Research on portfolio model based on information entropy theory

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1 Avalable ole Joural of Chemcal ad Pharmaceucal esearch, 204, 6(6): esearch Arcle ISSN : CODEN(USA) : JCPC5 esearch o porfolo model based o formao eropy heory Zhag Jusha, Zhag Jg, Su Halu ad Kag Ka School of Ecoomcs ad Maageme, Hebe Uversy of echology, aj, Cha ABSAC Eropy s a measure of he uceray. Eropy-based opmzao model ca help vesors o make decso he mperfec secures marke. hs paper mproved he exsg eropy opmzao model by addg he secures rasaco coss, ad aalyzed he maxmzao of he vesme porfolo gas a ucera evrome. Key words: Eropy; porfolo; rasaco coss INODUCION here are some uceraes he secures dusry. I order o avod rsks arsg from vesme secures, s ecessary o coduc research o he secures porfolo for vesors he process of vesme secures. Markowz's porfolo model lad a sold foudao for he quaave sudy of porfolo vesme. [] I he Classcal Markowz mea-varace model, Ivesors mmzed he varace as a rsk fuco uder he cera expeced reur. However, due o he dffculy of compug he covarace, applcao of Markowz s mea-varace model grealy reduced. Some scholars such as L hua, L Xgs, LIANG Chagyog, Ha Mao, who esablshed a seres of eropy opmzao model, ad hese models ca solve he compuaoal problems whch he Markowz mea-varace model ecouered. However, he sably of he secures dusry marke has brough dffcules o he research of porfolo. herefore, all coss arsg from he rasaco process becomes a mpora facor, ad hs arcle s based o he above aalyss ad explore he porfolo opmzao model.. MAKOWIZ S MEAN-VAIANCE MODEL Markowz assumed ha vesors are rsk averse ad hey always wa o ge he maxmum expeced reur uder cera codos or he mmum vesme rsk uder cera codos he expeced reveue. Markowz s mea - varace model s expressed as follows. m X CX s.. x r c = = x =, =, 2, 3, L, () Where C used o represe he covarace marx of radom vecor r, usually meas he vesme rsk 286

2 Zhag Jusha e al J. Chem. Pharm. es., 204, 6(6): marx. X = ( x, x2, L, x ) s rgh wegh marx, x represes he rao of vesme secures. r = ( r, r2, L, r ) s he expeced rae of reur vesors marx, c represes he expeced reur of porfolo vesme. 2. POFOLIO OPIMIZAION MODEL BASED ON INFOMAION ENOPY Geerally, he ga of he secures x ( =, 2,, ) s dffere a dffere me ervals, me ervals dffere gas, so ca be dvded o dffere ervals. We may assume ha secures -h me perod, he π s a proporo of he ga of he -h me erval oal reveue, r s yeld of r = = π r =,2,L, (2) From equao (2) ca be draw, B derved from he sascs he pas, so h perod come porfolo vesed ca be expressed as, = r x (3) = Average come secures = r x = may be draw herefrom porfolo. Mea - eropy model s as follows uder cera cosras. M ax π l( π ) = = S.. π = c (4) = = x r s subsued o he model (4). Max π xr l π xr = = = π xr = c = = S.. x =, x 0, =,2, L, = (5) Where, le c be exceped prof for vesor, hese opmzao models ca be rasformed o he form of mul-objecve opmzao. 287

3 Zhag Jusha e al J. Chem. Pharm. es., 204, 6(6): Max Max = = π xr l π xr = = = S.. x =, x 0, =, 2, L, = π x r (6) he lear weghg mehod ca be usually used o solve he mul-objecve plag problem. herefore, he problem s expressed as follow: Max ω π xr ω2π xr l π xr = = = = = S.. x =, x 0, =,2, L, = (7) 3. IMPOVED POFOLIO OPIMIZAION MODEL BASED ON INFOMAION ENOPY I he process of secures vesme, order o effecvely avod rsks, vesors ofe use he mehod of porfolo vesme. Iformao eropy opmzao model s roduced hs arcle ca help vesors make beer opmzao decsos he case of asymmerc formao. Bu acual operao, vesors wll ecouer more rsk. For example, payme rasaco coss wll affec he overall reveue he ere rasaco process. herefore, s ecessary o aalyze he rasaco coss of he whole process. rasaco coss were added o he model, so ha he resuls would be more realsc. Secures rasaco coss clude four caegores: commssos, rasfer fees, samp duy ad oher expeses, he cos of each par are dffere for dffere sock exchages. herefore, s ecessary o remove rasaco coss from he beefs of vesme porfolo. We assume ha he rasaco coss of buyg ad sellg s he same as α mes of he sock prce he vesme process, he you ca cosder mprovg he above lear programmg model. Le ω s he prce of he secures durg he -h me erval, ω ( + ) s he prce of he secures durg he (+)-h me erval, he vesme rae of reur by radg socks ca be expressed as follow he ere rasaco process. r [ ω - αω ]-( ω + αω ) = (+) (+) (8) ω + αω Sce follow. r ω -ω (+) = s he yeld whe rasaco coss are o cosdered, so he yelds ca be rewre as ω ' α 2α r = r + α + α (9) herefore, he above model (7) ca be rewre as follow. 288

4 Zhag Jusha e al J. Chem. Pharm. es., 204, 6(6): ' ' ' Max ω π xr ω2π xr l π xr = = = = = ' α 2α r = r + α + α S.. x =, x 0, =,2, L, = (0) Bu real lfe, rasaco coss of buyg ad sellg he same secures are always dffere a dffere me, eve a dffere me ervals. herefore, s ecessary o cosder wheher he model s adaped o he geeral case. Le ω s he prce of he secures durg he -h me erval, ω ( + ) s he prce of he secures durg he (+)-h me erval, Commsso s α mes of he sock prce, rasfer fee s β mes of he sock prce, Samp duy s γ mes of he sock prce, Oher coss are δ. So f you buy a u cos of secures a me, you ω + ω * α + ω * β + ω * γ + δ, Smlarly you wll ga wll sped ω ω * α ω * β ω * γ δ by sellg he secures a me +. ( + ) ( + ) ( + ) ( + ) I he course of hs rasaco, he vesme rae of reur becomes - ( ω + ω * α + ω " * β + ω * γ + δ) + ω ( + ) ω( + ) * α ω ( + ) * β ω( + ) * γ δ r = ω + ω * α + ω * β + ω * γ + δ herefore, he model ca be rasformed o S.. x =, x 0, =,2, L, = " " " Max ω π xr ω2π xr l π xr = = = = = () (2) 4. ANALYSIS OF HE MODEL Accordg o he prefereces of vesors, you ca selec he releva daa of several socks he sock exchage for he above model (2) emprcal research, ad hese socks may be a beer performace of he dusry secor, or growg ably of cera socks. Frsly, combed wh he sadard fee charged by sock exchages, each brach secures yelds s obaed by he model (), he used a uform dsrbuo (you ca also cosder oher dsrbuo) o calculae he value of π, whch represes he proporo of come he -h me erval of oal reveue. ω ad 2 ω are wegh coeffces, vesors ca appropraely adjused coeffce accordg o her degree of rsk averso. Fally, vesors ca coduc emprcal research based o he model (2). he problem are volved hs model s cosraed olear programmg problems, vesors ca cosder usg MALAB Opmzao oolbox fmco fuco o solve he above problems. hus, depedg o he vesor's choce o ake a dffere weghg facor, choose a dffere ad correspodg sock exchage, he resuls obaed wll ga a greaer chage. hs paper oly provdes he correspodg emprcal research mehods. CONCLUSION Due o he complexy ad sably of he sock marke, here are some defceces Markowz classc porfolo model. he porfolo model by he above aalyss shows ha he opmal model combao wh rasaco coss based o formao eropy ca combe he characerscs of formao eropy wh he uceray of he secures radg marke ogeher. o some exe, makes he applcao of he model becomes more realsc, bu 289

5 Zhag Jusha e al J. Chem. Pharm. es., 204, 6(6): also be able o adap o he real sock marke. Bu he sock marke s more complex, ay model has s lmaos, hs model requres ha he secures marke s relavely sable. I emprcal research, you eed o remove much of he volaly of dvdual raw daa, so as o make he model more realsc. hus, hs model ca provde useful lessos for vesme decsos, ad vesors choose he approprae weghg facor based o he acual suao ad her ow prefereces o maxmze reveue as much as possble cera rsks. Ackowledgmes he paper s suppored by he Naoal Socal Scece Foudao of Cha for corac 2CGL2, humaes ad socal scece fud projec of Msry of Educao for corac 2YJA630049, he Ph.D. programs foudao of Msry of Educao of Cha for corac , Hebe mucpal aural scece foudao for corac G ad G , Hebe Mucpal scece ad echology suppor program for corac , he colleges ad uverses Hebe provce scece ad echology research projec for corac SQ302, uder whch he prese work was possble. EFEENCES [] Markowz H. Joural of Face, v 7, p 7-79, 952. [2] L hua, L Xgs. Joural of Sysems Scece ad Iformao, v, 3, p 4-49, 2003 [3] L Hua, L Xgs. Eropy as a measure of rsk moder porfolo seleco Proceedgs of 2003 Ieraoal Coferece o Maageme Scece & Egeerg, v 2, p , [4] L Hua, L Xgs. Facal Sysems Egeerg, v 2, p 84-90, [5] Lag Chagyog, WU Ja, Huag Yogqg. Joural of Hefe Uversy of echology (Naural Scece), v 08, [6] Ha Mao, Zhou Shegwu, Cag Dgbag. Operaos esearch ad Maageme Scece. V 06,