determining of stock investments with grey relational analysis

Expert Systems with Applications 38 (2011) 9186–9195

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Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Determining of stock investments with grey relational analysis

Cos�kun Hamzaçebi a,⇑, Mehmet Pekkaya b

a Karadeniz Technical University, Department of Industrial Engineering, Trabzon, Turkeyb Z. Karaelmas University, Department of Business Administration, Zonguldak, Turkey

a r t i c l e i n f o a b s t r a c t

Keywords:Grey relational analysisAnalytic Hierarchy ProcessFinancial ratioISEMulti-criteria decision making

0957-4174/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.eswa.2011.01.070

⇑ Corresponding author. Tel.: +90 4623772950.E-mail addresses: [email protected] (C. Ham

com (M. Pekkaya).

Selecting stock is important problem for investors. Investors can use related financial ratios in stockselection. These kind of worthy financial ratios can be obtained from financial statements. The investorscan use these ratios as criteria while they are selecting the stocks. Since dealing with more than onefinancial ratio, the investing issue becomes multi-criteria decision making (MCDM) problem for theinvestors. There are various techniques for solving MCDM problems in literature. In this study grey rela-tional analysis (GRA) is used for ordering some financial firms’ stocks which are in Financial Sector Indexof Istanbul Stock Exchange (ISE). Besides, because of the importance of criteria weights in decision mak-ing, three different approaches – heuristic, Analytic Hierarchy Process, learning via sample – were exper-imented to find best values of criteria weights in GRA process.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

As in decision process in a condition of lots of alternatives, adecision maker aims to conduct and optimize his goal. However,present-day problems must take into consider more than one cri-terion/goal simultaneously instead of only one criterion/goal.Techniques of multi-criteria decision making (MCDM) is improvedfor a solution of these kinds of problems.

So many techniques are developed for MCDM that have variousadvantages. Some of these techniques are Analytic Hierarchy Pro-cess (AHP), Analytic Network Process (ANP), Elimination et ChoixTraduisant la Realite (ELECTRE), Preference Ranking OrganizationMethod for Enrichment Evaluation (PROMETHEE), Technique forOrder Preference by Similarity to Ideal Solution (TOPSIS), grey rela-tional analysis (GRA), etc.

MCDM literature is quite vast and growing. This literature isespecially about product design, product selection, facility locationand facility layout planning, river basin planning, achievementorder, financial applications, etc. For example, Raju and Pillai(1999) employed ELECTRE II, PROMETHEE II, AHP, CompromiseProgramming and EXPROM-2 techniques to select the best riverbasin planning in Kerala, India. Feng and Wang (2000) experi-mented TOPSIS and GRA methods for performance evaluation ofTaiwan airlines and concluded that if financial ratios are consid-ered, performance evaluation for airlines can be more comprehen-sive. Zopounidis and Doumpus (2002) reviewed the literature ofMCDM techniques on financial decision making. Albadvi et al.

ll rights reserved.

zaçebi), mehpekkaya@gmail.

(2007) studied decision making in stock trading and set up anapplication on Iran Stock Exchange with technique of PROMETHEE.Loken (2007) gave a brief knowledge about the usage of MCMDtechniques in energy planning problems. Yüksel and Dagdeviren(2007) demonstrated a process which uses the ANP for quantita-tive SWOT analysis that can be performed even when there isdependence among strategic factors. Kosmidou and Zopounidis(2008) used the method of PROMETHEE to evaluate the perfor-mance of commercial and cooperative banks, as a kind of creditrisk assessment of bank in Greece with the aid of specific financialratios.

One of the methods of MCDM technique used for decision mak-ing recently is GRA. GRA is quantitative analysis to show the sim-ilarity and dissimilarity between the reference series andalternative series. The alternative series which has the most closedsimilarity to the reference series is the best alternative for theproblem in hand. Some of the studies that used GRA are as follows.Feng and Wang (2000) show the usage of financial ratios to con-struct a performance evaluation process for airlines. Chang,Hwang, and Doong (2000) presented the methodology which usesthe GRA for the optimization of the injection molding processparameters of short glass fiber reinforced polycarbonate compos-ites. Authors used the GRA technique to select the representativeindicators. Cheng and Wang (2004) suggested grey Analytic Hierar-chy Process to analyze hazard potential of typhoon damage. Lin,Chang, and Chen (2006) developed a systematic algorithm for opti-mizing the multi-response quality characteristics in complemen-tary metal-oxide semiconductor ion implantation experiments interm of overall product quality. Li, Yamaguchi, and Nagai (2007)proposed a grey-based approach to deal with the supplier selectionproblem. Kuo et al. (2007) used GRA to select the facility layout.

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C. Hamzaçebi, M. Pekkaya / Expert Systems with Applications 38 (2011) 9186–9195 9187

Kung and Wen (2007) used six financial indicators to classify 20items of financial ratios as research variables through the GRA, tofind the significant financial ratio variables and other financialindicators affecting the financial performance of venture capitalenterprises in Taiwan. The authors applied Grey Decision-Making(GDM) to arrange the total performances of the sample venturecapital enterprises in order. Lin, Lee, and Chang (2009) used GRAto develop diagnosis models to identify the normal objects orconditions.

This study focused on to set criteria weights while determiningstock investments with GRA technique. For that reason three dif-ferent approaches are taken in consideration. One of them is set-ting the criteria weights heuristically; the other one is using AHP.The third approach is new and based on the experimental learning.An application is experimented for stocks of financial firms ofIstanbul Stock Exchange (ISE). The rest of this study is as follows.In Section 2, financial ratios that used in this study and importancein stock selection are presented. In Section 3, a brief knowledgeabout AHP and GRA is given. Section 4 contains an application offinancial firms of ISE. Section 5 is conclusion.

2. Financial ratios and stock selection

Investment decisions are delicate and gradual for investors. Foran ideal investment, firstly, investment decisions are made vialooking for global conditions and local area conditions accordingto political and economical necessities. Then, condition of the sec-tor are searched by requesting profitability, opportunity forgrowth, legal conditions, etc. At last, selecting asset and stock isdetermined according to its balance sheet and income statements.Balance sheet is snapshot of the firm at a given moment, usuallyannually and income statements summarizes the firm revenuesand expenses and the difference between the two (Brealey, Myers,& Marcus, 2001). Financial ratios are a kind of ratio analysis and areformed from balance sheet and income statement of the company.There are so much financial ratios exist, but only about 20 of themare financially meaningful. Some of these ratios show futuregrowth expectations; some show credit risk of firm, and someshow cheapness of stock price of firms in market, etc.

Stock investment decisions are determined according to bothexpected cash income (by future dividend payment and return of

Table 1Selected financial ratio as criteria in decision making.

Selected financialratio (symbol)

Ratio calculation fromfinancial statements

Desiredquantity ofratio

Class and informat

Price/earning ratio(P/E)

Market price per shareEarning per share

Minimumvalue

Stock market ratiothat stock is. Accorcheapest stock to iproduces desiringMarket price is marecorded at income

Market/book ratio(M/B)

Market price per shareBook value per share

Minimumvalue

Return on totalassets (ROA)

Net income after taxesTotal assets

Maximumvalue

Profitability ratiosstocks which havethe same quantityprofit margin on

sales (PMS)

Net income after taxesSales

Maximumvalue

Quick (acid-test)ratio (QR)

Current assets�InventoriesTotal liabilities

Maximumvalue

Liquidity ratios mconverted into cashthe highest QR and

Total dept ratio(TDR)

Total liabililitesTotal asset

Closeness of%50

Leverage ratios shdeveloping countryaccording to how bto lend the firm mobigger TDR suffersbigger TRD is havinleverage either to m

stock) and risk of it. Then, price assessment models of stocks canbe expressed in terms of future dividend payments of the firm,opportunity of the firm growth, financial ratios of the firm so on.

In practice, especially small investors select the stock in marketusually by investigating the financial ratios of the stocks. It is alsowidely accepted by academic literature. Financial ratios are used incompany performance and financial performance evaluation(Deng, Yeh, & Willis, 2000; Feng & Wang, 2000; Kung & Wen,2007), in stock selecting and trading (Albadvi et al., 2007), in finan-cial failure, credit risk assessment decisions, business bankruptcyprediction and business bankruptcy prevention (Park & Han,2002; Sun & Li, 2009; Xu & Wang, 2009), in financial valuationand credit analysis of companies (Al-Ajmi, 2008; Dagilen et al.,2006) and so on. However, in some of these studies, different crite-ria in addition to the financial ratios are used.

Large quantities of financial data can be summarized by finan-cial ratios. Moreover, performance of a firm among the otherscan be compared according to financial ratios. It is possible to findlots of meaningful financial ratios from financial statements. Theseratios can be classified as stock market ratios, efficiency ratios,profitability ratios, liquidity ratios and leverage ratios. There ismore than one ratio in the each of these ratio classes. These ratioclasses can be used for assessment goals. However, using morefinancial ratios as criteria makes problem more complicated. Thus,studying with ratios which can represent its class leads to makemodeling simpler as well as make model less complex. At thispoint, selection of financial ratios which ensure the least informa-tion lost in its class is desired and searched.

Selected financial ratios in this study were defined in Table 1,detailed information can be found in Brealey et al. (2001) andBrigham (1986).

As it deduced from Table 1 financial ratios give meaningfulknowledge about the status of the firms. So the usage of financialratios as major criteria in decision process of stock selection isfair.

3. MCDM techniques

This section is about the two of the MCDM techniques whichused in this study. These techniques are AHP and GRA. In this studyAHP is not used for decision making but it is used for determining

ion about financial ratios

s give idea to share holders about market performance of stock and how cheapdingly, investors can compare stocks P/E and M/B ratios and can search thenvest. The cheapest stock usually has to have the least P/E and M/B ratios oftenminimum P/E and M/B values.rket value of firm in stock exchange. Earning is net profit of firm for the year,

statements. Book value is net worth of the firm according to the balance sheetmeasure firm’s return on its investments. Stock holders of the firm desire to have

the highest ROA and PMS than the firm will have much profit with respect to haveasset or sale

easure the ability of easy cash circulation of the firm. Liquid assets can bequickly and cheaply. Stock holders of the firm desire to have stocks which havethan the firm will have less financial risk

ow the dept condition of company. TDR is desired to close about%50 especially forlike Turkey. If TDR ratio is much more than 0.50, the firm is perceived as risky

ig the ratio is. The firm that has bigger TDR, creditors of the firm would reluctantre money, or cost of dept of the firm increase. Moreover, when the firm which hasloss, the capital of firm may get in event of liquidation. So, the firm which hasg so much financial risk. On the other hand, shareholders may seek higheragnify earnings or fear of losing control degree of the firm

Table 2Scale numbers.

Intensity ofimportance

Definition Explanation

1 Equalimportance

Two activities contribute to the objectiveequally

2 Weak orslight

3 Moderateimportance

Experience and judgment slightly favor oneactivity over another

4 Moderateplus

5 Strongimportance

Experience and judgment strongly favor oneactivity over another

6 Strong plus7 Very strong

importanceAn activity is favored very strongly overanother

8 Very, verystrong

9 Extremeimportance

The evidence favoring one activity overanother is of the highest possible order ofaffirmation

9188 C. Hamzaçebi, M. Pekkaya / Expert Systems with Applications 38 (2011) 9186–9195

of criteria weights in GRA process. So the following subsectionsgive a brief knowledge about the AHP and GRA.

3.1. AHP

AHP was introduced by Satty (1980) and until this time it wastaken in consideration for various MCDM problems. AHP is aneigenvalue approach to the pair-wise comparisons. It supports amethodology to calibrate the numeric scale for the measurementof quantitative as well as qualitative performances (Vaidya &Kumar, 2006). The method is described by Saaty (2008) as in thefollowing steps:

1. Defining the problem and knowledge seeking.2. Determining the frame of the decision hierarchy: the top level

presents the goal of the decision, the intermediate levels showthe criteria and the lowest level presents the set of alternatives(Fig. 1).

3. Constructing the pair-wise comparison matrices: the compari-son matrices should be constructed for the criteria and for thealternatives according to each criterion.

4. Obtain the weights from the comparison matrices.

The AHP method uses scale numbers which indicate how manytimes more important or dominant one element is over anotherelement with respect to the criterion or property which they arecompared. Table 2 shows the scale numbers, their definitions andexplanations.

In addition to the Table 2, if activity i has one of the above num-bers assigned to it when compared with activity j, then j has thereciprocal value when compared with i (Saaty, 2008).

When pair-wise comparison matrixes are created, the weightscan be obtained from the comparison matrices if it is consistent.Let An�n is comparison matrix. The weight vector can be obtainedby solving Eq. (1).

Aw ¼ kmaxw ð1Þ

where kmax is the largest eigenvector of A matrix. kmax ¼ n if the pair-wise comparison is completely consistent. However all comparisonmatrixes do not guarantee the complete consistence. For this reasonthe consistency index (CI) and consistency ratio (CR) should bedetermined. The CR shows a measure of acceptance of the pair-wisecomparison. If the CR is less than 0.1, the comparison matrix will beacceptable. The CI and CR can be calculated by the followingequation

CI ¼ ðkmax�nÞðn�1Þ

CR ¼ CIRI

ð2Þ

Goal

Criterion 1 Criterion 2

Alternative 1 Alternative 2 Alternative

Fig. 1. The basic representation of hierarchica

In Eq. (2), RI is random index. RI values change according to the ma-trix dimension (n). Some of RI values are for various n as follows:

C

3

l fr

n

riter

A

ame (

1

ion 3

lternat

for 4 Cri

2

ive 4

teria an

3

Cri

Alter

d 5 Alter

4

terion 4

native

natives)

5

5

.

6
7 8 9
RI
0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45
The aim of this study is not to give details of AHP; detailed informa-tion about AHP and its various applications can be found in Saaty(1994) and Vaidya and Kumar (2006).

3.2. GRA

GRA is a tool of grey system theory for analyzing the relation-ship between a reference series and other series. Grey system the-ory was developed by Deng (1989). GRA aims to measure thesimilarity between the compared series. The GRA methodology isas follows:

1. Define the problem: alternatives (i = 1, . . . , m), criteria (j =1, . . . , n),

vi ¼ ðvið1Þ;við2Þ;við3Þ; . . . ;viðnÞÞ ð3Þ


2. Determine the reference series: reference series may come intoexistence via the minimum or the maximum – if the criterionrequires the maximization (minimization) the reference seriesvalue of the related criterion is maximum (minimum) value ofthe alternative series – values of the alternative series or a nom-inal value.

vo ¼ ðv0ð1Þ;v0ð2Þ;v0ð3Þ; . . . ;v0ðnÞÞ ð4Þ

3. Normalization: in order the make the values free of unit thenormalization process is done. This process is called grey rela-tional generating. The normalization process can occur in threetypes:i. Higher is better:

viðkÞ ¼v0

i ðkÞ �minv0i ðkÞ

maxv0i ðkÞ �minv0

i ðkÞð5Þ

ii. Lower is better:

viðkÞ ¼maxv0

i ðkÞ � v0i ðkÞ

maxv0i ðkÞ �minv0

i ðkÞð6Þ

iii. Nominal is better:

viðkÞ ¼ 1� jv0i ðkÞ � v0j

max v0i ðkÞ � v0

ð7Þ

where xiðkÞ is the value after the normalization, xoi ðkÞ is the value

before the normalization, and min xoi ðkÞ, max xo

i ðkÞ are the small-est and largest values of the kth response before the normaliza-tion respectively.

4. Calculate the grey relational coefficient: grey relational coeffi-cient (GRC) is an indicator of the similarity between the refer-ence series and alternative series.

eðv0ðkÞ;viðkÞÞ ¼Dmin þ nDmax

DoiðkÞ þ nDmaxð8Þ

5. Calculate the grey relational grade: grey relational grade (GRG)is used for overall evaluation of alternatives depending on allcriteria. If the all criteria have equal importance, the GRG canbe calculated by Eq. (9), for different importance degree of thecriteria, the GRG can be calculated by Eq. (10).

cðv0;viÞ ¼1n

Xn

k¼1

eðvoðkÞ;viðkÞÞ ð9Þ

cðv0;viÞ ¼Xn

k¼1

wiðkÞeðvoðkÞ;viðkÞÞ ð10Þ

ISE Financial

20000

30000

40000

50000

60000

70000

80000

90000

100000

Mar

-04

May

-04

Jul-

04

Oct

-04

Dec

-04

Mar

-05

May

-05

Jul-

05

Sep

-05

Fig. 2. Financial

The GRG values are used to rank the alternatives according tothe similarity to reference series. The higher GRG value indicatesthe higher similarity.

4. Application

4.1. Data and methodology

The application is on finance sector especially bank sectorstocks of Istanbul Stock Exchange (ISE) firms. Consolidated balancesheet and income statements of finance sector stocks were takenbetween the years of 2003–2006 (ISE, 2008; OYAK, 2008). Marketprices of the stocks were taken as average price of May and averageprice of December for the years of 2004–2007 used for calculatingthe stocks return (OYAK, 2008). Market stock price of May also wasused for calculating the P/E and the M/B ratios.

Market stock price period for calculating the return period ofthe stocks was taken between May–December periods of each2004–2007 years. Some financial sector stocks were not usedbecause of missing data stem from the financial ratio and/orthe stock value and/or abnormal deviation of them. Stocks ofbanks are AKBNK, FINBN, FORTS, GARAN, SKBNK, TEBNK, TEKST,HALKB, VAKBN and YKBNK. Insurance firms are AKGRT, ANHYT,ANSGR, GUSGR and YKSGR. Stocks of other financial firms areASYAB, ISFIN and ISMEN. The raw data used in GRA calculationsare given Appendix Tables A1–A4. The financial ratios of thesedata were normalized according to wishes that defined inTable 1.

In Turkey, there was a fluctuation and high variance in marketstemming from foreign exchange rate which can be observed onFinancial Index of ISE related with stocks of financial sector onsummer, 2007. For the other periods of data, market was peacefulas seen Fig. 2. The data used for Fig. 2 were taken from web site ofIBS (IBS, 2008).

The firms which have stocks in ISE should declare the previousyear balance sheet before the May of current year. So, financial ra-tios were calculated according to spot market prices of stock onMay and financial statements of previous year data. For example,for calculating the stock’s financial ratios for 2004, the averagestock market price of May-2004 and the firm’s financial statementsof 2003 were used. The financial ratios were used as criteria in GRAdecision making and calculating GRG. GRG of each stock was usedfor ordering the stocks among the others.

Endex

Dec

-05

Feb

-06

May

-06

Jul-

06

Sep

-06

Dec

-06

Mar

-07

Jun

-07

Au

g-0

7

No

v-0

7

High variance

index of ISE.


The average stock market price of December-2004 was used forcalculating the return of the stock for the May–December period ofthe year. The return period of the stock was ordered up to down.Ordered stock series according to GRG obtained from the financialratios and ordered stock series according to return of the stockswas compared. The success degree of GRA ordering techniquewas assessed by this comparison. This issue was done also forthe years of 2005, 2006 and 2007.

Because of importance of the criteria weights in GRA decisionmaking, in this study firstly, GRA was implemented for three sce-narios which have various criteria weights stated heuristically bythe decision maker in order to calculate GRG for each year. Sec-ondly, AHP based GRA was implemented, AHP was used to deter-mine criteria weights. Thirdly a new criteria weights determiningapproach was suggested. This approach was called LEvSA (LEarningvia SAmple). At the end, found results with three approaches werecompared.

4.2. Criteria weight determination with three scenarios

The stock grading and ordering was fulfilled according to threescenarios which have various criteria weights. These criteria

Table 3Criteria weights of three scenarios for GRA calculations.

Financial Ratio Scenario 1 Scenario 2 Scenario 3

P/E 0.300 0.200 0.350M/B 0.300 0.200 0.400ROA 0.075 0.150 0.050PMS 0.175 0.150 0.100QR 0.075 0.150 0.050TDR 0.075 0.150 0.050

Table 4Example calculation for Scenario 1 with using 2005 data.

Order of stocks accordingto actual return

Order of stocksaccording to GRG

Difference/deviationsbetween the orders

8 6 24 4 07 1 63 9 6

12 12 010 10 011 8 3

2 3 16 11 59 7 25 5 01 2 1

Table 5Deviations between the orders for 2004 with 12 stocks.

Deviation Scenario 1 Scenario 2 Scenario 3

ADeva CumDevb (%) ADev CumDev (%) ADev CumDev (%)

0 2 16.77 3 25.00 4 33.331 0 16.77 2 41.67 0 33.332 2 33.33 2 58.33 2 50.003 2 50.00 0 58.33 3 75.00More

than 36 100 5 100 3 100

a ADev: amount of deviation.b CumDev: cumulative deviation (%).

weights were adjusted via importance of financial ratios by expertsight and given in Table 3. For each of these scenarios, GRG of eachstock were calculated. The stocks were ordered up to down relatedto GRG for each scenario separately. This order was compared withreturn order of each stock. The ordering success of comparison be-tween actual order and determined order by GRA technique wasassessed. This operation was implemented for the years of 2004–2007 separately.

For example in Table 4, order of stocks according to stock returnat market and order of stocks according to grey coefficients wereused for calculating the difference between the orders. If the differ-ence is minimized, GRA’s power will increase.

General results of order comparison were resumed in Tables 5–8 and related graphs were given Figs. 3–6. The order estimationmade by Scenario 1 and 3 were more successful than Scenario 2,since the deviation from the actual order is less. Thus it can be de-duced that financial ratio of P/E and M/B are dominantly moreimportant ratios than others.

4.3. Criteria weight determination with AHP

As mentioned before the financial ratios were used as criteria torank the stocks. In order to determine factor weights with AHP,firstly, the comparison matrix of the criteria (financial ratios)should be created. This comparison matrix is obtained by opinionof financial course lecturer. This matrix is showed below.



ADev CumDev (%) ADev CumDev (%) ADev CumDev (%)

0 4 33.33 2 16.67 4 33.331 2 50.00 4 50.00 2 50.002 2 66.66 0 50.00 2 66.673 1 75.00 3 75.00 0 66.67More

than 33 100 3 100 4 100




0 1 10.00 0 0.00 1 10.001 4 50.00 3 30.00 4 50.002 1 60.00 4 70.00 1 60.003 2 80.00 2 90.00 2 80.00More

than 32 100 1 100 2 100




0 1 6.67 3 20.00 2 13.331 3 26.67 1 26.67 2 26.672 2 40.00 1 33.33 3 46.673 4 66.67 1 40.00 2 60.00More

than 35 100.00 9 100.00 6 100.00

Scenario 1

0

2

4

6Scenario 2

0

2

4

6

"

Scenario 3

0

2

4

6

0 1 2 3 3+ 0 1 2 3 3+ 0 1 2 3 3+

Fig. 3. Deviations between the orders for 2004 with 12 stocks.

Scenario 1

0

2

4

6Scenario 2

0

2

4

6Scenario 3

0

2

4

6

0 1 2 3 3+ 0 1 2 3 3+ 0 1 2 3 3+


Scenario 1

2

4

6Scenario 2

0

4

6Scenario 3

0

2

4

6

0 1 2 3 3+ 0 1 2 3 3+ 0 1 2 3 3+0

2


Scenario 1

0

2

4

6

8Scenario 2

0

2

4

6

8

10Scenario 3

0

2

4

6

8

0 1 2 3 3+ 0 1 2 3 3+ 0 1 2 3 3+



P/E
M/B ROA PMS QR TDR
P/E
1.00 2.00 8.00 5.00 9.00 7.00 M/B 0.50 1.00 7.00 4.00 7.00 5.00 ROA 0.13 0.14 1.00 0.33 1.00 0.50 PMS 0.20 0.25 3.00 1.00 3.00 2.00 QR 0.11 0.14 1.00 0.33 1.00 1.00 TDR 0.14 0.20 2.00 0.50 1.00 1.00
Using this comparison matrix the following results were found:CI = 0.02 and CR = 0.02. For the CR is less than 0.1 the pair-wisecomparison is acceptable and the weight vector which will be ob-tained from this comparison is employable. The obtained weightvector is as follows:

P/E
M/B ROA PMS QR TDR
0.443
0.301 0.042 0.108 0.046 0.060
Figs. 7–10 show deviations between the orders of AHP sorting andsorting as to actual stock returns.

4.4. Criteria weight determination with LEvSA

While implementing the LEvSA, data of the year 2004 were usedfor weights determining and the other years’ data used for testing.The first step of the modeling phase is to make grey the actualstock return values. Then, LEvSA aims to minimize the differencebetween GRGs of actual stock returns and GRGs obtained fromfinancial ratios. LEvSA model can be expressed as follows:

MinPm

j¼1ðaj � ojÞ2

Pn

k¼1wkxkj ¼ oj; j ¼ 1;2; ::;m

Pn

k¼1wk ¼ 1

wk P 0

ð11Þ

Deviation ADev CumDev

0 4 33.33%

1 0 33.33%

2 1 41.67%

3 3 66.67%

More than 3 4 100%

AHP

0

2

4

6

0 1 2 3 3+

Fig. 7. Deviations between the orders for 2004 with 12 stocks via AHP.


0 4 33.33%

1 4 66.67%

2 0 66.67%

3 0 66.67%

More than 3 4 100%

AHP

0

2

4

6

0 1 2 3 3+



0 1 10.00%

1 3 40.00%

2 2 60.00%

3 2 80.00%

More than 3 2 100%

AHP

0

2

4

6

0 1 2 3 3+



0 2 13,33%

1 2 26,67%

2 1 33,33%

3 3 53,33%

More than 3 7 100,00%

AHP

0

2

4

6

8

0 1 2 3 3+



where, aj is GRG value of jth actual stock returns, oj is GRG valueof jth stock obtained by financial ratios, wk is the weight of kthfinancial ratio and xkj is the GRC of kth financial ratio and jth

stock.The criteria weight vector determined by LEvSA is as follows:

P/E
M/B ROA PMS QR TDR
0.785
0.088 0.025 0.101 0.000 0.000
The criteria weight vector found by LEvSA was calculated withusing the data of 2004. According to this criteria weight vector,GRGs of each stock were calculated for 2004, 2005, 2006 and2007 separately. Figs. 11–14 show deviations between the ordersof GRG values obtained by LEvSA and GRG values of actual stockreturns.

4.5. Compared results

Stocks were ordered according to stated weights by three ap-proaches (heuristically, AHP, LEvSA) separately. The used weightsby these approaches are listed in Table 9.

In order to measure ranking power of three approaches Spear-man rank-order correlation was used. The Spearman rank-ordercorrelation is most commonly used for nonparametric measureof the correlation between two variables. The Spearman rank-ordercorrelation formulation is as follows (Aczel, 1993):

rs ¼ 1� 6ðPn

i¼1D2i Þ

n � ðn2 � 1Þ ð12Þ

where, rs is the Spearman rank-order correlation coefficient, D isrank deviation of ith stock, and n is the number of stocks in the ser-ies. This formula penalizes deviations tightly.


0 0 0.00%

1 6 50.00%

2 1 58.33%

3 2 75.00%

More than 3 3 100%

LEvSA

0

2

4

6

0 1 2 3 3+

Fig. 12. Deviations between the orders for 2005 with 12 stocks via LEvSA.


0 2 20.00%

1 4 60.00%

2 1 70.00%

3 1 80.00%

More than 3 2 100%

LEvSA

0

2

4

6

0 1 2 3 3+



0 4 26,67%

1 3 46,67%

2 2 60,00%

3 1 66,67%

More than 3 5 100,00%

LEvSA

0

2

4

6

0 1 2 3 3+


Table 9Determining the criteria weights for GRA calculations.

Financialratio

By heuristically ByAHP

By LEvSA of year2004

Scenario1

Scenario2

Scenario3

P/E 0.3000 0.2000 0.3500 0.4435 0.7852M/B 0.3000 0.2000 0.4000 0.3010 0.0885ROA 0.0750 0.1500 0.0500 0.0416 0.0251PMS 0.1750 0.1500 0.1000 0.1078 0.1012QR 0.0750 0.1500 0.0500 0.0455 0.0000TDR 0.0750 0.1500 0.0500 0.0606 0.0000

Table 10Comparisons of results with calculated spearman rank correlation values.

Period Table value(0.05)

Scenario1

Scenario2

Scenario3

AHP LEvSA

2004 0.497 0.441 0.294 0.525 0.483 0.7412005 0.497 0.594 0.552 0.601 0.559 0.5242006 0.564 0.539 0.624 0.539 0.576 0.6492007 0.441 0.225 �0.157 0.254 0.243 0.268


0 4 33.33%

1 4 66.67%

2 0 66.67%

3 2 83.33%

More than 3 2 100%

LEvSA

0

2

4

6

0 1 2 3 3+



Spearman rank correlation is calculated with using orderedstock series. First of these series is models outputs which are calcu-lated from GRA technique and the other is actual outputs obtainedfrom stock returns. The Spearman rank correlation coefficient wascalculated from the rank deviations of these two ordered series.These coefficients and their significances at significant levela = 0.05 are given in Tables 10.

Table 10 shows that LEvSA is really better than the others. Actu-ally, this is a normal situation for the year 2004 because learningperiod of LEvSA is 2004. In order to see LEvSA’s power, the testyears’ (2005, 2006, and 2007) data should be considered. AHPand LEvSA are meaningful for all test years but the others not.These results are given in Table 11.

It can be deduced from Table 11 that only LEvSA is meaningfulfor all years but 2007 among all approaches. The year of 2007 hadfluctuations as it can be seen in Fig. 2. So that may produce unex-pected situations. However, Spearman rank correlation coefficient

Table 11Performance comparisons: significance of spearman rank correlations between orderGRG values and order of stock returns.

Period Scenario 1 Scenario 2 Scenario 3 AHP LEvSA

2004 Not exists Not exists Exists Not exists Exists2005 Exists Exists Exists Exists Exists2006 Not exists Exists Not exists Exists Exists2007 Not exists Not exists Not exists Not exists Not exists


is not sufficient while speaking about the power of approaches.Although there is not a correlation between rank of stocks foundby LEvSA and actual return, the deviations of the rank series ismore satisfactory then others. This can be seen in Figs. 6, 10 and14. The count of deviation which has 2 or less value is 9 for LEvSAwhile 5 for AHP, 6 for Scenario 1, 5 for Scenario 2 and 7 for Scenario3. Well, why the Spearman correlation coefficient is not meaning-ful for 2007 also for LEvSA? Spearman correlation coefficient is af-fected hard from extreme deviations. In 2007, there are twoextreme deviations stemming from unexpected behavior of thesetwo stocks.

For the years 2005 and 2006; AHP, LEvSA and Scenario 2 (heu-ristic approach) give satisfactory results. However when the signif-icance level changes – for example when n = 10 and a = 0.025 thentable value = 0.648 – only LEvSA selection is meaningful for year2006. Hence, when generally speaking it is not wrong to say LEvSAhas better performance among the others.

5. Conclusion

In this study, stock selection issue was considered as MCDMproblem. The financial ratios of firms were deemed as criteria

Table A1Used data of 2004.

P/E M/B ROA PMS

AKBNK 5.5770 1.4808 0.0454 0.3583AKGRT 11.9712 2.0763 0.0933 0.0559ANHYT 4.6152 1.8254 0.0337 0.0300ANSGR 3.9463 1.1625 0.0850 0.0623FINBN 8.3064 0.9244 0.0090 0.2959FORTS 3.0520 0.7370 0.0363 0.2840GARAN 10.5776 1.4335 0.0148 0.1581SKBNK 1.9867 0.7413 0.0260 0.1589TEBNK 5.7132 0.8623 0.0113 0.1137TEKST 15.6176 0.7834 0.0049 0.0373YKBNK 29.9051 1.2469 0.0063 0.0550GUSGR 7.9731 1.0266 0.0433 0.0157


P/E M/B ROA PMS

AKBNK 10.1102 1.6307 0.0282 0.2256ANHYT 4.7748 1.4751 0.0334 0.0306ANSGR 3.2574 1.3851 0.1064 0.3168FINBN 8.3427 2.0108 0.0208 0.2063FORTS 32.9988 2.0551 0.0075 0.0613GARAN 15.2559 1.9418 0.0084 0.1207SKBNK 6.2096 1.7934 0.0239 0.1219TEBNK 8.3832 1.0787 0.0108 0.1065TEKST 52.6897 1.6779 0.0031 0.0291YKSGR 21.0204 1.5317 0.0226 0.0114GUSGR 15.5960 1.2449 0.0261 0.0094ISFIN 4.8802 1.2698 0.0427 0.4268

while selecting the best alternative stock among the stocks offirms. The GRA technique was preferred for solving the problem.The GRA process requires the optimization of criteria weights likethe other MCDM techniques, so three different approaches wereconsidered. One of them is called LEvSA and suggested in this studyas a new approach for determining the criteria weights. The otherapproaches are AHP and heuristic scenarios.

The compared results showed that heuristic scenarios cannotgive satisfactory result for investors, because the weight determin-ing operation is subjective and does not well grounded. In order toovercome this problem AHP may help decision maker, however italso involves subjectivity because of comparison matrix. LEvSA –suggested approach in this study – is based on learning relation-ship in data structure and determining weights according to thisrelationship. The compared results showed that LEvSA is betterthan the others in generally.

Determining of criteria weights gave information of the impor-tance of each financial ratio while selecting the stocks. It is con-cluded that P/E is the most important ratio for financial stockselection in ISE. PMS and M/B have secondary importance on deci-sion. The others do not have noticeable importance on financialstock selection in ISE. These results depict that the market inves-tors have a tendency to take into consideration essentially theseimportant ratios.

The financial ratios are used for stock selection generally in pro-duction sector. However, found results advocate that financial ratiocan be used also financial sector stocks. The further researches maydeal with the usage of financial ratios in different sectors and theircomprehensive comparison in stock selection.

Appendix A

Tables A1–A4

QR TDR Return of May–December 2004 (%)

0.6393 0.8290 49.300.9154 0.4619 30.380.9841 0.9149 53.690.7735 0.7115 72.880.1826 0.9190 84.910.3851 0.8496 40.600.7849 0.8905 34.430.5556 0.9304 95.140.3685 0.9253 67.760.3327 0.9020 33.990.3168 0.8485 26.060.4546 0.6636 53.75

QR TDR Return of May–December 2004 (%)

0.5752 0.8249 92.050.9960 0.8918 127.490.6769 0.7498 92.550.2737 0.9135 128.380.3561 0.8801 45.250.2021 0.9344 59.690.3108 0.9173 53.350.4564 0.9158 194.780.2966 0.9037 105.890.5172 0.6900 66.350.4626 0.6735 118.610.9044 0.8360 199.51


P/E M/B ROA PMS QR TDR Return of May–December 2004 (%)

AKBNK 13.9829 3.0753 0.0262 0.2329 0.5379 0.8809 19.63AKGRT 26.9477 1.1281 0.0353 0.1892 0.6740 0.1560 7.84ANHYT 38.3561 3.0153 0.0111 0.0460 0.8201 0.8582 �8.97ASYAB 16.2308 3.7555 0.0350 0.3039 0.2685 0.8487 35.88FINBN 10.5918 3.2754 0.0350 0.3046 0.3674 0.8867 0.19FORTS 18.4382 1.9783 0.0125 0.1060 0.3498 0.8838 3.87GARAN 12.2501 2.9621 0.0204 0.2097 0.3564 0.9158 55.47ISFIN 10.3204 1.8000 0.0300 0.1845 0.9262 0.8278 9.48SKBNK 25.9063 2.6811 0.0104 0.0819 0.4433 0.8999 73.17TEBNK 16.9341 3.3886 0.0120 0.1281 0.3820 0.9402 5.57TEKST 24.0998 1.0846 0.0053 0.0561 0.3889 0.8833 55.84YKSGR 44.3982 4.2546 0.0339 0.0503 0.5233 0.6460 �3.64ISMEN 21.0707 2.1723 0.0290 0.0007 2.3111 0.7185 �2.97HALKB 12.1650 2.7446 0.0251 0.1894 0.1430 0.8889 28.21VAKBN 11.7421 2.0035 0.0206 0.1727 0.5202 0.8790 11.55


P/E M/B ROA PMS QR TDR Return of May–December 2004 (%)

AKBNK 13.8300 3.1627 0.0265 0.2681 0.4920 0.8842 �2.88AKGRT 24.7857 1.0147 0.0355 0.2438 1.1868 0.1324 �11.74ANHYT 21.7218 2.8543 0.0202 0.0665 0.9850 0.8460 �0.14FINBN 13.9803 4.1447 0.0262 0.2412 0.2801 0.9115 9.01FORTS 24.4353 2.6270 0.0144 0.1152 0.3127 0.8664 �22.73GARAN 14.2617 2.8093 0.0186 0.2036 0.3669 0.9055 �8.36SKBNK 30.0808 3.6851 0.0120 0.0704 0.4718 0.9019 �37.04TEBNK 15.5226 3.1255 0.0147 0.1763 0.3890 0.9271 �9.90TEKST 58.0735 3.4017 0.0048 0.0581 0.2064 0.9185 �12.43VAKBN 14.7343 2.1805 0.0183 0.1673 0.4899 0.8766 �13.89


References

Aczel, A. D. (1993). Complete business statistics (2d ed.). Boston: Irwin Inc.Al-Ajmi, J. (2008). The usefulness of corporate governance and financial ratios to

credit and financial analysts: Evidence from Bahrain. European Journal ofEconomics. Finance and Administrative Sciences, 11, 107–125.

Albadri, A., Chaharsooghi, S. K., & Esfahanipour, A. (2007). Decision making in stocktrading: An application of PROMETHEE. European Journal of OperationalResearch, 117, 673–683.

Brealey, R. A., Myers, S. C., & Marcus, A. J. (2001). Fundamentals of corporate finance(3rd ed.). Singapore: McGraw-Hill International Edition.

Brigham, E. F. (1986). Fundamentals of financial management (4th ed.). New York:CBS Collage Publishing.

Chang, S. H., Hwang, J.-R., & Doong, J.-L. (2000). Optimization of the injectionmolding process of short glass fiber reinforced polycarbonate composites usinggrey relational analysis. Journal of Materials Processing Technology, 97, 186–193.

Cheng, S. P., & Wang, R. Y. (2004). Analyzing hazard potential of typhoon damage byapplying grey analytic hierarchy process. Natural Hazards, 33, 77–103.

Dagilien, L., Kovaliov, R., Maþerinskas, J., & Simanavi, Z. (2006). The application offinancial valuation methods in investment decisions. Vadyba/Management,2(11), 28–33.

Deng, H., Yeh, C. H., & Willis, R. J. (2000). Inter-company comparison using modifiedTOPSIS with objective weights. Computers and Operations Research, 27, 963–973.

Deng, J. L. (1989). Introduction to grey system theory. The Journal of Grey System,1(1), 1–24.

Feng, C. M., & Wang, R. T. (2000). Performance evaluation for airlines including theconsideration of financial ratios. Journal of Transport Management, 6, 133–142.

IBS (2008). Available from: http://analiz.ibsyazilim.com.ISE (2008). Istanbul stock exchange web site. Available from: www.imkb.gov.tr.Kosmidou, K., & Zopounidis, C. (2008). Measurement of bank performance in

Greece. South-Eastern Europe Journal of Economics, 1, 79–95.Kung, C. Y., & Wen, K. L. (2007). Applying grey relational analysis and grey decision-

making to evaluate the relationship between company attributes and itsfinancial performance – A case study of venture capital enterprises in Taiwan.Decision Support Systems, 43, 842–852.

Kuo, Y., Yang, T., & Huang, G. W. (2008). The use of grey relational analysis in solvingmultiple attribute decision-making problems. Computers & IndustrialEngineering, 55, 80–93.

Li, G. D., Yamaguchi, D., & Nagai, M. (2007). A grey-based decision-making approachto the supplier selection problem. Mathematical and Computer Modelling, 46,573–581.

Lin, C. T., Chang, C. W., & Chen, C. B. (2006). A simple approach to solvingmulti-response quality characteristic problems in CMOS ion implantation.International Journal of Advanced Manufacturing Technology, 28(5–6),592–595.

Lin, Y. H., Lee, P. C., & Chang, T. P. (2009). Practical expert diagnosis model based onthe grey relational analysis technique. Expert Systems with Applications, 36(2),1523–1528.

Loken, E. (2007). Use of multicriteria decision analysis methods for energy planningproblems. Renewable and Sustainable Energy Reviews, 11, 1584–1595.

OYAK (2008). Oyak investment Web site. Available from: www.oyakyatırım.com.tr.Park, C. S., & Han, I. (2002). A case-based reasoning with the feature weights derived

by analytic hierarchy process for bankruptcy prediction. Expert Systems withApplications, 23(3), 255–264.

Raju, K. S., & Pillai, C. R. S. (1999). Multicriteria decision making in river basinplanning and development. European Journal of Operational Research, 112,249–257.

Saaty, T. L. (1980). The analytic hierarchy process. New York: McGraw-Hill.Saaty, T. L. (1994). Fundamentals of decision making and priority theory with the

analytic hierarchy process. Pittsburgh, PA: RWS Publications.Saaty, T. L. (2008). Decision making with the analytic hierarchy process.

International Journal of Services Sciences, 1(1), 83–98.Sun, J., & Li, H. (2009). Financial distress early warning based on group decision

making. Computers and Operations Research, 36(3), 885–906.Vaidya, O. S., & Kumar, S. (2006). Analytic hierarchy process: An overview of

applications. European Journal of Operational Research, 169, 1–29.Xu, X., & Wang, Y. (2009). Financial failure prediction using efficiency as a predictor.

Expert Systems with Applications, 36(1), 366–373.Yüksel, _I, & Dagdeviren, M. (2007). Using the analytic network process (ANP) in a

SWOT analysis – A case study for a textile firm. Information Sciences, 177,3364–3382.

Zopounidis, C., & Doumpos, M. (2002). Multi-criteria decision aid in financialdecision making: Methodologies and literature review. Journal of Multi-CriteriaDecision Analysis, 11, 167–186.

http://analiz.ibsyazilim.com

http://www.imkb.gov.tr

http://www.oyakyatirim.com.tr



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