Can we apply Fibonacci retracement in the African market?

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1 Vol. 7(24), pp , 28 Jue, 203 DOI: /AJBM.2849 ISSN Academic Jourals hp:// Africa Joural of Busiess Maageme ull Legh Research aper Ca we apply iboacci reraceme i he Africa marke? Toshisugu Oake* ad all allou Graduae School of Maageme, Risumeika Asia acific Uiversiy, - Jumojibaru Beppu, Oia Japa. Acceped 20 Jue, 203 orecasig was oe of he mos impora issues facig compaies. Techical aalysis was he use of reds ad chars o udersad ad aalyze ivesors' behavior ad heir effec o subseque price acio of fiacial isrumes whe he red is so clear or suppor ad resisace levels obaied hrough iboacci raios. The applicabiliy of iboacci radig i he sock marke for he weser couries or Japa had bee he ceer of iese debaes for may years o predic fuure price. I his paper, we ried o check if here was ay logic i he urig pois paers i he Africa marke similar o i he weser or Japaese marke. Key words: iboacci reraceme, forecasig, echical aalysis. INTRODUCTION Techical aalysis is he use of reds ad chars o udersad ad aalyze ivesors' behavior ad heir effec o subseque price acio of fiacial isrumes. I is believed ha echical aalysis holds he key o moiorig ivesors. or echical aalyss, ivesor seime is he sigle mos impora facor i deermiig a isrume's price ad hey are oly ieresed i he price movemes i he marke. Alle ad Taylor (992) coduced a survey amog chief foreig exchage dealers based i Lodo i November 988. They foud ha raders relied more o echical aalysis ha o fudameal aalysis a shorer ime horizos, ad ha his would be reversed i he log ru. Lui ad Mole (998) came almos o he same coclusio whe hey coduced a survey i 995 o he use by foreig exchage dealers i Hog Kog of echical aalysis. Neely e al. (996) used echical radig rules ad geeic programmig, ad foud srog evidece of ecoomically sigifica ou-of-sample excess reurs o hose rules for each of six exchage raes over he period 98 o 995. Neely (997) explaied briefly he fudameals of echical aalysis ad a efficie marke hypohesis as applied o he foreig exchage marke, ad evaluaed he profiabiliy of simple radig rules, ad reviewed rece ideas ha migh jusify exrapolaive echical aalysis. May previous sudies, Bachelor ad Ramyar (2006), ivesigaed filer rules ha require a rader o buy if price goes up more ha k% above he mos rece low price. Techical aalysis relies o he use of reds ad char paers, or movig average whe he red is so clear or suppor ad resisace levels obaied hrough iboacci raios. Bachelor ad Kwa (2000) foud ha suppor ad resisace red lies are used much more ofe ha movig average rules ad oher idicaors i boh sock markes ad currecy markes. Kavajecz ad Odders- Whie (2004) saed ha suppor ad resisace levels coicide wih peaks i deph ad movig average forecass revealed iformaio abou he relaive posiio of deph o he book. The iboacci sequece begis wih 0 ad, ad he adds he previous wo umbers o ge he curre umber. The, he sequece coiues owards o ifiiy. Mahemaically, he iboacci sequece is as follows: 0 0,, 2, 3 2, 4 3, 5 5, 6 8, 7 3,... *Correspodig auhor. oake@apu.ap.jp. Tel: ax:

2 2338 Afr. J. Bus. Maage. More geerally, he iboacci sequece is defied by he followig recurrece: + + wih he iiial codiios 0 0 ad, for. These umbers are believed o have a very impora role i scieces ad are see as he key o aure. Moreover, he iboacci sequece of umbers is also referred o by Ralph Ellio as he mahemaical basis for he "Ellio Wave" priciple (938, 940). The "Ellio Wave" priciple is a powerful ool for forecasig sock marke behavior. This idea has bee challeged by Bachelor ad Ramya (2006). The iboacci raio is foud i he geomery of logarihmic spiral which is widespread i aure. iboacci proporios are also foud i he double helix of DNA molecules i he reproducio cycles of rabbis, ad he brachig paer i pla life ad hey are also used i ar ad archiecure. urhermore, iboacci raios are also foud i may differe fields i scieces ad i aure. I iace, iboacci raios are a popular radig ool ad hey are used i radig sraegies by may professioals. The mos commo iboacci raio is obaied by dividig ay iboacci umber by he iboacci umber oe place higher i he sequece, ha is, r + Whe goes o ifiiy i he above equaio, we obai ϕ lim r lim commo iboacci raio is derived as X ϕ 0.68 Hece, he The same process ca lead o aoher commo iboacci raio obaied by dividig ay iboacci umber by he iboacci umber wo places higher i he sequece ad is raio is equal o X Likewise, we ca cosider he raio obaied by dividig ay umber by he oe 3 places above i he sequece ad is value is X All he umbers above are called as he iboacci raios. I his paper we demosrae ha he iboacci raios ca be foud i he Africa sock marke, he BRVM (Bourse regioale des valeurs mobilieres) which is a Regioal Sock Exchage for 8 Wes Africa Couries. LITERATURE REVIEW Ayoe who is familiar wih he fiacial press ad he web-based fiacial services is aware of he populariy of echical aalysis ad he abuda lieraure abou i. I is revealed ha a leas iey per ce of ierviewees gave some weighs o echical aalysis whe performig views a oe or more ime horizos. Techical aalysis is like a geeric word ha comprises a se of echiques ad mehods based o visual recogiio of char paers ad reds show from pas price ad volume daa. Lebaro (996) ad Szakmary (997) showed ha exrapolaive echical radig rules rade agais U.S foreig exchage ierveio ad produced excess reurs durig ierveio periods. Leahy (995) demosraed ha echical rades make excess reurs whe hey ake posiios corary o U.S. Bachelor ad Ramyar (2006) showed ha rece sudies ivesigae movig average ha ell he rader o buy or sell if he marke price exceeds or falls below a log erm movig average. Gecay (999) foud ha simple echical rules provide sigifica improvemes for he curre reurs over he radom walk model. Some raders look a a red lie breakig rules ha require o buy or sell if he price breaks above some resisace level or falls hrough some suppor level. This is based o he belief ha as log as he share remais bewee hese levels of suppor ad resisace, he red is likely o coiue. A suppor level is he level a which brokers are willig o buy. O he oher had, a resisace level is he oe a which hey are willig o sell. If he price rises above resisace level, i will ofe become suppor. Traders look also a he paer rades ha require o go shor if some sequece of prices characerisic of a upward red appeared. A upward red is a successio of higher peaks ad roughs. Likewise, a dowward red is a successio of lower peaks ad roughs. I a comprehesive ad iflueial sudy, Brock e al. (992) aalyzed 26 echical radig rules usig iey years of daily sock prices from Dow Joes Average ad foud ha hey all ouperformed he marke. Nefci (99) also showed ha a few of he rules used i echical aalysis geeraed well-defied echiques of forecasig, bu eve well-defied rules were show o be useless i predicio if he ecoomic imes series is Gaussia. Brow ad Jeigs (989) poied ou ha echical aalysis has value i a model i which prices are o fully revealig ad raders have raioal cojecures abou he relaio bewee prices sigals. However, Blume e al. (994) showed ha volume provides iformaio qualiy ha cao be deduced from he price. They showed also ha raders who used iformaio coaied i marke saisics did beer ha raders who did o. I was foud by Lo e al. (2000), afer a examiaio of he effeciveess of echical aalysis o U.S socks from 962 o 996, ha several echical

3 Oake ad allou 2339 Table. eak of sock price. Day eak Table 2. Trough of sock price. Day eak idicaors did provide icremeal iformaio ad may have some pracical value. erdadez-rodriguez e al. (2000) applied a kid of eural ework o he Madrid Sock Marke ad foud ha, i he absece of radig coss, he echical radig rule is always superior o a buy-ad-hold sraegy for boh "bear" ad "sable" marke bu o i a "bull" marke. I he echical aalysis lieraure, here is more emphasis o echical idicaors ha o char paers ad suppor ad resisace levels ideificaio. Neverheless, Lucey ad Aggarwal (2006) examied wheher or o here is psychological barriers i gold prices. He used he sadard M-values of he various ime series ad claimed o fid some evidece o back he exisece of psychological barriers. As described earlier, echical aalysis relies o he use of reds ad char paers whe he red is suppored ad resisace levels are obaied hrough iboacci raios. I he ex secio, we summarize maerials ad mehods i his paper o demosrae iboacci reraceme. MATERIALS AND METHODS The daa of our aalysis are daily observaios o he BRVM0 which is a Wes Africa regioal sock exchage idex for 9 radig days bewee Sepember 7, 200 ad ebruary 7, 20. We used he closig prices durig his period for he BRVM0 idex. Divideds are o ake io accou i he idex because as i a echical aalysis, we are ieresed i ideifyig peaks ad roughs ha migh be observed by echical aalyss raher ha lookig a he irisic value of he idex. The deermiaio of iiial urig pois i he series is doe by pickig peaks ad roughs whe hey occur as he highes or he lowes prices i rage size of 8 mohs o boh sides of he dae (aga-sossouov, 2003). To make i appropriae for our daa, we will be cosiderig a smaller rage; he highes or lowes values i a four days widow o eiher side of he dae will qualify as a urig poi eiher as a peak or a rough. I is cosidered ha he price p is a is peak a ime if he followig iequaliy is verified: [, ] 4, < > This oaio ells us ha, 4 <, 3 <, ha is, a peak occurrig a ime, he correspodig price is he maximum of he followig se: Similarly, as for a rough, (,,, ) max [ >, ] 4, < ha is, a rough will be cosidered o have occurred a ime, he correspodig price is he miimum of he followig se: (,,, ) mi Give his lack of clariy i he way o choose a suiable widow size for he aalysis, we hik ha give he size of our daa se, a four days widow is appropriae. We use Scilab o impleme his algorihm. Scilab is a free sofware for umerical compuaio ha coais may mahemaical fucios. Afer obaiig he urig peaks ad roughs, we eed o calculae he reraceme ad projecio raios. Oce hose raios are obaied, we es if hose raios ad he iboacci raios have saisically he same disribuio checkig by he K.S es. Table shows he peaks from daily observaios o he BRVM0. Likewise, we have roughs from daily observaios o he BRVM0 as show i Table 2. We have o go hrough he ables ad compare he occurrece daes o pick hose ha fulfill hese codios. Also, we eed o perform he K.S. es o he disribuios of he raios foud i he marke o he iboacci raios. The raios foud i he marke are boh reraceme ad projecio raios. There exis wo ypes of reracemes: a bull reraceme ad a bear reraceme. A bull reraceme akes place whe he price moves from a fallig red o a risig oe. O he oher had, a bear reraceme appears whe he price moves from a risig o a fallig red. We ca see ha a reraceme is he raio of oe phase o he mos rece opposie phase. As for a projecio raio, i represes he raio of oe phase o he mos similar phase. Afer obaiig boh projecio ad reraceme raios, we examied he K.S es, D wih p-value rom he KS es resuls, we cao rejec he ull hypohesis ha iboacci raios ca be foud i he Africa marke. RESULTS OR IBONACCI RETRACEMENT I his secio, we es how close he reraceme ad projecio raios are o he iboacci raios, ad wha are

4 2340 Afr. J. Bus. Maage. he mos freque iboacci raios ha have occurred i he period of sudy. Techically we will see if he raios ha have occurred are wihi [ f f + ] R, of iboacci raios: where R is a raio, wheher a reraceme or a projecio raio ad f is a iboacci umber ad a kid of error erm. We do o expec he raios foud i he marke o be exacly he same as he iboacci raios, To defie he ierval umerically, we choose equal o as follows R [ f 0.025, f ] o be so ha we ca es if he give raio is wihi of some iboacci raio. Our objecive is o compare hose reraceme raios o he closes iboacci raio i order o examie if hey are wihi each oher. The mai iboacci raios sequeces may praciioers are usig are: Before we focus o he compuaio of he reraceme ad projecio raios, i is useful o have a look a he graph ha represes he prices red durig he period of ieres. rom Day 4 o Day 40, we ca see he firs upward red, a 7.92 icreme from he sarig poi. I lased 36 days from Day 4 o Day 40. rom Day 40, i reraced back uil Day 75, which was a log declie. The reraceme raio is obaied by dividig he legh of he declie by ha of he previous bull phase, which is give by Hece. he sock price was a 37.6% reraceme from he precede peak. The iboacci raio which is he closes o he 37.6% reraceme raio is he.382. The differece bewee he wo raios is simply give by We ca see ha he reraceme raio is very close o he correspodig iboacci raio. Nex, we will look a he projecio raio. Afer he log declie from Day 40 o Day 75, he sock price was he opposie moveme ad sared o go up agai, i.e., he bull phase from Day 75 o Day 99, which lased 24 days. The correspodig sock prices are ad 68.55, respecively. Therefore, he projecio raio is 0.236, 0.382, 0.68,.382, The projecio raio ca be compared o which represes he closes iboacci raio o ha from he previous equaio. The differece bewee he wo raios is simply give by We ca see ha he projecio raio is very close o he correspodig iboacci raio. A Day 99, here is a local peak ha is followed by a bear phase ha has lased uil Day 09. The sock price a Day 09 was Sice he legh of he dowred divided by ha of he previous upred is he reraceme raio, his is give by This raio ca be compared o is closes iboacci raio, The differece bewee he wo raios is simply give by Hece, we ca see ha he reraceme raio is very close o he correspodig iboacci raio. Noe of he iboacci raios ca be cosidered as he mos freque from our aalysis. However, we recogize iboacci reraceme exiss ad ha he iboacci radig rules ca be a very useful ool for raders i he Africa marke. DISCUSSION AND CONCLUSION orecasig is oe of he mos impora issues facig compaies. Improvig forecasig will always remai a difficul ask because he fuure will always remai ucerai. The applicabiliy of iboacci radig i he sock marke has bee he ceer of iese debaes for may years o predic fuure price. I his paper, we ried o check if here is ay logic i he urig pois paers i he Africa marke. We looked upo a rage of four mohs daa from Sepember o ebruary 7 20 obaied by he Africa regioal sock exchage i Abidja i Coe d' Ivoire. I addiio, we cosidered he closig sock prices of he BRVM0 for our aalysis. We firs foud he differe urig pois durig he sample period usig he aga ad Sossouov (2003) algorihm modified a bi o accou for he shorer imeframe of our research. We used he mahemaical sofware, Scilab, o fid he differe urig pois ad he calculaed he reraceme ad projecio raios. The K.S es was he

5 Oake ad allou 234 used o es he exe a which he iboacci raios sequece ad he differe raios foud i he marke. Aferwards, we cocluded he aalysis for iboacci reraceme proved he sock prices which were almos always reversed aroud iboacci raios. Alhough i was o clear how o ideify which iboacci raios were he mos freque, our coclusio from our aalysis is ha he iboacci radig ca be a very useful ool for raders i he Africa sock marke. ACKNOWLEDGEMENTS The firs auhor is graeful o Risumeika Asia acific Uiversiy for heir fiacial suppor durig his work. The auhors are graeful o he referees for heir useful commes o he paper. REERENCES Alle H, Taylor M (992). The Use of Techical Aalysis i he oreig Exchage Marke. J. I. Moey iace, (3): Bachelor R, Ramyar R (2006). Magic Numbers i he Dow, Cass Busiess School, Ciy of Lodo. Bachelor R, Kwa S (2000). A survey of Techical Aalyss. Cass Busiess School ad MMS ieraioal. Blume L, Easley D, O hara M (994). Marke Saisics ad Techical Aalysis: he role of volume, J. iac. 49(): Brock W, Lakoiskok J, B Lebra (992). Simple Techical Tradig Rules ad he Sochasic roperies of Sock Reurs. J. iac. 47(5): Brow D, Jeigs R (989). O Techical Aalysis. Rev. iac. Sud., 2(4): Doucouliagos C (2004). Number referece i Ausralia Sock Marke, Appl. iac. Eco., 4(): Ellio RN (938). The Wave riciple repried i R. R. recher Jr., Ed., 994, R. N. Ellio s Maserworks, New Classics Library, New York, pp Ellio RN (940). How he Wave riciple Works, ad is Correlaio wih Mahemaical Laws, repried i R. R. recher Jr., Ed., 994, R. N. Ellio s Maserworks, New Classics Library, New York, pp erdadez-rodriguez C, Gozalez-Marel S, Sosvilla R (2000). O he profiabiliy of echical radig rules based o arificial eural eworks: Evidece from he Madrid Sock Exchage, Eco. Leers, 69(): Gecay R (999). Liear, o liear ad esseial foreig exchage rae predicio wih simple echical radig rules, J. I. Eco. 47(): Kavajecz KA, Odders-Whie ER (2004). Techical aalysis ad liquidiy provisio, Rev. iac. Sud. 7(4): Leahy M (995). The profiabiliy of US ierveio i he foreig exchage markes, Joural of Ieraioal Moey ad iace, 4(6): Lebaro B (999). Techical radig rule profiabiliy of foreig exchage ierveio, J. I. Eco., 49(): Lo A Mamaysky H, Wag J (2000). oudaios of Techical Aalysis: Compuaioal Algorihms, Saisical Iferece, ad Empirical Implemeaio. J. iac. 55(4): Lucey BM, Aggarwal R (2006). sychological Barriers i Gold rices, Rev. iac. Eco. 6(2): Lui YH, M Mole (998). The use of fudameal ad echical aalyses by foreig exchage dealers: Hog Hok evidece, J. I. Moey iace 7(3): Neely C, Weller, Dimar R (996). Is Techical Aalysis i he oreig Exchage Marke rofiable? A Geeic rogrammig Approach, Discussio aper Series, Cere for Ecoomic Research Lodo. Neely C (997). Techical Aalysis i he oreig Exchage Marke: A Layma s Guide. ederal Reserve Bak of S Louis. Nefci SN (99). Naive Tradig Rules i iacial Markes ad Wieer- Kolmogorov redicio Theory: A Sudy of Techical Aalysis. J. Bus., 64(4): aga AR, Sossouov KA (2003). A Simple ramework for Aalyzig Bull ad Bear Markes, J. Appl. Eco. 8(): Szakmary AC, Mahur I (997). Ceral Bak Ierveio ad Tradig Rule rofis i oreig Exchage Markes, J. I. Moey iac. 6(4):