security i, in percentage of the total capital. An expert portfolio manager used in the study fixed these limits for each sector of the stock market as shown in Table III. Specific Preferences for Some Stocks The portfolio manager showing interest for some particular stocks expressed his intention to include them into his portfolio, investing at least a certain portion of the

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Variables Profits increase P/E per share Ratio

Dividend Market- Beta yield ability

Bank of Attica General Bank National Bank Bank of Greece N. I. B. I. D. (C) N. I. B. I. D. (P) Traders’ Credit Bank (P) Ergo Bank Mortgage Bank Ionian Bank Bank Macedonia – Thrace Bank of Piraeus Credit Bank National Housing Bank S.A. (C) National Housing Bank S.A. (P) Astir Ethniki General Insurance Co National Investment Co Hellenic Investment Co (B) Ergo Investment (B) Investment Development Fund (B) Ependyseis Pisteos (B) Alpha Leasing A.E. Naussa Spinning Mills (C) Elfico (C) Etma (C) Petzetakis

X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27

0.010 0.032 0.022 0.056 0.013 0.013 0.032 0.046 0.037 0.031 0.037 0.033 0.049 0.043 0.043 0.065 0.058 0.099 0.113 0.065 0.091 0.102 0.069 0.033 0.016 0.022 0.025

0.61 1.331 1.43 3.940 0.674 0.674 0.240 0.059 0:347 0.302 0.101 0.19 0.269 0:057 0:057 75.360 66.45 0.737 0.360 0:041 0.753 0.891 0.581 0.215 0:67 0:366 0.781

,

, ,

,

, ,

85.055 20.71 15.06 4.505 33.09 33.09 18.445 14.05 21.785 13.135 13.775 12.52 13.67 13.98 13.98 296.43 64.92 8.505 9.095 11.51 10.81 7.66 11.925 28.5 25.61 22.32 24.52

5.14 6.645 14.99 6.215 10.21 42.3 14.815 33.035 24.505 19.91 21.92 21.915 24.8 9.835 19.225 2.87 8.0 6.19 17.65 33.645 10.185 45.515 20.245 20.385 8.435 13.1 58.29

0.845 0.73 1.536 0.729 0.637 0.656 0.353 1.929 1.233 1.006 0.626 0.832 0.881 0.4 0.361 0.501 0.962 0.558 0.525 0.842 0.467 0.664 0.653 0.623 0.459 0.493 0.768

Return per share 0.009 0.014 0.015 0.092 0.011 0.011 0.097 0.1 0.012 0.018 0.008 0.018 0.011 0.008 0.07 0.014 0.015 0.005 0.008 0.007 0.014 0.011 0.009 0.002 0.002 0.001 0.017

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Table II. Securities and multicriteria evaluation

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Table II. (continued) Variables Profits increase P/E per share Ratio

Dividend Market- Beta yield ability

Heracles Cement Co Titan Halkis Cement Co Viometal METKA (C) Levederis (C) Radio Athenai (C) Radio Athenai (P) Fourlis (C) Fourlis (P) Elais Cambas Boutaris (C) Boutaris (P) St. George Mills KARELIA Keranis Athinea Vioter ZAMPA Klaoudatos G. Xelemporia (C) Xelemporia (P) Shelman (C) Shelman (P)

X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52

0.012 0.024 0.012 0.018 0.015 0.033 0.045 0.045 0.049 0.049 0.029 0.026 0.028 0.028 0.015 0.062 0.017 0.056 0.065 0.046 0.036 0.04 0.04 0.025 0.025

B

= Bearer; C = Common; P = Preferred.

0.880 0.69 0.59 0.79 0.08 0.175 0.201 0.201 0.533 0.533 0.045 0.035 0.066 0.066 1.28 0:051 0:673 0:134 0.608 0.255 0:684 0.425 0.425 0.652 0.652

, , , ,

41.02 20.96 10.86 39.55 27.47 16.2 15.285 15.285 13.76 13.76 18.67 19.33 26.08 26.08 71.05 13.325 65.64 11.57 13.065 4.475 27.14 20.055 20.055 18.61 18.61

17.46 29.15 30.015 20.58 46.0 36.545 3.915 37.765 22.885 80.16 15.395 12.83 33.31 73.365 35.275 3.790 5.405 17.465 59.245 10.575 4.145 35.49 81.555 8.405 61.3

1.238 1.259 1.557 1.137 0.417 1.002 0.447 0.94 0.771 0.831 0.701 0.332 0.357 0.357 1.231 0.41 0.179 0.284 0.757 0.94 0.516 0.865 0.674 0.724 0.715

Return per share 0.021 0.019 0.033 0.012 0.03 0.015 0.013 0.011 0.011 0.013 0.005 0.017 0.017 0.014 0.017 0.004 0:001 0.004 0.012 0.158 0.005 0.014 0.012 0.124 0.014

,

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Table III. Upper limits of the amount invested in each sector (% of capital) Sectors

Upper limit

Banks Insurance, Investment Companies Leasing Companies Textiles, Chemical products, Food-Spirits, Flour Mills, Tobacco, Miscellaneous Companies Building Materials, Cement Companies Mines-Metallurgical Companies

0.20 0.12 0.01

0.05 0.08 0.10

capital in these stocks. Thus he fixed these portions to 4% for the stocks of Credit Bank, 2% for the firm Titan, 1% for the firm Elais and 1% for the firm Karelia Cigarette. These specific preferences are modelled by the following constraints:

X13 > 0:04; X29 > 0:02; X38 > 0:01; X43 > 0:01 Beta Coefficient According to the portfolio manager’s preferences, stocks with low, medium and high beta must be included in the stock portfolio. To satisfy these a priori stated preferences, the following constraints are formulated:

X3 + X8 + X9 + X10 + X28 + X29 + X30 + X31 + X33 + X42 = 0:5; X1 + X2 + X4 + X5 + X6 + X11 + X12 + X13 + X16 + X17 + X18 +X19 + X20 + X22 + X23 + X24 + X27 + X35 + X36 + X37 + X38 +X46 + X47 + X48 + X49 + X50 + X51 + X52 = 0:3; X7 + X14 + X15 + X21 + X25 + X26 + X32 + X34 + X39 + X40 + X41 +X43 + X44 + X45 = 0:2: As stated in the above constraints the portfolio must be selected in such a way that 50% of the capital will be allocated to stocks with b > 1, 30% to stocks with 1 > b > 0:5 and 20% to stocks with a beta coefficient less than 0.5 (b < 0:5). 3. Outline of the ADELAIS System ADELAIS is an interactive computer program developed to support the search for a satisfactory solution in multiobjective linear programming (MOLP) problems of the general form: maxff1 (x); : : : ; fn (x)g

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2 A, where x = (x1 ; : : : ; xm ) is the vector of the decision variables, f1(x); : : : ; fn(x) are linear functions of the decision variables and A is the set of the feasible solutions (A  Rm ). subject to x

The system provides extensive data management capabilities and the concerned solution process provides a ‘two level’ interaction: interactive assessment of the decision maker’s utility function and interactive modification of the satisfaction levels. A complete reference of the MOLP method incorporated in ADELAIS, which is also described briefly in this section, can be found in Siskos and Despotis (1989). The method operates in two phases: a two-stage preliminary phase performed once and a three-stage iterative phase. 3.1. PRELIMINARY PHASE Stage 1. Each objective function is maximized and then minimized on the feasible set A to obtain upper and lower bounds respectively. Particularly, if all or some of the objective functions fail to achieve a finite minimum, as this may happen even though the original MOLP problem has been sufficiently formulated in order to have a finite maximum, the lower bounds are computed with a heuristic procedure (cf. Siskos, Despotis, 1989). Stage 2. A starting efficient solution (i.e., a solution that is not dominated by any other feasible solution) is estimated in a way that the resulting objective values are as close as possible to the upper bounds in the minimax sense (an LP problem is solved which locates its optimal solution on the efficient border of the decision space at a minimum Tchebycheff distance from the ideal objective values). 3.2. ITERATIVE PHASE Stage 3. At each iteration the decision maker (DM) is provided with a new efficient solution which, except the initial one, comes from Stage 5 (see below). The system provides the attained objective values relative to the new solution, the achievement percentages with respect to the upper bounds and the satisfaction levels (i.e., the revised lower bounds) established in previous iterations. The DM is then asked to indicate the objectives he/she insists on increasing and if he/she intends to decrease some of the others in compensation. The DM’s responses, combined with relative responses of previous iterations, form the basis for the establishment of new satisfaction levels. The new satisfaction levels limit the feasible set but the system provides the DM with the possibility to relax them if desired by analyzing the local trade-offs among the objectives. This possibility helps in removing the consequences of previous responses that eventually contradict the DM’s current desires by re-examining solutions that had been rejected in previous iterations. The iterative process is terminated by the DM within this stage when a satisfactory solution is achieved.

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Figure 1. The flow-chart of the ADELAIS system

Stage 4. This stage constitutes a learning process of the DM’s preferences. At first, a simple technique is set up to construct a reference set of decision alternatives (i.e., a set of vectors that might be assumed by the objective functions). Then the DM is asked to rank order these alternatives according to his preferences. The DM’s subjective ranking is taken as input and a concave additive utility model is assessed by a modified version of the UTA ordinal regression algorithm (cf. Jacquet-Lagr`eze and Siskos, 1982; Despotis and Yannacopoulos, 1990; Despotis et al., 1990). The UTA method fits ordinal utility functions of the additive form that best approximate the data (preference ranking over the set of reference alternatives) by using a linear programming formulation and post-optimality analysis. The partial utilities are assumed non-linear and are assessed in a piecewise linear form in a manner that

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the estimated ranking over the set of reference alternatives is as close as possible to the subjective ranking provided by the DM. In case of inconsistencies the DM is invited to interact with the model in order to improve the consistency. The utility assessment process is terminated by the system when full consistency is achieved or by the DM himself when acceptable consistency is achieved. Stage 5. The assessed utility function is maximized over the set A of the feasible solutions as it is reduced by the satisfaction levels. A new efficient solution is obtained and the process is repeated from Stage 3. For the maximization of the utility function a piece wise linear programming technique is employed (Fourer, 1985). The flow-chart of the ADELAIS system is presented in Figure 1. 4. Portfolio Selection in ASE Using ADELAIS The ADELAIS system was used to support the selection of stocks from the Athens Stock Exchange. The role of the decision maker was undertaken by a specialized portfolio manager. The manager, after being familiarized with ADELAIS system, used it experimentally to support the process of designing and selecting a portfolio on the basis of the model presented in Section 2. In the preliminary phase the system calculated the upper and the lower bounds of the objective functions within the region of feasible portfolios and then proceeded to the estimation of an initial efficient solution (portfolio). The system projected the objective values corresponding to the initial solution, the upper and lower bounds, the satisfaction levels and the rates of closeness to the ideal values (Table IV). Table IV. Basic information generated in the preliminary phase of the solution process Dividend yield P/E Upper bound 0.064 Compromise 0.045 Satisf. level 0.017 Lower bound 0.017 Rc 58.6%

Increase in profits Marketability Beta per share

10.859 21.791 71.181 71.181 81.9%

17.722 8.603 0:143 0:143 49.0%

, ,

45.358 32.840 11.920 11.920 62.6%

Return per share

0.767 0.570 1.136 0.533 1.216 0.009 1.216 0.009 17.8% 93.5%

The calculations in the preliminary phase was carried out automatically and the portfolio manager was not involved. Thus, in the absence of preference information the satisfaction levels for the objectives are initially set equal to the lower bounds. A pay-off table for the objectives was also given to the portfolio manager (Table V). The diagonal elements represent the ideal point at which all the objectives achieve their optimum values. It is apparent that these values are not attainable simultaneously due to the conflicting nature of the objectives.

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Table V. Pay-off table generated by ADELAIS Dividend yield P/E Dividend Yield P/E Incr. in prof./share Marketability Beta Return per share

0.064 0.048 0.041 0.034 0.041 0.036

Increase in profits Marketability Beta per share

14.022 0.223 10.859 1.027 62.131 17.722 20.242 0.351 56.915 9.244 16.010 0.887

25.140 18.700 15.067 45.357 18.213 22.739

1.013 1.053 0.980 1.071 0.767 1.075

Return per share 0.029 0.055 0.021 0.534 0.016 0.570

A great deal of information is obtained from the pay-off table concerning the competitive nature of the objectives. For example, when dividend yield receives its optimum value (0.064) the P/E ratio is expected to be 14.022, that is close to its ideal value. At the same time, when increase in profits gets its optimum value (17.722) the P/E ratio takes an undesirable (high) value and the same happens with marketability, dividend yield and return per share. If one selects a portfolio at a minimal beta coefficient (0.767), marketability is expected to take the value 18.213, which is low relatively to its highest possible value, and the other objectives will take values that could hardly be considered satisfactory when compared to the ideal values. Thus, if the portfolio manager requires his portfolio to include securities with the lower possible risk then he should not expect the higher return from that portfolio or the higher marketability and P/E ratio. With respect to the initial solution, the portfolio manager being satisfied by the attained values of P/E (21.791), increase in profits per share (8.603), marketability (32.840) and return per share (0.533) asked for an improvement of dividend yield and risk (beta). On the basis of this information the system generated a number of alternative portfolios, and asked the portfolio manager to define an overall preference ranking on them (Table VI). On the basis of the data and the inter-alternative preference information of Table VI the system assessed an additive utility model. The utility model was not fully consistent with the portfolio manager’s preference ranking. The difference appeared between the reference alternatives a6 and a7 which were ranked by the model 2nd and 3rd respectively. Focusing on this contradiction the portfolio manager appreciated that the model suggestion was relevant as an opportunity to achieve the same level of dividend yield and an acceptable level of beta at a lower expense of P/E, increase in profits per share and return per share. A new utility model was adjusted to that ranking. The system used the assessed utility model and completed the first decision cycle by estimating and presenting a new efficient solution of maximal utility. The corresponding objective values and the achievement rates in the first iteration are presented in Table VII.

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Table VI. Reference alternatives and portfolio manager’s preference ranking Alternative Dividend yield P/E a8 a7 a6 a5 a4 a3 a2 a1

0.06 0.06 0.06 0.06 0.05 0.05 0.05 0.04

71.18 62.56 53.95 45.33 36.71 28.09 19.48 10.86

Increase in profits Marketability Beta Return Rank per share per share

,0 14 :

2.41 4.96 7.51 10.07 12.62 15.17 17.72

11.92 16.70 21.47 26.25 31.03 35.8 40.58 45.36

0.77 0.82 0.87 0.93 0.98 1.03 1.08 1.14

0.01 0.09 0.17 0.27 0.33 0.41 0.49 0.57

1 2 3 4 5 6 7 8

Table VII. Objective values and rates of closeness in the first iteration Dividend yield P/E Upper bound 0.064 Compromise 0.057 Satis. level 0.045 Lower bound 0.017 Rc 84.4%

Increase in profits Marketability Beta per share

10.859 31.084 71.181 71.181 66.5%

17.722 5.825 0:143 0:143 33.4%

, ,

45.357 23.094 11.920 11.920 33.4%

Return per share

0.767 0.570 0.823 0.383 1.136 0.009 1.216 0.009 87.4% 66.8%

The new solution led to a considerable improvement of dividend yield and the beta coefficient but at the expense of the other objectives. Notice in Table VII that the new satisfaction levels for dividend yield and beta coefficient are set equal to the respective values in the previous solution. Any subsequent solution will lie between the new satisfaction levels and the upper bounds. But the portfolio manager has the possibility to interact with the system in order to relax the satisfaction levels by means of trade-off analysis if he wants to dilate the decision space under consideration. The portfolio manager performed three iterations until to arrive at a satisfactory solution. At each iteration the system provided the portfolio manager with a new efficient solution. These solutions (portfolios) together with the initial one, are presented in Table VIII. A detailed description of the whole decision process performed by the portfolio manager is given in Kamaratou (1993). The final stock portfolio with which the decision maker concluded the decision process is presented in the last column of Table VIII. The achievement rates of the objectives with respect to the ideal values are presented in Figure 2. On the basis of the selected portfolio, 42% of the capital budget is to be invested in Banks, 28.6% in Investment Companies, 10% in Metallurgical Companies,

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Table VIII. Sequence of stock portfolios generated by ADELAIS Initial

Iteration 1 Iteration 2 Iteration 3

Objectives Dividend yield 0.045 0.057 P/E 21.791 31.084 Increase in profits per share 8.603 5.825 Marketability 32.840 23.094 Beta 1.136 0.823 Return per share 0.533 0.383 Stocks National Bank 0.100 0.000 Ergo Bank 0.200 0.000 National Mortgage Bank 0.000 0.180 Ionian Bank 0.000 0.200 Credit Bank 0.040 0.040 BANKS 0.34 0.42 Astir Inc. Co. 0.003 0.054 Ethniki General Inc. 0.120 0.023 INSURANCE 0.123 0.077 Hell. Invest. (B) 0.000 0.106 Investment Dev. Fund (B) 0.120 0.120 Ependyseis Pisteos (B) 0.000 0.068 INVESTMENT CO. 0.120 0.294 Titan 0.020 0.000 Halkis Cement Co. 0.080 0.000 BUILDING MATERIALS 0.100 0.000 METKA (C) 0.017 0.000 Levederis (C) 0.100 0.100 Fourlis (P) 0.100 0.000 METALLURGICAL 0.217 0.100 Elais 0.010 0.010 Boutaris (P) 0.050 0.037 FOOD-SPIRITS 0.060 0.047 St George Mills 0.000 0.000 FLOUR MILLS 0.000 0.000 Karelias 0.010 0.010 TOBACCO 0.010 0.010 Athinea 0.003 0.033 Xelemboria (P) 0.027 0.000 MISCELLAN. CORPOR. 0.030 0.033

0.045 51.056 13.774 30.024 1.050 0.532

0.055 19.078 5.836 25.461 0.859 0.514

0.000 0.200 0.070 0.000 0.040 0.31 0.095 0.096 0.191 0.000 0.081 0.000 0.081 0.080 0.000 0.080 0.059 0.100 0.059 0.336 0.010 0.050 0.060 0.050 0.050 0.010 0.010 0.000 0.000 0.000

0.000 0.000 0.180 0.200 0.040 0.42 0.000 0.084 0.084 0.046 0.120 0.120 0.286 0.020 0.000 0.020 0.000 0.100 0.000 0.100 0.010 0.050 0.060 0.000 0.000 0.010 0.010 0.020 0.000 0.020

8.4% in Insurance, 6% in Food and Spirits, 2% in Building Materials, 2% in Miscellaneous Corporations and 1% in Tobacco (Figure 3).

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Dividend yield

P/E

Increase in Marketability profits/share

Beta

Return per share

Figure 2. Achievement rates of the objectives with respect to the ideal values.

Figure 3. Portion of capital invested in various sectors of ASE.

5. Concluding Remarks An application of the ADELAIS multiobjective linear programming system to the evaluation and selection of stock portfolios has been presented. During the decision process, stock market objectives were used by the portfolio manager. In a multicriteria analysis framework, additional criteria, such as price earnings ratio, marketability, dividend yield and increase in profits per share, were examined besides the two basic criteria of return and risk. Moreover, specific information about the portfolio manager’s preferences for certain securities or particular sectors (industrial, commercial, financial), his attitude towards risk and past experience in stock evaluation were taken into consideration. The fact that ADELAIS is capable of helping the investor to select the portfolio that satisfies, as much as possible, his spectrum of investment desires, makes it a powerful supportive tool

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for portfolio managers and financial analysts in the activities of portfolio selection and management. Of great significance is the contribution of the ADELAIS system in the process of designing portfolios and it could be proven valuable for portfolio managers, financial analysts and investors in managing their portfolios. Particularly,

 the investment decision process in securities, the significance of each criterion      

in this process and the portion of capital invested in each security are explained sufficiently; the portfolio manager learns his preferences through a trial-and-error process and, based on his own objectives, gradually structures his own portfolio selection model; the time and cost for the analysis and evaluation of stocks are minimised by using computerized procedures; the complex problem of portfolio evaluation and selection is being structured to some extent; the competitiveness and effectiveness of portfolio management companies, stockbrokers are increased through the use of scientific methods; the stock market ‘engineering’ is upgraded by the use of more sophisticated methods; the computerized system offers transparency in the evaluation and selection of securities, since every decision can be argued on solid scientific grounds.

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