Decision Science Letters

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1 Decson Scence Letters 2 (2013) Contents lsts avalable at GrowngScence Decson Scence Letters homepage: wwwgrowngscencecom/dsl An AHP-GRA method for asset allocaton: A case study of nvestment frms on Tehran Stock Exchange Froozeh Salardn * Masters n Fnancal Management, Department of Management and Accountng, Shahd Behesht Unversty, Tehran, Iran C H R O N I C L E A B S T R A C T Artcle hstory: Receved October 2, 2012 Accepted June 3, 2013 Avalable onlne June Keywords: AHP Grey relatonal analyss GRA Portfolo optmzaton Durng the past fve decades, there have been tremendous efforts to offer dfferent methods for portfolo management The prmary objectve of many of these methods s to provde a tradeoff between rsk and reward The proposed study of ths paper uses analytcal herarchy process (AHP) and grey relatonal analyss to offer a method for portfolo management The proposed method of ths paper uses a statstcal sample conssts of 16 frms whose shares were tradng durng the fscal year of 2010 on Tehran Stock Exchange The study uses AHP and gray relatonal analyss to assgn weght to each frm We also use a lnear programmng technque to model the resulted problem by consderng some realstc constrants 2013 Growng Scence Ltd All rghts reserved 1 Introducton Investment has been a major concern on many manageral problems and when t comes to uncertanty, many nvestors face some challenges (Mller, 1999; Machars et al, 2004) Ju-Long (1982) consdered stablty and stablzaton of a grey system whose state matrx s trangular and presented the dsplacement operator and establshed transfer Many nvestment models nvolve multple crtera decson makng problems and we need to use preference measure methods to handle such problems (Lee et al, 1999; Dong et al, 2008; Hsa et al, 2004; Huang et al, 2008) Gondzo and Grothey (2007) exploted the structure of optmzaton problems and showed how portfolo optmzaton problems wth szes measured n mllons of constrants and decson varables, featurng constrants on sem-varance, skewness or non-lnear utlty functons n the objectve, could be solved wth the state-of-the-art solver Tanaka et al (2000) proposed two types of portfolo selecton models based on fuzzy probabltes and possblty dstrbutons, respectvely, rather than conventonal probablty dstrbutons n Markowtz's model (Markowtz, 1952; Markowtz et al, 2000) * Correspondng author E-mal addresses: frozeh_salardn@yahoocom (F Salardn) 2013 Growng Scence Ltd All rghts reserved do: /jdsl

2 276 Snce fuzzy probabltes and possblty dstrbutons were computed based on possblty grades of securty data offered by experts, nvestment experts knowledge could be reflected Ja and Dyer (1996) presented a standard measure of rsk and rsk-value models Ince and Trafals (2006) looked at portfolo optmzaton problem by argung that the USA equty market could not be effcent They formulated the problem as a classfcaton problem by mplementng state of the art machne learnng technques such as mnmax probablty machne (MPM) and support vector machnes (SVM) The mplementaton of MPM technque reported a bound on the msclassfcaton probabltes On the other hand, SVM detected a hyperplane, whch maxmzes the dstance between two classes but they stated that both methods proved smlar results for short-term portfolo management Some of portfolo optmzaton problems can be formulated as NP-Hard problem where we may need to use metaheurstcs to solve the resulted problems (Rolland, 1997) Lorasch et al (1995) presented dstrbuted genetc algorthms wth an applcaton to portfolo selecton problems Inuguch and Tanno (2000) consdered portfolo selecton under ndependent possblstc nformaton Some of the portfolo selecton problems are nvolved wth ntegraton of mult crtera decson makng such as analytcal herarchy process (Saaty, 1980, 1994; Tung, & Tang, 1998) There are also some cases where we wsh to foretaste stock prce usng forecastng technques (Tang et al, 2002) Accordng to Lahmr (2012), n fnancal ndustry, the accurate predcton of the stock market s a major challenge to optmze and update portfolos and also to make an assessment of several fnancal dervatves Artfcal neural networks and techncal analyss are becomng wdely used by ndustry experts to predct stock market moves Lahmr used varous techncal analyss measures and reslent back-propagaton neural networks to forecast the prce level of fve major developed nternatonal stock markets, namely the US S&P500, Japanese Nkke, UK FTSE100, German DAX, and the French CAC40 They compared four dfferent techncal analyss measures ncludng ndcators, oscllators, stochastcs, and ndexes The out-of-sample smulaton results demonstrated a strong evdence of the effectveness of the ndcators category over the oscllators, stochastcs, and ndexes Besdes, he reported that combnng all these measures lead to an ncrease of the predcton error In sum, techncal analyss ndcators seem to provde valuable nformaton to predct the S&P500, Nkke, FTSE100, DAX, and the CAC40 prce level Gharakhan and Sadjad (2013) nvestgated advanced optmzaton technque for portfolo problem ntroduced by Black and Ltterman to study the shortcomngs of Markowtz standard Mean-Varance optmzaton Black and Ltterman proposed a new technque to estmate asset return They presented a way to ncorporate the nvestor s vews nto asset prcng process Snce the nvestor s vew about future asset return was always subjectve and mprecse, we may represent t by usng fuzzy numbers and the resultng model s mult-objectve lnear programmng Therefore, Gharakhan and Sadjad proposed a model to analyze through fuzzy compromse programmng approach usng approprate membershp functon For ths purpose, they ntroduced the fuzzy deal soluton concept based on nvestor preference and ndfference relatonshps usng canoncal representaton of proposed fuzzy numbers by means of ther correspondngα-cuts A real world numercal example was also presented n whch MSCI (Morgan Stanley Captal Internatonal Index) was chosen as the target ndex The results were reported for a portfolo consstng of the sx natonal ndces The performance of the proposed models was compared usng several fnancal crtera 2 The proposed method Markowtz, H (1952) s beleved to be the frst who ntroduced the dea of portfolo optmzaton Hs model tres to fnd asset allocaton based on the followng mathematcal model,

3 F Salardn / Decson Scence Letters 2 (2013) 277 N N N mn Z : ( X E ) X X C subject to X 1 j j 1 1 j1 N 1, X 0 (1) In model (1), X and E are the amount of nvestment and return on asset, respectvely C j s the covarance between asset and asset j The frst term n the objectve functon s assocated wth portfolo return; the second term determnes portfolo rsk and determnes the trade-off between these two terms The frst constrant s called budget constrant whle the second constrant X 0 specfes that there s no short sellng Ja and Dyer (1996) argued that Markowtz model does not consder many exstng constrans wth the model such as lqudty, lmtaton on buy/sell, etc In addton, when we add cardnalty constrant to model (1), we may face more complcated problem 21 Analytcal herarchy process Saaty (1980) s beleved to be the frst who ntroduced the dea of analytcal herarchy process (AHP) as the frst mult crtera decson makng technque Fg 1 demonstrates dfferent components of rankng varous alternatves usng ths technque Objectve Crteron 1 Crteron 2 Crteron n Alternatve 1 Alternatve 2 Alternatve n Fg 1 The structure of AHP The basc structure of AHP s based on parwse comparson of varous alternatve where decson maker (DM) gves hs/her relatve mportance of one alternatve versus another one based on some lngustc terms, whch could be transferred to some Lkert numbers from one to nne The method fnds average row-column and usng a consstency rato attempts to determne whether the comparsons are consstent or not 22 Grey Relatonal Grade Consder X 0 as reference and N alternatves wth k crtera as follows,

4 X { X (1), X (2),, X ( j ), X ( k )} X { X (1), X (2),, X ( j ), X ( k )} X { X { X (1), X (2),, X ( j ), X ( k )} X { X (1), X (2),, X ( j ), X ( k )} N (2) Grey relatonal coeffcent are calculated as follows, 0 mn max, X max 0 (3) where X 0 s the absolute dfference between X 0 and X n k th crteron, X 0 addton, max =max max j X 0 and mn = mn mn calculated as follows, X k 0 = X 0( k ) X ( k ) In Fnally, grey relatonal degree s k w, 0 j 0 j 1 where w j s the weght of crteron j and we may use normalzed as follows, x ( ) mn ( ) * j j x j x ( j), max x ( j) mn x ( j) j j max ( ) ( ) * j x j x j x ( j), max x ( j) mn x ( j) j j W j (4) 1 Fnally, all relatonshps must be k (5) (6) and we use Eq (5) n ths paper for our calculatons 3 The case study In ths paper, we have gathered the nformaton from Tehran Stock Exchange The proposed method of ths paper uses a statstcal sample conssts of 16 frms whose shares were tradng durng the fscal year of 2010 on Tehran Stock Exchange Frst, we have asked some experts to perform AHP on mportant crtera and let us fnd the relatve mportance of all crtera Table 1 summarzes the results of our survey, Table 1 The summary of mportant factors along wth relatve weghts Index Share prce EPS DPS Share beneft Management Operatng proft Technology P/E Frm sze C1 C2 C3 C4 C5 C6 C7 C8 C9 Weght Index Equty sze EVA β Current rato Quck rato Inventory turnover Weghted mean Rumors Internatonal rules C10 C11 C12 C13 C14 C15 C16 C17 C18 Weght EPS: Earnng per share, DPS: Dvdend per share, EVA: Economc value added The proposed study consders the nformaton of 16 nvestment frms denoted by A1 to A16 Table 2 demonstrates detals of weghts (C1-C16) assocated wth dfferent frms (A1-A16)

5 F Salardn / Decson Scence Letters 2 (2013) 279 Table 2 Relatve weght of each frm based on dfferent crtera C1 C2 C3 C4 C5 C6 C7 C8 (A 1 ) (A 2 ) (A 3 ) (A 4 ) (A 5 ) (A 6 ) (A 7 ) (A 8 ) (A 9 ) (A 10 ) (A11) (A 12 ) (A13) (A 14 ) (A 15 ) (A 16 ) C C C C C C C C Fnally, Table 3 summarzes the results of grey relatonal analyss for the proposed study of ths paper Table 3 The summary of grey relatonal analyss for 16 frms Frm Name (A 6 ) Bank Mell Investment frm (A 14 ) Tokafolad Investment frm (A 4 ) Credt Unon Investment frm (A 10 ) Khozestan development Investment frm (A 11 ) Toos development Investment frm (A 1 ) Iranan petrochemcal Investment frm (A 2 ) Maskan Investment frm (A 8 ) Khozestan development Investment frm (A 5 ) Alborz Investment frm (A 3 ) Damavant Investment frm (A 7 ) Bahman Investment frm (A 12 ) Industral development Investment frm (A 16 ) Cvl Investment frm (A 15 ) Rena Investment frm (A 13 ) Mell development Investment frm (A 9 ) Azarbayejan Investment frm Grey relatonal analyss Rank Accordng to the results of Table 3, Bank Mell nvestment frm s number one prorty followed by Tokafolad nvestment frm, credt unon and Khozestan development nvestment group The rankng of varous frms have ndcated that the management of some frms have had better performance n the past 4 Concluson In ths paper, we have presented an emprcal survey on rankng dfferent nvestment frms based on varous crtera The proposed study has mplemented analytcal herarchy process as well grey relatonal analyss to rank nvestment groups The results of rankng of these nvestment groups can be mplemented as nputs of a lnear programmng model where some regular constrants such as budget and lower/upper bounds are consdered

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