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Candlestick Technicl Trading

Stagies: an They reate Valuefor Ivestors?


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Abstract

hs thess exames the protabty of the oldest ow form of technca analyss

cadestck tradg strateges. Un ke tradtoa techncal aalyss whch s based

around cose prces these strateges generate buy and se sas that are based on

the relatonshp betwee ope hgh ow ad cose prces wthn a day ad over

cosecutve days radtoa techca aayss whch has bee the focus of

prevous academc research has a logterm focus wth postos beg held for

moths and years. cotrast candlestck techcal aayss has a shortterm focus

wth postos bg held for ten days or lss hs dffrence s sgcat as

surveys of markt partcpats dcate that they place 50 per cet more mportace

o techncal analyss for horzos of a week tha they do for horzos of a year


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Using an innovative extension of the bootstrap methodoogy which allows the

generation of random open high low and cose prices to test the protability of

candlestick technical trading strategies showed that candestick technica anaysis

does not have vaue. here is no evidence that a trader adhering to candestick

technical anaysis would outper the market.


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Acknowledgements

Compto of ths thss woud hav b mpossbl wthout th ovg suppot of

my wf aur I ow hr a hug amout

h tough tms whch ar aways part of rsarch wr abl to b ovrcom

wthout udu strss du to my fath h vrs ca do all thgs though hm who

givs m strgth" (Phl ppas 4 1 3 ) was a costat sourc of sprato

hs rsarch was supportd acally by th Foudato for Rsarch Scc

ad chology (FRS) th form of a op Achvr Doctoral Scholarshp hr


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Fialy I wat to ote my scere apprecatio to Rock ad Jared Caha for their

assistace wth my atab queries Rock particuar wl ever kow how much I

vaue his work i this area


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Table of Contets

Abstract Ackowledgemets vabe of Cotets v st of abes x

st of Fgures xCapter Oe Itroducto ... . 1Capter wo: terature Revew .. . . . . . . 1 02 1 Itroducto . .. 1 022 radtoal Face . 1 1

22 Backod . . . . . 1 12 2 2 Radom alk ypotess . . . 1 12 2 3 Efcet Market ypotess . . . . 1 42 24 Emprcl Evdece agast arket Efcecy 6

2 3 Beavourl Face 2023 1 Backod . . . . . . . . 202 3 2 Psycologca Bases . . . . . . 202 3 3 mts to Arbtrage . . . 222. 3 4 e Stock Market as Complex Adaptve System . . . . . 23

2 4 eccal Aayss . . . . . 24


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3 2 1 . Data Used .. . . . . . . . . . .. .. . .. . . . . . . . . . . . . . 6 13 .2 2 Data Soopg .. . . . .. . .. 63

3 3 Methodoogy . . . . . .. . .. .. . . . . . . .. . . 66

3 3 . adlestck Pattes . . .. . . . . . . . . 663 3 2 Measues of adlestck adg Stategy Potab ty . . . ... . . . . . . .. 7 1

3 32 1 est . . . .... .. . . . .. . . . . . 7 132 3 2 Bootstappg Methodology . . . . . . . . . . 72

3 .4 . ocuso . . . . . . . . . . . . . . . . . . . . . . . . 77hapte Fou Results . . . . . . . . . . . 794 1 Itoducto . . . .. . . .. .. . . . . . . 79

4 2 Suay Statstcs . . . . . . . . . . . . . .. .. . . . ... 8 4 3 Statstca ests . . . . . . . . . . . . . . . . . . . . . . 82

43 1 . Sceao A: ade tated at the ose Pce o the Day of the S aa e-Day oldg Peod ad a eDay Expoeta MovgAveage to Determe Po ed ... . . . . . . . .. . . 82

4. 3. 2 Sceao B ade tated at the ose Pce o the Day ae theSa a e-Day ol dg Peod ad a e-Day Expoetal

Movg Aveage to Determe Po ed . .. . . . 924 3 3 Sceao : ade tated at the Ope Pce o the Day ae theSal a eDay odg Peod ad a eDay ExpoetalMovg Aveage to Determe Po ed . . . . . 99

4 3 4 . Sceao D: ade tated at the Ope Pce o the Day ae theSgal a FveDay oldg Peod ad a eDay ExpoetaMovg Aveage to Deteme Po ed . 105

4 3 5 Sceao E: ade tated at the Ope Pce o the Day ae the


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Appdix hr: Matab Cod 177A.3. 1 . Cadsick Fuctios . 179A.3 .2 . s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

A.3.3. EMA 201A.3.4. Us 202A. 3 .5 . Radom Walk Boosrap .. .. 203A.3.6. Rsampl Fucio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223A.3 .7. AR Boostrap . . . . . . . . 224A. 3. 8. GARC-M Bootstrap 245A.3 .9. GARCM Fucio 266

A.3 . 1 0. EGARC Boostrap 268A.3 . 1 . EGARC Fuctio . . .. 289


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List of Tbles

Table : Number f Caneic Pae Tee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Tabe 2: Summar Saiic8 Tabe 3 : Scenari A : -Te Reul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Tabe 4: Scenari A: Bra Prrin fr al Nu Me . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Tabe 5 : Scenari A: Bra an Raw Sere Mean an Sanar

Deviain fr Ranm Wa an AR ) Nu Me .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Table 6: Scenari A: Bra an Raw Sere Mean an Sanar

Deviain fr GARCHM an GARCH Nul Mel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Table 7 : Scenari B: Te Reul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93Tabe 8: Scenari B: Bra Prrin fr all Null Mel .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95Tabe 9: Scenari B : Bra an Raw Sere Mean an S anar Deviain

fr Ranm Wa an AR( ) Null Mel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97Tabe 0: Scenar B: Bra an Raw Serie Mean an Sanar

Deviain fr GARCHM an GARCH Nll Me .. . . . . . . . . . . . . . . . . . . . . . . . . . . 98Table : Scenar C: Te Rel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 00Table 2: Scenar C: Bra Prrin fr all N Me . . . . . . . . . . . . . . . . . . . .. . .. .. . 02Table 3: Scenar C: Bra an Raw Serie Mean an Sanar

Deviain fr Ranm Wa an AR( ) Nu Me ... . . . . . . . . . . . . . . . . . . . . . . . . . 03Table 4: Scenari C: Bra an Raw Sere Mean an Sanar

Deviain fr GARCHM an GARCH Nl Mel ... . . . . . . . . . . . . . . . . . . . . . . 04


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A1 EGARCH Functon

functon = egach_functon (N etuns esduals C MA A K GACH ACH sgma)2 %EACHBOOAP oot st aps an egach model 3 %nput s esduals and f tted paametes fom og nal egach mode N s4 %the nume of eal sat ons to c eate etuns a y N matx of N etun5 %sees of length 6 lead 10 00 891 01 1

length (esduals ) eos (+leadN )

o n N 31 4 eps l on esa mp l e ( es dua l s es du a l s es du a l s ] )

1 5 h t = s t d ( e s dua l s * s a ) 2 1 6 ( n ) 0 8 o t2 +lead1 92 0 old_ht ht 2 1 h t exp ( K GACH*log (ht ) AC H * ( a s ( e ps l on ( ) * s q t ( o l d_ht ) ) / s q t ( h t ) - s q t p ) +

* ( ep s lon ( - 1 ) * sq t ( o l d_h t ) ) / s q t ( h t ) ) 2 2 ( t n ) = C + A * ( n ) + M A* ( e p s l on ( 1 ) * s q t o l d_ht ) ) + e ps l on ( t ) * s q t ( h t ) 2 324 % old_ht ht2 5 % ht = exp ( K + G A CH * og ( h t ) + ACH ( a s ep s l on ( 1 ) ) /s q t ( h ) -s q t ( 2 /p * ( ep s l on ( -

) ) / sq t ( h t ) ) 2 6 % ( t n ) C A * ( - 1 n ) + MA * ( ep s l on ( - ) ) + e ps l on ( t ) 2 2 8 end2 93 0 end

289


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List of Figures

Fure Oen , Low and ose Prces Dsayed as andes . 4Fure 2 e Marbozu andestck. 56Fure 3: Buis Enun andestck Pae . 58


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Chapter One: Introduction

Debae n he egree whch ae reu can be rece ha cnnue n

Wee nance cmmune fr ver ear The mrance f h ebae

he glba ecnm ha reue n a huge amun f reearch energ beng eve

h area e acaemc an racner cmmune have hrcall been

ve n h ue. Acaemc have ranall beeve ha reu are n

recable becaue f he were ranal mare arcan wul n lea f

h recabl an rae awa In cnra a large rn f he nvemen

nur bae n he reme ha value can be ae b acve managemen In

her wr rfenal manager are l a cng ure mvemen n ae


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prie moves above beow) a moving average of past pies, to es that are based

on pattes" in pie data An exampe is the head and shoulders patte his

involves thee peaks, the highest of whih is in the midde f prie penetrates the

bottom of the rst peak, aer ompeting this patte, a sell sia is given

raditional tehnial trading rules in the Weste word require lose pre data;

however, new more sophistiated ues - suh as the Diretiona Movement ndiator

- now ombine open, high, ow, and lose data

Sueys onduted among forei exhange and equity market patiipants and

nania oualists nd that the shorter the foreasting horizon the eater the

emphasis whih individuas plae on tehnial analysis Despite this aademi

researh has foused on testing the protability of longterm tehnia trading rules.

Most studies have tested ules based around 50 to 200 days of historial data whih


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aount A smaler strand of li terature shows that the appiation of tehnia

analysis does result in exess retus

his thesis is unique in that the protability of andlestik tehnia analysis is

onsidered Candlestik tehnial anaysis was introdued to the weste world by

Steve Nison in 99 when he pubished a book tited Japanese Candlesck Chang

Technques A Conempoa Gude o he Ancen Inesmen Technques ofhe Fa

Eas Candlestik trading rules rely on one to three days of historial data to

generate a sial Positions are generaly held for up to 0 days his short-term

fous makes them very popular with market partiipants who favour tehnial

anaysis for shortterm horizons Nison (2004 p 22) omments sine its

introdution to the Weste world andlestik tehnia analysis has beome

ubiquitous available in almost every soware and onine harting pakage


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Fgue 1. Ope, Hgh, Lw ad Cse Pces Dsplaed as Cadles

When the ose is above beow) the open the andle body i s white blak)

Hg

OLw

HgO

Lw

A daily andlestik is a aphial representation of the days open, high, low, and

lose pries Daily andestiks are ommonly referred to as singe lines" Some

single lines are said to have foreasting power in their own right Together,

onseutive single lines an form ontinuation and reversa pattes Continuation

pattes indiate the prevaiing trend will ontinue whie reversal pattes suggest


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point of January 1992 was arely hosen Despite it having been a popuar

trading tehnique in Japanese nanial markets for some onsiderable time, the

seminal andestik trading strategy book in English was not published until 1 99

herefore prior to 992 large setions of the Weste nane ommunity may not

have been aware of andestik tehnial analysis

Data hoie is ritiay important to tests of tehnia anaysis for severa other

reasons Firsty, it is important that the hosen data are able to be traded in reality in

the same manner in whih they are tested For instane, the use of index data in

tehia analysis researh is a dubious approah ifthe index is unable to be traded in

its own right in reality Seondy, it is important that the data are om instruments

of suient iquidity to enable market partiipants to make meaningl amounts of

money his liquidity aspet is also important to provide a fair test of tehnial


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he bootstrapping approah invoves tting a null model eg. GARCH-M) to a lose

prie stok series then randomy resampling the residuals 500 times hese

resamped residuals are then used to onstut 500 stok series that are by

onsttion random but have the same time-serie s propeties as the origina seies

he protability of a tehnial trading ule is statistially siiant at the lee of

5% if the number of times that the e produes more prot following a buy sia

on the 500 random series than the original series is fewer than 25

he bootstrapping methodology i s established i n the literature for trading rle s that

require only one pie series Candestik tehnial analysis involves open high

ow and lose pries so an extension is required he approah taken in this thesis

whih appears to be a rst was to simulate a random ose series in the manner

outlined above ne a randomy generated lose series had been formed vetors of


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Chapter wo is divided into three setions In the rst of these the traditiona

nane i terature is reviewed his inludes iterature on two of the most important

onepts in mode nane the random walk and efient market hypotheses he

andom walk hypohe holds that ae pce ucuae andomly whie the

ecen make hypohe ontends that no poble o make economc po

by adng on aalable nfomaon. his setion nishes with a brief review of

some of the eary empiria iterature whih explains evidene found that is

inonsistent with the random wak hypothesis

In Setion wo the li terature within the growing area of behavioural nane is

examined his work details attempts to explain departures om rational behaviour

using psyhology iterature he idea that there are limits to arbitrage that prevent

inefienies om being traded away is losely inked to this area A relatively new


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risks taken in eing them, and that whih does seem to indiate exess protabiity

Different ues ae onsidered separatey within these two broad ategoies Setion

hee nishes with a detaied desiption of andestik tehnia anaysis

Chapter hree ompises two setions The rst ontains an extensive disussion of

the hoie of data and the steps that have been taken to eevate this researh above

the itiism of data snooping. In genera tems, daa snooping ours when a

researcher ess a heo using he same daa ha were employed in he developmen

of he heo and hen claims ha he empirical resuls suppor he original heo

Setion wo ontains a detaied desription of the hoie of andestik rues and the

methodoogy used to test their protabiity This inudes a standard test approah

and an extension of the bootstrapping methodoogy to enabe the generation of

random open high ow and ose pries The four nu modes empoyed in the


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hree appendices are also incuded he rst provides a graphica depiction and

expanation of candestick single ines and reversal pattes. Appendix wo contains

a description of the Dow Stocks used in this research he nal appendix contains

the MA AB code that was used to generate the resuts.


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Chapte Two: Liteatue Review

2.1. Introuction

he iterature review is divided into three major setions In the rst the extensive

literature that overs the random walk and efient market hypotheses two of the

most important onepts in mode nane are onsidered In Setion wo, the

nane iterature in whih attempts are made to explain nanial phenomena usingpsyholo gy l iterature is disussed. his emerging area known as behavoural

nance suggests that eemngly rraonal nancal marke behavour can be

explaned by lookng a he pychologcal makeup o marke parcpan he


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22 raditiona Fnanc

221 Background

he traditiona nane paradi is a means by whih an understanding of nanial

markets using modes in whih agents are rationa is sought It is assumed that

agents proess new information orretly and that they have enough information

about the struture of the eonomy to gure out the true distribution for variables of

interest he random walk and efient market hypotheses are entral tenets of

traditional nane

22 2 Rando Walk Hypothe


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eading to subseuent disoveries" he seond disovery of the mode was by

Working 934) who showed empiriay that ommodity pries utuate randomy

Eonomists appear to have paid surprisingy li tte attention to Workings 93 4)

ound-breaking studies he next maor investigation was by Cowes 1933) who

found that stok market anaysts ould not predit pries Subsequently Cowes

944) provided orroborative resuts for a large number of foreasts over a muh

longer sampe period Kenda 1953) analysed 22 UK stok and ommodity prie

series and found that at fairly lose intervas the random hanges are so large that

they swamp any systemati effet whih may be present Kendal 1 953) onuded

that the data behave l ike a wandering series "

he main mode interest in the random walk model started in the late 1950s when

papers by Roberts 95 9) and sboe 1 959) expliitly stated that stok market


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Where

E) 0

Var) is nite

Now i f

a) e s 0) are independent then P is a strit random wak

b) e s 0) are unorrelated P is a seond order martingae

) e s 0) are independent and are all normay distributed then P is a

Wiener proess.

Following Robes 959) and Osboe 9 59) numerous papers generally

supportive of the mode were then written Cowes 1 960; Working 1 960;


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whee x% and y ae typiay both 05%) In this wok exess pots wee found

but these disappeaed ae one-way tansation osts of 0.05% wee taken into

aount

22 Efcet Market Hypothe

he tem ecien capial marke has seva eated meanings. In genea the

efient makets hypothesis hods that a marke i ecien i i impoible o make

economic pro by rading on available informaion. Unexpeted pie hanges

must behave as unoeated andom dawings if the maket is ompetitive and

expeted pots om tading ae zeo hese pie hanges eet new infomation

that annot be dedued om pio infomation, theefoe new infomation must be


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Building on Samueson s 1 95) micro economic approach together with taxonomy

suggested by Roberts 97) ama 970) assembed a comprehensive review of the

theory and evidence of market efciency hough his paper proceeds om theory to

empirica work he noted that most of the empirical work preceded development of

the theory he theory involves dening an ecen make as one in which adng

on avalable nfomaon fals o povde an abnomal po A market can be

deemed efcient therefore ony if a model is posited for retus ests of market

efciency are therefore joint tests of market behaviour and modes of asset prcing

Dimson and Mussavian, 1998).

A major contrbution of ama 1970) is the classication of the efcient market

hypothesis into three forms based on information A market is said to be weak form

efcient" if it reects all knowedge om past price information semi-strong form


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iewed as economic rens, exis o compensae inesors for he coss of rading and

informaion gahering.

This work on impedimens o purey ecien prices ed Jensen (198) o deeop a

broader deniion of he ecien markes hypohesis where marke prices can differ

om ndamenas ony o he exen ha i is undesirabe o rade in he mispriced

asse. Trading may be undesirabe because of ransacion coss, he cosy naure of

informaion, or arbirageur risk aersion. The adopion of his deniion aows

eeway for siican deiaions beween price and aue wihou ioaing he

efcien marke hypohesis.

Ba ( 1 995) idenied seera imiaions in he Jensen ( 98) approach. He

suggesed ha exremey arge ransacions coss impy few opporuniies o pro


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largey been developed by the pratitioner ommunity and subsequenty tested by

aademis he aademi ommunity has aso instigated researh into the predition

of ure stok reus based on urrent information his anomaly literature

typiay takes the approah of omparing the retus generated om a patiuar

strategy to those expeted based on the Capita Asset Priing Model CAPM) of

Sharpe 964) Lintner 965) and Mossin 966) his use of the dominant risk

reu model in nane means that suh tests are ointly investigating the CAP M and

the theory against market efieny

he tehnial analysis iterature is onsidered in detail in Part 3. In this setion the

voluminous literature that presents empiria results based on variables other than

past pries - that some laim ontradits the ef ient market hypothesis is briey

onsidered


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ne of the rst papers to doument a nonannounement anomaly was asu 1977)

He found that pie/eaings ratios are usel in prediting stok retus ow

prie/eaings seurities outperformed their high prie/eaings ounteparts by more

than 7% per year anz 1 98 1 ) then found that small stoks outperfomed large

stoks by an average of 1 % per month on a isk-adusted bas is his study has been

itiised as being affeted by suivorship bias . However Fama and Frenh 1 992)

showed that size and book-tomarket equity apture muh of the rosssetional

variation in stok retus and that beta has limited power to explain retus

akonishok Shleifer and Vishny 1 994) proposed that ratios involving stok pries

proxy for past perfomane Firms with high low) ratios of eaings to prie ash

ow to prie and book-to-market equity tend to have poor strong) past eaings

owth hey hypothesised that the market overreats to past growth and is surprsed

when the eaings owth mean revets As a result past poor strong) performers


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Othe studies hve doumented negtive utooeltion in weekly seuity etus

J egdeesh, 990), positive utooeltions in etus ove monthy time hozons

Jegdeesh nd Titmn, 993), nd negtive oetion in longe hozon etus

ove sevel yes DeBondt nd hle, 985) Whie this unde nd oveetion

itetue is typily inluded in disussions on nomies, in this thesis it is

inluded i n the tehni nysis setion These studies fomulte tding sttegies

bsed soely on pst etus, so they fll into the gene ssition of tehnil

nlysis

Othe evidene of ove nd undeetion is bsed on ompnyspei events

These inlude the oveetion to the poo longtem pefomne of initi publi

offeings Ritte, 1 99 1 Loughn nd Ritte, 1 995), nd sesoned equity offeings

Loughn nd Ritte 1 995; Spiess nd Afek Gves 1 995) Thee is lso othe


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abnormal prots ompensate for time-varying risk, question their perasiveness and

robustness ama, 998), or argue that markets may yet be minimay rational," in

the sense that they fai to supply opportunities for abnorma prots Rubinstein,

200 1 ) Others, now referred to as behaviourists", have sought to explain anomaies

using psyhoogy iterature B arberis and haler, 2002)

2. 3. Behavioural Finance

2 1 Backgrond

Behavioura nane was developed by psyhology researhers who saw the

relevane of their work to nane. Slovi 1 969, 1 972) il lustrated stokbroker and


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Heuristi simpliation heps expain many different biases suh as

representativeness udgements based on stereotypes) anhoring and adustment

saiene and avaiability effets heavy fous on information that stands out or is

oen mentioned at the expense of information that blends into the bakound)

aming effets where the desription of a situation affets udgements and hoies)

money ilusion where nominal pries affet pereptions) and mental aounting

traking gains or losses relative to arbitrary referene points)

Sef-deeption an explain overondene a tendeny to overestimate one's ability

or udent auray) and dynami proesses that support overondene suh as

biased sef-attribution a tendeny to attribute suess to ones own ability and

failure to bad uk or other fators) onrmatory bias a tendeny to interpret

evidene with ones pre existing beliefs) hindsight bias a tendeny to think you


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2 Lt to Artrage

Behavioua nane eeahe ague ha ome feaue of ae pie ae mo

plauibly inepeed a deviaion om ndamenal value and hee deviaion ae

bough abou by he peene of ade who ae no ly aiona Saegie

deied o oe mipiing ae aid o be oen oy and iky endeing hem

unaaive In ohe wod limi o abiage exi

Babei and Thae 2002) idenied ndamena ik a a key deeminan of

abiage aiviy Thi efe o he poibiliy ha he pie of wo ok wih

imia ndamenal may divege owing o hei unique haaeii ahe han

onvege beaue of hei imilaiie


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understanding of the eonomi situation Mithell, Pulvino and Stafford 2002)

found that information osts are a siiant fator behind the instanes when the

market value of a ompany is less than that of its subsidiary Beoming informed

about these opportunities is difult when there is little evidene to examine

2.34 The Stock Market as a Coplex Adaptive Syte

Based on the many obserations in the behavioural nane literature that individuals

do not at rationally, Mauboussin 2002) proposed that stok markets should be

viewed as omplex adaptive systems A omplex adaptive system exhibits a number

of essential properties and mehanisms irst, the behaviour of the market

emerges" om the interation of investors. Seond, agents within a omplex

i i f i h i i i i h h i


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t aso aows the reaxation of the assumption of rationa investors and the assoiated

assumption of risretu efieny

An interesting proposition stemming om the theory of ompex adaptive systems i s

that agegate rationaiy at the maret eve an be generated, not ony om

individua rationaity but aso om individua irrationaity his is in star ontrastto the widey aepted ead steer metaphor where pries are assumed to

be set by

rationa investors despite the presene of irrationa investors

2.4. Technical Analysis

2 1 Background


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to only 1 5 90000 urls for portfol io theory" both searhes were onduted on

29/3/05) Moreover sureys of forei exhange and equity market partiipants

e g Carter and Van Auken 1 990; Aen and aylor 1 992 ; Lui and Moe 998 ;

Oberehner 2001) onsistenty nd that the maority of market partiipants use

tehnia anaysis over some foreasting horizon

Despite i ts widespread aeptane and adoption by pratitioners tehnia anaysis is

desribed by Makiel 1 98 ) as an anathema to the aademi world" his is

beause of its onit with market eieny one of the entra pillars of aademi

nane

22 Theoretcal Foudaton


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here is more debate over pubi information Proponents of the efient market

hypothesis, suh as ain 98 8) dismiss the existene of trends in studies whih

show that pries adust rapidy to reet new information More reent studies have

found evidene that is in onit with this view egadeesh and itman 993)

showed that investors oen underreat to news leading to momentum over three to

twelve months, whie DeBondt and Thaer 985) showed that investors overreat

over periods of three to ve years.

Proponents of tehnial anaysis believe that trends are reversed at support and

resistane eves and gain momentum aer these levels due to order lustering

Using a unique data set of forei exhange orders ser 2003) found evidene to

support this. She found that exeuted take-prot orders luster more strongly at

d b th d t d Si t k t d h d t d t


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Grossman, Cone, Miler, ishel, and Ross, 1997) Seond, round numbers may be

easier to remember and to manipulate mentally Goodhart and Curio, 99 1 ; Kanel,

Sarig, and Woh, 2001) Third, humans may simply prefer round numbers, een

without rationa arguments for their superiority Yue, 927) ne the patte of

order ustering is established, it may be sefreinforing even in the presene of

rationa speuators

Many authors have speuated that intervention by monetary authorities is the soure

of tehnial trading rule protabili ty in forei exhange markets riedman, 95 3 ;

Dooley and Shafer, 98 3 Corrado and Taylor, 986 Sweeney, 1 986 Kritzman,

989) More reently, a seminal paper by LeBaron 1 999) showed a remarkabe

orreation between daiy US ofia intervention and retus to a typial moving

aerage rle urther researh has extended this result Szakmary and Mathur 1 997)


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the dietion of intevention Neely 2002) poposed that intevention is orrelated

with tading le etus beause monetay authorities intervene in esponse to shot

tem tends om whih tading les have eenty poted

Anothe hypothesis is that noise tades, who make thei tading deisions based

upon pio dietiona movements in an instment dominate the maket Sheife

and Summes 1 990) agued that this type of tading behaviou may push asset pies

beyond thei true value Moeove, even if individual tades eoise mispiing,

they may be unwiing o unable to tade against the maket beause of thei own

loss limit estitions In fat, individual tades may nd it in thei best inteest to

stimulate seria orrelation if they fee that investo sentiment wil emain stabe in

the short tem hey an tade with the maket in the shot tem and as a esut seve

t d i th k t th it d t l Shl if d S


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300 rie dealers traded 0000 bales of rie Yet throughout al of apan there

were ony 30000 baes of re Ni son 99 ) here is no known doumentation on

the transations osts of this early rie market

he majority of tehnial trading rule iterature uses DA stok market data for

empiria tests n the NYSE iquidity is provided by the quotes of the speialist

and limit orders om the publi ransation osts inude bid-ask spreads and

ommissions ones 2002) reported that the average one-way ommissions on

roundot transations in NYSE stoks were around 0 3% prior to the 930s they

then steadily rose to a peak of approximately 09% in the mid- 970s prior to the

Seurities and Exhange Commissions SEC) breaking of the ommission artel

Commissions then began dramatially fal ling and are down to approximatey 0 %

today Commissions vary based on who is doing the trading Floor traders fae


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the tansations osts faed by a lage investo would be in the 00 % - 0 % ange

pe ound tip

he teia tading iteatue has aso used tues maket data Futues makets

also adopt a deale stutue Investos ae faed with a ommission and the bidask

spead ike othe makets, it is easonabe to assume that tansation osts have

delined ove time Kusek and oke 993) estimated that bidask speads ae ess

than one tik ie. below $20) Aowing fo a ound-tu bokeage ommission

of $25 and a typial ontat vaue of $60,000 yields total diet tansations osts in

the 006-0 .07% ange

2.. Emprcal Tet Content wth the Efcent Market


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aone sraegy, may, in fa, be used as a vaue-adding overlay' sraegy o assis

nd managers in beer iming he buying or se ing of soks as par of heir normal

rading aiviies As hese sok rades would have effeively ourred in he

norma ourse of business, he ransaion oss are already faored in e hey have

zero inremenal os)

Markeos 2004) also found ha ehnia anaysis has vaue beyond obaining risk

adjused exess reus When aive porfoio managemen based on ehnial

analysis ombined wih passve buyandhod) sraegies subsania

diversiaion benes are shown o our Marke reus are able o be mahed a

a aion of he risk, whih ould expain he populariy of mixed" aivepassive

porfolio managemen ehniques


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2.4.4.2. Mvg Aveage ad adg Rage BeakOut ests

Moving average trading rues have proved very popuar in the iterature. hese rues

invove onstruting a short moving average e .g. 1 0 days) and a onger moving

average e.g. 200 days). A buy se) sia is generated when the shorter moving

average moves above beow) the onger moving average, beause at this point a

trend is onsidered to be initiated Gartey, 1 930)

rading range break-out res aso known as channel res) are osey inked to the

onepts of support and resistane. he prinipe is that one pries break ee of the

resistane support) whih has been at the top bottom) of a reent trading range they

tend to aeerate and move siianty higher ower) Wykoff, 1 9 1 0). ike


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oss 0 39%) are similar or smaller han esimaes of aual oss a resul ha is

onsisen wih marke efieny

he boosrapping mehodology of Brok e al 992) allows for a omparison of he

volailiy of reus following buy and sell sials his enables a udgemen o be

made on wheher risk is driving he poabiliy of a rading sraegy apers ha

nd rading rle proabiliy is eroded by ransaion oss e.g Bessembinder and

Chan, 1 998) end no o onsider he risk of rading rles beyond his approah In

onras, papers ha have found proabiliy an no be explained by ransaion

oss end o give exra fous o risk eg Kho, 1 996) o see i f i is an explanaion for

he rading rle proabiliy

Numerous sudies have applied he Brok e al 992) rading rles o oher sok


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In oher sudes he proaby of he Brock e a . ( 992) movng average and

radng range break-ou rues on exchange raes has been consdered Lee Geason

and ahur (200 ) found ha hese rues are no proabe n he currences of

Argenna Barbados Che Coumba Eas Carbbean Ecuador Jamaca Trndad

and Tobago and Urgay (a versus he UD) These ess are based on he md- o

ae- 990s perod and n cuded oneway ransacons coss of 0. % Lee Pan and

Lu (200 ) aso found ha hese res are no proabe on a range of currences

(Hong Kong Korea Thaand aaysa Tawan ngapore Phppnes Ausraa

and ew Zeaand) versus he UD for he 988-995 perod aer one-way

ransacon coss of 0. %.

Oher work has nvesgaed he proaby of mong average rues on cross raes.

L d h ( 996 ) d JPY/GBP DKGBP JPYDK CHF/DK


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Smar resus have been documened on ures markes ukac and Brorsen (1 990)

esed movng average and radng range break-ou radng sysems on 30 ures

markes over he 1 975 1 9 perod They found scan gross reus however

ne reus (aer ransacons coss) are argely nscan ayor (1994) aso

suded he radng range break-ou rue on ures conracs Usng currency ures

daa for he 1 92- 990 period he found rues are proabe (assumng 0.% round

rip ransacon coss) up o 1 97 bu no for he 1 9 1 990 perod Rsk was no

consdered

he aforemenoned papers are conssen wh Jensen's (97) vern of he

efcen marke hypohess ha s pas prce nformaon canno used by movng

average and radng range breakou echncal radng les o produce pros ha

ose ransacons coss he ndngs n hese papers are however evdence agans


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or mode seecion. When such daa reuse occurs here is aways he chance ha any

saisfacory resuls obained may simpy be due o chance raher han o any meri

ineren in he mehod yieding he resuls Su ivan immermann and Whie ( 1 999)

found ha daa snooping does no affec he Brock e a. ( 992) ndings he

robusness of he Brock e a (992) resus in dieren markes is rher

conrmaion ha daa snooping is no he driver

Day and Wang (2002) considered he impac of dividends and nonsynchronous

prices on he Brock e al ( 1 992) rading sraegies Dividends are no included in he

DJIA so Day and Wang (2002) hypohesised ha he Brock e al (992) resul may

be undersaing he reus o a buy-and-hold sraegy making echnica analysis

appear more proabe han i is Day and Wang (2002 p 432) also noed ha

while he rading in odays marke virualy assures ha al DJA socks rade a he


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reu and he uncondiona mean Ready 2002) exended he Brock e a 992)

daa o 2000 (he incuded 1 97) and found a simar resu Kwon and Kish 2002)

appied hese rues o CRSP NYSE and Nasdaq indces for he 92 -1 99 and 1 92-

99 periods respecivey and aso found weakening pros over me More

recen Fong and Yong 2005) have found a recursive rading sraegy ha uses he

bes moving average rue (ou of 00 aeaves) up o he previous day is no

proabe when appied o echnoog socks ha rose srongy and hen dramacay

decned during he 99 o 2002 period

2443 Geetc Pogammg

A of he sudies descrbed above used a range of rues chosen ex pos Even wih


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Aen and Kaanen (1999) ere the rst to use genetc proammng to dent

potabe tradng rues (movng average and tradng range beakout ules) n the

stock maket Usng day S&P 500 data fo the perod 1 99 1 995 they found no

evdence of economcay scant excess etus over a buy-and-hold stategy

ae transactons costs are accounted fo. Neey (001 ) extended the Aen and

Kaanen ( 1 999) study by ncludng four rsk-adjustment technques He found

that rsk-adjustment mproves the attractveness of the rues but skadjusted excess

etus are not avaable ae tansacton costs

Mhalov and Lnosk (00) tested the protablty of tradng based on ve

dfferent osclatos usng genetc algorthms to optmse the paameters n each on

the Latvan Stock Maket Osclators are based on the prncple that a sustaned

d t ll f l d b t b k th th d t


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2444 Dw her

chnca anayss n the Wste word can be traced to Chares Dow th foundng

edtor of The Wall See Joual. Dspt th length of tm t has ben n exstnc

t s only recnty that a robust statstca test has ben conducted on Dow hory

Accordng to Wam Ptr Hamlton (se Rhea 1932) Dows succssor as edtor a

key tent of Dow hory s that market movemnts reect all rea knowledge

avalabl At rst ganc ths noton sems to smply rct that markts are

nformatonay fcent. Closr examnaton howvr rvals that t s n fact

consstnt wth the noton that past market trends are predctv of tur prce

movemnts Prosperty s sad to drve nvestors to xcess and the repentanc for th

f h d d d h


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chance hey aso appied market tmng measures used to identfy ski to the tme

seres of retus to the Hamiton strategy and found sicant postive evidence.

An event study anaysis of the JIA around Hamton s edtoras shows a siicant

dfference in mean retus over a 40-day perod foowng bu versus bear market

cas Brown et a ( 1 99) proved that ow heory does not resut in beng n the

market in times of ncreased risk based on Betas and the Sharpe Rato However

they did not account for the transactions costs ncurred in acting on ow heory so

they were unabe to make a judgement on its impicatons for ensen s ( 97)

denition of market efciency

2445 Suppt ad Resstace


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a round numbers and rends deveop when round numbers are crossed Oser (2003)

dd no consder he proaby of a radng sraegy based around hese ndngs so

here s no evdence o sugges ha hey conradc he concep of marke efcency.

2446 Char aerns

As we as he mechanca rues ouned above echnca anayss use vsua rues

based on paes n prce daa here are numerous paes docuened n he

praconer eraure (Bukowsk 1999) bu he academc eraure focuses on he

mos popuar paes.

One of he mos common paes s he head and houlder paern hs nvoves


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ser ( 99) tested the protabiity of the head and shoulders trading strategy

(specicay seling aer a neckine break) using daiy data for 100 rms chosen at

random om the CRSP database oer the 92- 1 993 period and a bootstrap

methodology She found that the head and shouder patte is not protable on the

data she tested

Chang and ser ( 999) tested the rationali ty of exchange rate forecasts based on the

head and shoulders patte using daily spot rates for six currencies verss the US

over the period 1 973 1 994 Using a bootstrap methodology they found excess prots

aer one-way transaction costs of 0025% for the yen and bt not for the other

currencies.

o amaysky and Wang (2000) proosed a systematic and automatic approach to


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uncondiona reu dsribuions the mean reus are not siicanty dfferen

his suggess that he differences mus be he result of higher order momen

differences hese are dicu to interpre in erms of marke efcency which is

primay mean retu based.

Anoher charing heursc ha has been tesed is he bu ag". hs pae

consss of price uctuations wihn a narrow range preceded and foowed by sharp

rises eigh and Puris (2002) esed he bu ag charting heursic using a

empae maching system SE ompose ndex data for the perod 90 999

and a methodoogy whch compares the resuts of appying the bu ag tradng rue

o the resuts of buying every day n the comparison and hodng for he number of

tradng days speced in the rade rue hey found tha the tradng re generaes

t i ti t H d i t


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2447 Rern Anoes

ie he evidence of posiive and negaive seria coeaion in sock reus work is

generay discussed of he anomay ieraure in his hesis his ieraure is

incuded in he echnica anaysis secion his work uses ony pas prices no any

ndamena vaiabes o predic ure sock reus so i is consisen wih hegeneray acceped deniion of echnica anaysis

24471 Short er

egadeesh ( 990) and ehmann ( 1 990) showed ha conrarian sraegies ha seec

socks based on heir reus in he previous week or monh generae saisicay


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3- 1 2 months (wnners), and short postions n stocks that have underperormed

durng the same period (osers)

his phenomenon cannot be expained by a three-actor asset prcng odel (Fama

and French, 1 99) suggesting that they are not compensaton or excess risk, is

present n other countres (Rouwenhorst, 99), exists in nteationa arket indces

(Chan, Hameed, and ong (2000)), s present at the ndusry level (oskowitz and

Grnb att, 1 999), and does not seem to be reated to eaings oentu (Chan,

Chan, Jegadeesh and akonshok, 1 99). ore recenty, Grnblatt and oskowtz

(2004) ound that the consistency o past retus and tax-loss sellng are iportant

actors behnd omentum prots.

h b h d h b h bj


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arbtrage they are abe to crcument the jont hypothess demma of tradtona

market efcency tests because ts denton s ndependent of any equbrum

mode and ts exstence s ncompatbe wth market efcency Ho gan et a (2004)

found that momentum strateges are protabe usng transacton costs ower than

those of esmond et a (2004), whch rther underscores the mportance of

transacton cost estmaton to momentum prots

2.4.4.7.3. Long er

Transacton costs are ess key to expan ongterm retu anomaes due to the

nequent tradng noed The poneerng study n ths area s eBondt and Thaer

( 1 95) who consdered retus oer ong horzons Usng a wnner oser portfoo

h th f d th t t k h h h d f d th t 3 t 5


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tis work focuses on statistica properties of series and is typicay sient on te

abiity to prot om appying a trading rue

tudies in wic te rescaed range statistic procedure, originay deveoped by Hurst

( 95 ) and modied by Lo ( 99) as been appied ave produced mixed resuts In

eary work evidence of dependence (Greene and Fieitz, 977) was found, but in

more recent work by Jacobsen (99) and Batten, is, and Feterston (2004) it was

found tat tis anomay is dependent on metodoogica and time period issues Tis

raises te possibiity tat te earier ndings are statistica iusions as ypotesised

by Fama (998)

Pagan and ossounov (2003) and Gonzaez, Powe, i, and Wison (2002) ot

ii d d i f B d B (97) i i i i


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menoned n Secon 24 3 he eve of ransaons coss assumed s crca o hs

ndng he heory behnd he esmaon of ransacon coss n he echncal

rang rule eraure s ycay less robus han ha n he momenum eraure,

bu n se of h hs hess ncudes research n hs secon f he radng e oss

ros exceed wha he aer auhors deem o be far ransacon coss

251 Fier Re ests

Sweeney ( 1 988) found ha he long verson of he Fama and Bume ( 1 966) ler

rues (buyng aer an x% ncrease and sellng aer a y% decrease where x% and

y% are ycay 05%) are roabe on 1 90 1 982 daly RSP daa xcludng he

oss makng Fama and Bume (1966) shor rules alows for ros ha exceed one


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Tis is ikey to be due to metodoogica differences Cooper 1 999 examined a

broader range of ters, incuding some tat are muc more extreme tan te ters

of Fama and Bume 966 and weeney 988. noter difference om earier

work in Cooper 1 999 is te reuirement tat te retu ter be met in a xedtime

orizon, typicay one to two weeks

Fiter rues are aso sown to be protabe for trading excange rate data Using

simiar rues to weeney 1 988 , weeney 986 found prots in forei excange

markets for te 973 - 980 period Tese can not be expained by transactions costs

(estimated at one-way of 0. l 3% or risk (based on te CPM) Testing simiar rues

on currency tures data, Levic and Tomas 993 found annua prots (in excess

of oneway transactions costs of 0.025% for te UD/GBP UD/CD, UDDMK

d d th 1982 995 d R t d l ( 999) d


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awan and exco durng the 1982-995 perod Ratner and eal ( 999) used

countryspecc transactons costs whch range om 0 6 to 2.0% (one-way)

n severa papers t has been found that movng average and tradng range breakout

tests are protable on exchange rates ee Geason and athur (200 1 ) found these

res to be protable aer one-way transactons costs of 0. 1 % for the Brazlan rea,

excan peso Peruvan new so, and Venezuelan bolvr for the md-to-late- 1 990s

ore recenty, Okunev and hte (2003) evaluated 354 movng average for

eght currences om 98 0 to 2000 sng an approach that s smar to Jegadeesh

and tman ( 993 200 1 ) techncal ndcators were used to rank stocks om best to

worst A ong/short poston was then estabshed by buyng the strongest momentum

currency and shortng the weakest momentum currency hs smple strategy

d f 6% h h l h h

2 5 3 CSMA


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253 CSMA

A hybrid system which combines thee dierent trading res and which has received

wide coverage in the iterature is the CRISMA system deveoped by Pruitt and White

( 98 9) CRISMA is an acronym that represents the component parts of the syste

(Cumuative Voume, Reative Strenth, Moving Average) More specicay, the

three criteria are expained as foows First, the 50-day price moving average ah

must intersect the 200day price moving average graph om beow when the sope of

the atter aph is eater than or equa to zero Of ourse, this phenomenon occurs

ony when a stock's price is rising reative to previous time periods . Second, the

reative strength aph, om begining to ending point over the previous four weeks,

must have a sope eater than, or equa to, zero. This ter assures that the stok s

ccsi s th M Adj st d M d Mrk t Adj st d M d OS Mrk t M d


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occsions the Men Adjusted Mode, Mrket Adjusted Mode, OS Mrket Mode

and Schoes nd i ims 977) mode re used to djust retus for risk

More recenty, doubt hs been rised bout the robustness of the CRSMA trding

system Goodcre, Bosher, nd Dove 999) found tht CRSMA is not rotbe

on the UK equity rket for the 987 996 erod, whie Goodcre nd Kohn

Seyer 200 1 ) found tht CRSMA is not rotbe on different sme of S

stocks

254 Neral Neork

There is owing evidence tht non-rametrc methods, which im to cture

statstcay scat h comad to buy ad hod tus O


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statstcay scat h comad to buy-ad-hod tus O-ay

tasacto costs of % mat th otabty of som shot-t us but oth

mutod uls ma otabl

255 Neaes Neighbour Techniques

oth o-aamtc aoach s th nearest neighbour tchqu hch as

toducd by Fam ad Sdooch (1 87 Ths too s usd to automat th

tstg of tadg uls basd o atts data that s oly vdt ahca

fom. Ths aoach oks by sctg gomtc sts th ast of th tm

ss sma to th ast st avaabl bfo th obsvato to b focast

Thfo ath tha xtaolatg ast vaus to th mmdat tu as

neares neghbour rues prouce oss pros ha hae hgher harpe Raos han a


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neares neghbour rues prouce oss pros ha hae hgher harpe Raos han a

buy-anho sraegy Break een coss are as hgh as 1 76% n some sub-peros

bu fa o 002% in ohers suggesing ha he resu may no be robus

256 Genec Prograg

Geneic proamming is anoher nonparameric echnque his inoes seecng

opma raing rues om a arge popuaion of raing rues usng he principes of

naura seecion

sing genec proammng echnques seece in he 1978-1980 pero an he

boosrap mehooogy Neey eer an Dar (1997) foun srong eence of

tradng rue rsk s ower than the buy-andhod rsk so the tradng res ead to rsk


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tradng rue rsk s ower than the buy-and hod rsk so the tradng res ead to rsk

adjusted prots However Kaaanen 998) found that the rues do not

consstenty beat the market He states that they mght make prots by assumng a

rsk of rare events that dd not materase durng the tme perod studed

2.6. Candetck Chartng

Candestck chartng s the odest known form of technca anayss Datng back to

the 1 700s the earest candestck charts were used to predct rce prces n 1 75 0 a

weathy Japanese merchant Munehsa Homma began tradng at hs oca rce

exchange n Sakata usng hs own persona candestck anayss Homma became a

egendary rce trader and amassed a huge fortune oday's Japanese candestck

Candlestick technica anaysis involves the consideraton of the relationship between


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Candlestick technica anaysis involves the consideraton of the relationship between

open, high, low and cose prces hese four prces are dispayed as obects that

resembe candes as shown in Fgure 1 (page 4)

A daily candestick is a aphica representation of the day's open, high, low and

cose prices Daiy candesticks are commonly referred to as sngle ines Some

sngle nes are sad to have forecasting power in their own rght For instance, a

hite arbozu (shown n Fgure 2) is sad to be a single ine that suggests rther

price increases because prices open at the day's ow and rse throughout the day to

cose at the day's hgh A hte arubozu is sad to ndicate a stuaton where

buyers ovehelm seers and bd up prices during the day he odds are that this

supply demand mbalance wil ead to rther prce rises n the ture Other snge

l l di f

contnuaton and reversa pattes have a bulsh and a bearsh varety n ths


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contnuaton and reversa pattes have a bulsh and a bearsh varety n ths

context the term bullh (beaih) suggests ture prce ncreases decreases)

here are numerous combnatons of snge nes that are nether contnuaton nor

reversa pattes n addton some contnuaton and reversa pattes are sad to

have very lttle or no forecastng poer o determne hether a contnuaton or

reversa patte has strong forecastng poer proponents of candlestck technca

analyss deveoped a system of combnng the to or three ndvdua snge lnes

that make up the patte to form an overa snge ne for the to- or threeday

perod he characterstcs of ths overall snge lne ndcate hether or not the

patte does have forecastng poer

h l f b h l l h k ll l

Fgre 3 Bllsh Englg Cndlesck Pern


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g h g g d

A short back cande folowed by a ong whte cande that oens beow but closes

above the revous day ombnng these two candes resuts n a bush candle

wth cose above oen

A descrton of the candlestck sngle lnes and attes used n ths research

can be found n Aendx One

Deste ts oularty amongst racttoners to the best of the author's knowledge

are used, hie in ohers complex sraegies are adoped on hisorical daa he


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, p g p

probem ih his approach is ha j us because hese sraegies ere proable before

hey ere creaed (ie on daa ha pre-dae his poin) does no mean ha hey are

sil proabe or ha he principe ofmarke eciency has been violaed

Despie he debae on he proabiliy of echnical rading sraegies, aer

ransacions coss have been accouned for here is consisen evidence ha hese

sraegies are usel for predicing reus his means ha hey may sil l be

vauabe for nd managers for hom ransacions coss are a sunk cos. Fund

managers oen have o rebalance heir porfolios o remain ihin agreed asse

allocaion parameers his means ha echnica rading sraegies may be a usel

echnique for hem


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Chate Thee Data and Methdlgy

3 . 1 . Intoduction

he choce of data and methodology are crtcal to any research any techncal

tradng rule studes can be crtcsed for falngs n ths area Carel consderaton

has been gven to the data and methodology employed n ths research n an attempt

to elevate t above such crtc sm he data secton starts wth a detaled descripton

of the Dow ones ndustral Average (DA) component stock data used n ths

research hese data have several advantages over the more comonly used ndex

data Frstly, all the Dow stocks are tradable n ther own rght he prots

docuented are therefore not just hypothetcal they could have been eaed by

he mehodology secon nshes wh descron of he es nd boosr


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mehodoogy used o es he sscl scnce of he derences n reus

foowng cndlesck buy or sell sl nd he uncondonl reu. he es

mehodoogy s sndrd bu he boosrng mehodology nvolves n exenson

o he convenonl mehodoogy o ow he generon of rndom oen hgh low

nd close rces Prevous reserch hs doed boosrng mehodoogy h

focuses soey on cose rces

3.2. Data

32 1 Data Ued

he majoriy of he curren leraure uses ra reus raher han excess reus o


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j y

es rading sraegies his i s desirable as raders use ra daa hen implemening

heir sraegies hs approach is appropriae for shor-erm candlesick rules, as

varaions in he rsk premia are likely o hae a long periodciy relave o he

holding period Seeney 1 986).

he sample includes socks ha ere par of he Do Jones Indusral Aerage

DJA) index for he J anuary 1 992 - December 2002 perod he saring poin

as carelly chosen o ensure ha invesors ould have been aare of candlesick

echnical analysis and have had he abil y o apply hese o facors are

imporan for any es o f marke efcency

echnical analysis s said o be mos effecie on aciely raded socks For hs

322 Data Snoopng


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It is lear that the appliation of new trading les or new speiations of existing

trading les to historial data introdes the possibility of data snooping bias It is

qite possible that the rles have been tailored to the data series in qestion and ae

protable only bease of this here is nothing to sggest that the rles wil l e

protable ot of sample or that someone wold have hosen those exat

speiations ex ante to form a protable trading rle Pesaran and immermn

( 995 p 02) onlded that as far as possible rles for prediting stok rets

shold be formlated and estimated withot the benet of hindsight

here are three approahes to minimising the effets of data snooping bias e

In othe wods, it is not possibe to quanti the entie univese o technica anaysis


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ues om whic one ue might have been dawn

A moe ecent appoach invoves the assumption that agents tade ecusivey using

ue specications that ae consideed "best peoming based on inomation up to

the pevious day (Fong and Yong, 2005 The weakness in this appoach is that it

sti invoves a eseache seecting a ue tpe to test ex post In the cse o Fong

and Y ong (2005 moving aveage ues wee seected and agents ae simpy assumed

to seect moving aveage paametes on the basis o past peormance

In this eseach it is agued that candestick technica anaysis is moe obust to the

criticism o data snooping than ae tests o othe technica tading rues such as the

trading sias on the DJIA wod therefore be nabe to be impemented withot


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prhasing eah of the DJ IA omponents in the orret proportions

Seondly as Day and ang (2002) domented tests of tehnia trading res on

index data an be biased de to nonsynhronos trading kivoe ( 1 995 p 465)

expained that the probem is reated by the fat that the vae of an asset over a

ertain time annot be observed if the asset does not trade in that period Sine

most indies are ompted on the basis of the most reent transation pries of the

onstitent stoks the reported index beomes stale in the presene of ineqent

trading his reslts in the observed index not reeting the tre vale of the

nderlying stok portfoio One onseqene of ineqent trading is the sprios

serial orreation it indes in the observed index ret

rading rles ha are reliant on sbsanial omper power and reveal pros on 50


79/301

00 years of historial data are therefore no neessaril y evidene against market

efieny or this reason he sar poin of 1 Janary 1 992 was arelly hosen

Despie being a poplar trading ehniqe in Japanese nanial markets for some

onsiderable time the seminal andlestik rading srategy book in English was not

pblished nil 99 aor data providers sh as Reers also stared making

open high low and lose daa avalable om the middle of 1 99 1 Users of tehnial

analysis therefore wold have been aware of andlestik tehniqes and have had he

abiliy o implemen hem om he sart of 992

inally tehnial analyss laim ha their methods are most reliable on avely

traded stoks (orris 995 ). his makes the DA omponent soks an obvios

hoie hey are also imporan hoie om a marke mirostrre perspeive

single ines are said to have foreasting power in their own right or instane a


80/301

White Marboz (as shown in igre 2 on page 56) is said to be a singe ine that

sggests rther prie inreases bease pries open at the day's ow and rise

throghot the day to ose at the days high A White Marboz is said to indiate a

sitation where byers overwhem seers and bid p pries dring the day he odds

are that this sppy demand imbalane wi ead to rther prie rises in te tre

Other singe ines are netral giving no indiation of tre prie movements

ogether onsetive single ines an form ontination and reversa pattes

Contination pattes indiate that the prevailing trend will ontine while reversal

pattes sggest that there wi be a hange in trend All single lines and most

ontination and reversa pattes have a bllish and a bearish variety In this

ontext the term bullih (bearih) sggests tre pre inreases (dereases)

ombined low is he low on individal single ines he ombined open is he open


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om he rs singe line and he ombined ose is he ose om he las single ine

(Morris 1995)

An exampe of a bllish reversa pae is he B ish Englng pae (as shown in

igre on page 58). he Bish Englng pae invoves a shor bak andle

being followed by a ong whie ande whih opens below b oses above he

previos day he overal singe line formed by ombining he wo individal single

ines ha make p he Bll ish Engng pae is bllish his ons ha he

Bl ish Englng pae is said o have power o predi prie inreases

In seeing he single i nes and paes o es he following approah was adoped

i l ll i l i d d d b i i b k


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when a white single ine mst have similar open and low pries and simiar lose and


83/301

high pries Morris ( 1 995 p 25 ) stated that the differene shold be less than 0%

of the open-ose range However andestik books point ot that there is some

exibiity in dening other aspets of singe lines sh as the distane etween open

and ose for the andle to be assied as a ong andestik

Single lines are said to have foreasting power regardless of the nderying trend in

the market In ontrast reversal pattes reqire the existing trend to be identied

Candestik tehia anaysis is a shortterm tehiqe so andlestik books

advoate that a tenday moving average of pries be sed to determine the trend If

prie is above (below) the tenday moving average an ptrend (downtrend) is said to

exist (Morris 1995). olowing Morris ( 1 995) the base tests se an exponential

i hi h i i h h b i


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( )


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( )

where b and Nbs) are the mean ret folowing a by (sel) sial for the ten day

hoding eriod and the nmber of sias for bys (sells). J and N are the

nonditional mean and nmber of observations. i

)is the variane of res

foowing a by sia and is the variane for the entire same.

3.2.3.2. Bootstrapping ethodoo

In addition to this statisti methodology a bootstrapping methodology - whih has

Previous papers have a recorded the testing of trading res that are based soely on


86/301

cose prices Athough in this thesis open, high, ow, and cose prices are considered,

their approach was fo owed"to start with This nvoved resamping cose retus for

the random walk mode and tting the respective nu modes to the orig ina close

price series for the AR( GARCH-M and EGARCH models4 This process was

conducted separatey for each stock because it akes no sense to try and t a null

mode to a long series of retus that has been created by joining together seres of

individual stock retus

The AR( 1 model is provided n equatio 2 :

(2)

(b)


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z/ N(O,l) ()

In this model the error et is onditionally normally distribted and serially

norrelated he onditional variane 2 , is a l inear ntion of the sare of the

last periods errors and of the last perods onditional varane whi implies

positive serial orrelation in the onditional seond moment of the ret proess.

Periods of high (or low) volatility are likely to be followed by periods of high (low)

volatili ty. he onditional rets in this model are a l inear ntion of the

onditional varane and the past distrbane e- Under this retgeneratingproess volatility an hange over time and the expeted rets are a ntion of

volatil ity as well as of past rets he parameters and standardied residals were

ti t d f h DJIA t t k i th i lik lih d it i

Secony t aows prevous retus to affect ture voatty fferently epenng


88/301

on ther s Ths s ese to captue a phenomenon n asset res obseve by

Back (976) where negatve retus ae generaly followe by larger volatlty than

are postve retus

In accorance wth Brock et a. (92) the resuals of the GARCM an

EGARCH moes were stanarse usng estmate stanar evatons for the

error process. The estmate resuas for the AR( ) moel an stanarse

resuas for the GARCM an EGARC moes were then rerawn wth

replacement to form a scrambe resuas seres whch was use aong wth the

estmate parameters to form new repesentatve close retu seres These retus

were then expontate to form new cose prce seres for each stock These

b h h h l h

This process was replicate times for each stock so there were simulate


89/301

sets o f open high low an cose seres for each stock in te sample for each null

moel Eon an Tibshirani ( 98 6) suggeste that - 1 000 simulations e enough

to approximate the tre estimator Convergence before simulations was also

foun in this research

The proportion o f times that a canlestick traing rule prouces more prot on the

bootstrappe seres than on the orginal seres following a sial is a simulate

value for the null hypothesis that the traing rle has no value For a bullish

canlestick to have statistically siicant forecasting power at the % level the

simulate -value shoul be less than In other wors more prot shoul be

prouce on the ranom series than the orginal ess than % of the time For a

bearsh canlestick to have forecasting power at the % level the simulate value

Boosrapping aso alows he consieraion of retu variaion following a

l i k i U i h h i f i l


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canlesick sia Using he same approach as ouine for mean reus simulae

vaues were calculae for he nul hypohesis ha he raing re is more risky on

ranom series han on he original series This was achieve by measuring he

sanar eviaion of reus following a signal on he original an on he

boosrappe series an calcuaing he proporion of imes ha he sanar

eviaion was arger on he boosrappe series han on he origina series

As a check of he robusness of he resuls he variaion in pros semming om

enering he marke foowing a sial a cose cose + an open + (where is

he ay ha he sia is receive) were invesigae hen enering a he cose

price was consiere he boosrap process was conuce as escribe above an he

The use of DJIA componen sock aa has severa oher avanages Frsy unlke

h bl h l b


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nex aa hese nsrmens are raable so he resuls obane are no us

hypoheca hey coul have been acheve by anyone applyng canlesck

echnca anayss Secony Dow sock aa are very lqu whch makes hem

ea for ess of echnca anays s. Techncal analyss s suppose o capure mass

marke psychoogy so s mporan ha s appe o lqu seres where one or

wo marke parcpans are unlkely o be able o move he prce Ths hgh eve of

quy aso ensures ha any rus ocumene are avalabe o arge amouns of

capa In oher wors marke mpac coss are no hgh

Chapte Fou Rests


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Chapte Fou Rests

4.1. Inrducin

his section contans the summay statistcs for the stocks use in this research anthe results of the tests of the statistical scance of retus folowing canestick

buy an sel sas As iscusse in the literatre review an ata an methooogy

sectons bullsh (beash) singe lnes an pattes are those that practtoner books

(e g Morrs 1 995 ) suggest ea to ther price ncreases ( ecreases)

The core statstic an bootstrap resuts are base aroun entering the market at the

wou enter the market at the rst avalable opportunty following a techncal sa

More specicaly the traer woul buy at the open price on the ay foowing the


93/301

More specicaly the traer woul buy at the open price on the ay foowing the

sia In this thess ths assumption is use as the base case but sensitivity analysis

was conucte to etermine if the results are sicanty ifferent if the traer

enters on the ay of or ay aer a sial

Sensitivity anayss was aso conucte on the number of ays a trae is hel open

for (holing pero) an the length of the movng average use to etermine the

prior tren (for reversal pattes only) More specically n Scenario A t is

assume that a trae is nitiate at the cosing prce on the ay that the entry sia s

generate that the trae is kept open for ten ays an a ten-ay exponental movng

average is use to etermine the pror tren for reversal pattes Scenaro B s

i ti l t S A t th t S i B t th t t i it t

Scenaro s entcal to Scenaro C except for the assumpton that postons are

kept open for ve ays nstea of ten ays Scenaro E s entca to Scenaro C


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kept open for ve ays nstea of ten ays Scenaro E s entca to Scenaro C

except for the assumpton that postons are kept open for two ays nstea of ten

ays Uner Scenaro F each canestck parameter s ncrease by 20% whe a

other Scenaro C assumptons are mantane. Uner Scenaro G a canlestck

parameters are reuce by 20% whe a other Scenaro C assumptons are

mantane. The mpact of varyng the length of the exponenta movng average s

nvestgate n Scenaros H an In Scenaro t s reuce om ten ays to ve

ays whe n Scenaro t s ecrease om ten ays to two ays

42 Summary Statstcs

cacuae ogeher. As expece he mean reus of each of he four seres are

simiar Volai iy is aso similar across he four series wih hgh an ow only


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simiar Volai iy is aso similar across he four series wih hgh an ow only

sl ighy ess volaie han open an cose All four series ispay negave skewness.

The four seres are al epookuric wih hgh an ow ispaying his characerisic

more srongy han open an cose.

4.3. Statstcal Tests

.3.1. Scenario A: Trade initiated at the Close Price on te Day of

the Sinal, a Ten-Day Holdin Period, and a TenDay Exponential

Movin Averae to Deermine Prior Trend

Uner Scenario A a rae is assume o be niae a he close prce on he ay of

abe 3 Scenaro A Test Rests


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Candesick Buy) Buy>O Mean Sa

Pa h g LLng White . .

Whte Marbz . .

Csng White Marbz .

Openng Whte Marbz .

Dagnfy Dj . . .*

White Pape Umbrela

. Blac Pape Umbrea . .

P h v Pa

Hamme . .

Bish Englfng .

Piercng Lne .

Blsh aami . . .

hree Insie Up . .

hee Otse Up .

Tweeze Bttm .

Candesick Se) Se>O Mean Sa

zero less than y percent of the tme hle th ncatve of a poorly

perfong rule t s not entve as t oes not take the sze of retus nto account


97/301

perfong rule, t s not entve as t oes not take the sze of retus nto account

It s possble that a rle that s correct less than y percent of the tme yels

substantally bgger prots than losses makng t protable overall In aton, the

Buy > 0 column results make no comparson to uncontonal retus The only

bullsh reversal pattes to yiel retus greater than zer more than y percent of

the tme are the ammer an Bullsh aram pattes

The mean res contonal on bullsh sngle lne sals are all postve wth the

excepton of the ragony oj espte ths, none of the bullsh sngle lnes ye l

statstcally scant prots at the 5% level Rather, al l of the statstcs except

those for the hte Marubozu are negatve Ths ncates that the mean retus

contonal on all the non hte Marbozu bullsh sngle lne sals are lower than

han eo ess han y pecen of he ime which means ha hey ae ess han zeo

moe han y pecen of he ime his is wha one woul expec fo a beaish


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moe han y pecen of he ime his is wha one woul expec fo a beaish

canesick he beaish evesa paes ae aso geae han eo ess han y

pecen of he ime wih he excepion of he hee Ousie Don pae

Ohe han he hee Insie Down pae he means of he beaish single lines an

evesal paes ae all posiive he Long Back coniional minus unconiiona

mean is saisicaly siican a he 5% evel an he Back Maubozu an losing

Back Maubozu coniional minus unconiional means ae saisicaly siican

a he % eve his suggess ha conay o canlesick heoy hese beaish lines

inicae highe han aveage eus ove he nex en ays he sais ics fo he

Beaish Haami an hee Insie Down beaish evesal paes ae negaive (as

b f h i i i i

RW AR) GARCM EGARC

Candestck Se a Se O Se O Se a


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Pa ah g LLong Blak . .

Blak Mauozu . .

losng Bak Mauozu . . .

penng Bak Maruozu . .

Gavestone Doi

hite Shoot ng Sta . .

Bak Shooting Sta . . .

Pa ah va Paangng Man . .

Bearsh Enguing .

Dark lo ud over .

Beaish Hara . . . .

Tree Inside Down . . .

Tree Outsde Down weeer op .

Table 4 contans the Scenaro A bootstrap results The numbers refer to the

Panes A ncate that the resuts are very consstent across the four nu moes

The buy popotons for the snge nes are a aoun 0 5 whch ncates that none


100/301

y p p g

of these canestcks generate contona rets that are statstcay scanty

erent om the uncontona retus It s event om the Pane A resuts that

the ragony o Cosng Whte Mabozu an Long Whte ne have the hghest

vaues ncatng that t s more common for the ranomy generate bootstrap seres

to have hgher rets than the orgna for these nes

If a trang re has statstcay scanty fferent retus an obvous queston to

ask s whether or not ths fference s ue to atona rsk beng unertaken he

coumn spays the proporton of tmes that the stanar evaton of retus

foowng a buy sa s eater on the bootstrappe seres than on the orgna

Ths s the opposte to what one woul expect for bearsh rules but s broay

consstent wth the -statstc results whch show that n some nstances bearsh snge


101/301

g

nes forecast negatve rather than postve ture retus The sel l values om the

bearsh reversa pattes are also ess than 0 5 wth the excepton of the Bearsh

Engung an Bearsh Haram pattes The stanar evaton values for the

bearsh sngle lnes an reversa pattes show no clear tren.

The fact that none of the bootstrap resuts are statstcaly scant ncates that

the statstc results whch showe statstcal scance n ve cases may be

nuence by one of the statstc assumptons beng volate The summary

statstcs n Tabe 2 show that the retu seres are not normay strbute (as

requre for the test to be accurate) but rather splay characterstcs of negatve

an the orgnal sees. For nstance, f the bu proporton for a bul sh rule s eater

than 05 ncatng that the bootstrap retu s eater than the orgnal retu n


102/301

excess of 50% of te tme, then the bootstrap mean s n fact eater than the orgnal

mean. An exampe of ths s the Long hte canle uner the ranom wak null

moe whch has a -vaue of 0 5374 an mean retu of 00002 an 0 000 1 on the

bootstrap an orgnal seres respectve Ths s not alwas the case thoug. It s

possbe that the bootstrap retu s eater than the orgna retu over 50% of the

tme but that the remanng bootstrap retus are ver smal, resultng n an overall

bootstap mean that s ess than the orgna mea. A exampe of ths s the hte

Paper Umbrea whch has a bootstrap -value of 04735 an means of 00002 an

0000 1 on the bootstrappe an orgna seres respectve (uner the ranom walk

nul moel).

concue that it pouces a annua etu n excess of 250% (obtaine by

annuaising the aiy etus)


103/301

Thee is a sma chance that the esuts ae not consistent acoss the entie eeven

yea peio of this stuy This is investigate by iviing the ata into two equa

subsampes an uning the tests on each of these The esuts ae vey consistent

acoss these subsampes an contibute itte They ae theefoe not pesete.

able 5: Scenaro A Boosrap and aw Seres eans and Sandard Deaonsfor ando Walk and AR!) Nll odes

RW AR)

Bootstap Dow Bootstap Dow

Candestck Buy Ob Buy Ob Buy Ob Buy Ob h g L

Candesck

Booap

Se

RW

Dow

Se Boosap

Se

AR()

Dow

Se


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Lg Back

Black Marub

Cg Black Marub

Oeig Black Marbu

Gravete D

ite Stg Star

Black Stg Star

agg Ma

Bea gufg

Dark Cud Cver

Beari arami

ree de Dwree Outde Dw

weeer

Pa ah g

Se

00001 00102 00003 0010B 00002 00102 00003 00108

00002 00098 00004 00098 00001 00097 00004 00098

00002 00101 00006 00103 00002 00100 00006 00103

00002 00099 00001 00109 00002 00099 00001 00109

00002 00098 00006 00075 00002 00099 00006 00075

00002 00098 -00001 00099 00002 00098 00001 00099

00002 00101 -00001 00091 00002 00101 -00001 00091

Pa ah a Pa00002 00087 00006 00083 00001 00088 00006 00083

00002 00095 00001 00094 00003 00096 00001 00094

00002 00101 00001 00094 00001 00102 00001 00094

00002 00096 00000 00097 00002 00096 00000 00097

-00002 00088 00001 00096 -00002 00084 00001 0009600000 00091 00010 00096 00002 00091 00010 00096

00002 00093 00003 00083 00002 00093 00003 00083

GARC-M EGARC

Boosrap Dow Boosrap Dow

Candesck Se a Se a Se a Se a


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a Se a Se aP h g L

ong Back 00002 00 00003 0008 00002 0004 00003 0008

Back Maoz 00002 0008 0000 00098 00002 000 00004 00098

Cosing Back Maoz 00002 000 00006 0003 00002 0003 00006 0003

Opnng Black Maoz 00002 00 0000 0009 0000 0004 0000 0009

Gavston Doji 00002 0003 00006 00075 00002 00097 00006 00075

Wht Shooting Sta 00002 0007 -0000 00099 00002 0000 -0000 00099

Back Shootng Sta 00002 0008 0000 0009 0000 0002 -0000 0009

P h v Panging Man 00002 0000 00006 00083 00004 0000 00006 00083

Baish Enging 00002 0003 0000 00094 00003 0003 0000 00094

Dak Cod Cov 00002 0002 0000 00094 00003 0002 0000 00094

Bash Haai 00002 0004 00000 00097 00003 0004 00000 00097

h sd Do 00003 00090 0000 00096 00004 00094 0000 00096h Otsd Don 0000 0009 0000 00096 00003 00092 0000 00096

T Top 00003 00097 00003 00083 00003 00098 00003 00083

3 2 S C

subsequent sias are iore This is the most practical working assumption

because a secon buy sia folowing an earlier buy sial tat resulte in an


106/301

investor becoming ly investe wou simpy be seen as conrmation of the earlier

sia An ateative approach is the inclusion of all sias an thus overapping

oing perios . or instance if the Long hite canle sials a by on ay t+ an

sials anoter buy on ay t+ a long position woul be entere on both ays.

able 7 Senaro B T-es Resls

Candestick (Buy) Buy>O Mean Ttat

P h g LLong Wht 947 04754 0.0001 19

Whit Marboz 64 04586 0.000 0.07

Closg Whit Mabo 1565 04711 0000 0.

Ong Wht Mabo 1611 04681 00001 710**

Candesc SeJ) Se>O Mean a

Pa ah g L B k 2


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Log Bak 2 0.4883 0.0007 205

Ba Maruozu557 04783 00009 2.083*

losg Blak Mar uozu 022 0.4833 0.000 .338

Opg Bak Maruozu 737 0.48 00005 .220

Gravsto Doj 9 0.4597 00008 .07

Wht Shootg Star 520 0.4808 0.0004 0.233

Bla Shootg Star 45 0.483 00005 0.7

Pa ah a PaHagig Ma 84 0.478 0.000 0.384

Bash Egg 289 0495 0.0009 .45

Dar ou ovr 7 04872 00004 0072

Barsh arai 39 0499 0.0000 -02

hr Isi Dow 34 0.4353 -000 -.324

hr Outsid Dow 36 05 0.007 342

wzr op 407 0.4747 0.0007 .305

**statisticay siicant at the 1 % evel *statistically siicant at the 5% leve

he Scenario B resuts are vey simiar to their Scenaro A counterparts, which

Te esults isplaye in Table 8 inicate tat te bootstap esults ae also vey

simila between Scenaios A an B. Tee is some vaiation acoss les but te


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simulate values ten to be geate tan 05 following buy sials an less tan 05

following sell sials Tis suggests tat te les ae not even close to aving

foecasting owe If tis was te case you wol expect te vales to be less tan

05 an close to zeo fo by sials In ote wos te potability of te sial

on te anomly geneate seies wol be expecte to excee tose on te oiginal

seies less tan 50% of te time Consistent wit te Scenaio A te eslts ae vey

simila acoss te fou null moels Tee is no consistent tend in te stanad

eviation values acoss eite te buy o se ll signals

abe 8: Sceario B Bootsrap Proportios for al N odels

RW AR) GARC-M EGARCH

Candesck Se O Se O Se O Se O h g


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ong Bac 04179 0.1818 0.4156 01819 0.3634 0.3507 0.3487 0.2407

Bac Mabo 04622 0.4321 0.4586 04230 0.3804 0.5611 0.3689 0.5302

Cosing Bac Maoz 0.4646 0.3691 0.4564 0.3663 04347 0.4575 0.4307 0.3890

Openng Bac Marbo 04838 02609 0.4807 02655 0.4270 0.3611 0.4203 0.2634

Gavesone oi 0.3673 07685 0.3714 07667 0.4201 0.6928 04224 0.6967

Whe hooi ng a 05164 0.5794 05222 0.5780 05306 0.5761 05308 0.5500

Blac h ooing a 0.4380 0.7438 0.4430 0.7470 0.4599 0.6867 0.4551 06798

h v anging Man 0.4884 0.5165 04902 0.5160 04736 05670 0.4923 05945

Bearish Engfng 0.4709 04384 0.4733 04396 04414 0.4851 0.4721 0.5410

a Clod Cover 0.4774 04818 04708 0.4649 0.4981 0.5004 0.5194 0.5298

Bearsh aam 0.5259 0.4455 0.5374 04486 05621 0.5035 0.5881 0.5470

Three Inside own 05000 0.2963 0.4725 04396 05547 04236 05703 0.4444

Thee Osde own 04010 05411 0.4056 04779 04137 0.4510 04371 0.4943

weee op 0.4769 0.5919 04829 05892 04725 05611 0.4981 06127

e reul diplayed in al e 9 and 1 0 indicae a e alue for a paricular

booraed ere 0 00 1 comared o 0002 on e orgnal . ugge ere

are a e very mall reu on e boora erie and or very large reu on e


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orginal erie a are nuencng e mean reu

e conency o e reul acro e our null model alo ver evden. e

mean reu on e booraed ere ollong e H mer ngle lne are

00002, 0.0002 00003 and 00001 or e random alk ARl GARCHM and

EGARCH model reecvely. e correondng andard devaon on eac o

e booraed ere are 00083 0008 1 , 0.0089, and 00077 reecvely

able 9: Senario B Boosrap and Raw Series eans and Sandard Deviaionsfor Rando Wal and AR) Nll odels

Candestick

Bootstap

Se

RW

Dow

Se

Bootap

Se

AR()

Dow

Se


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Long Back

Back Marboz

Cloing Back Marboz

Oeg Bac Maboz

Graveone oj

Whie hoong ar

Black hoong a

angng Man

Beah ngfing

ark Cod Cover

Beah aam

hree Inide own

hree Oide own

Tweeer To

P h g L2 .2 .3 .8 2 2 3 8

.2 99 2 .98 . .98 .2 98

2 . 5 3 . 5 .3

.99 2 8 98 .2 8

2 99 .5 6 .2 .98 .5 6

.2 9 -3 98 .2 98 -.3 98

. 2 92 .2 -.2 .92

P h v P.3 .8 .5 .83 .2 8 .5 83

2 95 . 95 3 96 . .95

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