The Tenth nterntonl Symposum on Opertons Reserch nd ts Applctons (SORA 2011) Dunhung, Chn, August 28 31, 2011 Copyrght 2011 ORSC & APORC, pp. 314 321 Applcton of ntervl-promethee Method for Decson Mng n nvestng Shunghong Qu 1 Hu L 2 Xol Guo 1 1 Deprtment of Mthemtcs nd nformton Scence, Zhengzhou Unversty of Lght ndustry, Chn, 450002 2 Deprtment of Mthemtcs, Zhengzhou Unversty, Chn, 450001 Astrct Ths pper ntroduces the ntervl-promethee method to the nvestment decson mng of vlue nvestng. Fve performnce crter re used for mesurng the growth potentl of frms nd re represented y ntervl numers sed on the rel fnncl dt. The ntervl-promethee method s ppled to rn the 20 rndomly selected stocs n Shngh Stoc Exchnge. The portfolo wth the top 5 stocs ws proven to hve hgher return thn the top 10 stocs wthn the 17-month nvestment perod. The emprcl study showed the effectveness of the ntervl-promethee method n the decson mng process of vlue nvestng. Keywords Vlue nvestng; Mult-crter decson mng; ntervl-promethee 1 ntroducton Vlue nvestng ntlly proposed y Grhm nd well developed lter y Buffet hs proven to e successful nvestment strtegy nd hs een pd more nd more ttenton n the lst three decdes. As suggested, the mn process of BV conssts of two phses. The frst s to fnd the equtes wth extrordnry overll performnce sed on severl fnncl rtos. The second s to evlute the ntrnsc vlue of ech selected equty. n ths pper, the emphss s ld on the frst phse, nd we focus on the overll performnce evluton of equtes sed on fve crter suggested y Buffet. PROMETHEE s one of the most recent MCDM methods tht ws proposed y Brns et l.[1] nd hs successvely een ppled n mny felds[2], especlly n the nvestment nlyss nd performnce evluton. Mreschl nd Brns[3], Vrnegl et l.[4], Bc nd Plzt[5], Bour et l.[6] nd Aldv et l.[7] ll ppled PROMETHEE s decson mng tool to solve the dfferent prolems n the feld of fnnce. n ths pper, we pply PROMETHEE to select frms wth outstndng performnce n the decson process of vlue nvestng. n the ove mentoned pplcton n fnnce, the performnces prmeters re ll represented y sngle vlue numers. However, fnnce nvestment decson mng s complex process due to the uncertn nture of fnncl mrets, or
Applcton of ntervl-promethee Method for Decson Mng n nvestng 315 ecuse the mrets re not well understood whch s clled non-rndom uncertnty. t s hrd to convey the proftlty nformton ust y sngle-vlued numer or smple verge of the pst. So n ths pper, we ntroduce ntervl numer to model the uncertnty n vlue nvestng decson mng prolem sed on the PROMETHEE method. The rest of ths pper s orgnzed s follows: n secton 2 the orgnl PROMETHEE method s reclled nd then t s generlzed to ntervl-promethee n secton 3; n secton 4, the mult-crter rnng prolem of rnng outstndng frms re presented nd the pplcton of ntervl-promethee method s performed for stocs sed on 5 crter n Shngh Stoc Exchnge; fnlly the conclusons re drwn n secton 5. 2 PROMETHEE A = { 1, 2,, n } s set of lterntves to rn, F ={f 1, f 2,, f m } s set of crter, whch hve to e optmzed ccordng to ther potentl contrutons to the fnl results. f the hgher of the performnce evluton for crteron, the hgher of the rnng, ths crteron wll e mxmzed; otherwse ths crteron should e mnmzed. A pr-wse comprson etween ny two lterntves nd s mplemented nd the ntensty of the preference of n lterntve over nother lterntve denoted y P (d ), nd here d = f ( )-f ( ) (1) s determned frstly, where f ( ) s the evluton of lterntve correspondng to the crteron f. Sx dfferent types of the preference functon for the -th crteron P re recommended y Brns et l. The decson mers cn lso defne ther own preference functon. A lner preference functon [1] s selected n ths pper: 0, f d < 0 d (2) P d =, f 0 d q q 1, f d > q Ths shows tht the ntensty of the decson mer's preference etween the lterntves nd whch ncreses lnerly wth the growth of d up to q. After the threshold q, the preference wll e equl to 1. For rnng purposes, q cn e set ccordng the rel stuton. The vlue of the preference scles vres from 0 (no preference) to 1 (strong preference). The preference of lterntve nd s evluted for ech crteron nd the preference ndex s determned y (, ) = m w P ( d =1 m ) w P ( f =1 ( ) f ( )),, A (3) where w W = {w 1, w 2,,w m } s weght for -th crteron whch s mesure for the reltve mportnce of ech crteron. The levng flow nd the enterng flow of re respectvely gven y n n 1 ( ) = (, ), 1 ( ) = (, ) (4) n1 n 1 =1 =1
316 The 10th nterntonl Symposum on Opertons Reserch nd ts Applctons The sc premse s tht the hgher the levng flow nd the lower the enterng flow, the etter the lterntve. PROMETHEE method s totl rnng method sed on the evluton of the net flow = ( ) (, ) A (5) The hgher the net flow the etter the lterntve. 3 ntervl-promethee As we cn see ove, the orgnl PROMETHEE method s desgned for sngle-vlued numer. When some uncertntes nherent re represented s ntervl numers, the ntervl-promethee method s then requred. Ths comes from the fct tht n most cses the nput dt cnnot e defned wthn resonle degree of ccurcy. Ths mprecson s sometmes treted s n ntervl numer. So the regulr PROMETHEE lgorthm wll e generlzed to the ntervl-promethee. 3.1 ntervl numer An ntervl numer x hs such form: x = [, ], <, where nd re ll rel numer. The ntervl numer set re recorded s (R). Ovously for x = [, ] (R), f =, then x = = s n ordnry rel, so R (R). The sc opertons wth ntervl numers re summrzed n Tle1. Tle 1: the sc opertons wth ntervl numers Addton [, ]+[c, d] = [+c, +d] Sutrcton [, ]- [c, d] = [- d, -c] Multplcton [, ] [c, d] = [mn{c, d, d, c}, mx{ c, d, d, c }] Dvson [, ]/ [c, d] = [mn{/c, /d, /d, /c}, mx{ /c, /d, /d, /c }], 0[c, d] 3.2 ntervl-promethee When the performnce of nd correspondng to the crteron f re represented y ntervl numers, the d = f ( )-f ( ) s the ntervl numer (u, v), nd P (d ) n (2) etween nd sed on f s expressed s: 0, f u 0 ( u, v) P d =, f 0 u, v q q 1, f v > q (6) where q could e expressed s ntervl, ut for smplcty we te sngle vlue numers. Then the procedure of the PROMETHEE method descred n (3)-(5) re followed step y step y the ntervl numer clcultons. Smlrly, other prmeters, re ll consdered s regulr dt wth precse numercl vlues. Fnlly, when ntervl dt re ncluded, the net flows re ll ntervl numers, so the fnl rnng prolem s oled down to the rnng of ntervl numers. Thus the comprson of two ntervls plys crucl role. An enhnced rnng pproch for ntervl numers presented y L (2004)[8] ws used n ths pper whch s sed on the posslty degree whch represents the degree of one ntervl s greter thn nother ntervl. Ths methodology s refly descred elow.
Applcton of ntervl-promethee Method for Decson Mng n nvestng 317 Let = [, ] nd = [, ] re two ntervls, f = nd =, then = ; f the posslty degree of denoted s P > s greter thn 0, then ; f P < 0, then. The posslty degree of s defned s > 1, f ( ) ( ) (7) P, f, f f = [, ] degrdes to sngle vlue,.e., = [, ], the posslty degree of s gven y 1, f < (8) P f > =, < 1, f > f = [, ] nd = [, ], the comprson of two ntervls ecome rnng two rel numercl vlues. n ths scenro, the posslty degree s then defned s 1, f P 0, f (9) 1, f The comprson mtrx of posslty degree for m ntervl numers s determned y 0 P12 P1 m P21 0 P2 m P = Pm 1 Pm 2 0 (10) > 1 P 1 where P s the posslty degree of nd meets nd P P = 0. Let R = One gets r, r,, r T 2 m r = m P, = 1,2, m, =1 1, the comprson of ntervl numers then ecomes rnng r,.e., the hgher the r, the hgher the ntervl numer. 4 Applcton to Vlue nvestng The phlosophy ehnd vlue nvestng s tht the ntrnsc vlue determnes the stoc prce of frm nd the stoc prce fluctutes round the vlue; the outstndng (11)
318 The 10th nterntonl Symposum on Opertons Reserch nd ts Applctons performnce suggests tht the frm hs gret potentl nd lty to grow nd proft more, whch led to hgher ntrnsc vlue, nd thus the current elow-ntrnsc-vlue prce s expected to rse, therefore f n nvestor uys nd holds t now nd he or she wll surely me money n long tme horzon. The fve crter for mesurng the growth potentl of frm suggested y Wrren Buffet re return on ssets(denoted s f 1 ), ncresng rto of sles( f 2 ), ncresng rto of equty( f 3 ), ncresng rto of ernngs per shre( f 4 ), ncresng rto of free csh flow( f 5 ). These fve crter provde reltvely overll evluton of the lty of frm to grow nd proft. The fve crter re lsted n Tle 2. Tle 2: Fve crter for selectng stocs n vlue nvestng Crteron Defnton Mn Unt f1 f2 Return on ssets ncresn g rto of sles Ernngs efore nterest nd txes totlssets Sles t Sles Sles t1 t1 /Mx Mx Mx Percentge Percentge f3 ncresn g rto of equty Equty t Equty Equty t1 t1 Mx Percentge f4 ncresn g rto of ernngs per shre [ernngsp ershre] t [ernngsp ershre] [ernngsp ershre] t1 t1 Mx Percentge f5 ncresn g rto of free csh flow [freecshflow] t [freecshflow] [freecshflow] t1 t1 Mx Percentge The performnce cn e clculted sed on the frms fnncl sttements. n ths pper, the fnnce dt re otned through CSMAR4.0. We rndomly select 20 frms from the Shngh Stoc Exchnge. We compute the fve crter nnul performnces for ech frm for the fnncl yers 2007, 2008, 2009. And we use the pst dt to develop n ntervl numer representton for ech crteron nd ech frm. The ntervl representtons re lsted n Tle 3. Tle 3 Fve crter performnce for 20 rndomly selected frms (percentge) 600375 (4.67,15.06) (-11.35,41.23) (-42.68,265.32) (0.81,13.19) (-251.72,419.13) 600252 (7.77,13.17) (-11.02,119.81) (29.41,122.69) (8.96,27.65) (-111.95,240.16) 600031 (16.02,27.58) (20.01,99.91) (-48.74,60.74) (22.54,83.33) (-360.05,178.91) 600712 (15.44,34.78) (10.56,118.26) (15.45,79.25) (12.74,21.34) (7.33,12.27) 600600 (9.50,13.23) (12.50,17.40) (22.70,71.44) (3.91,33.43 ) (-3.59,125.90) 600195 (14.52,18.41) (6.01,15.95) (6.88,43.76) (2.03,15.93) (-128.68,290.35)
Applcton of ntervl-promethee Method for Decson Mng n nvestng 319 600233 (9.72,19.24) (-2.66,26.23) (-44.26,126.46) (10.63,17.15) (55.79,469.65) 600750 (11.46,17.27) (-1.06,29.66) (-37.33,53.86) (10.68,15.69) (14.55,42.40) 600528 (7.94,12.94) (29.87,73.11) (-14.97,133.41) (10.54,94.02) (-507.79,39.58) 600859 (8.84,17.39) (9.09,39.93) (12.80,34.72) (-31.90,74.79) (-46.60,91.76) 600101 (6.73,10.62) (-18.57,35.52) (-136.11,89.41) (6.67,28.88) (-52.27,29.26) 600697 (9.96,14.11) (14.42,60.82) (3.48,47.02) (6.89,12.47) (-190.01,352.76) 600708 (12.53,14.78) (-1.22,20.71) (-22.20,9.84 ) (-12.29,26.32) (-67.62,204.84) 600835 (11.64,15.75) (5.16,26.08) (-16.58,34.90) (9.20,9.47) (-51.52,59.45) 600664 (11.31,15.29) (-9.86,16.95) (2.97,45.82) (1.81,14.54) (7.89,29.40) 600829 (16.83,18.93) (1.69,14.38) (3.25,26.24) (0.47,29.76) (-21.89,45.08) 600269 (11.98,13.79) (5.39,35.27) (-43.94,35.77) (14.05,21.40) (-126.30,55.72) 600611 (10.40,12.23) (-29.69,19.83) (-42.51,58.64) (-4.97,51.03) (-265.10,147.93) 600519 (31.05,5.44) (13.88,47.82) (13.8,88.4) (27.37,39.60) (3.12,90.24) 600066 (14.58,30.72) (5.35,59.06) (-7.5,93.75) (-39.86,107.63) (-113.08,407.29) Wth the ntervl-promethee methods presented ove, we rn the ove stocs nd get the order lsted n Tle 4. Here we lst only the top10 Tle 4 The rnng result of the top10 frms Code ntervl of net flow Vlue of r Rn 600712-0.27885 0.514948 30.52631 1 600252-0.30656 0.555963 30.39054 2 600375-0.38101 0.520593 16.65066 3 600031-0.32511 0.433371 15.11768 4 600519-0.29406 0.348474 9.074004 5 600600-0.33066 0.332213 1.346427 6 600750-0.32896 0.316332-0.63525 7 600195-0.3301 0.315249-0.96069 8 600528-0.33835 0.321953-1.23726 9 600101-0.38084 0.360621-2.02337 10 The hgher the vlue of r, the hgher the rn of the frm nd the hgher the potentl of the stoc prce to grow. The prce wth rn 1 s supposed to hve hgher potentl to grow thn tht wth rn 2. For the complex nture of fnnce mret, t s not relstc to expect stoc wth rn n to grow fster thn tht wth tht wth rn n+1. But t s nturl to expect tht the portfolo vlue wth top m stocs grows fster thn tht wth top n stocs, where m s less thn n. Thus, the effectveness of ths ntervl rnng method cn e verfed y the nvestment effect of portfolos wth top m stocs nd top n stocs. For verfyng the feslty of the ntervl-promethee method, we construct portfolos wth top 5, top 10 nd 20 stocs rndomly selected, nd ech stoc wth 1000 shres. Suppose we nvested these three portfolos rght fter the end of 2009, nd on the dt Jn 04, 2010. We ept them untl June 10, 2011 wthout ny chngng of the portfolos. For comprng the nvestment effect, the portfolos re
320 The 10th nterntonl Symposum on Opertons Reserch nd ts Applctons dusted to e equl t the rght egnnng nd dusted wth the sme rto n the followng. For exmple, suppose we te the Shngh ndex vlue 3000, on Jn 04 2010 s the se pont, the portfolo vlue ws 30000, then we dvde the portfolo vlue y 10(30000/3000=10), nd thus the dusted portfolo vlue s 3000 equl to the Shngh ndex t the very egnnng, then for ech dy fter, the dusted portfolo s set to the rel vlue dvded y 10, so tht they re comprle. We dusted the three portfolos s ove mentoned nd the evoluton of the portfolos re plotted n Grph 1. Grph 1 The portfolo vlues As we cn see from the Grph1, the portfolo vlue wth the top 5 stocs stys ove tht wth the top 10 stocs n the long run. Smlrly, the top10 stocs stys ove the 20 rndomly selected stocs throughout the nvestment perod. Ths fct suggests tht the rnng methods we used s effectve. By the wy, the frst two portfolos perform etter thn the Shngh ndex whch represents the verge performnce of the Chnese stoc mret. Tle 5 The dstrutons of return rtes 2010-6-30 2010-12-31 2011-6-10 men std men std men std top5-0.428817 0.223669 0.362508076 0.273947 0.3625081 0.261254 top10-0.293117 0.215117 0.319870755 0.248416 0.3198708 0.238435 rndom20-0.30083 0.221058 0.263547856 0.221058 0.2635479 0.070005 SZ -0.639363 0.229973-0.07600934 0.219195-0.076009 0.122188 Furthermore, we compute the dstruton of the nnul rte of the portfolos from the egnnng up to 2010-06-30, 2010-12-31 nd 2011-06-10 respectvely. The correspondng nvestment perods re 6 months, 12 months nd 17 months respectvely. The men vlue nd the stndrd devton for the nnul return dstruton re lsted n Tle 5. Up to 2010-06-30, the verge vlue of the return of the top 5 portfolo s -42.88%, the top 10 portfolo hs the verge return rto -29.31%, lthough they re oth loss nd the top 5 loss s hgher thn the top 10 loss, ut ths sttes clerly tht the mret s nstlty. Up to 2010-12-31, the top-5
Applcton of ntervl-promethee Method for Decson Mng n nvestng 321 portfolo hs the verge return rte 36.25%, whch s hgher thn tht of the top-10 portfolo whch s 31.98%. Smlrly we cn see the etter performnce of the top-5 portfolo up to 2011-06-10 thn the top 10, rndom20 portfolo nd the Shngh ndex. On the other hnd, the rs of portfolo s mesure y the stndrd devton (std) of the return rte. The smller the std, the less rsy the portfolo. For the ove mentoned 3 nvestment perods, the stds of the top-5 portfolo re lmost the sme wth the top10. All n ll, the top 5portfolo rngs hgher return n the sme rs wth the top 10 portfolo n the long run. Ths emprcl study shows the effectveness of the pplcton of ntervl-promethee method to vlue nvestng. 5 Conclusons Ths pper ppled the ntervl-promethee method to the nvestment decson-mng process of vlue nvestng. Fve crter were used to evlute the growth-potentl performnce suggested y Buffet nd were represented y ntervl numers sed on the rel fnncl dt gthered from the dt se CSMAR4.0. The ntervl-promethee method ws ppled to rn 20 rndomly selected stocs n Shngh Stoc Exchnge. The portfolo wth the top 5 stocs ws proven to hve hgher return thn the top 10 stocs wthn the whole 17-month perod. The emprcl study showed the effectveness of the ntervl-promethee method n the decson mng process of vlue nvestng. References [1] Brns, J.P., Vnce Ph., Mreschl B.. How to select nd how to rn proects: the promethee method. Europen Journl of Opertonl Reserch, 1986,24(2): 228-238. [2] Md Behzdn, R.B.Kzemzdeh, A.Aldv, M.Aghds. PROMETHEE: A comprehensve lterture revew on methodologes nd pplctons, Europen Journl of Opertonl Reserch, 2010,200: 198-215. [3] Mreschl,B., Brns, J.P.. BANKADVSER:An ndustrl evluton syutem. Europen Journl of Opertonl Reserch, 1991,54: 318-324. [4] Vrngel,S.,Stnoevc,M., Stevnovc,V.,LuEn,M..NVEX:nvestment dvsory expert syutem. Expert Systems, 1996,13(2):105-120. [5] Bc,Z., Plzt,N.. Rnng of enterprses sed on multcrtersl nlyss. nterntonl Journl of Producton Economcs, 1998: 29-35,56-57. [6] Bour,A., Mrtel,J.M., Chchou. A mult-crteron pproch for selectng ttrctve portfolo. Journl of Mult-crter Decson Anlyss, 2002,11: 269-277. [7] Aldv,A., Chhrsoogh,S.K., Esfhnpour,A.. Decson mng n stoc trdng: An pplcton of PROMETHEE. Europen Journl of Opertonl Reserch, 2007,177:673-683. [8] L, Z-L. A new mproved rnng pproch for ntervl numers. Mthemtcs n prctce nd theory (n Chnese) 2004, 34 (6): 124-127.