Comparison Multi criteria Decision Model VIKOR With The Capital Asset Pricing Model For Portfolio Selection in the Tehran Stock Exchange

Transcription

1 Comparison Multi criteria Decision Model VIKOR With The Capital Asset Pricing Model For Portfolio Selection in the Tehran Stock Exchange Dr Abolfazl Shahrabadi Department of finance Islamic Azad University,Tehran, Iran FAZEL BAGHBAN * Department of finance University of Economic Scienes, Tehran, Iran *Corresponding author Abstract The purpose of this study is to present an appropriate decision making for investment in capital market. For this goal first effective factors to select portfoilo are extracted on the basis of capital assets pricing by conducting the review of literature. Afterwards, the importance of factors from an investment expert point of view is assessed. Due to reliability between the factors, a mixture of ANP and DEMATEL techniques are applied in order to determine their importance. To continue, the VIKOR technique is utilized to categorize the society under survey which consists of metal ores, essential metals, chemical and medical industries. Also, by extracting the expected we shall rank the above industries based on capital assets pricing se four industries in the time line of year and finally we will compare the outcomes se two methods, and the results study show that on the basis VIKOR, the essential metals and medical industries and based on capital assets pricing, the medical industry is the best choice for the industry. Key Words: capital assets pricing, multi-criteria decision making, experimental decision making and laboratory assessment, the analysis procedure, VIKOR COPY RIGHT 2013 Institute of Interdisciplinary Business Research 44

2 1.Introduction One main subjects which exists on the financial sphere is that why different assets n show different. For this purpose, pricing theories have made efforts to determine why some assets have a higher or lower in comparison with other assets by applying their theoretical and fundamental concepts. In the past financial institutions and companies, financial researchers and investments considered higher as appropriate for higher. But it was only by the help of that economists could succeed in measuring the and reward which investment took on in regard to tolerance and turned it into quantity. In 1964, an economist named William Sharp succeeded in presenting the pricing single-agent capital assets. This is incredibly simple and comprehendible in comparison with the Markowitz boring and usual. Up until today many researchers and academic societies investigated and tested this in different financial markets, which dependant on the conditions and characteristics of different markets, the hypothesis and claims of this were confirmed or rejected (Hajazi and Gholamhosseini, 2010). In this research each coefficient capital assets pricing were divided to some subinvoices and then by using the VIKOR method, we categorize the mentioned industries. 2.Description and Explanation Issue Study Nowadays, existence of an active and booming capital market is known as one signs of the development of a country in international levels. In the developed countries most investments are executed by financial markets. Active participation people society in exchange guarantees the life capital market and the undying development of a country. The most significant matter that investment in these markets faces is making decisions regarding the selection of suitable negotiable papers for investment and establishment of share optimum baskets. The process of investment in a coherent manner requires analysis main essence of investment decision makings. In this case activities related to the process of making decisions are analyzed and important in the investors activity environment which influences their decisions are investigated (Tehrani, 2008). Every single day wide efforts are made to improve the investigation and analysis methods of shares and shares basket in the financial markets world. Efforts made in order to improve analysis methods of shares and shares basket, especially in markets which the number of shares is very high, causes emerge of modern methods which in comparison with COPY RIGHT 2013 Institute of Interdisciplinary Business Research 45

3 previous methods are about to find an answer to individual s tendency to profit maximization in financial markets. The first individual who presented the subject of establishing basket of negotiable papers in the framework of mathematics was Harry Markowits. He showed in a quantitative manner that how and why having variety in the basket of negotiable papers decreases the of negotiable papers basket and presented the concept of work portfolio (the desirable mixture of negotiable papers in a manner that the of that portfolio is minimum in exchange for the ) (Jones, 2009) The was presented by Sharpe, Lintner and Mossin, which was set on the basis Markowitz two-parameter portfolio analysis and is the most applicable of selecting portfolio. By applying this, we can make some predictions regarding y asset output. The considers three fundamental factors which influence the expected of shares and does not present other factors which may influence these three factors. Experimental findings show that the less under the influence of budget cuts is the of and of money. The expected market is also influences by country and of macroeconomics. Also, financial s and company s exclusive s, effects the beta of each negotiable paper (Wen- Rong and colleagues, 2011). And for this reason, in this paper we attempt to identify the influences se factors on less, market s and shares beta and then by applying the VIKOR, we shall compare the selected portfolios and investigate that are the results VIKOR method better than the results or not? 3. Necessity and Application In the financial markets world many researches have been conducted for the purpose of improving the methods of investigation and analysis of shares and establishment of negotiable papers basket. These researches led to the emergence of modern methods which side by side previous methods are looking for an answer to the tendency to maximization of individual s in financial markets. However, the mentioned methods have not been able to adapt to the circumstances capital market in Iran and have had a noticeable influence in selecting investors. On one hand the executed clarification in the recent years in negotiable papers exchange has led to access to a huge mass of specialized COPY RIGHT 2013 Institute of Interdisciplinary Business Research 46

4 information. Appropriate application of this information was not possible for normal people and required using the opinions of financial experts. Existence of a whole lot of information and other influential, has turned individual decision making for the goal of selecting a suitable basket of shares to a complicated issue to the extent that often individuals have decreased their criteria for making decisions about selection of share, to the amount mass of sale and purchase queues, heard news and rumors in markets and such issues. How to manage this massive amount of information and their effective application in improving decision making is one debatable issues (Amiri and colleagues, 2010). This research is a sequel to suggesting a to be able to analyze and summarize the effecting and their weigh and importance in the capital market and to help decision making in selecting appropriate shares for most investors. The main goal of this study is to compare the results MCDM with the capital assets pricing for the aim of choosing portfolio. The secondary aim study is divided into two parts. The first part consists of identification of influential factors on less, market and also beta and the second part secondary aim is related to determination importance of each identified factors in the first part and putting importance on these factors to execute the considered MCDM modem. 4. Executive Methods and Techniques study The applied method for this study consists of two stages. The first stage is to determine critical factors and subinvoices effective on the coefficient by library studies and then during the interview process, effective factors in this specific study are given weight to. After finding the weight of important factors and subinvoices in the first stage, the second stage consists of finding internal relations between the considered main factors in the beginning study by the help DEMATEL method is a group fuzzy and eventually by combination of outcomes in ANP, the final weighs of factors and subinvoices are valued and these values are applied in the VIKOR method to select portfolio. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 47

5 4.1 A general outlook research road Identifying effective factors in coefficients by review of literature Categorizing the factors Confirming that the factors and structures are suitable Internal assessment of factors with the help of DEMATEL group fuzzy Giving weight to the indexes Assimilation of DEMATEL and ANP and calculating the final weight factor Execution VIKOR and comparing the result with the results of Figure 2.3 A general outlook research road COPY RIGHT 2013 Institute of Interdisciplinary Business Research 48

6 Coefficient less ijcrb.webs.com 4.2 The MCDM First stage: At this stage it was requested of some experts to complete a square table in which each square of it showed the effect of each horizontal factor on the vertical factor and a sample is presented in table 4.1 for an expert person. Table 4.1: Effects factors on each other from an expert s point of view NO H H H H L L L NO H L H NO NO L H NO VH L VH L VH H VH NO L H L VH H NO H NO L L NO NO NO NO NO NO VH NO NO NO NO NO H NO Coefficient less The used symbols are described as follows: NO L H VH No effect Low effect High effect Very High effect Second Stage Afterwards by applying the CFCS non-fuzzy making method and with the help of relations in 13-7 of chapter 3 the absolute amount were calculated and shown on table 4.2 and so for the rest experts non-fuzzy amounts were calculated. Eventually these amounts will be mixed by the use 14 relations of chapter 3 and the mass of people s opinions (matrix Z) will be calculated. These results are shown in table 4.3 Table 4.2: Absolute amounts by the CFCS method COPY RIGHT 2013 Institute of Interdisciplinary Business Research 49

7 Table 4.3: The Mass of People s Opinions (Matrix Z) Coefficient of the less Macroecono mics Total Coefficient less In table 4.4 the normal matrix of direct relations (X) was calculated by using relations 1 and 2 of chapter 3. By applying this matrix and also using relation 3 of chapter 3, matrix T or the general relations matrix was calculated as described in table 4.5. Table 4.4: Normal matrix of direct relations (matrix X) Table 4.5: Matrix of general relations (Matrix T) D D+R D-R R COPY RIGHT 2013 Institute of Interdisciplinary Business Research 50

8 The Third Stage: The possible structure and procedure of are determined by using the total of rows (D) and total of rows (R). The total of D+R for each factors, importance and weight of that element in the relation system between factors is shown in table 4.5. The value of D for each element is the indicator of effecting amount of that element of other and the value corresponding R is an indicator intensity impressibility mentioned element by other. Therefore, D+R determined the total of effectiveness and impressibility considered in the system. In other words, the element which holds the most D+R has the most interaction with other system. The final amount of effectiveness on the total of other system is also calculated by D-R, in a manner that if D+R>0 then the above element is effective and if D-R<0 then the above element is impressible. Coefficient less The Fourth Stage: In the DEMATEL method a threshold amount was determined to show the strong and important connections between any. In the calculated matrixes each number is an indicator amount of effect each element has on another element. For using the outcomes of Matrix T a threshold is determined and only values equal or more than the connection matrix is considered important. Determination amount of threshold is also a group decision making issue in which between the two status, big, the results becoming less important and the relations becoming more (by considering a small threshold) and the matter of losing meaningful connections (big threshold amount) an optimum value should be calculated. In this study the amount of 0.16 has been selected as the threshold. In table 4-6 numbers less that the threshold amount are shown with the symbol *. Table 4-6: Connection matrix with regard to the amount of threshold * * * * * * * * 0.19 * * * * * 0.18 * COPY RIGHT 2013 Institute of Interdisciplinary Business Research 51

9 The Fifth Stage: As we proceed, by the help of matrix T the graph of cause and effect between factors is acquired. Picture 1-4 shows this diagram. Coefficient less Picture 4.1: Cause and effect graph between factors Table 4.7: Normal matrix T The weigh integrative matrix importance of to each other which was calculated by relations 15 and 16 in chapter 3 and are as described in table 8-4. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 52

10 Coefficient less ijcrb.webs.com Table 4.8: Initial matrix (initial W) weighs of factors The Sixth Stage: In the later stages, by applying the normalized matrix T which is presented in table 4.7 and also matrix (initial W), imbalanced matrix (W W ) was calculated with regard to relation 17 of chapter 3 as described in table 4.9. Table 4.9: Imbalanced matrix Coefficient less Coefficient less Total In the calculated imbalanced matrix, the column of normal balanced matrix is calculated by dividing each number to the total and the result is shown in table 4.10 Table 4.10: Normal balanced matrix (balanced W) COPY RIGHT 2013 Institute of Interdisciplinary Business Research 53

11 Coefficient less ijcrb.webs.com The normal balanced matrix (W balanced) is be exponent of 2 k+1 and the final or limited matrix is calculated, all the numbers of which in every row is equal with each other and equal to the criterion weight related to the same row. (Table 4.11) Table 4.11: The calculated weighs by ANP After obtaining the weight of factors and by using the mixture two methods DEMATEL and ANP, in the proceeding stages we shall use these weights in the VIKOR method. To apply the VIKOR method, the following stages should be conducted. Stage One: Forming the decision matrix by using the ideas of experts according to table 4.12 In this matrix the numbers in each square show the effect existing factor in the related column on the existing industry in the considered row. Table 4.12: The decision matrix Chemical industry Medical industry Metallic industry Essential metals industry Best Bad COPY RIGHT 2013 Institute of Interdisciplinary Business Research 54

12 Stage Two: Calculating the value of R and S by using relations 18 and 19 in chapter 3 as described in table 4.13 Table 4.13: Calculating the value of R and S S R Stage Three: Calculating the value of Q by using relation 20 in chapter 3 In this stage with regard to the Q compound function and the values two tables of R and S and taking V into consideration, the value of Q is calculated. With regard to the reliability of Q on the different values of V, the presented results were according to different values of V on the scale of 1-0 in table 4.14 Table 4.14: Calculating the value of Q Chemical industry Medical industry Metallic industry Essential metals industry Q(V=0) Q(V=0.1) Q(V=0.2) Q(V=0.3) Q(V=0.4) Q(V=0.5) Q(V=0.6) Q(V=0.7) Q(V=0.8) Q(V=0.9) Q(V=1) With regard to the above table under the agreement conditions meaning (V=1, 0.9, 0.8, 0.7) the medical industry is selected as the dominant industry. Under average agreement conditions (V=0.4, 0.5, 0.6) the essential metals industry is selected and under weak agreement conditions (V=0, 0.1, 0.2, 0.3) again the basic metal industry is chosen. In this stage for choosing the final option we will take action with regard to conditions which were declared in stage 8 in chapter 3 VICOR method COPY RIGHT 2013 Institute of Interdisciplinary Business Research 55

13 For the 3 different values of V, we shall investigate the following presented conditions: Q(V=1) Q(V=0.5) Q(V=0.2) Industry Chemical industry Medical industry Metallic industry Essential metals industry 1) V=0.2 As an agreed on solution the essential metals industry shall be selected due to the fact that it hold the minimum value of V in the rank list if the below two conditions exist: First condition (C1), the privilege of being acceptable: Q(a )-Q(a ) DQ In which a option holds the second place in the rank list of Q and DQ=1/(J-1) and J is the number of options /(4-1) The second condition (C2) stability of acceptable in decision making: The selected option should also be ranked in the best manner by using R,S As you can see in table 13-4 the essential metals industry is only dominant to the medical industry in the minimum individual deplorable status. With regard to the fact that only condition 2 has not been complied, in the below agreement status both medical and essential metals industries have been chosen. 2) V=0.5 First condition: /4 1 As you can see in this status the first condition has not been complied and selection is not possible. 3) V=1 First condition: /4 1 COPY RIGHT 2013 Institute of Interdisciplinary Business Research 56

14 Second condition: With regard to table of values of R and S it can be observed that group pleasantness status the second condition, at least, exists but the minimum individual deplorable status does not exist. With regard to investigation twofold conditions it could be said that in the maximum agreement status also like the minimum agreement status, essential metals and medical industries are the selected and dominant industries. 4-3 Capital Assets Pricing Model The results due to calculations of capital assets pricing depending on the industry are as described in the following tables. To obtain the expected according to the capital assets pricing first we have calculated beta based on the annual of industries and then ranked the industries according to the expected during the study course and the outcome se calculations is as follows in the below tables. The expected table by the capital assets pricing Industry Medicine Chemical Essential metals Metallic The Study Result The calculated weights by the mixture method of DEMATEL and ANP for factors are as described in the following tables Table 5.1: calculated weights for factors Factor Weight As it is shown, the macroeconomics with the weight of 0.22 and after that the financial with the weight of 0.20 have the highest weights and the currency with the weight of 0.09 has the lowest weight of all. And in comparison with the results COPY RIGHT 2013 Institute of Interdisciplinary Business Research 57

15 Wen-Rong and colleagues study (2011) they only differ in the score of currency. In the Wen-Rong study, currency had the highest weight after macroeconomics. In this study the four industries of metallic, essential metals, chemical and medical industries were selected and then by the use VIKOR method and the capital assets pricing the mentioned industries were ranked and the results se two methods are as described in the following tables. Table 5.2: Comparing the results two investigated methods Capital assets pricing Medical industry VIKOR Essential metals and medical industries Chemical industry Chemical industry 2 Essential metals industry Metallic industry 3 Metallic industry 4 Rank 1 With regard to table no. 5.2 in the VIKOR method the essential metals and medical industries and in the capital assets pricing the medical industry were selected as the dominant industries. COPY RIGHT 2013 Institute of Interdisciplinary Business Research 58

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