Seasonality onthe J ohannesb urgStockE xchange
O w enB eeld ers¤
Departm ent ofE c onom ic s
E m ory U niversity
Atlanta G a 30 32 2 -2 2 4 0
J une 1,2 0 0 0
Ab strac t
W e test f
or seasonality onthe J ohannesb urg Stoc k E xc hange (J SE )
using f
our b road ind exesand f
our f
uturesind exesthat are c onstruc ted
f
rom a sm aller group ofhighly trad ed stoc ks.Seasonality ispresent inthe
f
our b road ind exs,b ut not inthe f
uturesind exes.Further ¯nd ingsare that
the seasonale®ec tsare the strongest inthe F inancialInd ex w here thin
trad ing ism ore likely. T he G old Ind ex isunique and d oesnot d isplay
the seasonalf
eatures f
ound inthe other three ind exes.T he AllShare,
Ind ustrialand F inancialInd exeshave a negative M ond aye®ec t,a positive
W ed nesd ay settlem ent-d ay e®ec t and a ¯rst-¯ve-d ays-of
-J anuary e®ec t.
For the b road ind exes, the c ond itionalvariance peaksona M ond ay and
d ec lines through the w eek. W ithinthe ¯rst ¯ve d ays ofJ anuary the
c ond itionalvariance d oub lesand thism ay explainthe large returnd uring
thisperiod .T he resultsofthisstud yraisesinterestingquestionsregard ing
the interplay ofseasonality, thintrad ing and the m arket m ic rostruc ture
ind i®erent geographic areasor tim e z ones.
J E L Classi¯c ationNumb er: G 14 ,G 15
K ey W ord s: Stoc k R eturns; Seasonality;Day ofthe W eek e®ec ts.
¤Ithan
kDavid Sam b ur and NingLiuf
or their c apab le researc h assistance,M ichel
le Franc is
ofthe J SE and G ryphonAsset M anagem ent f
or their generous and in
val
uab le assistance.
Allrem aining errorsare m ine. Al
lc orrespond anc e should b e ad d ressed to O w enB eeld ers,
Departm en
t ofE c onom ic s,E m ory U niversity,Atl
anta G a 30 32 2 -2 2 4 0 ;telephone numb er (4 0 4 )
72 7-6650 ;f
axnum b er (4 0 4 ) 72 7-4 639 ;e-m ail
, ob eel
d e@em ory.
ed u.
1
1
In
trod uc tion
Seasonalityinstockpricereturnsisaviolationofthee±cientmarketshypothesis
becausereturnsdisplaysystematicvariationintheirconditionalmeanovertime.
Seasonalityhas beendocumentedintheU S as earlyas 1 931 (Fields (1 931 ))and
in many stock markets around the world (e.
g.A ggrawaland T andon (1 994);
M ookerjeeand Y u (1 999),etc.
).
L akonishok and Smidt (1 988)suggest three reasons why seasonality may
notbe ofthatmuch importance, namely, boredom, noise and data snooping.
A s researchers becomeboredwithstudies con¯rmingexistingtheories,theyare
morelikelytoreportanomalies toovercometheboredom.Second,ifweunderestimate thenoisein returns (as de¯ned by B lack(1 986)),wemay giveundue
weight to anomalies that are mere statisticalartifacts, but not economically
relevant.Finally,withalargeamountofresearchbeingconductedonrelatively
fewdatabases such as CR SP and Compustattheanomalies maysimplybethe
T ypeI errors thatareboundtooccur.A ccordingtoL akonishokandSmidtthe
bestwaytoovercomethedata-snoopingbias is touseanewinformationset.
Itisforthelatterreason,thatweinvestigateseasonalityontheJohannesburg
StockExchange(JSE).T hereislittlepublishedresearchontheJSEandweseek
todocumenttheempiricalregularities ofthis market.T heoutlineofthis paper
is as follows.In section 2,webrie° ydocumentthetypes ofseasonalitythatwe
address and in section 3 we discuss the data and results ofouranalysis. W e
concludewith section 4.
2
A Catal
ogofSeasonalAnom al
ies
O neofthe¯rsttypes ofseasonalitytobedocumentedwas thatoftheweekend
e®ect.In the U S stock returns tend to be negative on M ondays and positive
onFridays (Cross (1 973)).French (1 980 )rediscoveredth3 weekende®ectwhile
tryingtotesttwohypotheses ofinformation ° ow,namely,thetradingtimehypothesis andthecalendertimehypothesis,althoughneitherofthesehypotheses
could explain the weekend e®ect.M any foreign markets display aT uesday effect, i.
e.a negative return on a T uesday, when theirtrading period does not
overlap with thatoftheU S.Itappears thatforeign markets respond on T uesday tothe information released in the U S markets on M onday.A notherdaily
seasonalis theholidaye®ect.A riel(1 990 )foundthatreturns onthedaybefore
a holiday in the U S were signi¯cantly positive.T he positive return priortoa
holidayis similartothepositivereturns found on aFridaybecauseboth occur
priortothemarketclosingforatleastoneday.
T urning to longer time intervals, the January e®ect (R oze® and Kinney
(1 976)), i.
e. positive returns in the month ofJanuary, has been particularly
perplexing to researchers. A numberofpossible explanations have been suggested: tax-loss selling (R einganum (1 983), R oll(1 983)), window dressing by
portfolio managers (L akonishok, Shleifer, T halerand V ishny (1 991 ))and the
small¯rm e®ect(R ogalski (1 984)).N oneoftheseexplanations is complete,but
2
they doprovide apartialexplanation.Keim (1 983)investigated theexcess returnsofsmall¯rmsbecausetheJanuarye®ectwasoriginallyfoundinanequally
weightedindexthatgives moreweighttosmall¯rms.H efoundthathalfofthe
small¯rm annualexcess return is earned in January and halfofthe January
returns areearned in the ¯rst¯ve days ofJanuary.R einganum (1 983)further
pointedoutthattheexcessreturnsinJanuaryarehigherforthesmall¯rmsthat
havedeclined in the previous year.T heseresults givecredencetothe tax-loss
sellinghypotheses and the window-dressinghypothesis.H owever, the tax-loss
sellinghypothesis is nota complete explanation because the January e®ectis
found in countries wherethetax-yeardoes notrun from JanuarytoD ecember
(Katoand Schallheim (1 985);B erges, M cConneland Schlarbaum (1 984)).A t
this point,acompleteexplanation is stillwanting.
A riel(1 987)discovered thatpositive rates ofreturn only occurin the ¯rst
halfofthemonthwherethe¯rstofhalfofthemonthisde¯nedtoincludethelast
tradingdayofthepreviousmonth.W hereasmanyoftheotherseasonalitieshave
been documented in othercountries this e®ecthas notbeen tested elsewhere
beside the U S.Finally, A riel(1 987)documents a turn-of-the month e®ectin
U S returns. T his seasonality is alsofound in the stock markets ofthe major
industrialized countries andsomeemergingmarkets.
T he only seasonality thathas a signi¯canttheoreticaland practicalfoundation is the settlemente®ect(L akonishok and L evi (1 982)).T he settlement
e®ectwas introducedasanexplanationfortheweekende®ect,butithasproven
tobeabetterexplanation ofan anomaly on theP aris B ourse.W ith only one
settlementdayeach month,astockpricewillriseon thetradingdayfollowing
thesettlementdaytore° ectthe30 days ofinterestpriortothenextsettlement
day.In e®ect, stock prices are futures prices priorto the settlementday and
incorporatethecostof¯nancingthetransaction.CrouhyandG alai (1 992)¯nd
thatthereis apro¯tabletradingruleinbuyingthestockatthecloseofthesettlementdayandsellingitonthenexttradingday.O ntheJSE,settlementtakes
place every T uesday so we expectto observe a positive return on W ednesday
thatis equivalenttoaweekofinterest.
U singthis catalogofseasonalanomalies as aguide,weturn totheJSE and
testfortheseanomalies in fourbroad indexes and fourfutures indexes.
3
3 E m piric alM ethod ol
ogy and R esul
ts
3.
1
M ethod ol
ogy
W eestimatethefollowingmodelfortheconditionalmeanandconditionalvariance,
R t = ¯ 1 M ont + ¯ 2 T uet + ¯ 3 W edt + ¯ 4 T hurt + ¯ 5 F rit
+ ¯ 6 Holidayt + ¯ 7Januaryt + ¯ 8 F 5Jant + ¯ 9 S emimt
+ ¯ 1 0 T O M t + "t
ht ´ V ar("tjFt¡1 )
= !0 + ® 1 "2t¡1 + ® 2 "2t¡1 ¢
N E G t¡1 + ° ht¡1
+ !1 M ont + !2 T uet + !3 W edt + !4 T hurt + !5 F rit
+ !6 Holidayt + !7Januaryt + !8 F 5Jant + !9 S emimt
+ !1 0 T O M t
(1 )
whereM ont,T uet,W edt,T hurt,F rit areday-of-the-weekdummies,Holidayt,
Januaryt,F 5Jant,S emimt and T O M t arethedummies fortheday before a
holiday,themonthofJanuary,the¯rst¯vedays ofJanuary,the¯rsthalfofthe
month (includingthe lasttradingday ofthe previous month)and the turn of
themonth (thelasttradingdayoftheprevious month and the¯rstthreedays
ofthenewmonth),respectively,andN E G t is adummyforthenegativevalues
of"t¡1 forthe threshold A R C H or T A R C H modelintroduced by G losten,
JaganathanandR unkle(1 993).R t denotes therawreturnthatis computedas
thenaturallogofthepricerelative,i.
e.R t ´1 0 0 ¢ln(P t=P t¡1 )whereP t is the
price index attime t.W e may alsoinclude lagged returns in the speci¯cation
oftheconditionalmean tomop up anyserialcorrelation.
3.
2
Data
W efocus onthebroad,marketindexandthreebroadindexesthatrepresentthe
largestpercentageofmarketcapitalization oftheJSE,i.
e.theA llShareIndex
(A L SI),theIndustrialIndex(IN D I),theG oldIndex(G L D I)andtheFinancial
Index(FIN I).T hedailydatafortheA L SI,IN D I,G L D I andFIN I indexes were
obtained from D atastream forthe period January 1 988 toD ecember1 999.In
1 995 theJSE introduced indexes thatarebased on thelargerand morehighly
tradedcompaniesineachofthesesectorsforthepurposeofbeingtheunderlying
index forfutures contracts on the South A frican Futures Exchange.W e focus
on the A L SI40 , G L D I1 0 , IN D I25 and FIN D I25 indexes thatmirrorthe four
broad indexes wherethenumberattheend ofeach indexrefers tothenumber
ofstocks thatis used in constructingthe index and FIN D I denotes Financial
andIndustrialIndex.A lthoughthefuturescontractbasedontheG L D I1 0 index
was discontinued in 1 7September1 998 andwas replaced byafutures contract
ontheR esources Indexon27February1 998,theindexis stillcalculatedbythe
JSE.T heFIN D I30 andFIN I1 5 indexes wereintroducedon2 O ctober1 995 and
4
27February 1 998,respectively.W e use the FIN D I30 index as aproxy forthe
broaderFinancialIndex because ofthesmallsample sizeoftheFIN I1 5 index.
M ichelle Francis ofthe JSE kindly provided the data forthe indexes forthe
period 1 5 June1 995 to31 D ecember1 999 T heindexes arevalue-weighted and
1
areadjusted formergers,de-listings,butnotdividends.
A ppendix1 contains alistoftheSouth A frican publicholidays.T helistof
holidays includes thepost-apartheidchanges thatwereintroducedintheP ublic
H olidays A ctof1 994 and cameintoe®ectin 1 995.
3.
3 Desc riptive Statistic s
T his sectioncontains anexploratoryanalysis oftheunderlyingdistributionand
the conditionalmean and variance ofthe returns. In particular, we look for
deviations from normality in the unconditionaldistribution and determinethe
amountofdependence in the ¯rstand second conditionalmoments. T he descriptive statistics are reported in T able 1 and include tests ofskewness and
excess kurtosis basedontheG M M estimatorandthetraditionalestimatorthat
is derived underthe assumption ofiid returns.W e include tests based on the
G M M estimatorbecause the traditionalestimatorsu®ers from the drawback
thatits varianceis underestimatedwhenreturns arenon-normalandconditionallyheteroskedastic(P agan (1 996)).
In T able 1 we ¯nd thatexceptforthe G old Index, the broad indexes are
negatively skewed. A ll four indexes also have statistically signi¯cant excess
kurtosis based on the G M M estimator.Forthe futures indexes, we ¯nd that
the G L D I1 0 Index is positively skewed, butthe otherindexes are symmetric.
A llfourfutures indexes haveexcess kurtosis.T urningtoT able2,we¯nd that
eachofthebroadindexeshasastatisticallysigni¯cant¯rstorderautocorrelation
withtheFinancialIndexdisplayingthemostpersistence.T heQ -statisticsofthe
returns arestatisticallysigni¯cantatthe1 % levelofsigni¯canceatboth5 and
1 0 lags forallfourindexes.T he highly signi¯cantQ -statistics ofthe squared
returns is consistent with conditional heteroskedasticity and the presence of
excess kurtosis in thedistribution.
T he four futures indexes display similarregularities. A ll fourfutures indexes have a statistically signi¯cant ¯rst order autocorrelation although the
coe±cients are smallerthan those ofthe broad indexes.W e expectless serial
correlationinthefutures indexes becauseofareductionorremovaloftheproblem ofthin trading. T he Q -statistics ofthe returns are signi¯cantatthe 1 %
levelatboth 5 and 1 0 lags fortheA SI40 ,G L D I1 0 and FIN D I30 indexes.T he
IN D I25 index displays much less persistence and itis only the Q -statistic at
5 lags thatis signi¯cantatthe 1 0 % level. Finally, allthe Q -statistics ofthe
squared returns are signi¯cant at the 1 % levelat both 5 and 1 0 lags. T his
is consistentwith theconditionalheteroskedasticity and excess kurtosis in the
distribution.
1 Detail
ed inf
orm ationab out the ind exc onstruc tionisavailab le at the w eb site ofthe J SE ,
http://w w w .
jse.
c o.
za/.
5
G iven these empiricalregularities,we adoptthe followingmethodology for
estimatingtheappropriatemodels from thegeneralspeci¯cation in (1 ).First,
wemodeltheconditionalmeanandthenwetestforthepresenceofconditional
heteroskedasticity usingan L M test. Forthe conditionalmean, the autocorrelationfunction(A CF)andpartialautocorrelationfunction(PA CF)providea
guidetothenumberoflagged returns toincludein theconditionalmean.W e
usedthegeneraltospeci¯cmodellingstrategyanderronthesideofcautionby
includingatleastonemorelagthansuggestedbytheA CF andPA CF.D iebold
(1 986)has noted that the con¯dence intervals forthe A CF are considerably
largerwhen thereis conditionalheteroskedasticitysoanyinsigni¯cantlags will
beomitted oncewehavemodeled theconditionalvariance.
W e¯ndthatthereareA R CH e®ectsinalltheseriessoweincludeaG A R CH (1 ,1 )
modelfortheconditionalvarianceandincludeallthedummies as regressors in
the conditional variance. A t this point we also include the dummy for the
T A R CH componentintheconditionalvariance.U singlikelihoodratiotests,we
omittedlaggedreturns intheconditionalmeananddummies intheconditional
variance.W edid notomitanyoftheinsigni¯cantdummies in theconditional
mean forexpositionalpurposes.T he estimated models are in T ables 3.
A and
3.
B forthebroad indexes and tables 4.
A and 4.
B forthefutures indexes.
3.
4
Seasonal
ity inthe B road Ind exes
D uetothepresenceofthin tradingon JSE,each oftheconditionalmeans has
larggedreturns inits speci¯cation(T able3.
A and3.
B ).O nlyonelagis required
forthereturnsoftheG oldIndexwherestockssu®erleastfrom thintrading,but
threelagsareneededfortheFinancialIndex.T heFinancialIndexisexpectedto
su®ermostfrom thin tradingbecausethe¯nancialindustrycould notdiversify
internationallyforalargepartofthesampleperiod.D uringthesampleperiod,
largeindustrialcompanieswithlargeexportoperations weremorehighlytraded
becausethey provided ahedge againstthe severe depreciation in the currency
duetopoliticalriskandthein° ationdi®erential.T hestocks in thegold sector
have always been highly sought after by foreign investors because of South
A frica's dominancein gold production in theworld and wereleastlikelytobe
thinlytraded.
A llthe indexes have aM onday e®ect,i.
e.M onday returns are negative on
average. It is strongest in the Financial Index, followed by the G old Index
and then the Industrialand A llShareIndexes.Ifthe average interestrate for
this period was on theorderof20 % perannum,then the daily interestrate is
approximately0 .
0 55%.T hus thenegativeM ondayreturns equalapproximate3
to4 daysworthofinterestforthegoldand¯nancialstocksandbetweenoneand
twodays worth ofinterestfortheIndustrialstocks and fortheoverallmarket.
T he magnitude ofthe return is consistentwith calenderhypothesis ofFrench
(1 983),howeveritgoes in theoppositedirection!
O nly the G old Index has a statistically signi¯cant and negative T uesday
e®ect.T his is consistentwith theT uesdaye®ectfound in A sian stockmarkets
(A ggrawal and T andon (1 994))and can be interpreted as a response to the
6
behavioroftheU S markets onM onday.B oththeJSE andA sianmarkets open
andclosebeforetheU S markethasopenedsotheycanonlyrespondonT uesday
2
toanyinformation thatis released intheU S on M onday.
T hegoldstocks are
themostinternationallytradedoftheSouthA fricanstocks andaremorelikely
tobea®ected byinternationalevents thathavean impacton theN Y SE.
T heW ednesdaye®ectis thethird dailye®ectthatweobserveintheconditionalmean and is presentin the A llShare, Industrialand FinancialIndexes.
O n average, the coe±cient of the W ednesday dummy lies between 0 .
0 8 and
0.
1 1 % which equals one totwodays worth ofinterest.T he positive return is
consistentwith ourexpectations becauseT uesdayis thesettlementday(Clark
(1 998)), butthe size ofthe coe±cientis much less than aweek'
s worth ofinterest(Crouhy and G alai (1 992)).T he settlemente®ectis notpresentin the
G old index: this may be due tothe higherproportion offoreign traders that
are activein the marketwhodonotrely as much on domesticsettlementand
thehighervolatilityofthegold indexthatmasks this e®ect.
N one ofthe indexes display signi¯cant January e®ects, but the A llshare
andIndustrialIndexdodisplayverylargepositivereturns forthe¯rst¯vedays
ofJanuary. T he return forthe O veralland IndustrialIndexes is 0 .
364% and
0.
41 6%,respectively;this is equivalenttosixorsevendays riskless return.O ne
explanationforthehigherreturnis ahigherlevelofrisk:boththeallshareand
industrialindexes havesigni¯cantincreases intheconditionalvarianceoverthe
¯rst¯ve days ofeach year.O nly the A llShare Index displays a positive and
statisticallysigni¯cantturnofthemonthe®ectandtheFinancialandIndustrial
Indexes displaysemi-monthlye®ects.
T urningtotheconditionalvariance,allfourindexes displaythetypicalparameterestimates forG A R C H(1 ;1 )models,i.
e.thesum ofthe coe±cients of
the A R C H and G A R C H terms is close to 1 , the A R C H coe±cient is close
to0 .
1 and the G A R C H coe±cientis close to0 .
9.A surprising¯ndingis the
asymmetricresponse toshocks is only found in the IndustrialIndex.T here is
a strikingdi®erence between the importance ofthe dummies in the A llShare
and G old Index versus the Industrials and Financials. T he strongestresults
are evidentin the FinancialIndex thatagain may be due tothe thin trading.
Eachofthedailydummies -T uesdaytoFriday-arestatisticallysigni¯cantand
negativeand indicate thatM onday is more volatilethan theotherdays ofthe
week.T heJanuary dummy is notsigni¯cant,butthedummy forthe ¯rst¯ve
days ofJanuary is highly signi¯cantand large relative tothe constantin the
conditionalvariance.T he ¯rst¯ve days ofJanuary are twice as volatile as a
M onday during the year. T he turn-of-the-month and semi-monthly dummies
have positive and signi¯cantcoe±cients although theirmagnitude is only one
tenth ofthesizeofthecoe±cientofthe¯rst¯vedays ofJanuary.
T he results forthe IndustrialIndex tend to mirrorthose ofthe Financial
Index, butwith a lowerlevelofsigni¯cance.O utofthe fourdaily dummies,
2 Durin
gthe North Am eric anSum m er,w henthe E ast Coast isonE asternStand ard T im e,
the NY SE and J SE overlap b y half
-an-hour, b ut d uring the Falland W inter w henDaylight
SavingsT im e isine± ec t, the NY SE c losesb ef
ore the J SE .W e d o not expec t the Sum m er
overlap to b e large enough to negate the T uesd ay e®ec t.
7
onlythesigni¯canceoftheW ednesdaydummyis questionableatthe1 0 % level.
T here is noJanuary e®ect, butthecoe±cientofthe ¯rst¯vedays ofJanuary
dummyis signi¯cantand one-and-a-halftimes largerthan theinterceptin the
conditionalvariance.T heturnofthemonthdummywas omittedandthesemimonthlycoe±cientis signi¯cant,butsmallrelativetothelong-run variance.
T heonlydummyvariablethatplays aroleintheG oldIndexis theJanuary
dummy:itis statisticallysigni¯cantatclosetothe1 % leveland is threetimes
largerthan the coe±cientofthe long-run variance. Forthe A llShare Index,
the dummy ofthe ¯rst¯ve days ofJanuary and semi-monthly e®ectare both
statisticallysigni¯cantatapproximatelythe1 0 % levelofsigni¯cance:the¯rst
¯vedays ofJanuaryare1 1 timesmorevariablethantherestoftheyearandthe
¯rsthalfofthemonth seems tobetwiceas variableas therestofthemonth.
In conclusion, there is seasonality in the broad indexes and itis strongest
in theFinancialIndex.T heA llShare,IndustrialandFinancialIndexes havea
negativeM ondaye®ect,apositiveW ednesdaysettlement-daye®ectanda¯rst¯ve-days-of-January e®ect.T he conditionalvariance peaks on a M onday and
declines throughtheweek.W ithinthe¯rst¯vedays ofJanuary,theconditional
variancedoubles andthis mayexplain thelargereturnduringthis period.T he
G old Index is unique and does notdisplay the seasonalfeatures found in the
otherthreeindexes.
3.
5 Seasonal
ity inthe FuturesInd exes.
T hemostinteresting¯ndingforthefutures indexes is thelackofseasonalityin
theconditionalmean(T able4.
A and4.
B ).A fterincludingonelagofthereturns
to modelthe serialcorrelation, we ¯nd that the only statistically signi¯cant
seasonale®ectis the M onday e®ectin the IN D I25 and FIN D I30 indexes.T he
FIN D I30 overlaps the IN D I25 index toalarge extentsothe signi¯cance ofits
M onday e®ect is not surprising. T his result suggests that the seasonality is
drivenbythintrading.SeasonalityinU S stockprices was originallydiscovered
in equally weighted indexes thatgive greaterweightto smallercompanies in
comparison tovalueweighted indexes and itmay be the thin tradingofsmall
stocks thatis drivingtheseasonalityinthebroadindexes.H owever,thestocks
in the JSE futures indexes are large soitis more likely thatitis thin trading
and notasmall¯rm e®ectthatis causingtheseasonality.
A llfourfuturesindexeshavestatisticallysigni¯cantconditionalheteroskedasticitywiththeA R CH andG A R CH coe±cientssummingtocloseto1 ,theA R CH
coe±cientbeingclose to0 .
1 and theG A R CH coe±cientclose to0 .
9.W e¯nd
signi¯cantasymmetry in the conditionalvariance forthe A L SI40 , IN D 25 and
FIN D I20 indexes,butnotthegold index.T his mayberelatedtothefactthat
theG old indexwas theonlyindexthatwas positivelyskewed.A furtherregularityis thenegativecoe±cientonthedummies fortheT hursdayandFridayin
theconditionalvariance.T his suggests thatT hursdayand Fridayhavealower
variancethan theotherdays oftheweek.
8
4
Concl
usion
W etestforseasonalityinfourbroadJSEindexesandfoursimilarfuturesindexes
thatare constructed from a smallgroup ofhighly traded stocks.Seasonality
is presentin the fourbroad indexes, butnotin the futures indexes. Further
¯ndings are thatthe seasonale®ects are the strongestin the FinancialIndex
wherethin tradingis morelikelytobepresent.T heG old Index is uniqueand
does not display the seasonalfeatures found in the otherthree indexes.T he
A llShare, Industrialand FinancialIndexes have a negative M onday e®ect, a
positiveW ednesday-Settlemente®ectanda¯rst-¯ve-days-of-Januarye®ect.For
the broad indexes, the conditionalvariance peaks on a M onday and declines
through the week. T he conditionalvariance doubles in the ¯rst¯ve days of
January and may explain the large return during this period. T hese results
are consistentwith the results forU S stock returns in French (1 980 ), butnot
Chinesestockreturns inM ookerjeeand Y u (1 999).
T heresults ofthis studyraises twointerestingquestions:¯rst,is seasonality
simply an artifactofthin trading? Second,is seasonality amarketmicrostructure e®ect that is unique to a geographical market ortime zone? T he lack
ofseasonality in both G old Indexes seems tosuggestthatthe answertoboth
questions is `
yes.
'
R ef
erences
[1 ]A ggrawal, A .and K.T andon (1 994)\ A nomalies orIllusions? Evidence
from Stock M arkets in Eighteen Countries," Journal of International
M oneyandFinance,1 3,83-1 0 6.
[2]A riel,R .
A .(1 987)\ A M onthlyE®ectinStockR eturns,"JournalofFinancialEconomics,1 7,1 61 -1 74.
[3]A riel, R .
A .(1 990 )\ H igh Stock R eturns B efore H olidays: Existence and
EvidenceofP ossibleCauses,"JournalofFinance,45,1 61 1 -1 626.
[4]B erges,A .
,J.
J.M cConnelland G .
G .Schlarbaum (1 984)\ T heT urnofthe
Y earin Canada,"JournalofFinance,39,1 85-1 92.
[5]B lack,Fischer(1 986)\ N oise,"JournalofFinance,41 ,3,529-543.
[6]Clark, R obertA .(1 998)A frica'
s Emerging Securities M arkets, Q uorum,
W estport,Conn.
[7]Crouhy, M icheland D an G alai (1 992)\ T he SettlementD ay E®ectin the
French B ourse,"JournalofFinancialServices R esearch,6 ,4,41 7-35.
[8]Cross,F.(1 973)\ T heB ehaviorofStockP rices onFridays andM ondays,"
FinancialA nalysts Journal,N ovember-D ecember,67-69.
9
[9]D iebold,Francis X .(1 986),\ T estingforSerialCorrelation in theP resence
ofA R CH ,"P roceedings oftheA merican StatisticalA ssociation,B usiness
andEconomics Statistics Section,p.
323-328.
[1 0 ]Fama,E.(1 965)\ T heB ehaviorofStockM arketP rices,"JournalofB usiness,38,January,34-1 0 5.
[1 1 ]Fields,M .
J.(1 931 )\ StockP rices:A P roblem in V eri¯cation,"Journalof
B usiness,4,O ctober,41 5-41 8.
[1 2]French,K.
R .(1 980 )\ StockR eturns and theW eekend E®ect,"Journalof
FinancialEconomics,1 2,469-481 .
[1 3]G losten,L awrenceR .
,R avi JagannathanandD avidE.R unkle(1 993)\ O n
theR elationbetweentheExpectedV alueandtheV olatilityoftheN ominal
Excess R eturn on Stocks,"JournalofFinance,48,5,1 779-1 80 1 .
[1 4]Kato,K.amdJ.Schallheim (1 985)\ SeasonalandSizeR elatedA nomoliesin
theJapaneseStockM arket,"JournalofFinancialandQ uantitative A nalysis,June,243-260 .
[1 5]Keim,D .B .(1 983)\ SizeR elatedA nomoliesandStockR eturnSeasonality:
FurtherEmpiricalEvidence," JournalofFinancialEconomics, June, 1 322.
[1 6]L akonishok, J.and S.Smidt (1 988)\ A re Seasonal A nomalies R eal? A
N inetyY earP erspective,"R eviewofFinancialStudies,1 ,40 3-425.
[1 7]L akonishok, J.
, A .Shleifer, R .T haler and R .V ishny (1 991 )\ W indow
D ressing by P ension Fund M anagers," A merican Economic R eview, 81 ,
M ay,227-231 .
[1 8]M ills, T erence C.(1 999), T he Econometric M odelling ofFinancialT ime
Series,CambridgeU niversityP ress,Cambridge.
[1 9]M ookerjee, R ajen and Q iao Y u (1 999) \ Seasonality in R eturns on the
Chinses Stock M arkets: the case ofShanghai and Shenzhen," G lobalFinance Journal,1 0 ,1 ,93-1 0 5.
[20 ]P agan, A drian (1 996)\ T he Econometrics ofFinancialM arkets," Journal
ofEmpiricalFinance,3,1 5-1 0 2.
[21 ]R einganum,M .
R .(1 983)\ T heA nomolousStockM arketB ehaviorofSmall
Firms inJanuary:EmpiricalT ests forT axL oss SellingE®ects,"Journalof
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J.(1 984)\ N ewFindings R egardingD ay-of-the-W eekR eturns
overT radingand N on-T radingP eriods:A N ote,"JournalofFinance,39,
5,1 60 3-1 61 4.
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[23]R oll, R ichard (1 983)\ V as istD as? T he T urn-of-the-Y earE®ectand the
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S.and W .
R .Kinney (1 976)\ CapitalM arketSeasonality:T he
CaseofStockR eturns",JournalofFinancialEconomics,2,279-40 2.
11
A ppendix1 : South A frican H olidays
O ldH olidays (pre-1 995)
Fixed H olidays
D ate
1 January
6 A pril
1 M ay
31 M ay
1 0 O ctober
1 6 D ecember
25 D ecember
26 D ecember
N ewY ears D ay
Founders'D ay
L aborD ay
R epublicD ay
KrugerD ay
D ayoftheCovenant
Christmas D ay
D ayofG oodwill
A lgorithmicH olidays
M arch-A pril
M arch-A pril
M ay-June
G ood Friday-Christian
EasterM onday-Christian
A scensionD ay-Christian
P ublicH olidays A ctof1 994 introduces newH olidays from
1 January1 995
Fixed
1 January
21 M arch
27A pril
1 M ay
1 6 June
9 A ugust
24 September
1 6 D ecember
25 D ecember
26 D ecember
N ewY ear's D ay
H uman R ights D ay
Freedom D ay
W orkers'D ay
Y outh D ay
N ationalW omen's D ay
H eritageD ay
D ayofR econciliation
Christmas D ay
D ayofG oodwill
A lgorithmicH olidays
M arch-A pril
M arch-A pril
G ood FridayFridaybeforeEasterSunday
FamilyD ayM ondayafterEasterSunday
12
T able1 :D escriptiveStatistics oftheJSE Indexes
B road Indexes
SampleSize
M ean
Standard D eviation
A llShare
G old
Industrial
Financial
2993
0.
0 224c
0.
21 1
2993
-0 .
0 0 6c
1.
0 52
2993
0.
0 267c
0.
1 78
2993
0.
0 326c
0.
226
Skewness
iid t-statistic
G mm t-statistic
-1 .
274
(-28.
441 )c
(-1 .
997)b
0.
562
(1 2.
543)c
(3.
871 )c
-1 .
667
(-37.
20 9)c
(-1 .
781 )a
-1 .
462
(-32.
655)c
(-1 .
90 6)a
Kurtosis
iid t-statistic
G M M t-statistic
1 3.
644
(1 52.
242)c
(2.
726)c
3.
20 1
(35.
70 0 )c
(4.
858)c
22.
345
(249.
347)c
(2.
831 )c
21 .
280
(237.
265)c
(4.
0 82)c
Futures Indexes
A L SI40
G L D I1 0
IN D I25
FIN D I30
SampleSize
mean
V ariance
1 1 72
0.
015
0.
362
1 1 72
0.
005
0.
924
1 1 72
0.
014
0.
429
1 0 99
0.
014
0.
475
Skewness
iid t-statistic
G M M t-statistic
-1 .
20 0
(-1 6.
754)c
(-1 .
243)
0.
597
(8.
339)c
(3.
746)c
-0 .
899
-0 .
873
(-1 2.
453)c (-1 1 .
778)c
(-1 .
0 58)
(-1 .
110)
Kurtosis
iid t-statistic
G M M t-statistic
1 4.
30 5
(99.
759)c
(2.
1 37)b
2.
61 9
(1 8.
236)c
(6.
21 5)c
1 2.
427
11.
51 7
(86.
656)c
(77.
61 8)c
(2.
1 67)b
(2.
325)b
R eturns arecalculatedas 1 0 0 ¤ln(P (t)=P (t¡1 ))andasuperscripta,b and
cdenotes signi¯canceatthe1 0 %,5% and 1 % levelofsigni¯cance,respectively.
13
T able2:A utocorrelations oftheJSE Indexes
B roadIndexes
L ag
1
2
3
4
5
A llShare
G old
Industrial Financial
0.
1 45c
0.
0 70 c
0.
019
-0 .
0 22
0.
001
0.
0 98 c
-0 .
019
0.
008
0.
0 21
0.
006
0.
1 68 c
0.
0 95c
0.
0 25
-0 .
007
0.
0 32
0.
1 98 c
0.
1 1 6c
0.
0 58
-0 .
003
0.
0 46
Q R (5)
Q R (1 0 )
80 .
469c
91 .
742c
31 .
663c
40 .
973c
1 1 6.
99c
1 29.
44c
1 67.
1 4c
1 85.
52c
Q R 2 (5)
Q 2R (1 0 )
438.
75c
459.
64c
276.
45c
378.
35c
40 0 .
26c
434.
0 5c
735.
1 9c
863.
1 7c
Futures Indexes
lag
1
2
3
4
5
A L SII40
G L D I1 0
IN D I25
FIN D I30
0.
1 1 3c
0.
0 53c
-0 .
0 22
-0 .
0 73b
-0 .
015
0.
1 51 c
0.
016
0.
008
0.
012
-0 .
0 22
0.
0 67b
0.
011
-0 .
0 44
-0 .
0 39
0.
015
0.
1 33c
0.
0 42
-0 .
0 33
-0 .
0 53c
0.
009
Q R (5)
Q R (1 0 )
25.
346c
27.
644c
27.
926c
34.
40 9c
9.
655a
1 3.
220
25.
721 c
27.
969c
Q R 2 (5)
Q R 2 (1 0 )
30 4.
75c
321 .
67c
275.
42c
397.
96c
284.
66c
31 9.
44c
248.
91 c
277.
0 2c
A superscripta, b and cdenotes signi¯cance atthe 1 0 %, 5% and 1 % levelof
signi¯cance,respectively.
14
T able3.
A :T hecoe±cientestimates fortheB road Indexes
R egressor
A llShare
Coe±cient P -value
G old
Coe±cient P -value
ConditionalM ean
lag1
lag2
M onday
T uesday
W ednesday
T hursday
Friday
H oliday
January
First5 days ofJanuary
T urn oftheM onth
Semi-M onthly
0.
1 82
0.
0 41
-0 .
0 78
-0 .
0 32
0.
0 86
0.
0 42
-0 .
0 44
0.
0 75
-0 .
0 71
0.
364
0.
0 93
0.
0 57
0.
000
0.
0 55
0.
108
0.
455
0.
0 32
0.
31 7
0.
240
0.
481
0.
255
0.
0 75
0.
001
0.
104
0.
113
-0 .
1 95
-0 .
1 86
-0 .
101
-0 .
009
-0 .
112
0.
0 21
-0 .
1 22
0.
41 3
0.
114
0.
0 86
0.
000
0.
0 56
0.
0 53
0.
292
0.
925
0.
243
0.
897
0.
496
0.
237
0.
1 30
0.
246
0.
0 65
0.
0 67
0.
920
0.
1 95
-
0.
002
0.
000
0.
000
0.
012
-
ConditionalV ariance
!
®
°
T arch (asymmetry)
T uesday
W ednesday
T hursday
Friday
H oliday
January
First5 days ofJanuary
T urn oftheM onth
Semi-M onthly
0.
0 29
0.
1 57
0.
80 7
0.
20 9
0.
0 26
15
0.
007
0.
000
0.
000
0.
0 78
0.
102
T able3.
B :T hecoe±cientestimates fortheB road Indexes (continued)
R egressor
Industrial
Coe±cient P -V alue
Financial
Coe±cient P -V alue
ConditionalM ean
lag1
lag2
lag3
M onday
T uesday
W ednesday
T hursday
Friday
H oliday
January
First5 days ofJanuary
T urn oftheM onth
Semi-M onthly
0.
244
0.
0 62
-0 .
0 84
0.
005
0.
0 84
0.
0 44
-0 .
0 36
0.
1 58
-0 .
0 59
0.
41 6
0.
0 33
0.
0 48
0.
000
0.
004
0.
010
0.
835
0.
003
0.
1 45
0.
241
0.
000
0.
280
0.
000
0.
1 72
0.
0 42
0.
251
0.
0 49
0.
0 55
-0 .
20 8
0.
019
0.
113
0.
0 69
0.
0 47
0.
0 56
0.
000
0.
1 54
0.
0 27
0.
0 88
0.
000
0.
0 24
0.
008
0.
000
0.
51 5
0.
000
0.
015
0.
1 37
0.
243
0.
995
0.
363
0.
30 3
0.
000
0.
285
0.
224
0.
70 6
-0 .
460
-0 .
298
-0 .
287
-0 .
1 98
0.
1 44
-0 .
014
0.
30 3
0.
0 34
0.
0 36
0.
000
0.
000
0.
000
0.
000
0.
000
0.
000
0.
000
0.
000
0.
1 58
0.
000
0.
000
0.
000
CondionalV ariance
!
®
°
T arch (asymmetry)
T uesday
W ednesday
T hursday
Friday
H oliday
January
First5 days ofJanuary
T urn oftheM onth
Semi-M onthly
0.
1 38
0.
1 58
0.
71 4
0.
1 64
-0 .
1 96
-0 .
0 54
-0 .
1 22
-0 .
1 23
0.
0 55
0.
1 91
0.
0 22
16
0.
000
0.
000
0.
000
0.
000
0.
000
0.
103
0.
000
0.
000
0.
001
0.
007
0.
003
T able4.
A :T hecoe±cientestimates fortheJSE Futures Indexes
R egressor
A L SI40
Coe±cient P -V alue
G L D I1 0
Coe±cient P -V alue
ConditionalM ean
lag1
M onday
T uesday
W ednesday
T hursday
Friday
0.
1 69
0.
0 80
-0 .
017
0.
0 90
0.
0 44
-0 .
019
0.
000
0.
1 44
0.
755
0.
236
0.
50 9
0.
723
0.
1 79
0.
1 22
-0 .
0 74
-0 .
1 39
0.
0 36
-0 .
004
0.
000
0.
271
0.
529
0.
264
0.
741
0.
963
0.
226
0.
0 84
0.
898
0.
012
0.
261
0.
0 90
-0 .
984
-0 .
1 58
0.
000
0.
000
0.
000
0.
586
0.
498
0.
740
0.
004
0.
50 1
CondionalV ariance
!
®
°
T arch (asymmetry)
T uesday
W ednesday
T hursday
Friday
0.
0 29
0.
0 65
0.
889
0.
0 77
0.
0 81
0.
227
-0 .
112
-0 .
239
0.
627
0.
000
0.
000
0.
000
0.
463
0.
012
0.
30 2
0.
010
17
T able4.
B :T hecoe±cientestimates fortheFutures Indexes (continued)
R egressor
IN D I25
Coe±icient P -V alue
FIN D I30
Coe±cient P -V alue
ConditionalM ean
lag1
M onday
T uesday
W ednesday
T hursday
Friday
0.
117
0.
1 44
0.
0 23
0.
0 47
0.
0 22
0.
0 85
0.
000
0.
016
0.
696
0.
569
0.
759
0.
1 37
0.
1 84
0.
1 63
-0 .
016
0.
1 23
0.
013
-0 .
0 68
0.
000
0.
0 25
0.
81 0
0.
1 85
0.
865
0.
261
0.
285
0.
0 66
0.
881
0.
760
-0 .
011
0.
1 90
-0 .
359
-0 .
263
0.
0 62
0.
000
0.
000
0.
000
0.
935
0.
1 38
0.
007
0.
011
CondionalV ariance
!
®
°
T arch (asymmetry)
T uesday
W ednesday
T hursday
Friday
0.
0 24
0.
0 73
0.
892
0.
0 58
0.
0 36
0.
278
-0 .
1 39
-0 .
1 78
0.
6949
0.
000
0.
000
0.
000
0.
753
0.
001
0.
222
0.
0 62
18