further insights on the puzzle of technical analysis

8/2/2019 Further Insights on the Puzzle of Technical Analysis

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Further insights on th e puzzle of technical

analysis protabilityBERTRAND MAILLET1, and THIERRY MICHEL2

1TEAM, Universit e Paris I, Panth eon-Sorbonne and A.A. Advisors/ABN AMROGroup, France2TEAM, Universit e Paris I, Panth eon-Sorbonne and Direction de la Pr evision,Minist `ere de lEconomie et des Finances, France

This pa pe r extends current results concerning technical analysis efciency on th e

foreign exchange marketa nd attempts to determinewhether lteringth e r awexchange

rate series with some trading rule signicantly changes its characteristics . Because of

th enon-normalityofexchange r a t eseries , bootstrap m e t hods areus e don th e main daily

exchange rates since 1974 to s how technical analysis performance. Th e technical

analysis strategy tested generates returns whose distribution is signicantly different

from the basicseries . Th erobustness oft he resultsis tested in and ou t-of-sampleand a n

explanation of t he technical analysis performance ba s e d on it s ltering properties issuggested.

Keywords: international nance , technical analysis , performance, foreign exchange

market, nancial forecasting, efcient markethypothesis

1. INTRODUCTION

Academic nance still recognizes market efciency as one of its principal

paradigms (see for example Fama , 1965a , 1965b , 1970, 1991; Grossman , 1976;

Grossman a nd Stiglitz, 1980 ). This contr asts with evidence from author s (Allenand Taylor, 1989, 1990, 1992;Frankel, 1989;Franket a nd Froot , 1990 )wh o r e p o r tthat most oper ator s u s e technical analysis for their s h o r t-term investment

decisions .Grossman and Stiglitz(1980 )have shown t h a t with information c o s t s , markets

cannot b e perfectly efcient in Famas s e n s e , though an efcient market price

still fully reects all th e costless information . Nevertheless , technical analysis

m e t h o d s assume t h a t markets ar e no t perfect an d us e th e chronicle o f p a s t

prices t o benet from t h e s e imperfections. In a n efcient market , a n active

strategy of buying an d selling a security would n ot outperform b uy and hold

(Cornell, 1979, p . 387 ). And s o , ifth etechnicalanalysis rule prots a re positive ,then markets are clearly inefcient, even in t h e restricted weak form , b e c a u s e

current prices d o n ot incorporate all publicly available information (Fama ,1965a , p . 35 ).

The European Journal of Finance

ISSN1351-847Xprint/ISSN1466-4364online2000Taylor &Francis Ltdh t t p :/ /www.tandf .c o.u k/journals

The European Journal of Finance 6, 196224 (2000 )


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Th erst technicalanalysis rules weredeveloped at th ee nd o fth e nineteenth

centur y a nd have b e e n rened since (s e eMurphy, 1987;Pring, 1991for abasic

presentation o f technical analysis m e t h o d s ). Their foundations were purely

empirical, without an y relevant theoretical justication. Nevertheless , s o m e

author s have shown , in a noisyrationalexpectationmodel, t h a texpectationson

a s s e t returns o f informed agents d e p e n d on equilibrium a s s e t prices (s e e, forexample, Admati, 1985; for a reviewe s s a y s ee Admati, 1991; Admati and Ross ,

1985;Treynoran d Fergusson, 1985;Brown a nd Jennings , 1989 ). Inthis particularcontext , Technical Analysis , or more precisely th e u se of p a s t prices t o infer

private information , h a s valuein a m o d e lin which prices are not fullyrevealing

a nd t r a d e r shave rationalconjecturs about t h e relationshipbetweenprices a nd

signals . Therefore , seminalempirical studies (Alexander, 1961, 1964; Fama a nd

Blume, 1966) a nd many r ecent p a p e r s tr y t o t e s t t h e ver y usefulness of t h e

technicalanalysis strategies, applied t o differentnancialassets (cash , stocks ,

exchange r ates , interest r ates , commodities ), in sever al markets (mainly NewYorkand London Markets ), varyingt h e instruments (s p o tan d futures )a nd with

multipled a t afrequencies(weekly, dailya nd recentlyintra-dailydata )(Sweeney,

1986; Neftci, 1991; Brock et al., 1992; Curcio an d Goodhart, 1992, 1993; Acar,

1993; Lebaron, 1993, 1996;Levich a nd Thomas , 1993; Taylor, 1994;Silber, 1994;

Kho , 1996; Genay, 1996; Lee a nd Mathur, 1996, Neely et al., 1996; Neely a nd

Weller, 1997; Curcio et al., 1997;Clyde a nd Osler, 1997). Some author s provide ,

for th e foreign exchange r ate market, a n economicexplanationof th eappar ent

puzzle oftechnicalanalysis performancewhich is b a s e d on th e behaviour oft h e

centr albanking authorities (LeBaron, 1996; se e also Lee a nd Mathur, 1996a ndNeely an d Weller, 1997 ).

Th e technicalanalysis trading rules , according to some author s , ma y play a

p a r t in t h e price formation pr ocess b e c a u s e they ar e widely used among

practitioners. Theymight also detect s o m e properties oft h eprice pr ocess such

a s cycles , nonlinearities or tr ends (LeBaron, 1992a , 1992b , 1992c , 1993; Clydea nd Osler, 1997) n ot detected b y econometric models incorporating ARMA,

ARCHa nd GARCH pr ocesses (Brocket al., 1992; Taylor, 1994; Lee a nd Mathur,

1996;Kh o , 1996;Neelyet al., 1996 ).

Thisp a p e r

focuses

on

t h e

main

statistical

properties

o f

chartist

rule

r etur ns

.

Th e question we t r yto answeris whether lteringt h e r awexchange r ate series

with s o m e tradingrule signicantly changes their characteristics.

This p a p e r is organized as follows . In Section 2, we shallsummarizeLeBarons

main results an d apply, in Section 3, h is appr oach t o a larger exchange r ate

database;we s h o w, in particular, that s o m erules outperformth emarket , even if

t h eexcessmean return is not always signicantly superior to th e market r etur n.

In Section 4 we s t u d y t h e r obustness of technical analysis trading rules

performance an d it s consistency. A generalization of t h e s e results shows t h a t

theyare homogeneous over th e period ofestimation . In Section 5, wes t u d y in

detail t h e characteristics o f empirical chartist r etur ns in th e foreign exchange

market. Their rst an d third empirical moments a re different from th e na ve

ones . Once this result is established , we p r o p o s enallyageneralexplanationof

this outperformance .

197The puz z le of technical analysis protability


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2. DEFINITION OF TECHNICAL TRADING RULE AND METHODOLOGY OFTESTS

LeBarons (1996)p a p e r focuses o n an economic explanationo fperformanceoftechnicalanalysis o n th e exchange r ate . Itfollows earlier paper s on stockprice

indices(Brock

et al

.,1992 )

a nd

o n

nonlinearities

in

t h e

foreign

exchange

markets(LeBaron, 1992b ). His m e t h o d s, which a re developed in Brocket al. (1992)and

Levich an d Thomas (1993), mainlyus e simulation and bootstr apping.

2.1. Denition of the moving average trading rule

On e o f t h e most popular technical analysis trading rules is b a s e d on th e

crossingoftwo movingaverages ofp a s t prices . Accordingto this rule , b uyand

sellsignals aregenerated b y two movingaverages of t h e levelof t h e exchange

r atea longperiod average a nd a s h o r t period average . Here , t h e longmoving

average is computed on periods varyingfrom15t o 200 days , while t h e length of

th es o r t movingaverage windowis from 1d ay(in this case , it is t h e ra wreturn )to 14 days at m o s t. When th e s h o r t period average is above t h e long moving

average , th e rule r ecommendsholdingt h e foreign cur r ency. Th e rule advocates

holdingth e domesticcurrencywhen th e s h o r t period average is belowt h elong

on e. Thus , ab uysignalis generated when th es h o r t movingaverage breaksth e

longo ne from below a nd a sellsignal when itbreaks th e long moving average

from above.

Th e s h o r t moving average is th e s p o t exchange r ate at time t, noted Pt, and

MAMt (Pt), t h e long movingaverage is dened in th e u s u a lwa ya s :

MAMt (Pt) 51

M OM2 1

i 5 0

Pt2 i

where Mis th e lagu s e d to c o m p u t e t h e movingaverage .1

If t h e b uy signal is dened as (st5 1st2 1 5 2 1) a nd th e sell signal as(st5 2 1st2 1 5 1)where st is dened a s :

st5 H1 if Pt$MA

M

t (Pt)2 1 if Pt,MA

Mt (Pt)

and p t5 ln (Pt), th e return x t of t h e tradingstrategy is then:

x t5 st (p t1 1 2 Pt)

As shown in Fig. 1, b uy and sell signals alternate and th e trading position is

either s h o r t or long in th e foreign cur r ency.

If t h e interest rate differentials between th e t wo countries are taken into

account, th e cumulative return of t h e chartist strategybecomes:

1 See , for example, Brock et al. (1992 ) an d LeBaron (1996 ) for ot he rspecications of this simple

rule . Hereafter, this rule will b e noted VMA(x,y) for variable moving average , with x an d y

respectively th e lengthof th e s h o r tmoving average an d th elengthof t he longone.

198 Maillet and Michel


4/29

x t5 st[pt1 1 2pt1 ln(1 1 r*t) 2 ln(1 1 rt)]

with rt an d r*t respectively t h e domestic a nd t h e foreign interest r ates .

2.2. The performance tests

Ausefultradingrule must generate a positive return . Twokinds ofperformance

benchmar k are traditionally u s e d : t h e na ve strategyan d a strategyb a s e d on

s o m e str uctur al economic o r statistic model. As implied b y th e market

efciency hypothesis , no str uctur al model outperforms signicantly t h e na ve

strategy, as shown b ymanya u t h o r s(s ee , for example , Meese an d Rogoff, 1983for 1970s m o d e lprediction accuracy and Frankeland Rose, 1994a nd Chinna nd

Meese, 1995 for recent surveys on empirical results ). Indeed , t o provide

continuity with previous works , we test both whether th e chartist return issignicantly positive , and also th e signicance o f th e spr ead between char tist

a nd market r etur ns. Some author s 2 test th e positivity of th e chartism r etur ns,

2 See LeBaron (1996), Lee a nd Mathur (1996)o r Neelyet al. (1996 ).

Exchange ratept and moving averageMAMt (Pt):

Corresponding cumulative return of the strategyxt:

Fig. 1. Trading rule example on the daily USD/DEM rate from 01.11.1990 to01.11.1992



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whereas th e usualperformancetest is to compar e t h e m with t h e buy-and-hold

strategy returns , generally used in t h e portfolio performance literature. Th e

p u r p o s e of this comparison is to a s s e s s th e economic value o f chartist

prediction r ather t h a n it s relative predictive power.3 We shall consider in this

workt h a ta strategyis usefulonlyifit yields amean return signicantlyhigher

than t h e market on t h e s a m eperiod .

2.3. Recent evidence and explanations of the protability of technicalanalysis on exchange rate data

LeBaron (1996) consistently nds signicant positive char tist r etur ns o n mainr eser ve currencies. Every t-statistic is above th e critical 5% value. Usingbootstr ap m e t h o d s, th e estimated p-values are under 1.5%. These results holdwhatever t h e exchange r ate considered , and whether t h e interest r ate differ-

entialis included in th e cumulative return or not . Th echartist return volatilities

are ver yclose to t h o s e o ft h e r aw returns . Th e Sharpe ratiosconrm th egoodperformanceofth e chartist strategies , evenwhen a realistic transaction c o s t is

paid for each t r a d e.

Neelyet al. (1996 )us e a genetic programmingappr oach t o s h o wevidence ofexcess returns o f trading rules over t h e main dollar currencies. Th e genetic

programming method allows nonparametric exibility: th e trading rules are

endogenously generated a nd selected b a s e d on their tness on a subsample,

and tested o ut-of-sample . Neely et al. (1996) then conclude t h a t p a s t pricescontainprotable information .

These positive results are somewhat questioned b y Lee and Mathur (1996),wh o have shown that th e technicalanalysis performances a re no thomogeneous

over t h e series . Th e technical analysis results on th e main European daily

exchange r ates a renot as good a s t h o s e on main dollar currencies .

LeBaronp r o p o s e san economic explanationo f th e chartism performanceon

th e dollar currencies (s ee also Lee a nd Mathur, 1996 and Neely an d Weller,1997 ). Heshows a linkbetweenFederalReserve interventions and t h echar tistreturns . Th eFed interventionsmight b et h e c a u s efor s o m e ofth e predictability

seen in several foreign exchange series . LeBaron r epeats t h e previous tests

removing t h e foreign exchange intervention periods . Then , t h e results of th e

chartist strategies a re dramaticallydowngraded . LeBaronu s e s complementar ytests t o ensur e t h a t this result is no tjust a simulation artefact. Th e rst test is

to simulate a virtual intervention series on another cur r ency. Removing th e

simulated intervention periods causes no drastic changes in th e technical

analysis returns , which s e e m s t o prove th e causal link between th e real Fed

interventions an d th e chartist performance . Th e statistical exploration of th e

centr alb a n k behaviour shows t h a t it s policy is likelyt o b eleaningagainst th e

3 As recommended in Admatian d Ross (1985 ) an d a s we ar e interested in th eeconomicvalue o f

technicalanalysis forecasting, we used th e n ave strategyas abenchmark(s ee Cornell, 1979for a

justication a nd Cumbya nd Modest, 1987for applications ), instead ofother statisticalpredictioncriteriasuch as th eaverage absolute error, th esquare rooto fth e meanofsquared errors o rth e U-

Theilstatistic of th e tradingstrategy returns (s ee Lakonishok, 1980;Meese and Rogoff, 1983;a nd

Diebold an d Mariano, 1994 and Brooks , 1997 fo r a survey on predictive accuracy measures). For

alternative benchmarks, s ee alsoAcar (1993), Chapter2.



6/29

wind. Th e prot realized b y technicalanalysts would b e th e price paid b y t h e

centr alauthority in or der t o stabilize th eforeign exchange r ate .

In a related s t u d y on weekly futures contr acts , Kho (1996 ) suggested a nalternativeexplanation:t h e excessreturn generated b yth e us eofth e technical

analysis advice is actually t h e counter par t of a time-varying systematic risk,

even if th eoverallrisk of this strategy d o e s not differ from th e na ve one .

3. FURTHER EVIDENCE OF TECHNICAL ANALYSIS PROFITABILITY

These recent results on exchange r ate a nd on stock market indices challenge

t h e efcient market hypothesis . It s e e m s therefore interesting t o test t h e

stability a nd r obustness of th e technical analysis performance . We r epr oduce

t h emaintest o fLeBarons p a p e r on t h e performanceofth echar tistrule , b ut we

allowpar ameter s t o var ys o a s to generalize th eprevious results .

Ou r empiricalresults are t h a t char tismmean returns a re almostalways higher

than th e na ve strategys r etur ns a nd t h a t t h e signicance of t h o s e differencesholds for a wide range ofpar ameter s . For each series, we determine t h e optimalrule . We then suggest an alternativeexplanation of thisobvious performance .

3.1. Database description and performance test results

Weus e th e followingdailyforeign exchange series , extracted fromDATASTREAMTM;

DEM/USD, FRF/USD, JPY/USD, GBP/FRF, DEM/FRF, JP Y/FRFfrom Januar y1974t o

September 1996.4

Some previous studies us e weeklydata (LeBaron, 1996 ), most a u t h o r sc h o o s e

dailyd a t a, a nd Curcio et al. (1997 )applyachartist rule on an intradaily d a t as et .Wec h o o s e th e dailyfrequencybecause it is recognizedt h a tchartism is mostlyapplied o n a ver ys h o r t horizon (Allen an d Taylor, 1992;Curcio et al., 1997)a ndalso in or der t o allow comparisons with m o s t of th e previous studies on

exchange r ates .Ino ur data , t h e characteristicsofhigh frequencyexchange r ates a re , as usual

weakreturn autocorrelations, signicant(b utlow)absolute a nd squar ed returnautocorrelations, high kurtosis indexan d a weakskewness coefcient(LeBaron,1993, 1996;Sweeney, 1986;Neelyet al., 1996;Pagan , 1996 ).

We implement th e performance test descr ibed below on this d a t a b a s e a nd

focus on th e return differential between technical analysis strategy an d t h e

marketreturns on th e s a m e period . Table 1displayst h estatistics relative to o ur

tests 5 for th e often used technical analysis strategy tested b y LeBaron (1996 ),a nd b a s e d on th e crossing o f th e s p o t exchange r ate an d a moving average

computed over t h e 150 last days .

4 Weused th elastquote ofeach d a y(mid-askbid quotation )on th eLondon market an d t h ecross-

rates a re built from th e Sterling rates .5 Without taking intoaccount t he interestratedifferential, which doe s n ot modifyth e results (s ee

Sweeney, 1986 , p . 172 for acomplete justication a nd resultsin LeBaron , 1996 ). Besides, ou r simple

pur pos ehere is t ouncoverpotentialdiscrepanciesbetween r aw an d tradingrule ltered series . Wed o no t intendye t to design th e be s t winningstrategy, which would requiren ot only interest rate

differentials, b ut also ination ratesan d transactions costs ofthis strategy(e.g. different cost ofa

cash , futureo roption based strategy). Even th e design ofth e strategy(i.e. t h ewa yto answer to t he

tradingrule signals )allows some degree offreedom, as s hown in Brocket al. (1992).



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Table1.T

es

to

fc

hart

ists

tra

tegywi

thM

the

lago

fthe

longm

ov

ingaverageMAMt(pt)

eq

ua

lto150days

Series

Samp

le

Num

ber

ofs

ignals

Meanre

turn

ofthe

chart

ist

stra

tegy

Stan

dard

dev

iatio

no

f

thec

ha

rtist

stra

tegy

return

Meanre

turn

ofthena

ve

stra

tegy

Stan

dard

dev

iationo

f

the

na

ve

stra

tegy

retu

rn

Sign

icance

*

ofthec

hart

ist

return

(to

0)

Sign

icance

*

ofthere

turn

difference

DEM/USD

DEM/FRF

USD/DEM

USD/FRF

USD/JPY

FRF/DEM

FRF/USD

FRF/GBP

FRF/JPY

GBP/FRF

JPY/USD

JPY/FRF

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

74

.01

96

.09

171

147

165

187

163

152

182

154

126

163

141

134

0.0

00152

0.0

00057

0.0

00173

0.0

00144

0.0

00196

0.0

00105

0.0

00113

0.0

00155

0.0

00278

0.0

00142

0.0

00258

0.0

00258

0.0

0723

8

0.0

0288

4

0.0

0723

8

0.0

0706

5

0.0

0792

2

0.0

0253

8

0.0

0739

4

0.0

0514

2

0.0

0692

4

0.0

0515

3

0.0

0773

2

0.0

0696

0

0.0

00097

0.0

00111

0

.000097

0.0

00014

0

.000153

0

.000112

0

.000015

0.0

00052

0

.000168

0

.000052

0.0

00154

0.0

00168

0.00

7239

0.00

2882

0.00

7239

0.00

7067

0.00

7923

0.00

2538

0.00

7395

0.00

5144

0.00

6927

0.00

5155

0.00

7734

0.00

6963

1.6

2

1.5

2

1.8

4

1.5

7

1.9

1

3.1

8

1.1

8

2.3

3

3.0

9

2.1

2

2.5

7

2.8

6

0.4

2

1

.02

2.0

3

1.0

0

2.4

0

4.6

5

0.9

4

1.0

9

3.5

0

2.0

5

0.7

3

0.7

1

*t-s

tatis

ticv

alues;boldprint5%

signic

ance.



8/29

On each series , th e VMA(1,150 ) trading rule yields a positive return higher

than th e market one . Moreover, in s ix cases out of 12, char tist r etur ns ar e

signicantly positive . But theysignicantly outperform th e market only in ve

cases (where t h e n a ve return is negative ). As r epor ted in Table 1, char tist

r etur ns a re n ot different when th e rule is applied on th e direct (or European )

exchange rate quotation o r th e indirect(o r American )quotation , b ut t h e na vereturn obviously is . We consider indeed both n ave strategies: holding th e

national cur r ency or holding th e foreign currency for t h e cambist oper ator

(Neely et al., 1996 ). Therefore , and as expected , when th e na ve return is

positive , th e difference between b o t h strategiesis less signicantt h a n when t h e

na ve return is negative . That is to s ay, it is more difcult to beat signicantly a

good strategythan a bad one, b ut also that it is difcult t o select signicantly

more bullish periods a nd less bearish periods in series containing lots o f up-

tr ends a nd fewdown-tr ends .

Nevertheless , t h e comparison between chartist and na ve returns is slightlyless favourable to technicalanalysis on alarger d a t a b a s ethan we could expect

from LeBarons rst results . However, this d o e s not mean that no rule

signicantly outperforms t h e market . We s h o w in th e next section t h a t s o m e

combinationsof par ameter s d o beat t h e market b ya signicantmargin .

3.2. Trading rule performance sensitivity to its parameters

Westudyhereafter th e tradingrule returns conditionalon t h e s e to fpar ameter s ,

in or der t o test th ehypothesis of th e stabilityof t h e performance .

Sensitivity to the lag of the long moving average

We var y th e la g over which t h e long moving average is computed , setting t h e

s p o t price as t h e s h o r t moving average . Th e returns conditional on t h e s e lags

a re r epr esentedbelow.

As we would expect , t h enumber ofsignals d r o p s drasticallyas t h ela goft h e

long moving average increases. Th e s h o r t moving average can diverge more

easily from t h e long moving average when th e lag is longer because t h e n th e

long moving average is less sensitive to a on e-d ay variation s h o c k . There is

obviously a relationship between chartist returns and t h e lag of th e long

movingaverage as shown in Fig. 2.

Figure 3r epr esentsth e signicance ofth echartist tradingrule , as afunction

of th e la gof th e longmovingaverage in o ur sample .

Two t-statistics are r epr esented in Fig. 3. These statistics are computed as

usuala s th e ratio ofdifference in means over standar d deviations . Th e rst one

is th e statistic for t h ehypothesis that th e trading rule return is equal to zero .

Th e second one tests th e hypothesis that th e chartist r etur n is no t different

from th e market return . Although m o s t of th e trading rule returns a re

signicantly positive and superior to t h e na ve ones for a lagu n d e r 145 , none

outperforms signicantly t h e nave strategyfor a la gsuperior t o 145 . However,

t h e s e r etur nsare always positive and higher than th e market return ifnot with



9/29

a signicantmargin . Itmight then b e worthwhile to s t u d yt h e sensitivity foth e

performanceof t h e rule to b o t h it s par ameter s .

Fig. 2. Number of signals and trading rule returns: function of M, the lag of the long movingaverage MAMt (pt) on the USD/DEM rate from 01.03.1974 to 09.30.1996

Fig. 3. Signicance of trading rule returns: function of M, the lag of the long movingaverage MAMt (pt) on the USD/DEM rate from 01.03.1974 to 09.30.1996



10/29

Chartist performance sensitivity to the lags of both short and long movingaverage

Figures 4 and 5 (an d Fig. A.1 in th e Appendix ) s h o w th e performancesignicance function o f th e lags of th e moving averages compar ed using th e

rule . This signicance is measur ed her e b y th e t-statistic of th e differential of

return between th e na ve an d th e chartist strategies when b o t h par ameter svar y. Th elonga nd s h o r tmovingaverage lengthsare read respectivelyo n t h e x-axis and th e y-axis of Fig. 4. Th e level o f grey of each point is a decreasing

function of th e t-statistic .

Th e black d o t s in Fig. 5 r epr esent t h e pairs o fpar ameter s for which moving

average comparison does no t yield r etur nssignicantly higher t h a n t h e market

r etur ns.

Th e results ar e no t stable over th e whole range o f par ameter s; th e return

differencesare n ot signicant in some areas o ft h e s etofpossiblevalues for t h e

length of moving averages . There is , however, a widearea of values wher e th erules aresignicantly useful.

Figure A.1 in t h e Appendix generalizes this binary representation o f th e

results to t h e whole d a t a b a s e. Th e results are fairlyhomogeneous for most of

t h eseries:either none (or almostnone )oft h e combinationofpar ameter s yieldssignicant performances , either for every (or almost ever y ) combination ofpar ameter s th e return differences are signicant. In th e case in which none of

t h e results is signicant, using th e rules on th e universe exchange r ate yields

Withythe length of short moving average MAyt (pt) varying from 1 to 14,x the length of the long movingaverage MAxt (pt) varying from 15 to 300; the level of grey of each point is a decreasing function of the

t-statistic of the difference between the chartist and nave returns.

Fig. 4. Level of signicance of the tradingrule return as a function of both length ofthe moving averages used on the seriesUSD/DEM rate from 01.03.1974 to09.30.1996

Fig. 5. Signicance of the trading rule returnas a function of both length of the movingaverages used on the series USD/DEM ratefrom 01.03.1974 to 09.30.1996



11/29

s o m esignicantpositive performance. This is th e case for th e DEM/USD, DEM/FRFand JPY/USDseries .

It is wor th noting that for nine exchange r ates o ut of t h e 12 comprising o ur

d a t a b a s e, t h e difference betweenchartist r etur nsan d market returns is always

positive .

FigureA.2in t h eAppendixr epr esentsth e sign ofthis return difference for th ethr ee series wher e it is no t always positive . For t h e JP Y/USD a nd JPY/FRF

exchange r ates , t h e negative sign is exceptional. Th e DEM/FRF is th e only

exchange r ate where t h e results ar econtr asted .

4. ROBUSTNESS OF THE TRADING RULE PERFORMANCE

Th e results in this section concer n t h e r obustness of t h e trading rule

performance over th e d a t a b a s e. We rst s t u d y th e r obustness o f technical

analysis performance when th e rules are applied on different subsamples. Wefocus her e on t h e case of t h e USD/DEM exchange r ate trading rule perform-ance.

4.1. Time consistency of the technical analysis performance

Th e following results are obtained b y using th e lengths of moving averages

which maximize th e return differences between chartist a nd na ve strategies ,

divided b y th e s um of th e return standar d deviations (in other words , t h e t-statistic associated with t h e difference between strategies mean r etur ns ). Forinstance, we have found t h a t t h e t-statistic of th e difference in mean return is

maximalfor t h e lengthsof9days for th e s h o r t and 16days for t h elongmoving

averages in t h e case ofUSD/DEMexchange rate .6

To ensur e t h a t t h e previous results are no t d e p e n d e n t on t h e period of

estimation , we r an sever altests o n different subsamples. Th e rst test consists

in checking t h e r obustness of th e results over t h ewhole period . Starting from

Januar y 1974, we compute t h e cumulative r etur ns of chartist a nd na ve

strategies and t h e 5% condence intervals each d ay until t h e en d of th e totalperiod . Figure 6compar es th e optimal tradingrule return with th e na ve one and

th e superior b o u n d of th e5%condence interval.

Th e cumulative return of th e optimal trading rule is over th e u p p e r 5%condence b o u n d from May 1975. Table 2 displays statistics about th e time

consistency of th e chartist performance. The columns of this table give th e

number o fperiods whereth echar tistreturn is respectivelypositive , higher and

signicantly higher t h a n t h e na ve return over t h e total n u m b e r of estimation

periods .Th e performanceo f t h e chartist rule is homogeneousover t h e sample since

th etradingrule regularlybeats th e market . When th e chartist r etur ns are higher

than t h e n ave o ne over th e whole s et ofpar ameter s , theya re also insensitive t o

th e selectionof asubsample. This is th e case for t h e USD/DEM, USD/JPY, FRF/DEM, FRF/JP Y, GBP/FRF r ates . On th e c o n t r a r y, when no signicant results are

6 In order to save space , t he in-sample maximization results a re no t reproduced for th e ot he r

exchange rates b ut ar e availableon request.



12/29

found b y varying t h e moving average lengths , they are rarely signicant. But ,

her e again , as shown in t h e t wo rst columns, it is ver y likely for th e entire

d a t a b a s e t h a t t h e chartist r etur ns are positive a nd higher than th e market

return .

Fig. 6. Cumulative returns of the optimal trading rule compared to the nave returns on theseries USD/DEM rate from 01.03.1974 to 09.30.1996

Table 2. Time consistency of the optimal trading rule performance over thesample from 01.03.1974 to 09.30.1996

Series Prob[ xc > 0] Prob[ xc > xN] Prob[Tc > 1.96]

DEM/USD 1.00 0.99 0.56DEM/FRF 1.00 0.99 0.02USD/DEM 1.00 1.00 0.92

USD/FRF 1.00 1.00 0.59USD/JPY 1.00 1.00 0.79FRF/DEM 1.00 1.00 0.89FRF/USD 0.95 0.93 0.68FRF/GBP 0.97 0.94 0.69FRF/JPY 1.00 0.95 0.85GBP/FRF 1.00 0.98 0.95JPY/USD 0.98 0.98 0.01JPY/FRF 0.99 0.99 0.02

Prob[ xc > 0] is the estimated frequency of cumulative positive chartist return for the optimal

rule.Prob[ xc > xN] is the estimated frequency of cumulative chartist return higher than the navereturn for the optimal rule.

Prob[Tc > 1.96] is the estimated frequency of cumulative chartist return signicantly higherthan the cumulative nave return for the optimal rule.



13/29

This does not mean that from 1974 to 1996 t h e information s e t available

allowed to conclude that t h e chartist method signicantly outperformed th e

marketsince we used th ewholeperiod to determine t h e optimal rule . Therefore ,

we again carried out th e test this time using an ar bitr ar y ex ante rule: th e

commonly u s e d rule that compar es t h e s p o t price t o th e 150-d ay moving

average .7 Figure 7 and Table 3 illustrate t h e test . As in Table 3 relative t o th e

optimal rule , t h e columns o f Table 3 give th e n u m b e r o f periods where th e

chartist return is respectivelypositive , higher an d signicantly higher than th e

na ve r etur nover t h e totaln u m b e r ofestimation periods .

Th e results using an ar bitr ar y rule strongly differ from those previously

obtained . In our example of t h e USD/DEM exchange r ate whose cumulative

trading rule r etur n is plotted o n Fig. 7, th e compar ison of trading a nd na ve

returns would have led to rejection oft h e usefulness oftechnicalanalysis more

than halfo f th e time , even though it s returns were always positive and higherthan t h e na ve ones .

Th e empirical frequencies in th e rst t wo columns in Table 3 are obviously

lowerthan t h o s e in Table 2, b ut are also above50%. However, th e probabilityofconcludingth e usefulness oftechnicalanalysis is this timemuch lower. As t u d y

focusingon th esignicance ofchartist outperformance would have determined

its inefciencyb ut would havemissed th eregularityofthis performance. Table

4r epor ts th efrequency of, respectively, positive , higher an d signicantly higher

return of th e VMA(1,150 ) rule using, this time, 15 000 r andom periods of thr ee

years dr awn from th e series . These statistics are t h e n independent from th eperiod ofestimation oft h echar tistperformance . Th econclusion ofa n obser ver

7 Noted thereafter t heVMA(1,150 ) rule for variable movingaverage with a on e-d a ys h o r tmoving

an d 150-d ay longmovingaverage.

Fig. 7. Cumulative returns of the VMA(1,150) trading rule compared to the navereturns on the USD/DEM rate from 01.03.1974 to 09.30.1996



14/29

Table 3. Time consistency of the VMA(1,150) trading rule performance over thesample from 01.03.1974 to 09.30.1996


DEM/USD 1.00 0.94 0.00

DEM/FRF 0.98 0.87 0.00USD/DEM 0.98 0.99 0.52USD/FRF 0.99 0.88 0.00USD/JPY 0.95 0.87 0.48FRF/DEM 0.91 0.92 0.86FRF/USD 0.99 0.95 0.26FRF/GBP 0.99 0.80 0.00FRF/JPY 1.00 0.95 0.85GBP/FRF 1.00 1.00 0.25JPY/USD 0.82 0.81 0.00

JPY/FRF 0.97 0.88 0.00Prob[ xc > 0] is the estimated frequency of cumulative positive chartist return for the

VMA(1,150) rule.Prob[ xc > xN] is the estimated frequency of cumulative chartist return higher than the nave

return for the VMA(1,150) rule.Prob[Tc > 1.96] is the estimated frequency of cumulative chartist return signicantly higher

than the cumulative nave return for the VMA(1,150) rule.

Table 4. Time consistency of the VMA(1,150) trading rule performance overbootstrapped subsamples from 01.03.1974 to 09.30.1996


DEM/USD 0.92 0.70 0.00DEM/FRF 0.92 0.32 0.00USD/DEM 0.84 0.81 0.24

USD/FRF 0.83 0.71 0.00USD/JPY 0.84 0.99 0.30FRF/DEM 0.77 0.94 0.69FRF/USD 0.93 0.78 0.13FRF/GBP 0.93 0.82 0.01FRF/JPY 0.84 1.00 0.35GBP/FRF 0.90 0.72 0.07JPY/USD 0.95 0.52 0.00JPY/FRF 0.92 0.56 0.00

Prob[ xc > 0] is the estimated frequency of cumulative positive chartist return for the

VMA(1,150) rule.Prob[ xc > xN] is the estimated frequency of cumulative chartist return higher than the navereturn for the VMA(1,150) rule.

Prob[Tc > 1.96] is the estimated frequency of cumulative chartist return signicantly higherthan the cumulative nave return for the VMA(1,150) rule.



15/29

aftera thr ee-year s t u d y would b e again t h a t no signicant performance would

b e generated b y th e char tist method as shown in Table 4. To give signicant

results , t h e rule h as to b e applied on a time period greater than thr eeyears .8

Th eprobabilityofth ereturns beingpositive after thr ee years is stillhigh . Th e

results r epor ted in th e second column are less homogeneous. On t h e thr ee

series DEM/FRF, JP Y/USD, and JP Y/FRF, th e probability o f th e chartism out-performing t h e market is no t higher than 50%.

Ou r previous results (Fig. A.1 in t h eAppendix) have alreadyshown t h a t, on

t h e s e thr ee series , th e chartist trading rule return was no t also signicantly

higher than th e market return whatever th e movingaverage lengths are. From

Table 3 an d Fig. A.1 in th e Appendix, we c an s ay that when technical analysis

performance is insensitive t o th e rules par ameter s , it is also consistent over

time . This regularity suggests that t h e technical analysis outperformance is a

realphenomenon .

4.2. Out-of-sample tests of technical analysis prots

To make sure t h e s e results are not spurious 9, we s et up out-o f-sample tests

(Brock et al., 1992; Silber, 1994; Lee an d Mathur, 199610; Neely et al., 1996),

optimizing t h e rule on a ve-year s u b-sample (01.197401.1979) and applyingthis optimal rule for th elatter period (01.197909.1996 )for th e main currencies.

Table 5 pr esents results of t h e s e out-o f-sample tests a nd Table 6 summarizes

s o m estatisticalproperties of th e r aw exchange r ate series .

For th e tests in Table 5, we u s est ude nts t-statistic to compar e chartist and

na vemean return and alsobootstr ap m e t h o d sbecause ofth e n on-normalityofth e series .11 We test also for th e difference between th e o t h e r empirical

moments of th e estimated market returns , and t h o s e of th e chartist strategy

returns . Wethen c o m p u t eth estatistics ofconditionalreturns and s e tup 15 000

series o f na ve returns with r andom dr aws, having t h e same investment

horizons . For each moment computed , th eassociated p-statistics a re given , i.e .

8 Tests s et up on ve-years bootstrapped subsamples (no t reproduced here )yield th e same general

result concerning th e high probability level to reject th eutilityof technicalanalysis .9 See for example Silber (1994 )for t heselection bias problem of testing in-sample performance .10 Lee an d Mathur(1996 )optimize on aon e-year period . Accordingtoou r rst result , we optimized

over a longer period:from January 1974 to January 1979.11 However, we should note here , according to o ur o wn rst results an d Brock et al. (1992) an d

LeBaron (1996)analyses , that th e student t-statistics leads to a similargeneral conclusion a bout

chartism performance . Wecould then writeas Curcio et al. (1997, p . 8, note 8):It is wellknown that

th edistributionofexchangeratereturns deviates fairlyfrom t henormal. This implies that amore

appropriatewa yoftestingth esignicance o ftradingrule returns would b et ous eaboot s t r a p, a s

in Brocket al. (1992). However, th e results in Brock et al. (1992) a re no t qualitatively altered by

using bootstrapped standard errors an d he nc e we focus o n traditional t-statistics t o provide

inference. Moreover, as s uppos e d implicitlyb ySilber (1994)a nd LeBaron (1996 ), t he students t-

statistic is equivalent , if th e mean return a nd th e standard error ar e annualized , to t h e ex post

Sharperatio (1966), used traditionallyin th eportfolio performance literature. Finally, ift hetradersutilityfunction is quadratic, he is interested onlyin t he rst a nd second empiricalmoments ofh is

strategys returns , even if these a re n ot multivariate normal. Nevertheless , we present bot h t-

statistics an d p-statistics when th e calculation of th e bootstrapped p-values ar e not unbearably

computer timeconsuming.



16/29

Table5.O

ut-o

f-samp

letes

to

fdaily

chart

istperformanceon

thema

incurrenc

ies

from

0

1.1

979to09

.1996

Series

Num

ber

of signa

ls

Num

bero

f

signa

lsfor

large

varia

tions

i

Op

tima

l

(short-long

)

mov

ing

averages

Mea

n

leng

tho

f

sign

als

ii

Max

ima

l

leng

tho

f

signa

ls

Chart

ist

mean

return

(p-

statis

tic

)iii

Stan

dar

d

dev

iatio

n

ofc

hart

ist

returns

(p-

statistic

)iii

Skewness

coe

fc

ien

t

ofc

hart

ist

returns

(p-

statis

tic

)iii

Kurtos

is

indexo

f

chart

ist

returns

(p-

statis

tic

)iii

t- statis

tic

ivT(x

c>

0)

t- statis

tic

vT(x

c>xN

)Marg

ina

l

pro

ba

bility

of

Wilcoxon

tex

t

vi

c2

Goo

dness

oft

vii

Correc

t

sign

pro

ba

bility

viii

Correc

t

sign

pro

ba

bility

(for

large

varia

tions

)

ix

DEM/USD

175

8

(6;

32)

25.1

130

0.0

05718

(0.0

930)

0.0

01365

(0.7

583)

1.5

87112

(0.0

038)

6.2

21387

(0.1

070)

4.1

9

4.6

3

0.0

099

11.5

96

0.3

7

1.0

0

DEM/FRF

107

4

(14;

49)

48.1

232

0.0

00764

(0.9

953)

0.0

00209

(0.3

871)

1.0

11268

(0.9

777)

14

.239914

(0.2

431)

3.6

6

1.0

5

0.9

980

18.6

74

0.3

0

0.7

5

USD/DEM

182

10

(6;

31)

15.7

81

0.0

05227

(0.0

243)

0.0

01346

(0.6

728)

1.6

64556

(0.0

008)

6.4

25803

(0.1

344)

3.8

8

4.2

3

0.0

017

11.6

26

0.3

7

1.0

0

USD/FRF

184

8

(6;

26)

25.1

129

0.0

09056

(0.0

035)

0.0

01232

(0.7

944)

1.6

62830

(0.0

066)

6.5

73139

(0.1

370)

7.3

5

7.5

4

0.0

091

2.6

31

0.4

4

1.0

0

USD/JPY

202

9

(13;

24)

25.8

92

0.0

07975

(0.0

000)

0.0

01244

(0.6

380)

1.7

41976

(0.0

000)

8.0

60766

(0.0

376)

6.4

1

6.2

3

0.0

001

7.9

28

0.4

0

0.8

9

FRF/DEM

104

4

(14;

51)

41.4

233

0.0

02407

(0.0

000)

0.0

00224

(0.2

566)

2.9

37442

(0.0

000)

13

.942528

(0.2

339)

10.7

5

3.8

3

0.0

000

10.0

85

0.3

5

1.0

0

FRF/USD

29

2

(12;

247)

25.4

128

0.0

38702

(0.0

386)

0.0

19715

(0.1

188)

3.0

58403

(0.0

065)

12

.278893

(0.0

306)

1.9

6

18.0

8

0.0

050

2.7

78

0.3

4

1.0

0

FRF/GBP

127

9

(8;

42)

34

275

0.0

09313

(0.0

042)

0.0

01208

(0.4

656)

2.0

73633

(0.0

204)

7.0

58230

(0.5

772)

7.7

1

9.0

3

0.0

022

9.6

65

0.3

6

1.0

0



17/29

FRF/JPY

36

4

(12;

159)

146

.2

882

0.0

27451

(0.0

003)

0.0

09189

(0.2

306)

1.4

86794

(0.0

307)

4.1

49727

(0.6

651)

2.9

9

16.7

2

0.0

621

4.0

50

0.3

3

1.0

0

GBP/FRF

138

6

(10;

33)

34.2

275

0.0

09472

(0.0

003)

0.0

01023

(0.5

375)

2.3

91386

(0.0

000)

10

.002610

(0.0

307)

9.2

6

9.3

5

0.0

001

3.5

07

0.4

2

1.0

0

JPY/USD

81

2

(7;

88)

29

98

0.0

12209

(0.3

734)

0.0

03598

(0.5

984)

3.1

47269

(0.0

240)

17

.269441

(0.0

357)

3.3

9

8.7

4

0.0

081

3.6

94

0.4

0

1.0

0

JPY/FRF

65

4

(9;

93)

30.2

182

0.0

15249

(0.5

199)

0.0

06015

(0.1

907)

2.2

42204

(0.1

093)

7.2

32679

(0.4

483)

2.5

4

10.1

9

0.0

052

10.3

47

0.3

1

1.0

0

For

largevaria

tions,

i.e.

forx

c

suc

has

12s

xc

0

where

H

12s

=1

if(x

c(x

c+

2sc

)orx

c(x

c2sc

))

12s

=0

otherw

ise

(ii)Weuse

the

term

leng

tho

fs

igna

lfor

thenum

be

ro

fdays

be

tween

twoconsecu

tive

signa

ls(buyan

dse

lls

igna

lorsellan

dbuys

igna

l).

(iii)Boo

tstrappe

dp-s

tatis

tic,

i.e.

thees

tima

tedfreq

uencyo

f15000boo

tstrappe

dorig

ina

lseriesex

hibitinga

higherempir

ica

lmomen

ttha

tthe

ltere

dseries

one.

(iv

)t-s

tatis

ticto

tes

tifc

hart

istmeanre

turnx

cissign

ican

tlypos

itive.

(v)t-s

tatis

tic

to

tes

tifc

hart

istmeanre

turnx

cissig

nican

tly

higher

than

thena

vemeanre

turnxN.

(vi)WilcoxonS

ign

Ran

kTes

t,i.e.

thepro

ba

bilityto

havec

hart

istmeanre

turn

different

from

thena

veoneus

ing

Wilcoxon

seriess

igncomparison.

(vii)Chi-square

ds

tatis

tico

fthesum

ofthesquare

ddifferences

be

tweenc

hart

istand

na

vere

turn

discre

tedistribu

tions.

(viii)Es

tima

ted

pro

ba

bilitytha

tc

hart

istforecas

ting

hascorrec

ts

ign,

i.e.

Sign

(xcT

xNT

)=

Sign

(sT

1)w

ithTas

igna

lda

tetw

here

H(s

T=

1sT

1=

1

(sT

=

1sT

1=

1).

or

(ix

)Es

tima

tedpro

ba

bilitytha

tc

hart

istforecas

ting

hascorrec

ts

ign

for

largeexc

hange

ratevaria

tions,

i.e.

withtheprev

iousno

tation,

tha

t:

12s

Sign

(xcT

xNT

)=

12s

Sign

(sT

1)w

here

12s

isde

ne

das

in(i).

Thep-s

tatis

tic

assoc

iatedw

itheac

hmomen

tisno

tedun

der

itsva

lue

inbrac

ke

ts.

Bold

printindicatessignicantdifferen

cebetweenchartistandnavereturnmomentsat5%

signicancethreshold.



18/29

Table6.S

tatis

tica

lpropert

ieso

fthe

ma

incurrenc

ies

from

01.1979to09

.1996

Series

i

Studen

tize

d

Range

Meanof

na

ve

returns

Stan

dard

dev

iation

ofna

ve

returns

Skewnes

s

coe

fcien

t

ofna

ve

returns

Kurtos

is

indexo

f

na

ve

returns

Bart

lett

Lag

statistic

ii

Box-P

ierce

statis

tic

iii

Q(30)

Adjus

ted

Lo-

Mac

Kinla

y

statis

ticiii

Q(30)

Ko

lmogov-

Sm

irnov

tes

to

f

Norma

lity

iv

DEM/USD

13

.34

0.0

0003

8

0.0

07569

0.3

0040

9

6.2

17609

2

57

.0357

(0.0

021)

41

.6711

6

(0.0

764

)

0.4

874

DEM/FRF

30

.62

0.0

0008

4

0.0

02288

6.3

1464

8

131

.925857

1

166

.6223

(0.0

000)

69

.4894

(0.0

000

)

0.4

957

USD/FRF

16

.98

0.0

0004

6

0.0

07422

0

.09853

2

7.9

56858

2

72

.4987

(0.0

000)

53

.7133

(0.0

050

)

0.4

872

USD/JPY

10

.73

0

.00011

9

0.0

08200

0

.22188

5

5.1

49565

2

203

.4496

(0.0

000)

152

.9981

(0.0

000

)

0.4

868

FRF/GBP

21

.10

0.0

0001

1

0.0

05087

0

.05999

3

14

.118965

1

78

.2937

(0.0

000)

46

.6877

(0.0

267

)

0.4

897

FRF/JPY

13

.55

0

.00016

5

0.0

06995

0

.34637

6

6.5

05981

2

108

.7409

(0.0

000)

78

.6054

(0.0

000

)

0.4

884

(i)Alltheser

iesare

rs

torder

integra

tedI(1),us

ing

Phillips

Perron,

Aug

men

tedDickey-Fu

lleran

dKw

iatows

kiPhillips

Sc

hm

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19/29

th e frequencies of th e simulated moments which a re superior t o th e chartist

return moments .

Th egeneralchar tistperformanceresults over th e entire (in-sample )d a t a b a s eare not given her e in or der to save s p a c e . Th e out-of-sample performances ,

generallydowngraded , are ver ysimilar t o th e in-sample totaldatabase period .

Student tests at a 5% threshold lead t o th e conclusion that th e chartist meanreturns are positive a nd higher 12 t h a n th e market return . At th es a m econdence

level, t h e tests using th e bootstr apped r etur ns are less favourable t o char tist

results , leading this time to t h e rejection ofhigher r etur ns in four cases out of

twelve:DEM/USD, DEM/FRF, JP Y/USD, JPY/FRF.13 Moreover, t h echartist strategy

does n ot seem to b e more risky14 than t h e na ve o ne since t h e standar d

deviations are not signicantly different . When t h e chartist mean return is

higher, t h e empirical probability density function o f th e conditional r etur ns is

alsosigncantlymore skewed to t h e right . As expected from t h e compar isonof

th e

rst

empirical

moments

given

above,

th e

Wilcoxon

sign

r ank

t e s t

an d

th ech i-squar ed goodness-of-t conrm t h a tth e distributions oft h e ltered chartist

returns a nd th e na ve one a resignicantly different. Nevertheless , th epredictive

power o ftechnicalanalysis is ver ylow. Th e cor r ectsign frequencies a reindeed

inferior to 50%. However, t h e largest char tist returns (a s indicated in t h e largevariation cor r ect sign column of Table 5) have mostly t h e good sign and it isthen likelyt h a tt h e overallgood chartist tradingrule performance is linked with

this ltering pr oper ty.

Inor dert o conrm t h e s e results , we s et up more extensivetests t o a s s e s s th e

r obustness ofth e ou t-of-sample chartist performance. Weevaluate th e empirical

probabilityofa n ar bitr ar y rule outperforming in-samplea nd ou t-of-sample andth e probabilities of a rule giving a consistent performance in and ou t-of-

sample .15 We r epor t in Fig. 8 th e differences of t h e in- a nd out-o f-sample

characteristics of th e trading rules results . The frequency of rules yielding

superior r etur ns is a b o u t th e s a m e in- and out-of-sample , except for t h e USD/

DEM, FRF/USDan d GBP/FRFseries .16 Th e t wo subsamples ar enearlyequivalent

in ter ms o f chartist trading rule performance for t h e o t h e r exchange r ate . We

notice also t h a t for t h eseries DEM/USD, DEM/FRF, FRF/GBP, JPY/USD, JPY/FRF,

th e mean chartist returns are never signicanton b o t h subsamples.

We wanted t o knowifgoodtradingruleresults obtained o ut-of-sample couldb e linked with t h e good results in-sample . Table 7 shows t h e estimated

12 With th e notable exception of th e DEM/FRFexchange rate .13 In t he s ecases , th e n ave return wa s superior.14 In other words , th e total risk of th e chartist strategy is comparable t o th e na ve on e, even

assumingth e presence ofsystematictime-varyingriskpremium(Kho , 1996). Moreover, as t hesu m

of squared returns ar e t he s a m e for bot h strategies , t he variance differential is equal to th e

difference in squared mean returns , which is found empirically to bevery low, i.e . with previous

notations:

s2

( x c)2 s

2

( xN)5

( x c)

22

( xN)

2


20/29

probabilities of consistent signicant results between in- and o ut-of-sample

periods .

Few rules t h a t signicantly outperformed t h e market in-sample stilld o s o out-

of-sample . Ino t h e rwords, t h e in-sample performance is not apredictor ofou t-

of-sample performance , although t h e in-sample optimal rule still gives goodresults out-o f-sample (s ee Table7). Th e lackofpositive results with th e optimalrule on series DEM/USD, DEM/FRF, FRF/GBP, JP Y/USD, JPY/FRF is consistent

with their general lo w performance her e, whether in- or o ut-of-sample. A rule

which h a s yielded ahigher return t h a n t h e naive in-sample on eis , however, ver y

likelyto also yield higher ( ifnot signicantly )ou t-of-sample return . On th e o t h e rh a n d , it is unlikelyt h a tarule t h a td id n ot outperformin-sample does s o out-o f-

sample . Therefore, while optimization is n e c e s a r y to obtain signicant ou t-of-sample results , a nyrule yieldinghigher returns t h a n th emarket willcontinue t o

d o s o .

5. STATISTICAL PROPERTIES OF THE OPTIMAL TRADING RULERETURNS

From n ow on , we shall u se th e b e s t pair of par ameter s for each rule for th e

wholesample , in or der t o displayclearlyth e specicityoft h e characteristics of

t h e trading rule returns .

5.1. Properties of signals

Werst s o r t th esignals accordingto theirlength (i.e. th elength oftimebeforet h enextsignal). Wet h u s compar e , in Fig. 9, t h emean dailyreturn o ft h e char tiststrategy for each horizon with t h e mean return of t h e market over th e s a m e

horizon .

Figure 9 illustrates t h e two followingpr oper ties:

P0,i is the empirical frequency that a rule yields out-of-sample a return signicantly higher

than the nave strategy (0), whatever the in-sample results (i);pi, 0 is the empirical frequency

that a rule yields a return signicantly higher than the nave strategy in-sample (0),whatever the out-of-sample result (i).

Fig. 8. Comparison of chartist trading rule in- and out-of-sample performances



21/29

c th esignal frequencyh as a tendency t o decr ease with length;

c th e mean returns o f th e signals whose length is more t h a n 20 days a re

higher than th e mean market return (for th e same horizon ), a nd t h o s e

whose length is u n d e r15 days are lower.

Th e mean length of th e signals is 15 days a nd th e median is 12 days . Mostsignals whose length is under 12 days have a return inferior t o t h e market

return . This means that more than half of t h e signals have a return under

th e mean market return . Th e variance of t h e market return increases with th e

length ofth e investmentperiod . Th e extreme returns are generallyt h o s eofth e

longest signals . As t h o s e signals a re nearly always efcient, t h e m o s t extreme

returns should b e asymmetric (skewed to th e right ). This is conrmed in

Fig. 10.

5.2. Estimation of the conditional return distribution

We u se b o o t s t r a p m e t h o d s (r a n d o m d r a w with replacement ) to constr uct a n

estimation of th e distributions of trading rule r etur ns an d t h e original market

Table 7. Consistency of chartist trading rule in- and out-of-sample performancesfor the main currencies

Series p0, 0/p9

0, 0 p0, 1/p9

0, 1 p1, 0/p9

1, 0 p1, 1/p9

1, 1

DEM/USD

DEM/FRFUSD/DEMUSD/FRFUSD/JPYFRF/DEMFRF/USDFRF/GBPFRF/JPYGBP/FRFJPY/USD

JPY/FRF

0.00 / 0.76

0.00 / 0.000.13 / 1.000.00 / 1.000.83 / 0.991.00 / 1.000.00 / 0.840.00 / 0.200.88 / 0.990.16 / 1.000.00 / 0.19

0.00 / 0.45

0.00 / 0.23

0.00 / 0.000.03 / 0.000.00 / 0.000.07 / 0.000.00 / 0.000.25 / 0.160.08 / 0.800.11 / 0.010.04 / 0.000.00 / 0.74

0.00 / 0.03

0.00 / 0.00

0.00 / 0.970.80 / 0.000.14 / 0.000.03 / 0.000.00 / 0.000.00 / 0.000.00 / 0.000.00 / 0.000.30 / 0.000.00 / 0.00

0.00 / 0.31

1.00 / 0.00

1.00 / 0.030.04 / 0.000.85 / 0.000.07 / 0.000.00 / 0.000.75 / 0.000.92 / 0.000.01 / 0.000.50 / 0.001.00 / 0.07

1.00 / 0.20p0, 0 (p

9

0, 0) is the empirical frequency that a rule yields a return signicantly higher than the

nave strategy (resp. higher ) out-of-the sample when this rule has given a returnsignicantly higher than the nave strategy (resp. higher) in the in-sample.

p1, 0 (p9

1, 0) is the empirical frequency that a rule yields a return not signicantly higher thanthe nave strategy (resp. not higher ) out-of-sample when this rule has given a return

signicantly higher than the nave strategy (resp. higher) in-sample.p0, 1 (p

9

0, 1) is the empirical frequency that a rule yields a return signicantly higher than the

nave strategy (resp. higher ) out-of-sample period when this rule has given a return notsignicantly higher than the nave strategy (resp. not higher) in-sample.

p1, 1 (p9

1, 1) is the empirical frequency that a rule yields a return not signicantly higher than

the nave strategy (resp. not higher) out-of-sample period when this rule has given a returnnot signicantly higher than the nave strategy (resp. not higher) in-sample.



22/29

r etur ns. We dr ew o n th e original series returns with th e s a m e investment

periods as t h e trading rule signals until we h a d more t h a n 15 000 returns . We

then used akernelmethod t o estimate t h e densityprobabilityfunction oft h e s e

r etur ns. Figure 10 illustrates th e distributions obtained .17

Th etradingrule r etur nsare skewed to t h e right , t h e 5%m o s t negative returnshave been ltered b y th e technical analysis rule . Th e empirical cumulative

distribution o f th e chartist r etur ns is lower t h a n t h e na ve on e whenever th e

return considered is inferior t o t h e mean , i.e . t h e chartist strategyis superior t o

t h e na ve strategy according t o th e rst- and second-or der 18 stochastic d o m-

inance criteria.

Table 8pr esents s o m enonparametric tests for th e estimated originaland th e

estimated conditionalreturn distributions . Th e conclusions o fth efour tests a re

homogeneous a nd allow for rejection of th e null hypothesis of th e equality of

b o t h distributionsat t h e 5%signicance level.Th e comparison of cumulative density functions conrms our previous

results; t h a t is , without any additional assumption on t h e s h a p e of th e return

17 For th egraph , we u s eaGaussiankernelan d choose th ebandwidthwhich minimizes th ecross-validation criterion(Efron an d Tibshirani, 1993).18 If th e second-order stochastic criterion is veriedwhen th e chartist mean return in- or o ut -o f-

sample is higher than th enave one, t h e rst-order stochastic dominance criterion isn ot however

veried for allot he r ou t-of-sample conditionalreturn series.

Fig. 9. Signal properties function of their lengths on the USD/DEM rate from01.03.1974 to 09.30.1996



23/29

Fig. 10. Comparison of the original and the conditional return distributions on theUSD/DEM rate from 01.03.1974 to 09.30.1996

Fig. 11. Comparison of the original and the conditional empirical cumulativereturn distributions on the USD/DEM rate from 01.03.1974 to 09.30.1996



24/29

distributions , technical analysis yields signicantly superior r etur ns . Th e

chartist strategyis superior o n t h e basis ofth emean-variance criterion a nd also

on t h ebasis o ft h e second stochastic dominance criterion. From Table5, we ca n

s ayalso that th e asymmetr yo fchartist returns is not d ue to chance .

Th e heuristic explanation of this result is that moving average rules ac t as

s t o p-loss lters. As s o o n as th e s p o t price cr osses th e moving average from

below, th emovingaverage willrise ceteris paribus, b e c a u s eit takes into accountt h ecur r entprice . For instance, ifa b uysignalh ad a long length , it means that

t h epriceh as increasedpersistentlyfor a longtime. Indeed , when th es p o tprice

(o r th e s h o r t moving average ) decr eases , it cr osses th e long moving average ,which rises as long a s it remains under t h e s p o t price .19 In th e case of a long

signal, t h es p o t price follows a long tr end . It is then likely that , when t h enext

crossing occur s (sell signal), t h e price will b e high enough to ensur e a returnhigher t h a n t h e mean market return . On t h e other hand , th e moving average

trading rules d o not lead t o holding a losing position for a long time, t h u s

avoiding th e largest losses.For th e chartist rule to b e protable , t h e r aw exchange r ate series must

exhibit enough long tr ends s o that t h e good results on t h e s e signals , cor r e-

sponding to largeexchange r ate variations , offset th efrequent small losses .

6. CONCLUSIONS

Th e signicance of chartist performanced e p e n d s on t h e length of t h eper iods

over which t h e moving averages are computed . Still, th e return differentialbetween th e na ve an d th e chartist strategies is positive for almost ever y

19 We d o no t take into account t he prices leaving th e computation of th e moving average a nd

reasonceteris paribus.

Table 8. Nonparametric tests of the equality of the nave and chartist returndistributions for the DEM/USD from 01.03.1974 to 09.30.1996

Test KolmogorovSmirnov Kuiper

Statistic 0.2252 0.2933

5% threshold 0.1010 0.18325% signicance test conclusion rejectH0 rejectH0

Test Wilcoxon MannWhitney

Statistic 1596263929 2.8333p-statistic 0.0046 0.00465% signicance test conclusion rejectH0 rejectH0

H0:H xN ~ +()xC ~ +()where xN is the na

ve return, xC is the chartist return and+

() is an unknown densityfunction.



25/29

combination of s h o r t a nd long moving average on t h e main international

currencies. This puzzling result holds whatever th e exchange r ate tested and

th eperiod considered . Moreover, t h e s echartist returns are signicantlyhigher

than th e na ve ones for severalseries an d for alargerange ofpar ameter s . None

of th e usual statistics allow discrimination between t h e series , b u t th e

variabilityo fth era wseries seems to b erelevant. Differences between b o t h rstand third centred moments o f chartist and na ve r etur ns ar e shown t o b e

signicant using bootstr ap methodology. The trading rule returns a re higher,

and th e extreme losses a re avoided . Th e general char acter of t h o s e results

induces us to conclude t h a t technicalanalysis performanceis not simplyd u et o

spurious patter ns of series tested , selection bias performance , data-mining or

data-snooping issues .

Several economichypotheses on exchange rate determination could explain

ou r results , s u c h a s centr alb a n k behaviour or self-realizing tr ad er s beliefs as

invokedb y

s o m e

author s

(De

long

et al

.,1990;

Lee

a nd

Mathur

,1996;

Neely

andWeller, 1997 ). This is also compatible with th e fact t h a tt h e chartist rule actually

selects th e periods where ther e is a tr end in th e prices, b ut cannot forecast

them ex an te . These few good results must offset th e lowcommon results for th e

rule t o b e efcient. Nevertheless , before drawing conclusions regarding th e

inefciencyo fth e market and t h e ex ante chartist performance , we test whether

it is possible to u s e this statisticalresult t o dene a protyieldingcash-future-option b a s e d strategy, including, this time, bidask spr ead , transaction costs ,

yield a nd ination spr eads , liquidity oppor tunity an d o t h e r nonperfect market

costs .

Naturalextensionsof this workwould incorporate o t h e radditionalvariablessuch as volume statistics or, as in Acar and Satchell (1995), Taylor, (1994)andClydea nd Osler(1997 ), a s t u d yof th e links between chartist performanceandth e specicationo f t h e data generatingpr ocess followed b y t h e prices .

ACKNOWLEDGEMENTS

Inpreparingthis p a p e r, we have beneted from th ecomments , suggestions and

references of Thierry Chauveau (CEBI, Univers it e Paris I / CDC-FMR), Helen eRaymond(CEBI, Univers it e Paris I), EmmanuelAcar (BZW-London ), PaulWeller(University o f Iowa / Federal Reserve Bank of Saint Louis ), Sylvain Friederich

(CEBI, Universite Paris I / LSE-FMG) and CEBI seminar participants . We t h a n k also th e editor for h is comments a nd an anonymous referee for h is detailed

r epor t . Responsibilityfor a nynonsense r ests with us . An earlier version of this

p a p e r was pr esented at th e CNRSconference Monnaie et Financement, Aixe n

Provence , June 1996, a tth e A.E.A. conference , Evry, October 1996, at t h eA.E.A.-

ImperialCollege-BNPconference , London , May1997a nd a tt h eAFFIconference ,

Grenoble, June 1997.



26/29

APPENDIX

(yis the length of the short moving average MAyt (pt) used in the trading rule varyingfrom 1 to 14 days (vertical axis) and x is the length of the long moving average MAxt (pt)varying from 15 to 300 days (horizontal axis)

* Darker areas stand for the values pairs of parameters for which the return differencesare not signicantly positive. The series not represented here (e.g. DEM/USD, DEM/FRF,JPY/FRF, JPY/USD) yield nonsignicant return differences when the chartist rule isapplied, whatever the moving average parameters considered.

Fig. A.1. Signicance of the return differential between chartist and nave strategiesfunction of both lengths of the moving averages used for the main currencies from 74.01to 96.09

(yis the length of the short moving average MAyt (pt) used in the trading rule varyingfrom 1 to 14 days (vertical axis) and x is the length of the long moving average MAxt (pt)varying from 15 to 300 days (horizontal axis)

** Sign of the return differential between the chartist and nave strategies is positive in thelighter areas, i.e. the chartist return is higher than the nave return, and negative in the

darkest ones. For the others series in our database (e.g. USD/DEM, USD/FRF, USD/JPY,FRF/DEM, FRF/USD, FRF/GBP, FRF/JPY, GBP/FRF), the chartist return is always higherthan the nave one whatever the value of the trading rule parameters considered.

Fig. A.2. Sign of the return differential between the chartist and nave strategies functionof both lengths of the moving averages used on the main currencies from 74.01 to 96.09



27/29

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