Volatility onthe J ohannesb urgStockE xchange
and the Introd uc tionofFuturesContrac ts
O w enB eeld ers¤
Departm ent ofE c onom ic s
E m ory U niversity
Atlanta,G a,30 32 9-34 89
e-m ail: ob eeld e@em ory.ed u
J uly 31,2 0 0 0
Ab strac t
W e analyz e the e®ec t ofthe introd uc tionofa f
uturesm arket onthe
spot volatility ofthe J ohannesb urg Stoc k E xc hange usingthe m ethod of
B essimb ind er and Seguin(19 9 2 ).W e ¯nd that spot volatility ispositively
related to the sec ular leveloftrad ing inthe spot and f
utures m arket.
Sec ond , using openinterest asa m easure ofm arket d epth w e ¯nd that
it is negatively related to spot volatility, i.e. f
utures trad ing d oes not
increase spot volatility. F inally, the unexpec ted numb er oftransac tions
inthe f
uturesm arket isstrongly related to spot volatility - thisresult is
c onsistent w ith J ones,K auland Lipson(19 9 4 ).
¤Iw oul
d like to thank M ariz a G oosenofthe South Af
ric anFuturesE xc hange, M ic helle
Francisofthe J ohannesb urg Stock E xchange and StephenE vansofM c G regor B FA f
or their
generousand invaluab le assistance. Iw ould also like to thank my tw o c apab le researc h assistantsonthe projec t, J ing Xu and Ning Liu f
or their hel
p inpreparing the d ata ¯les.All
rem ainingerrorsare m ine.
1
1
In
trod uc tion
T heintroductionofafutures marketis supposedtohavemanybene¯ts suchas
risk-sharing(hedging),anincreaseinmarketdepthand adecreasein volatility
due to the more rapid rate atwhich information is re° ected in prices. H owever,opponents offutures markets argue thatany increase in marketdepth is
duetospeculation and speculation leads togreaterspotmarketvolatilitythat
negates thebene¯ts.T heobjectiveofthis paperis to° eshouttherelationship
betweenthespotvolatilityoftheJohannesburgStockExchange(JSE)andthe
introductionofnewstockindexfutures contracts ontheSouthA fricanFutures
Exchange (SA FEX )in 1 995.In particular,we investigate the relationship between futures volumeandspotpricevolatilityaftercontrollingforspotmarket
volume.
T herearemanytheories thatrelatevolatilityorpricechanges tothelevelof
tradeandmanytheories purportingtoshowthecosts andbene¯ts oftheintroduction offutures markets.Karpo®(1 987)provides acomprehensivereviewof
thetheories thatpredictapositivecontemporaneous relationship between volumeandpricechanges andtheempiricalstudies thatsupportthetheory.W ith
regard totheempiricalanalysis oftheintroduction offutures markets,theresults are less supportive.B essembinderand Seguin (1 992)(hereafterB &S92)
argue that many of the empirical studies are ° awed because they are event
studies with asamplesizeofone.Forexample,manystudies thatcomparethe
ex ante and ex post levels ofvolatility are unable to partialoutthe e®ectof
a secularchange in volatility in the latterperiod;this may lead to erroneous
conclusions.T oremedythesituation B &S92 proposeanewmethodology.
T headvantageofusingtheB &S92 methodis thatwecantestforapositive
relationship betweenspotvolatilityandfutures tradingactivityafterpartialling
outthee®ectofspottradingactivity.W ithinthis frameworkweinvestigatethe
following fourhypotheses: (i)spot volatility and futures trading volume are
positively related;(ii)spot volatility and the numberoffutures transactions
are positively related;(iii)the numberoffutures transactions has a stronger
relationship withvolatilitythanfutures volume;(iv)openinterestis aproxyof
marketdepth andis negativelyrelated tovolatility.
B ecause ofthe trends in the spotand futures activity variables, they are
decomposed intothree components.T he ¯rstcomponentis the seculartrend
and the second and third components are the predicted and unexpected components ofthedeviation from the trend.A llthetrend components are highly
correlated and areusefulin capturingthe relationship between overalllevelof
tradingactivity and volatility.T hepredicted components areespeciallyuseful
as ameasureofmarketdepthespeciallywhenappliedtoopeninterest.Finally,
theunpredicted componentcaptures the relationship between newtradingactivityand volatility.
T he outline ofthe paperis as follows.In section 2 we discuss the theories
thatsupportand oppose the introduction offutures markets with the aim of
summarizing the testable hypotheses. Similarly, in section 3 we discuss the
theories thatrelatethevolumeoftradetopricechanges andvolatilitywiththe
2
aim ofsummarizingthetestablehypotheses.Section 4 contains abriefhistory
ofthe South A frican futures exchange, section 5 contains a briefsynopsis of
ourempiricalmethodologyand section 6 contains adiscussion ofthedata.W e
reporttheresults in section 7and concludewith section 8.
2
T he R el
ationship b etw eenSpot Vol
atil
ity and
FuturesM arkets
M anyofthebene¯tsoftheintroductionoffuturesmarkets° owfrom theirtransactions costadvantages.Futures markets reducesearch,liquidity,moralhazard
andbrokeragecosts (Cagan(1 981 ),Ja®e(1 984),V eljanovski (1 986)).T hebene¯ts ofcheapertrading opportunities leads to quickerinformation revelation,
less mispricing, greaterliquidity and newrisk-return combinations.H owever,
theimpacton spotvolatilityis unclear.
B lack (1 976), Cox (1 976), P eck (1 976), T urnovsky (1 979), Campbell and
T urnovsky(1 985)showthatfutures markets areclearinghouses formarketinformationandprovideadditionalinformationforspotmarketparticipants.D ue
to the more rapid dissemination of market-wide in¯rmation, D anthine(1 978)
shows thattheintroductionoffutures tradingleads toincreasedmarketdepth.
A dditionalliquiditymayalsobeprovidedbyspeculatorswho° ocktothefutures
marketwhereitis cheapertotrade.T hus speculators provideboth avaluable
serviceas arbitraguers,whoenablehedgers totransferrisk,andgreatermarket
depth.
T he bene¯cial e®ect on volatility may go either way. O n the one hand,
the additional liquidity provided by speculators may also lead to a decrease
involatility(H odgsonandN icholls (1 991 )).D anthine(1 978),G rossman(1 988)
andG rossmanandM iller(1 988)provideargumentsforadecreaseincashmarket
volatility because ofan increasein marketliquidity and adecreasein the cost
toinformedtraders ofrespondingtomispricing.T his wouldbeofbene¯tiftoo
1
little information leads to toomuch volatility as argued byA ttanasio(1 990 ).
O n theotherhand,ifspotprices dobecomemorevolatilethis is good because
itre° ects alltheinformation available(R oss (1 989)).
Finally,totheextentthatthemarketisincomplete,thefuturesmarkethelps
tocompletethemarketbyallowingpreviouslyunavailablecombinations ofrisk
and return tobereplicated.
O pponents offutures markets assertthatthey are destabilizingbecause of
speculationandarbitragestrategies suchas computertrading.W hereas proponents see bene¯ts from the availability oflow-costtrading,Stein (1 987)shows
thattradingin futures by uninformed speculators destabilizes the market.In
this case, prices become less informative. T he resulting loss in con¯dence in
¯nancialmarkets may lead to a reduction in liquidity thatcan have negative
welfaree®ects byincreasingtransactions costs andtherebyraisingtherequired
1 T hisissim il
ar to Singleton's(1987) point regard ingexc hange ratesw here the m ainthrust
isthat m ore inf
orm ationc anac tual
ly l
ead to a red uc tioninvolatility
3
realreturn on an asset.M alkiel(1 979)and P indyck (1 984)alsosuggestthat
an increaseinvolatilityincreases therequiredriskpremium and this leads toa
highercostofcapitaland lowerstockprices.
M any ofthese implications are very di±culttotest.Forexample,changes
in spotmarketdepth maybeduetosecularchanges thatare unrelated tothe
introduction offutures markets. Similarly, an increase in volatility following
the introduction ofa futures marketmay be due to the greaterrevelation of
information (R oss (1 989))ordue to the destabilizing in° uence ofspeculators
(Stein(1 987)).O nealternativeistousethemethodologyofG allowayandM iller
(1 997)whouseamatchingsampletoeliminate any secularchanges.U nfortunately,theJSE is highly concentrated and thinlytraded (B eelders (20 0 0 a))so
this method is infeasible.
T he advantage ofusing the B &S92 framework is thatwe can testforthe
sensitivityofspotvolatilitytotradingactivityonthefutures marketafterpartialling outthe e®ectofspottradingactivity.W ithin this framework we can
determineiffutures tradingactivityhas apositivee®ectonspotmarketvolatility.
3 Spot Vol
atil
ity and Spot T rad ingAc tivity
T hepositivecorrelationbetweenvolumeandabsolutepricechanges arederived
from the interplay oftwoprinciples: the asymmetry ofinformation generates
tradingandtheextentofthedisagreementdetermines thesizeofthetrades.In
this section we brie° y reviewthe theories thatprovide testable hypotheses of
therelationship betweenspotvolatilityand spottradingactivity.
First,(Clark(1 973),Epps and Epps (1 976),T auchen and P itts (1 983)and
H arris (1 986))proposed a mixture ofdistributions hypotheses where the sequentialarrival of new information generates both trading volume and price
movements with both increasingduringperiods characterized bynumerous informationshocks.A nymeasureofactivitysuchas volume,openinterestorthe
numberoftransactions canactas themixingvariable.
Second,Copeland(1 976,1 977),M orse(1 981 ),Jennings,Starks andFellingham (1 981 )and Jennings and B arry(1 983)proposemodels wherein newinformationis disseminatedsequentiallytotraders andimperfectlyinformedtraders
cannotinferthepresenceofinformedtrading.T hesequentialarrivalofinformationgenerates bothpricechanges andvolumewherebotharepositivelyrelated
tothenumberofinformation shocks arrivingperunittime.
T hird, within the class ofstrategic models, A dmati and P ° eiderer(1 988)
show that traders who have discretion in choosing when to trade, choose to
trade when volume is large.Consequently, transactions and price movements
are bunched in time and the e®ectofvolume on price movements depends on
recentvolumelevels.Kyle's (1 985)modelimplies thatlargervolumesupports
moreinformedtradersandthemarketdepthvarieswithnon-informationaltradingactivity.Kyle(1 985)de¯nesmarketdepthastheorder° owrequiredtomove
prices by one unit.B essembinderand Seguin (1 993)argue thatmarketdepth
4
varies withrecenttradingactivityanditcanbeproxiedbyendogenouslydetermined open interestand open interestis morelikelytore° ecthedgingactivity
than speculation.T hehypothesis is thatvolatilityis lowerwhen open interest
is largeafterconditioningon contemporaneous volume.
Finally,withintheclassofcompetitivemodelstradesizeis positivelyrelated
to the quality orprecision of the information possessed by informed traders
(P ° eiderer(1 984),Kim andV errechia(1 991 )).A n adverseselection problem is
introducedbecauseinformedtraders wanttotradelargeamounts atthecurrent
price. It is shown that absolute price changes and volume - the aggregate
demand ofallinvestors -arepositivelyrelated within this class ofmodels.
A s wementionedintheintroduction,Karpo®(1 987)documents manystudies thatsupportthe positive relationship between absolute price changes and
volume.R ecently, Jones, Kauland L ipson (1 994)suggestthatthe numberof
transactions is morerelevantthanthesizeofthetransaction(volume).Intheir
study of835 securities on theN A SD A Q -N M S master¯le oftheCenterforR esearchin SecurityP rices (CR SP )they¯nd thatvolumeorthesizeofthetrade
has noexplanatorypowerbeyondthatcontainedinthenumberoftransactions.
B ased on the theories and empiricalwork todate, we obtain fourtestable
hypotheses: (i)spotvolatility and spot volume are positively correlated;(ii)
spotvolatilityandopeninterestarenegativelyrelated.W ederivethetwomore
hypothesesfrom Jones,KaulandL ipson(1 994)whosuggestthatthenumberof
transactions canbesubstitutedforvolume:(iii)spotvolatilityandthenumber
oftransactionsarepositivelyrelated;(iv)thesizeofthetradehasnoexplanatory
powerbeyond thatcontained in thenumberoftransactions.U nfortunatelywe
donothavethenumberoftransactions forthespotmarket,butwedohavethe
numberoftransactions forthe futures market, sowe analyze the relationship
between spotvolatilityand futures transactions.
4
History ofthe South Af
ric anFuturesM arket
In A pril1 987 an informalfutures marketwas started in South A frica by the
R and M erchantB ank(R M B ):itwas theexchange,theclearinghouseand the
only marketmaker. A lthough the futures marketsurvived the O ctober1 987
marketcrash,volumes remained relatively thin.In September1 988 itwas decidedtobroadenthemarketandensurewidespreadtrustintheindependenceof
theexchangeandclearinghousebyformingtheSouthA fricanFuturesExchange
(Safex)and theSafexClearingCompany(P ty)L imited (Safcom).T wenty-one
majordomestic¯nancialinstitutions,includingtheSouthA fricanR eserveB ank
and the JohannesburgStock Exchange (JSE),subscribed to80 \ seats"in the
ventureatapriceofR 25,0 0 0 ,therebyprovidingthestart-up capitalofR 2 mil2
lion.
W hen the infrastructure,rules and procedures were completed in 1 989,
2 T he South Af
ric anc urrency is c alled the \rand " and is m ad e up of10 0 c en
ts. T he
ab reviationf
or the rand isan\R " b ef
ore the am ount. In1980 , the exc hange rate w ith the
U S$ w asapproxim ately one-f
or-one;inJ une 2 0 0 0 ,it isapproxim ately R 6.
90 per U S$ .
5
afurther39 seats were issued ataprice ofR 35,0 0 0 each,givingan additional
R1.
365 million in capital.
Safcom took overthe managementofthe informalfutures marketin A pril
1 990 withthefollowingobjective:\ Safexseekstoprovidethesecureande±cient
marketfortradingderivativesinSouthA frica.
" T heSafexwaso±ciallylicensed
on A ugust1 0 ,1 990 afterthepassingoftheFinancialM arkets ControlA ct.A t
this point, the only listed products were futures contracts on the majorJSE
(A llshare(A L SI),G old(G L D I)andIndustrial(IN D I))Indexes,themostactive
long-datedbond (theE1 68 issued byEscom (ElectricitySupplyCommission)),
thethreemonth liquid bankers acceptancerateand on theU S$ priceofgold.
In O ctober1 990 theSA R B granted non-residents permission toparticipate
ontheSafexviatheFinancialR andsystem.G rowthinthemarketwas initially
very slow with volumes of 2,0 0 0 -5,0 0 0 contracts per day, but they began to
soarafterthe Safexintroduced options-on-futures togetherwith aworld-class,
portfolio-scanning-type margining system in O ctober 1 992. W ithin approximately1 2 months,volumes hadgrownby70 0 % andinD ecember1 993 volumes
exceeded1 million contracts permonth forthe¯rsttimeandopeninterestwas
greaterthan 50 0 ,0 0 0 contracts.
O n June1 5,1 995 the underlyingindexes ofthe A L SI,IN D I and G L D I futures contracts were restructured and based on the largestand mostactively
traded stocks in theirsector. T he newunderlying indexes were the A L SI40 ,
IN D I25 andG L D I1 0 indexes wherethenumberattheendoftheindexdenotes
thenumberofstocks usedinits construction.A futures contractontheFinancialand Industrial(FIN D I30 )Index contractwas introduced slightly lateron
O ctober6,1 995.O wingtothe size ofthe South A frican markets,many large
companies appearin morethan twoindexes.
In M ay 1 996 a fully-automated tradingsystem was introduced.T his coincided with thephasingin oftheJohannesburgEquities T rading(JET )system
on the JSE from M arch 1 996 toJune1 996.In January 1 997open interestexceeded 1 million contracts forthe¯rsttime.T hemostsuccessfulcontracts are
thosebasedontheA L SI40 andIN D I25 indexes.T heM ining1 5 (M IN I 1 5)and
Financial1 5 (FIN I 1 5)contracts wereintroduced on M arch 3,1 998 toreplace
the G L D I 1 0 and FIN D I 30 contracts,respectively, thatwere discontinued on
M arch1 9,1 998.O nM arch1 8,1 999 theR esources 20 (R ESI 20 )contractbegan
trading and replaced the M IN I1 5 contractwhich ceased trading the previous
day. V olumes continue to be dominated by equity index products with the
concentration being in the A L SI40 and IN D I25 indexes. O ptions accountfor
approximately 50 % ofvolumes and 80 % ofopen interest,and tradeis increasinglydominatedbyinternationalmarketplayerswhoaccountforapproximately
40 % ofvolumes traded.
Inkeepingwithits statedobjectiveofprovidinga\ secureande±cientmarketfortrading derivatives in South A frica" an A griculturalM arkets D ivision
was introducedin1 995 andoptions onagriculturalproducts wereintroducedin
M arch 1 998.In February 1 999 Sun° owerSeeds and CapeW heatfutures were
introduced intheA griculturalM arket.
6
5 E m piric alM ethod
T he empiricalmethod is thatofB essembinderand Seguin (1 992)whoiterate
between thetwoequations,
R t = ±+
Xn
j=1
¾
bt = ® +
X4
° jR t¡j +
´idi +
i=1
X4
½idi +
i=1
Xn
j=1
Xn
j=1
¯ j¾
bt¡j +
Xn
j=1
¼ j¾
bt¡j + U t
!jU t¡j + "t
(1 )
(2)
where R t is the return on day t and is calculated as R t = 1 0 0 ¢ln(P t=P t¡1 );
P t is the index atdp
ate t, di denotes day-of-the-week dummies forM onday to
T hursday,b
¾ t ´jU tj ¼=2 istheestimatedvolatilityandU t and"t aretheresiduals.T oobtain consistentestimates ofthe parameters we adoptthe following
iterativemethodofestimation:¯rst,estimate(1 )withoutthelaggedvolatility,
savetheresiduals as Ubt andcomputeb
¾ t.Second,estimate(2)andsavethepredicted volatility.T hird, estimate (1 )and include the predicted volatility from
thesecondstep.Savetheresiduals as Ubt andcomputeb
¾ t.Finally,estimate(2)
and interprettheparameterestimates.
T oanalyzetherelationship between volatilityand theactivityvariables we
includetheactivityvariables in(2)toobtain,
¾
bt = ® +
X4
i=1
´idi +
Xn
j=1
¯ j¾
bt¡j +
Xn
j=1
!jU t¡j +
m
X
¹ kA k+ "t;
(3)
k=1
wheretheactivityvariablesareindexvolume,futuresvolume,openinterestand
numberoffuturestransactions.W eadoptthesamefourstepiterativeprocedure
for(1 )and(3)as mentioned above.
W euse thesamedecomposition as B &S92 toremovethe timetrend in the
activity variables. First we take the natural log of the activity variable to
remove heteroskedasticity.Second, we ¯ta 1 0 0 -day movingaverage tomodel
the trend componentand ¯nally we use an A R IM A (0 ;1 ;1 0 )modeltoobtain
a predicted and unpredicted component forthe detrended component ofthe
activityvariable.In sum,thevariableis decomposed as follows:
V t = trendt + trenddeviationt
= M A V (1 0 0 )t + (P V t + U V t)
(4)
whereM A V (1 0 0 )t isthe1 0 0 -daymovingaverage,P V t isthepredicteddeviation
from the trend and U V t is the unexpected deviation from the trend. B efore
includingthesethreecomponent
s ofvolumeas activityvariables in (3),wedeP
meaneachseries sothat®=(1 ¡ j ¯ j)canbeinterpretedas theunconditional
orlong-run variancewhentheactivityvariables areattheiraveragelevels.
7
6 Data
P riortoJune 1 995, futures contracts on the South A frican Futures Exchange
(SA FEX )were based on the broad, marketindexes thatrepresentthe largest
percentage ofmarketcapitalization, i.
e. the A llShare Index (A L SI), the IndustrialIndex(IN D I),theG old Index(G L D I)andtheFinancialIndex(FIN I).
O n June 1 5, 1 995 the JSE introduced indexes based on the largerand more
highly traded companies in each ofthese sectors forthe purpose ofbeingthe
underlying index forfutures contracts on the SA FEX .T he A L SI40 , G L D I1 0 ,
IN D I25 andFIN D I30 mirrorthefourbroadindexes mentionedabovewherethe
numberattheend ofeach indexrefers tothenumberofstocks thatis used in
constructingthe indexand FIN D I denotes theFinancialand IndustrialIndex.
M ichelle Francis ofthe JSE kindly provided the closing price and volume for
theindexes fortheperiod 1 5 June 1 995 to31 D ecember1 999.T henumberof
transactions, volume and open interestofthe futures contracts was obtained
from theSA FEX website.
W ehaveacompletedatasetfortheA L SI40 and IN D I25 futures contracts
from 1 5 June 1 995 to 30 N ovember1 999. T he futures contractbased on the
G L D I1 0 indexwas discontinuedin1 7September1 998 sothesampleperiodruns
from September1 ,1 995 to1 7September1 998.A llotherfutures contracts are
ignoredduetosmallsamplesizesorlackofdataduetothintrading.T heindexes
3
arevalue-weightedandareadjustedformergers,de-listings,butnotdividends.
In conclusion, we focus on the futures contractbased on the A L SI40 , IN D I25
and G L D I1 0 contracts becausetheyhavesu±cientdatafortheanalysis.
7 R esul
ts
7.
1
Desc riptive Statistic s
W ereportthedescriptivestatistics ofthereturns ofthethreeindexes in T able
1 . W e include tests of skewness and kurtosis based on the G M M estimator
becausethetraditionalestimatorsu®ers from thedrawbackthatits varianceis
underestimatedwhenreturns arenon-normalandconditionallyheteroskedastic
(P agan (1 996)).T he G L D I1 0 index is uniquely di®erenttothe othertwoindexes:thereturns fortheG L D I1 0 indexaretwotothreetimes as largeas those
oftheIN D I25 and A L SI40 indexes and itdisplays statisticallysigni¯cantpositiveskewness.A lthoughthecoe±cients ofskewness oftheIN D I25 andA L SI40
indexes arenegative,theyarenotstatisticallysigni¯cant.W hereas theA L SI40
andIN D I25 indexes displaystatisticallysigni¯cantexcess kurtosis,theG L D I1 0
index has statistically signi¯cantly less kurtosis than the normaldistribution.
Each ofthe indexes has a statistically signi¯cant¯rstorderserialcorrelation
coe±cientandtheB oxL jungQ -statistics aresigni¯cantatthe1 % levelatboth
5 and 1 0 lags. T he signi¯cance ofthe Q -statistics of the squared returns is
3Detail
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/.
8
consistentwith conditionalheteroskedasticityin thereturns.
W edonotreportdescriptivestatisticsfortheactivityvariablesbecausesome
ofthem were growingovertime.H owever,the generalfeatures ofthe activity
variables can be seen in Figures 1 ,2 and 3.Forexample,the growth in index
volume ofthe A L SI40 index is evidentin Figure1 C while the lackoftrend in
ofthe numberoftransactions forthe A L SI40 and IN D I25 contracts is evident
inFigures 1 D and3D .T hevolatilitythatfollowedtheA siancrisis is evidentin
Figures 1 B and 3B forthe A L SI40 and IN D I25 indexes,respectively. Figures
1 F,2F and 3F display theuniquebehavioroftheopen interestthatdecreases
atthe maturity date ofeach futures contract.W hereas the open interestfor
theA L SI40 and IN D I25 contracttrend upwards,thereis notrend in theopen
interestoftheG L D I1 0 index.T hefailureofthefutures contractbased on the
G L D I1 0 indexis clearlyevidentinFigure2D wherethenumberoftransactions
declines overtimedespitehigh volumes followingtheA sian crisis (Figure2C).
7.
2
Correl
ationM atric es
A s a precursor to the analysis, we brie° y highlight the ¯ve most important
features ofthecorrelation matrix ofthereturns,absolutereturns and activity
variables forthethreeindexes inT ables 2,4 and6.First,returns andabsolute
returns are negatively correlated.T his is consistentwith negative skewness in
thedistributions oftheA L SI40 andIN D I25 indexes,butnottheG L D I1 0 index.
Second, the correlation between the absolute return and the activity variables
arepositiveandaveragearound0 .
20 0 ;thisisconsistentwithapositiverelationship betweenvolatilityandtheactivityvariables(Karpo®(1 987)).T heabsolute
return has the strongestrelationship with the unexpected futures volume and
unexpectedtransactions volumes and1 0 0 -daymoving-averages,i.
e.volatilityis
positively related tothe overallleveloftradingand unexpected shocks tothe
market. T he relatively large correlation between the absolute return and the
1 0 0 -daymoving-averages oftheindexvolume,futures volumeandopeninterest
canbeexplainedbythehighleveloftradingactivityduringthehighlyvolatile
period ofthe A sian crisis and the upward trend in activity overthe sample
period.
T hird,thethreemoving-averages arehighlycorrelatedwitheachotherwith
manycorrelationcoe±cients inexcess of0 .
90 0 .Fourth,thepredictedindex,futures and transaction volumehavecorrelation coe±cients thataverage around
0.
40 0 ,buttheyhavealowercorrelationwiththepredictedopeninterest. Fifth,
thecorrelation between the unexpected index volume,unexpected futures volumeandtransactionvolumeaveragearound0 .
250 .Incontrast,theunexpected
futures volumeandunexpectedtransactions volumehaveacorrelationof0 .
71 1 .
T osum up,theactivityvariables arepositivelyrelatedtovolatilityandweneed
tobeconcernedaboutthemulticolinearitybetween themoving-averages.
9
7.
3 T he ALSI4 0 Ind ex
T heestimated parameters ofequations (2)and(3)arecontainedinT able3 for
theA L SI40 Index.M odel1 is thecombinationof(1 )and(2)wherenoactivity
variables areincludedinthespeci¯cationoftheconditionalvariance.T heestimates havethreebasicfeatures:¯rst,volatility is positivelyseriallycorrelated
- the¯rst¯velags ofvolatilityarestatisticallysigni¯cantand positive.T his is
consistentwiththeexcess kurtosis inreturns andconditionalheteroskedasticity
inassetreturns.Second,thecoe±cientonthe¯rsttwolaggedresiduals arestatistically signi¯cantand negative,i.
e.the conditionalvariance increases when
thereis anegativeshocktoreturns.T his is consistentwith asymmetrice®ects
involatility(Christie(1 982))andwiththeresults ofB eelders (20 0 0 a)who¯nds
T A R CH e®ects inthefutures indexes and broadermarketindexes.T hird,only
the W ednesday dummy is statistically signi¯cantand positive.T his is consistentwith the results ofB eelders (20 0 0 b)who ¯nds a settlemente®ecton the
JSE - transactions mustbesettled everyT uesdayorthe¯rstdaythereafter.
Itis interestingtonotethatthecoe±cients on thelagged conditionalvarianceandlagged returns arequitesimilaracross thevarious models.Exceptfor
the W ednesday e®ect, these three empiricalregularities are presentin each of
thesixmodels.Each ofthesixmodels has astatisticallysigni¯cantF-statistic
forgoodness-of-¯tatthe 1 % level. T he consistency in the magnitude ofthe
parameters across models suggests thatnoneofthemodels is seriouslymisspeci¯ed.
M odel2 is the combination of (1 )and (3)where the Index volume (X V )
is included as an activityvariable.T he1 0 0 -daymoving-average,predicted volumeandunexpectedvolumeeachhavepositivecoe±cients thatarestatistically
signi¯cantatthe1 % level,i.
e.theconditionalvarianceoftheindexis positively
relatedtovolume(Karpo®(1 987)).T hesigni¯canceofthemovingaverageand
the predicted volume may be due to the high levelofvolatility following the
A sian crisis in 1 997 and 1 998, the introduction ofelectronic trading in 1 996
andtheresolutionofpoliticaluncertaintythathas leadtogreaterinternational
interestin South A fricain thelatterpartofthe1 990 's.
M odel3 isthecombinationof (1 )and(3)wherethefutures contractvolume
(FV )is includedas theactivityvariable.T he1 0 0 -daymoving-averageand unexpected volumeeach havepositivecoe±cients thatarestatisticallysigni¯cant
atthe1 % level.T hestatisticalsigni¯canceofthemovingaveragemaybedueto
thesecularchanges thatwementionedabove.T hecoe±cientoftheunexpected
futures volumeis 0 .
552 soan unexpected 1 0 % increasein volumeincreases the
conditionalvarianceby6.
5% from 0 .
81 6 to0 .
871 assumingthattheconditional
varianceequalled thelong-run varianceon theprevious ¯vedays.
M odel4 is the combination of (1 )and (3)where the open interest (O I)
is included as the activity variable. O nly the 1 0 0 -day moving-average has a
positive and statistically signi¯cantcoe±cientatthe 1 % level.T he statistical
signi¯canceofthemoving- averagemay beduetothesecularchanges thatwe
mentioned above and the lack ofsigni¯cance ofthe othercomponents may be
duetothelargechanges in open interestatthematurityofacontract.
10
M odel5 is thecombinationof (1 )and(3)wherethenumberoftransactions
(T )is included as the activity variable.T he numberoftransactions does not
haveanytrendsowedidnotcomputea1 0 0 daymovingaverage,butwedouse
the A R IM A (0 ;1 ;1 0 )modeltodecompose itintoa predicted and unexpected
component. T he coe±cient of the predicted component is insigni¯cant, but
the coe±cientofthe unexpected componentis signi¯cantatthe 1 % leveland
is statistically indistinguishable from 1 , i.
e. a 1 0 % increase in the numberof
transactions leads to1 0 % increasein thelong-run variance.
Finally, model 6 refers to the combination of (1 )and (3)where all the
activity variables are included as regressors. T he 1 0 0 -day moving average of
the open interest is statistically signi¯cant at the 5% leveland captures the
secularchangeswereferredtoearlier.T hepredictedlevelofopeninterestisalso
statistically signi¯cant, butthe coe±cientis negative.T his is consistentwith
theresults ofB &S92 whoconjecturethattheintroduction offutures contracts
decreases spot volatility when the market is deep. Finally, the unexpected
numberoffutures transactions is statistically signi¯cant with a coe±cientof
0.
981 , i.
e. the unexpected number of transactions maintains its importance
even afterpartiallingoutthee®ectofthe otheractivity variables.T his result
is consistentwith Jones, Kauland L ipson (1 994)who ¯nd thatitis notthe
volume,butthenumberoftransactions thatis thekeyvariablefordetermining
volatility.
W hen we compare the adjusted-R 2 ofeach modelwe note thatthe benchmark is given by model1 with an adjusted-R 2 of0 .
235.O utofmodels 2, 3,
4 and 5, model5 has the highestadjusted-R 2 of0 .
30 9. T he adjusted-R 2 of
model5 is notmuchsmallerthanthatofmodel6 (0 .
31 8).T helargestincrease
in the adjusted-R 2 occurs when weadd the numberoftransactions.B ased on
explanatorypower,itappears thattheunexpectednumberoftransactions that
is mostimportantadditionalvariable.
In conclusion, spot volatility has a positive relationship with the secular
trendinopeninterest,anegativerelationship withpredictedopeninterestanda
positiverelationship withtheunexpectednumberoftransactions onthefutures
market.In terms ofexplanatorypower,thenumberoftransactions is themost
4
importantvariable.
7.
4
T he G LDI10 Ind ex
T heestimated parameters ofequations (2)and(3)arecontainedinT able5 for
theG L D I1 0 Index.M odel1 is thecombinationof(1 )and(2)wherenoactivity
variables areincludedinthespeci¯cationoftheconditionalvariance.T heestimates havethreebasicfeatures:¯rst,volatility is positivelyseriallycorrelated
withthelargestcoe±cients atthesecondandfourthlag.Second,thecoe±cient
on the ¯rstlagged residualis negative across allthe models butonly statistically signi¯cantin model4.T hird, none ofthe daily dummies are signi¯cant;
4 T he c aveat to thisc on
c lusionisthat w e are not partialling out the e®ec t ofthe n
umb er
ofspot transac tions.
11
this is consistentwith B eelders (20 0 0 b)whofails to detectseasonality in the
conditionalmean returns ofthe G L D I1 0 index.T he lowadjusted-R 2 of0 .
0 71
formodel1 is much lowerthan theequivalentmodelfortheA L SI40 indexand
may be due to the greaterlevelofvolatility in the G L D I1 0 index. W ith the
addition ofindexvolume(X V )in model2,theadjusted-R 2 increases to0 .
1 65.
T he predicted and unexpected volume each have positive coe±cients thatare
statisticallysigni¯cantatthe1 % level.T hecoe±cientofunexpectedvolumeis
1.
0 61 whichimplies thata1 0 % increaseinindexvolumeleads to5.
5% increase
in thelong-runlevelofvolatility.
T hecoe±cientofunexpected futures volumein model3 is 0 .
399 and is signi¯cant at the 1 % level. In comparison to model 2, the coe±cient ofindex
volume is more than twice as large as the coe±cient on the futures volume.
T urningtomodel4, none ofthe coe±cients ofthe components ofopen interest(O I)are statistically signi¯cant.In model5, the coe±cientofunexpected
transactions is 0 .
979 whichimplies thata1 0 % increaseinthenumberoftransactions leads toa5.
8% increasein thelong-run variance.Finally, weconsider
model6 thatincludes alltheactivityvariables as regressors.O nlythepredicted
open interesthas nostatisticalsigni¯cance.T he coe±cients on predicted and
unexpected index volume are both positive.T he coe±cients on predicted and
unexpected futures volumeareboth negative.T his is consistentwith B essembinderand Seguin's conjecture thatfutures trading does notexacerbate spot
volatility when the marketis deep.T he coe±cienton unexpected open interestis 1 .
298 and may re° ectincreased volatility atthe maturity ofthe futures
contracts.Finally,the coe±cientofthe unexpected numberoftransactions is
0.
994,i.
e.a1 0 % increasethenumberoftransactions leads toa5% increasein
spotvolatility,ceteris paribus.
W hen we compare the adjusted-R 2 ofeach modelwe note thatthe benchmarkis given bymodel1 with an adjusted-R 2 of0 .
0 71 .O utofmodels 2,3,4
and 5, model6 has the highestadjusted-R 2 of0 .
21 8.T he addition ofindex
volume and transactions to the base models provides the biggestincreases in
theadjusted R 2 .
In conclusion,spotvolatilityhas apositiverelationship with indexvolume,
anegativerelationship withfutures volumeandapositiverelationship withthe
unexpectednumberoftransactions on thefutures marketand open interest.
7.
5 T he INDI2 5 Ind ex
T he estimated parameters ofequations (2)and (3)are contained in T able 7
forthe IN D I25 Index. M odel1 is the combination of (1 )and (2)where no
activity variables are included in the speci¯cation ofthe conditionalvariance.
T he estimates have the same three basicfeatures as the A L SI40 and G L D I1 0
contract.Inmodels 2 and3,the1 0 0 -daymovingaverageandunexpectedindex
volumeand futures volumeeach havepositivecoe±cients thatarestatistically
signi¯cantatthe1 %.Inmodel3,the1 0 0 -daymoving-averageofopeninterestis
statisticallysigni¯cantatthe1 % level.O nceagain,thestatisticalsigni¯canceof
themovingaveragemaybeduetothesecularchangesthatwementionedabove.
12
Formodel4 we¯ndthatallthreecomponents ofthenumberoftransactions are
statistically signi¯cant.T he 1 0 0 -day moving-average has acoe±cientof1 .
569
and the unexpected numberoftransactions has acoe±cientof1 .
0 28.Finally,
in model6 only three coe±cients are signi¯cant: unexpected futures volume
has a positive coe±cientof0 .
669, the 1 0 0 -day movingaverage oftransactions
has a positive coe±cientof1 .
684 and predicted open interestonce again has
a negative coe±cient. W hen comparing the adjusted-R 2 across the models,
we ¯nd thatfutures volume and transactions provide the greatestincrease in
explanatory powerovermodel1 .T hebasemodelhas an adjusted-R 2 of0 .
225
and this increases to0 .
273 and 0 .
274 when futures volume and the numberof
transactions areadded,respectively.
Inconclusion,spotvolatilityispositivelycorrelatedwiththe1 0 0 -daymoving
averageoftransactions thatcaptures theseculartrendandpositivelyrelatedto
theunexpected futures volume.
8
Concl
usion
Consistentwiththeexistingstudies,we¯ndthatspotvolatilityandtheoverall
leveloftradingactivityon thespotand futures markets arepositivelyrelated.
W henmarketdepthis measuredbypredictedopeninterestorpredictedfutures
volume we ¯nd thatfutures market activity dampens spotmarket volatility.
T his is consistentwith Kyle(1 985)whoconjectures thatgreatermarketdepth
cansupportmoreinformed traders and theresults in B &S92.
Finally, the unexpected number of transactions on the futures market is
more strongly related to spotvolatility than unexpected futures volume and
unexpected index volume forthe A L SI40 and G L D I1 0 contracts. In fact, for
A L SI40 indexa1 0 % increaseintheunexpectednumberoftransactionsleadstoa
1 0 % increaseinvolatility.T heresponseofthevolatilityoftheG L D I1 0 indexto
thesameincreaseintheunexpectednumberoftransactions is only5% although
itis twiceas variableas theA L SI40 index.T heseresultsareconsistentwiththe
results ofJones,Kauland L ipson (1 994)and may re° ectthefactthattraders
who have access to new information are more likely to trade on the futures
marketbecause itis less expensive than the spotmarket. T he one caveatto
this conclusionis thatwedonotincludethenumberofspottransactions inour
analysis;ahorseracebetweenthenumberofspottransactions andthenumber
offutures transactions would clearlybeamorede¯nitivetest.
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J.andM .
H .M iller(1 988)\ L iquidityandM arketStructure,"
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16
T able1 :D escriptiveStatistics oftheJSE Futures Indexes
A L SI40
SampleSize
mean
V ariance
G L D I1 0
1 1 72
0.
015
0.
362
Skewness
-1 .
20 0
iid t-statistic
(-1 6.
754)c
G M M t-statistic
(-1 .
243)
Kurtosis
iid t-statistic
G M M t-statistic
L ags
IN D I25
1 1 72
0.
005
0.
924
1 1 72
0.
014
0.
429
0.
597
-0 .
899
(8.
339)c (-1 2.
453)c
(3.
746)c
(-1 .
0 58)
1 4.
30 5
2.
61 9
(99.
759)c (1 8.
236)c
(2.
1 37)b (6.
21 5)c
1 2.
427
(86.
656)c
(2.
1 67)b
A utocorrelations
1
2
3
4
5
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
Q R (5)
Q R (1 0 )
25.
346c
27.
644c
27.
926c
34.
40 9c
9.
655a
1 3.
220 c
Q R 2 (5)
Q R 2 (1 0 )
30 4.
75c
321 .
67c
275.
42c
397.
96c
284.
66c
31 9.
44c
Superscripta,b andcdenotestatisticalsigni¯canceatthe1 0 %,5% and1 %
levelofsigni¯cance,respectively.
17
T able2:T heCorrelation M atrixfortheA L SI40 Index
R eturn A bs(R t) M A X V
R eturn
1.
000
A bs(ret) -0 .
1 78c
PX V
UXV
M A FV
P FV
U FV
M A OI
PO I
1.
000
M A XV
PXV
UXV
0.
011
-0 .
018
0.
0 33
0.
1 66c
0.
1 44c
0.
1 48 c
M A FV
P FV
U FV
-0 .
002
0.
006
0.
018
0.
1 61 c
0.
0 55a
0.
237c
0.
931 c
-0 .
1 72c
-0 .
006
-0 .
0 26
0.
40 3c
-0 .
019
0.
015
0.
1 23c
0.
237c
1.
000
-0 .
1 72c
-0 .
0 32
1.
000
-0 .
0 35
1.
000
M A OI
PO I
UOI
0.
008
-0 .
014
-0 .
015
0.
20 0 c
-0 .
000
0.
0 33
0.
957c
0.
014
-0 .
006
0.
0 36
-0 .
0 34
0.
008
0.
0 29
0.
0 78 b
-0 .
1 30 c
0.
929c
0.
0 32
-0 .
0 21
-0 .
1 29c
0.
20 1 c
-0 .
0 93c
-0 .
004
0.
1 0 4c
0.
0 57b
1.
000
0.
0 34
-0 .
0 22
1.
000
-0 .
1 0 6c
PT
UT
-0 .
0 29
-0 .
0 25
0.
1 79c
0.
350 c
0.
011
-0 .
001
0.
41 3c
0.
016
0.
1 0 7c
0.
288 c
0.
0 60 b
0.
014
0.
762c
0.
0 65b
0.
0 26
0.
71 1 c
-0 .
0 48
0.
017
0.
1 86c
0.
0 99c
1.
000
-0 .
0 30
1.
000
0.
0 0 7 -0 .
0 27
1.
000
T he pre¯xes M A , P and U denote moving average, predicted and unexpected,respectively,and thesu±xes X V ,FV ,O I and T denoteindex volume,
futures volume,open interestand transactions,respectively.A superscripta,b
and cdenotes signi¯cance atthe 1 0 %, 5% and 1 % levelofsigni¯cance forthe
nullhypothesis thatthecorrelation equals zero.
18
T able3:M odelEstimates fortheA L SI40 Index
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
Intercept
0.
325c
0.
41 3c
0.
41 2c
0.
40 4c
0.
425c
0.
535c
¾
bt¡1
0.
221 c
0.
1 85c
0.
1 97c
0.
20 8 c
0.
1 96c
0.
1 70 c
¾
bt¡2
0.
0 93c
0.
0 82a
0.
0 98 c
0.
0 89a
0.
1 0 4c
0.
0 87b
¾
bt¡3
0.
21 4c
0.
20 4c
0.
20 0 c
0.
1 96c
0.
1 96c
0.
1 83c
¾
bt¡4
0.
0 59a
0.
0 49
0.
0 48
0.
0 48
0.
0 52
0.
0 43
0.
0 55a
0.
0 41
0.
0 49
0.
0 43
0.
0 60
0.
0 46
U t¡1
-0 .
1 1 7c
-0 .
1 32a
-0 .
1 48 b
-0 .
1 1 6a
-0 .
1 47b
-0 .
1 56b
U t¡2
-0 .
0 649b
-0 .
0 68 b
-0 .
0 53a
-0 .
0 66b
-0 .
0 43
-0 .
0 48
U t¡3
-0 .
0 28
-0 .
0 41
-0 .
0 38
-0 .
0 33
-0 .
0 35
-0 .
0 41
U t¡4
-0 .
017
-0 .
019
-0 .
009
-0 .
016
-0 .
001
-0 .
005
U t¡5
0.
0 49b
0.
0 47
0.
0 52
0.
0 43
0.
0 58
0.
0 51
M onday
0.
0 65
0.
1 89
0.
1 69
0.
0 74
0.
103
0.
1 65
T uesday
0.
115
0.
118
0.
0 75
0.
112
-0 .
0 22
-0 .
013
0.
222b
0.
20 2a
0.
111
0.
20 1 a
0.
0 47
0.
017
0.
018
-0 .
019
-0 .
0 47
0.
017
-0 .
0 57
¾
bt¡5
W ednesday
T hursday
19
-0 .
0 878
T able3 (continued):M odelEstimates oftheA L SI40
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
M A XV
0.
1 33c
-0 .
0 73
PXV
0.
51 3c
0.
51 4b
UXV
0.
437c
0.
1 77
0.
1 78 c
-0 .
1 84
P FV
0.
006
-0 .
1 24
U FV
0.
552c
0.
0 85
M A FV
M A OI
0.
1 90 c
0.
424b
PO I
-0 .
0 96
-0 .
349b
UOI
0.
678
0.
825
PT
-0 .
0 90
-0 .
018
UT
0.
967c
0.
981 c
0.
228
0.
30 9
0.
31 8
23.
971 c
1 8.
50 8 c
31 .
689c
1 9.
784c
0.
81 6
0.
797
0.
843
0.
955
adj-R 2
F-statistic
L R variance
0.
235
0.
246
25.
1 76c
20 .
239c
0.
90 8
0.
280
0.
781
T able3 contains theestimates ofmodels (1 ),(2)and (3).T heregressors ¾
bt¡j,
j = 1 ;2:::;5 arethe¯velagged conditionalvariances and U t¡j,j = 1 ;2:::5 are
the¯ve lagged residuals from (1 ).Fourday-of-the-weekdummies areincluded
to mop up any seasonality in the conditionalvariance. T he pre¯xes M A , P
and U denotemovingaverage,predicted and unexpected,respectively,and the
su±xes X V ,FV ,O I and T denoteindexvolume,futures volume,open interest
and T ransactions,respectively.A superscripta,band cdenotes signi¯canceat
the1 0 %,5% and 1 % levelofsigni¯canceforthehypothesis thatthecoe±cient
equals zero.
20
T able4:T heCorrelation M atrixfortheG L D I1 0 Index
Rt
Rt
1.
000
A bs(R t) -0 .
1 39c
A bs(R t)
PX V
UXV
P FV
U FV
PO I
U PO I
PT
1.
000
PXV
UXV
-0 .
011
0.
21 2c
0.
20 7c
0.
256c
1.
000
-0 .
0 77b
1.
000
P FV
U FV
-0 .
0 41
0.
1 0 8c
-0 .
0 44
0.
258c
0.
0 84b
0.
003
0.
0 23
0.
31 3c
1.
000
-0 .
0 53
1.
000
PO I
UOI
-0 .
0 61
0.
1 33c
-0 .
0 28
0.
006
0.
0 95b
0.
0 64
-0 .
0 22 -0 .
1 56c
0.
30 5c
-0 .
0 66a
0.
0 92b
0.
0 23
1.
000
-0 .
1 84c
1.
000
PT
UT
0.
0 46
0.
1 1 7c
0.
0 0 7 -0 .
0 72a
c
0.
374
-0 .
009
0.
793c
-0 .
1 59c
0.
0 43
0.
782c
0.
1 36c
0.
0 34
-0 .
0 20
-0 .
018
0.
017
0.
387c
T hepre¯xes M A ,P and U denotemovingaverage,predicted and unexpected,
respectively, and the su±xes X V ,FV ,O I and T denote index volume,futures
volume,open interestand transactions, respectively.A superscripta, band c
denotes signi¯cance atthe 1 0 %, 5% and 1 % levelofsigni¯cance forthe null
hypothesis thatthe correlation equals zero.
T he pre¯xes M A ,P and U denote
moving average, predicted and unexpected, respectively, and the su±xes X V ,
FV ,O I and T denote index volume,futures volume,open interestand T ransactions,respectively.A superscripta,b and cdenotes signi¯canceatthe1 0 %,
5% and 1 % levelofsigni¯cance forthe hypothesis thatthe correlation equals
zero.
21
1.
000
-0 .
1 23c
T able5:M odelEstimates fortheG L D I1 0 Index
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
Intercept
1.
0 61 c
1.
324c
1.
1 92c
1.
223c
1.
0 29c
1.
428 c
¾
bt¡1
0.
1 69c
0.
0 96b
0.
0 98 b
0.
1 37c
0.
0 78a
0.
0 26
¾
bt¡2
0.
0 98 b
-0 .
0 27a
-0 .
1 0 6b
0.
0 91 b
0.
1 42c
0.
1 0 2b
¾
bt¡3
-0 .
006
-0 .
0 27
0.
016
-0 .
0 22
-0 .
003
-0 .
0 32
¾
bt¡4
0.
1 20 c
0.
1 0 4c
0.
1 1 6c
0.
111b
0.
1 1 7c
0.
0 81 b
¾
bt¡5
0.
1 1 2c
0.
0 93b
0.
1 1 7c
0.
0 98b
0.
1 1 8c
0.
0 89b
U t¡1
-0 .
017
-0 .
012
-0 .
0 37
-0 .
1 20 b
-0 .
0 34
-0 .
0 40
U t¡2
-0 .
011
0.
006
-0 .
006
-0 .
0 23
-0 .
0 21
-0 .
015
U t¡3
0.
0 34
0.
0 25
0.
0 43
0.
007
0.
0 31
0.
0 29
U t¡4
0.
0 24
0.
0 31
0.
0 26
0.
018
0.
005
0.
010
U t¡5
-0 .
0 37
-0 .
0 22
-0 .
0 46
-0 .
0 48
-0 .
0 49
-0 .
0 46
M onday
0.
0 41
0.
356a
0.
1 71
-0 .
001
0.
353
0.
444
T uesday
-0 .
0 62
-0 .
0 81
-0 .
1 36
-0 .
0 84
-0 .
006
-0 .
003
W ednesday
-0 .
0 68
-0 .
0 80
-0 .
0 31
-0 .
1 79
0.
0 96
0.
0 64
T hursday
-0 .
1 46
-0 .
1 83
-0 .
1 64
-0 .
1 24
0.
014
-0 .
019
22
T able5 (continued):M odelEstimates fortheG L FI1 0 Index
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
PXV
0.
591 c
0.
71 6c
UXV
1.
0 61 c
0.
674c
P FV
-0 .
1 97
-0 .
427b
U FV
0.
399c
-0 .
1 92c
PO I
-0 .
1 78
-0 .
1 87
UOI
0.
540
1.
298 b
PT
0.
0 55
0.
377b
UT
0.
979c
0.
994c
adj-R 2
F-statistic
L R variance
0.
0 71
0.
1 65
0.
109
0.
0 45
0.
1 69
0.
21 8
4.
71 9c
9.
371 c
5.
767c
2.
844c
7.
360 c
7.
669c
2.
118
1.
80 4
1.
538
2.
1 72
1.
754
1.
961
T able3 contains theestimates ofmodels (1 ),(2)and (3).T heregressors ¾
bt¡j,
j = 1 ;2:::;5 arethe¯velagged conditionalvariances and U t¡j,j = 1 ;2:::5 are
the¯ve lagged residuals from (1 ).Fourday-of-the-weekdummies areincluded
to mop up any seasonality in the conditionalvariance. T he pre¯xes M A , P
and U denotemovingaverage,predicted and unexpected,respectively,and the
su±xes X V ,FV ,O I and T denoteindexvolume,futures volume,open interest
and T ransactions,respectively.A superscripta,band cdenotes signi¯canceat
the1 0 %,5% and 1 % levelofsigni¯canceforthehypothesis thatthecoe±cient
equals zero.
23
T able6:T heCorrelation M atrixfortheIN D I25 Index
Rt
Rt
1.
000
A bs(R t) -0 .
1 46c
A bs(R t) M A X V
PX V
UXV
M A FV
P FV
U FV
M A OI
PO I
1.
000
M A XV
PXV
UXV
0.
002
-0 .
0 34
0.
0 20
0.
21 1 c
0.
0 40
0.
0 96c
M A FV
P FV
U FV
0.
014
-0 .
0 42
-0 .
0 43
0.
256c
0.
1 34c
0.
240 c
0.
924c
-0 .
0 46
0.
0 38
-0 .
1 1 9c
0.
373c
-0 .
0 69b
-0 .
0 40
0.
1 1 9c
0.
277c
1.
000
-0 .
0 82c
-0 .
003
1.
000
-0 .
012
1.
000
M A OI
PO I
UOI
0.
015
-0 .
019
-0 .
0 29
0.
20 3c
0.
0 45
0.
0 21
0.
80 0 c
0.
003
0.
016
0.
016
-0 .
0 55a
-0 .
0 26
0.
014
0.
014
-0 .
1 41 c
0.
821 c
0.
1 34c
-0 .
011
-0 .
1 1 6c
0.
255c
-0 .
0 96c
0.
008
0.
1 0 4c
0.
0 31
1.
000
-0 .
1 0 4c
-0 .
0 36
1.
000
-0 .
1 33
M AT
PT
UT
-0 .
017
-0 .
0 67
-0 .
0 93
0.
342c
0.
1 24c
0.
1 93c
0.
464c
-0 .
0 78 b
0.
0 26
-0 .
0 89c
0.
349c
-0 .
1 1 9c
-0 .
0 30
0.
1 1 6c
0.
275c
0.
693c
-0 .
1 27c
-0 .
0 20
-0 .
0 49
0.
861 c
-0 .
0 53a
-0 .
0 46
0.
101c
0.
769c
0.
539c
-0 .
1 40 c
-0 .
002
0.
1 69
0.
281
0.
0 65
1.
000
-0 .
101c
1.
000
-0 .
0 27 -0 .
110c
1.
000
T hepre¯xes M A ,P and U denotemovingaverage,predicted and unexpected,
respectively, and the su±xes X V ,FV ,O I and T denote index volume,futures
volume,open interestand transactions, respectively.A superscripta, band c
denotes signi¯cance atthe 1 0 %, 5% and 1 % levelofsigni¯cance forthe null
hypothesis thatthecorrelation equals zero.
24
T able7:M odelEstimates fortheIN D I25 Index
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
Intercept
0.
323c
0.
396c
0.
51 1 c
0.
40 9c
0.
621 c
0.
655c
¾
bt¡1
0.
248 c
0.
1 224c
0.
20 7c
0.
238 c
0.
1 75c
0.
1 72c
0.
0 36
0.
0 32
0.
017
0.
0 23
0.
017
-0 .
000
¾
bt¡3
0.
229c
0.
222c
0.
224c
0.
222c
0.
1 98 c
0.
20 0 c
¾
bt¡4
0.
0 62
0.
0 60
0.
0 30
0.
0 53
0.
0 22
0.
014
¾
bt¡5
0.
0 71
0.
0 50
0.
0 61
0.
0 56
0.
0 42
0.
0 36
U t¡1
-0 .
1 1 5b
-0 .
1 29b
-0 .
1 24b
-0 .
1 20 b
-0 .
1 24c
-0 .
1 24c
U t¡2
-0 .
018
-0 .
0 24
-0 .
016
-0 .
0 23
-0 .
0 21
-0 .
018
U t¡3
-0 .
006
-0 .
007
-0 .
005
0.
007
-0 .
001
-0 .
004
U t¡4
-0 .
008
-0 .
006
-0 .
002
0.
003
0.
001
-0 .
002
U t¡5
0.
0 26
0.
0 26
0.
0 23
0.
0 24
0.
0 28
0.
0 22
M onday
0.
1 28
0.
21 9
0.
222a
0.
1 33
0.
1 96
0.
234a
T uesday
0.
1 29
0.
1 37
0.
0 41
0.
1 36
-0 .
0 36
0.
0 40
0.
232b
0.
220 a
0.
114
0.
21 0 a
0.
1 21
0.
103
0.
0 71
0.
0 46
-0 .
0 47
0.
0 56
-0 .
0 47
-0 .
0 75
¾
bt¡2
W ednesday
T hursday
25
T able7(continued):M odelEstimates fortheIN D I25 Index
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
0.
262c
-0 .
0 88
PXV
0.
21 0
0.
31 3
UXV
0.
30 6c
0.
0 68
M A XV
0.
482c
0.
1 75
P FV
0.
1 31
0.
230
U FV
0.
784c
0.
669c
M A FV
0.
355c
0.
273
PO I
0.
1 32
-0 .
31 9b
UOI
0.
288
0.
265
M A OI
M AT
1.
569c
1.
684c
PT
0.
272b
-0 .
001
UT
1.
0 28 c
0.
325
0.
290
adj-R 2
F-statistic
L R variance
0.
225
0.
232
0.
273
0.
222
0.
274
23.
741 c
1 8.
867c
23.
1 69c
1 7.
894c
23.
31 9c
1 6.
797c
0.
61 5
0.
71 6
0.
898
0.
757
0.
992
1.
0 43
T able3 contains theestimates ofmodels (1 ),(2)and (3).T heregressors ¾
bt¡j,
j = 1 ;2:::;5 arethe¯velagged conditionalvariances and U t¡j,j = 1 ;2:::5 are
the¯ve lagged residuals from (1 ).Fourday-of-the-weekdummies areincluded
to mop up any seasonality in the conditionalvariance. T he pre¯xes M A , P
and U denotemovingaverage,predicted and unexpected,respectively,and the
su±xes X V ,FV ,O I and T denoteindexvolume,futures volume,open interest
and T ransactions,respectively.A superscripta,band cdenotes signi¯canceat
26
the1 0 %,5% and 1 % levelofsigni¯canceforthehypothesis thatthecoe±cient
equals zero.
27