Efficient Frontier and Lower Partial Moment of the First Order

Transcription

1 Ieaoal Joual o Scece a Egeeg Ivesgaos vol ssue Febuay 0 Ece Foe a Lowe Paal Mome o he Fs Oe Mla Jasem Depame o Iusal Egeeg Islamc Aza Uvesy Masje Soleyma bach Masje Soleyma Ia Mlaj@auac Absac- I hs pape ae a quc evew o he cocep o Ece Foe (EF) s scusse how o eve EF o he bass o Lowe Paal Mome o he s oe The shape o he ew amly o EFs s vesgae Ths s a cobuo o he leaue as o such meho s ow o exs Keywos- Face Ece oe; Lowe Paal Momes; Poolo Seleco; Evoluoay Algohms I INTRODUCTION Ivesos clug lage suos such as muual us a peso us use poolo maageme sysems o suppo he asse allocaos I hs ega evg EF o he bass o hsocal omao s a esseal al sep o emove ece poolos ohewse he complexy o ecso mag ceases coseably [] A poolo s ece hee s o ohe poolo wh same o hghe expece eu a lowe s; he colleco o poolos wh hs popey s calle ece se o EF O he mpoa poso o EF he el o poolo seleco s goo o ee o Balleseo a Romeo [] a Jasem e al [3] ha ecomme maxmzg vesos expece uly o EF o come o he bes choce o vesme A ypcal moelg o EF ha mus be solve o ee amous o R s as ollows: M Rs P x x x x () R y a () (3) l y x u y (4) Whee Rs : Rs uco x : Shae o soc he poolo x 0 y (5) 0 x 0 x 0 (6) P x x : Icao o soc pas eus peomace : The poolo whose socs shaes ae x x a : Dese umbe o socs he poolo l a u : Lowe a uppe bou o x ; I he moel cosas a 6 ae maaoy whle he ohes ha ae also scusse mahemacally by Peol [4] ae o I hs suy he Rs s Lowe Paal Mome () o he s oe whch Fshbu [5] beleves o su a seual veso Speze a Rez [6] has some scussos abou a Jasem e al [7] poves o be sesbly cohee II EF AND ITS NEW RISK MEASURE A The so calle moelg o Eq7 evelope by Fshbu (997); ; R R FR E max R 0 (7) Whee F R s he cumulave sbuo uco s he age paamee a ha hs suy equals eemes he wegh o evaos The amly o s measues s o specal mpoace o applcao o acal ecso mag he way ha Bawa [89] Halow a Rao [0] a Use [] mly ecomme s applcao o evelopme o asse pcg moels B Rs o a poolo To calculae R o P x x wo appoaches ca be evse as Eqs 8 a 9 whle as s obvous he ome s soc-ve a he lae s poolo-ve x (8) 39

2 x RP x x x x whee RP x x s eu o P x x Sce o he s a he seco appoach hee ae a e sbuo ucos o be esmae especvely applcao o Eq8 he moel s much smple bu hee s a ma poblem wh The poblem ases whe eu o a asse s smalle (bgge) ha bu he weghe aveage o he poolo eu s bgge (smalle) ha To exemply he poblem cose wo ollowg epee vaables o a 50% P 50% 0% 30% P 30% 70% 0 ; 0% so he pobably uco o he poolo whch x 0% a x 80% woul be as ollows: 5% RP % ; 35% RP 4% Pp RP 5% RP 6% 35% RP % a 5% RP0%80% 45% whle Eq8 calculaes as 6% To appoxmae RPx x by Eq9 s o all RPx x mus be esmae Hee s oe by applyg he cocep o hsogams Fo ou poblem o he bass o Bowe a Lebema [] wo mehos seem moe appopae o awg he ee hsogams I oe he evals legh o he hsogam s spece he way ha splays a plae mage ha asces evely beoe he maxmum po a ae eachg esces evely Obvously bewee wo ee eve hsogams he oe wh moe evals s peee I he ohe meho ha has bee pove o be moe appopae [3] a s gog o be apple ou EF moel he evals ae oo sho o ecompass moe ha oe sc aa Fg epcs a ypcal eoes he h smalles eu o he asse oe whee eemes equecy o a N s he umbe o ee eus o he asse Fg A ypcal hsogam ha s aw by he s saegy (9) To calculae by he seco meho (Fg) shoul be covee o s equvale scee veso Eq0 R R R P (0) 00 Now R s calculae by Eq () () RPR 00 I s assume ha he me hozo s o legh T eu o P x RP x o he h me u s calculae by Eq () x x x a x a x a x a T whee a s eu o asse o he h me u The he al EF moel howeve s smples om whou he caaly a boug cosas s as ollows: M x x p x x x 0 whee px x s he h smalles eu o P x x I he above omulao he paamees a p ae ucos o x x ; e o each se o amous o he vaables hee wll be a ew objecve uco ha maes us use he evoluoay appoach o Geec Algohm o solve he moel C Rug he ew moel As a mae o ac Eq s ece o be Ahmec aveage o pas eus ha ae geae ha o mee he wo mpoa ollowg cea: All aa shoul be equal om he pespecve o he mes beg apple by he moel Boh chaacescs o Mea a Volaly beg cosee To suvey he geeal shapes o he ew EFs hee ollowg secos ae evse I he s a seco oes wo a moe ha wo (clug sx a eghee) asses especvely ae cosee whle he h seco hee ae eghee asses wh caaly a boug cosas Ieaoal Joual o Scece a Egeeg Ivesgaos Volume Issue Febuay 0 40 wwwijseicom Pape ID: 0-08

3 E(R) E(R) E(R) C Two asse EF I hs pa hee wo-asse combaos om NYSE wh ee coelao aos bewee he aly eus ae cosee Table a Fg coespo o Dell a Hp 007 wh coelao ao o +05 a % Table : EF wh 0 poolos Po HP Dell (%) Reu(%) Fg3: The EF o Table The aly eus o Geeal Elecc (GE) a Hoa ug 007 have he coelao ao o bu o see he shape o EF whe coelao ao s o posve egave o Hoa soc eus s cosee a so he ew coelao ao becomes Fo hs case Table 3 a Fg4 show he EF o % Fg: The EF o Table Table 3: EF wh 0 poolos Po GE -Hoa Reu(%) (%) Table a Fg3 coespo o Boeg a Mcoso 999 wh coelao ao o a 0 Table : EF wh 9 poolos Po Boeg Mcoso (%) Reu(%) Fg4: The EF o Table 3 C Moe ha wo asse EF Table 4 a Fg5 coespo o sx socs o HP Dell Boeg Mcoso GE a Hoa NYSE ug 007 a % Each po he able coespos o a ece poolo whle he gue epeses he assocae EF Ieaoal Joual o Scece a Egeeg Ivesgaos Volume Issue Febuay 0 4 wwwijseicom Pape ID: 0-08

4 E(R) Table 4: EF wh 0 poolos Po HP Dell Boeg Mcoso GE Hoa (%) Reu(%) Fg5: The EF o Table 4 Abou he case wh eghee asses moeove o he above sx socs hee socs o GM IBM a Ne om NYSE ae also cosee The e socs ae aalyze ug 006 a 007 he way ha each soc a yea s cosee as a epee asse The esule EFs o 0 a % ae show Fg6 whle ss a eus ae pesee peceage Fg6: Two EFs C3 The complee EF moel I hs seco s vesgae ha wha woul happe o EF whe he umbe o asses each poolo s esce a he amou o vesme each soc has lowe a uppe bous Hee he eghee asses o pevous pa ae use aga whle he lowe a uppe bous ae epee o a as s omulae by Eq(3) l ; a u (3) a a The EFs o hs seco ae eve wh hee amous o a as 6 a 8 Fg7 shows he esuls o 0 a % Fg7: Sx EFs o wo amous o a hee amous o a Ieaoal Joual o Scece a Egeeg Ivesgaos Volume Issue Febuay 0 4 wwwijseicom Pape ID: 0-08

5 III CONCLUSION The cocep o EF was he ma ocus o hs pape The eece bewee hs suy a he ohes o he el ca be summaze he wo ollowg ems Coseg he s measue o o he s oe o evg EF Peseg a paccal appoach o eve EF o he bass o he whle he appoach s o esce by acos le sochasc chaacescs o he socs eus o umbe o socs ha compose he poolo The popose mechasm s apple o eve EF o vese amous o s a cosas combaos o gve a geeal uesag o he ew geeao o EF The peomace o he popose mechasm s mly appove by he sesble esuls om he pespecves o shape a echcal accepace The geeal shape o he EFs s a cocave asceg paabola; e he se he poolo moe eu ca be expece A las s hghly ecommee o eplace Vaace ay acal moel wh o he s oe he a compehesve compaso bewee hem beg couce a he esuls beg aalyze Suely hs pah hee s a poeal o mpoveme o acal moels REFERENCES [] E Balleseo M Guhe D Pla-Saamaa a C Summe Poolo seleco ue sc uceay: A mul-cea mehoology a s applcao o he Fau a Vea Soc Exchages Euopea Joual o Opeaoal Reseach pp [] E Balleseo a C Romeo Poolo seleco: A compomse pogammg soluo Joual o Opeaoal Reseach Socey pp [3] M Jasem A M Kmaga a A Memaa Cocepual Moel o Poolo Maageme Sesve o Mass Psychology o Mae Ieaoal Joual o Iusal Egeeg-Theoy Applcao a Pacce 0 8 pp-5 [4] A F Peol Lage-scale poolo opmzao Maageme Scece pp43 60 [5] P C Fshbu Mea-s aalyss wh s assocae wh belowage eus Joual o The Ameca Ecoomc Revew pp6-6 [6] U W Speze a V Rez O he opmzao o a CAPM poolo usg lowe paal momes as measue o s a usg he possbly o saeguag s loss Physca A pp43 46 [7] M Jasem A M Kmaga a A Memaa Developme o A Moe Apple Veso o Coheecy Calle Sesble Coheecy o Assessme o Facal Rs Measues Souh Aca Joual o Iusal Egeeg 00 pp57-65 [8] V S Bawa Opmal ules o oeg ucea pospecs Joual o Facal Ecoomcs 975 pp95- [9] V S Bawa Saey-s sochasc omace a opmal poolo choce Joual o Facal a Quaave Aalyss pp55 7 [0] W V Halow a R K S Rao Asse Pcg a Geealze Mea- Lowe Paal Mome Famewo: Theoy a Evece Joual o Facal a Quaave Aalyss pp85-3 [] M Use Lowe paal momes as measues o peceve s: A expemeal suy Joual o Ecoomc Psychology 000 pp53-80 [] A H Bowe a G J Lebema Egeeg Sascs seco e Pece-Hall Ic New Jesey 97 [3] M Jasem a A M Kmaga Ue evew sce Ju 9 00 Developme a compaso o some mehos o appoxmao o Lowe Paal Mome o he s oe Apple Mahemacs a Compuao M Jasem was bo Ia o Feb 7 h 98 He accomplshe hs BSc MSc a PhD Iusal Egeeg especvely a Ia Uvesy o Scece a Techology Teha Ia (999_003) Sha Uvesy o Techology Teha Ia (003_005) a Amab Uvesy o Techology Teha Ia (005_00) Hs eseach eess ae Facal Egeeg Rs Maageme Ivesme Aalyss a Iveoy Cool Hs poessoal expeeces clug Naoal Iaa Dllg Compay Msy o Roa a Taspoao Naoal Iaa Poucvy Ogazao Iaa Iusal Cosula Egees Compay Lala Facoy Pasaloy Facoy RAJA Compay a cuely he s a Asssa Poesso a Iusal Egeeg Depame a Islamc Aza Uvesy Masje Solema Ia He has 8 publshe papes whle he bes o hem s A Moe Neual Newo Moel o Do Soc Mae Tmg o he Bass o he Ace Ivesme Techque o Japaese Calesc he joual o Expe Sysems Wh Applcaos o whch he has bee ve as he coeece speae a EPS Moeal Ieaoal Foum o Ecoomy a Tae whch was hel o Augus D Mla Jasem s a membe o Iaa Eles Naoal Isuo Ieaoal Joual o Scece a Egeeg Ivesgaos Volume Issue Febuay 0 43 wwwijseicom Pape ID: 0-08