Alternative Settlement Methods and Australian Individual Share Futures Contracts. Donald Lien and Li Yang * (Draft: September 2003)

Transcription

1 Alernaive Selemen Mehods and Ausralian Individual Share Fuures Conracs Donald Lien and Li Yang * (Dra: Sepember 2003) Absrac Individual share uures conracs have been inroduced in Ausralia since Iniially he conracs were seled in cash. In 1996, cash selemen was gradually replaced by physical delivery. This sudy invesigaes he eecs o he selemen mehod change on Ausralian individual sock and is uures markes. Speciically, we examine wheher he reurns and volailiy o each marke, he correlaion beween he wo markes, he basis behavior, and he hedging perormance o uures markes dier across he cash selemen period and he physical delivery period. We use he error correcion model o accoun or he coinegraed sysem o wo markes in he mean equaions and he bivariae GARCH model o esimae he condiional imevarying variance and covariance marix o sock and uures reurns. We ind ha, aer he swich rom cash selemen o physical delivery, he uures marke, he spo marke, and he basis all become more volaile. However, each individual share uures conrac becomes a more eecive hedging insrumen. The improvemen in hedging eeciveness is paricularly impressive or he mos recenly esablished individual share uures conracs. JEL classiicaion: G13 Keywords: Bivariae GARCH model; Fuures selemen mehods; Hedging eeciveness o individual share uures; Basis behavior * Donald Lien is a Proessor o Economics and Finance a he Universiy o Texas a San Anonio, U.S.A. Li Yang is a Senior Lecurer a School o Banking and Finance, Universiy o New Souh Wales, Sydney, Ausralia. The auhors wish o acknowledge an anonymous reeree or helpul commens and suggesions. Corresponding auhor: Li Yang. Tel.: +61 (02) ; ax: +61(02) [email protected] (L. Yang)

2 Alernaive Selemen Mehods and Ausralian Individual Share Fuures Conracs 1. Inroducion There are wo selemen mehods associaed wih a uures conrac, cash selemen and physical delivery. Beore sock index uures conracs were inroduced, all uures conracs were seled by delivery o he underlying asse. This selemen procedure promoes he convergence o cash and uures prices and hereby enhances he risk-ranserring and pricediscovery uncions o uures markes. However, he high delivery coss and vulnerabiliy o marke manipulaion o physical delivery have led o he adopion o cash selemen as an alernaive (Garbade and Silber (1983), Jones (1983), Edwards and Ma (1996), and Manaser (1992)). For example, he sock index uures have been seled in cash since hey were inroduced because delivering a sock index porolio would require high ransacion coss i possible a all. Commodiies are by naure heerogeneous and perishable. The delivery process hereore incurs large ransacion coss such as ransporaion, inspecion, sorage, and insurance. In addiion, he physical delivery selemen mus speciy deliverable grades and locaions. Resricions on he deliverable grades and locaions reduce he uncerainy o a successul delivery process bu promoe marke manipulaion (e.g., corners or squeezes). On he oher hand, lexibiliy on he grades and locaions increases he uncerainy o he good o be delivered, and hence reduces he hedging eeciveness o a uures conrac. The necessiy o consanly balancing resricions and lexibiliy on he deliverable grades and locaions or physical delivery speciicaion renders cash selemen more desirable. Currenly, eeder cale and lean hog uures conracs boh adop cash selemen. In addiion, proposals or cash-seled uures conracs on corn, soybean, and oher livesock were considered. 2

3 Lien and Tse (2002) examine he eecs o swiching rom physical delivery o eeder cale uures conracs o cash selemen on he eeder cale marke perormance. The resul is consisen wih he expecaions o Chicago Mercanile Exchange when he change was iniiaed. Cash selemen reduced he uures marke volailiy and he basis variabiliy. Furher sudies by Chan and Lien (2002, 2003) ind he conclusions o be robus o dieren volailiy esimaion mehods. The challenge involved in cash selemen is o ensure ha he selemen process be air and orderly so ha uures prices properly relec underlying asse values during he inal days o rading. I his does no occur, he hedging and price discovery uncions o uures markes are compromised. Cornell (1997) summarizes hree ypes o problems ha can cause cash-seled uures prices o diverge rom rue equilibrium prices. The underlying asse or an individual share uures (ISF) conrac is a sock. There is no grade heerogeneiy problem and he delivery cos is negligible. Physical delivery mehod is considered o be appropriae. Ausralian ISF conracs were seled in cash when hey were irs inroduced in Sydney Fuures Exchange (SFE). Aer wo years, SFE decided o swich rom cash selemen o physical delivery. Several raionales were provided by SFE. One o hem is he improvemen o hedging uncion. Consider an equiy call wrier who buys he ISF o reduce risk exposure in he opions marke. Under physical delivery mehod he obains he sock a he mauriy o he ISF. Wih he sock in hands, he can make delivery o he sock a he selemen o he opions conrac and perecly achieve his hedging objecive. Cash selemen mehod o he ISF concludes wih cash ranserring. To sele he opions conrac, he call wrier has o ener ino he spo marke o purchase he sock. I he cash-seled uures prices are no equal o 3

4 he sock price, he price risk in he uures marke is incurred. The eec o hedging risk exposure in he opions marke wih he ISF could be aeced adversely. This paper presens he irs aemp o measure he impac o selemen mehod change on Ausralian individual sock and is uures markes. Speciically, we invesigae he eec on he reurns and volailiy o each marke, he correlaion beween he wo markes, he basis behavior, and he hedging perormance o he uures conracs. An error correcion-bivariae GARCH model (EC-BGARCH) is proposed. Error correcion erms are included in he condiional mean equaions o preserve he long-erm equilibrium relaionship beween spo and uures markes. The ime-varying variance and covariance srucure o he wo markes is described by a bivariae GARCH model. Daily daa is used o esimae he EC-BGARCH model. Dynamic opimal hedge raios and hedging eeciveness are obained rom he esimaion o he ime-varying variance-covariance marix and hen are evaluaed beore and aer he conracs were swiched rom cash selemen o physical delivery. In addiion, he eec o he selemen mehod on he basis behavior is analyzed. We ind ha he swich rom cash selemen o physical delivery improves hedging perormance o he uures marke, srenghens he comovemen beween uures and spo markes while promoing marke volailiy in boh uures and spo markes. The variabiliy o basis also becomes higher during he physical delivery period. The remainder o he paper is organized as ollows. In he nex secion we discuss he daa and provide a preliminary saisical analysis. The EC-BGARCH model is described in Secion 3 along wih he esimaion resuls. Opimal hedge raios and hedging eeciveness are analyzed in Secion 4. Secion 5 devoes o he saisical analysis o he basis. Finally, Secion 6 concludes he paper. 4

5 2. Daa and Preliminary Analysis Ausralian ISF conracs were inroduced in 1994 on SFE. Each ISF conrac is priced on he basis o 1,000 shares o he underlying sock. Prior o March 1996, he ISF conracs were seled in cash. On March 29, 1996, SFE modiied rules o swich ISF conracs o Broken Hill Proprieary, Ld. (BHP), Wesern Mining (WMC), and Rio Tino (RIO) rom cash selemen o physical delivery o shares. Seven addiional ISF conacs were swiched a laer daes when heir respecive cash-seled conracs expire. Telsra Corporaion is he sole excepion. The uures conrac o Telsra Corporaion has been seled in cash since i was irs inroduced in November Table 1 repors names o he socks, codes o he socks, lising daes o heir corresponding uures conracs, and he swiching daes rom cash selemen o physical delivery or each pair o sock and is uures prices being analyzed, respecively. Daily closing prices o individual socks and heir corresponding uures conracs are used in his sudy. The price series are colleced rom Daasream. The sample period covers rom he irs day o each ISF conrac being lised (see Table 1) o May A single uures price series or each ISF conrac is consruced using closing prices rom he nearby conrac wih rolling over a he beginning o he delivery monh o he nex nearby conrac. The daa poin is removed i a missing value occurs in eiher sock or uures price a ha day. Table 2 repors he summary saisics o mean, sandard deviaion, skewness, and kurosis on each pair o reurn series during he cash selemen period, he physical delivery period, and he complee sample, respecively. The mos eviden change is ha, aer he ISF conracs were swiched rom cash selemen o physical delivery, he sandard deviaions across each o spo and uures markes excep he FBG uures marke increased rapidly, ranging rom 3% up o more han 5

6 70%. Thus i appears ha boh spo and uures markes were more volaile during he physical delivery period. Beore discussing he model used in his sudy, we perorm uni roo and coinegraion ess on he price and reurn series. According o he cos-o-carry heory, uures and spo prices should move up and down ogeher in he long run whereas shor-run deviaions rom he longrun equilibrium may ake place due o mispricing o uures or spo price. This lays ou he oundaion or a coinegraed sysem o uures and spo prices. Thereore, we irs perorm augmened Dickey-Fuller (1981) es on each spo and uures price series and heir irs dierences o invesigae he saionariy o he price and price change series. I he price series o spo and uures are no saionary bu he changes o prices are saionary, he coinegraion concep becomes relevan. We hen use he Engle and Granger (1987) mehod o es wheher spo and uures prices are coinegraed. Le p s and p denoe he naural logarihm o he sock and is uures prices a ime, respecively. The changes o spo and is uures prices a ime are calculaed as p s = p s p s, 1 and p = p p, 1, respecively. For each price series, we consider he ollowing equaions. k 1 (1) p = γ p + ψ i p i + µ i= 1 1. (2) p = α + γp + 1 ψ i p i + µ = 1 (3) p = α + β + γp + 1 ψ i p i + µ = 1 k 1 i The null hypohesis in all hree cases is ha γ = 0 ; i he null canno be rejeced, he price series conains a uni roo, and hence i is non-saionary. We use he Schwarz Bayesian crierion k 1 i 6

7 (Schwarz, 1978) o deermine k, he number o lags in equaions (1)-(3). We hen esimae he above equaions or each pair o price series and es he null hypohesis. To save he space, he es saisics rom equaion (3) are repored in he irs wo columns o Table 3. The null hypoheses o a uni roo or hese series are no rejeced a he 5% level (excep wo series a he 1% level) indicaing ha all he pairs o spo and uures price series are non-saionary 1. The augmened Dickey-Fuller es is also applied o he changes o spo and uures price series as well as he basis series, B, calculaed as B = p p. The resuls rom equaion (3) are s repored in columns 3-5 o Table 3, respecively. The null hypoheses o a uni roo or he change in price and he basis series are rejeced a he 1% level, which concludes ha he price change and basis series are saionary. We now use he Engle-Granger (1987) coinegraion es o examine he sysem o uures and sock prices. The es is based on assessing wheher single-equaion esimaes o he equilibrium errors appear o be saionary. As repored in he las column o Table 3, he null hypohesis o no coinegraion beween uures and spo prices is rejeced or each pair o price series a he 1% level. This suggess ha each pair o sock and is uures prices are coinegraed. This inding is consisen wih he predicion o he cos-o-carry heory. 3. EC-BGARCH Model Our main objecive is o examine marke volailiy and he hedging perormance o a uures marke under dieren selemen schemes. Esimaion o he variance-covariance marix o uures and spo reurns becomes crucial o achieve he objecive because he variance o he asse reurn measures marke volailiy. Moreover, hedge raio and hedging eeciveness are wo 1 The criical values o he -saisics depend on he equaion being esimaed. The criical values o Enders (1995) are used. 7

8 imporan elemens or consrucing hedging sraegies, carrying ou he ask o risk managemen, and evaluaing he hedging perormance. The calculaions o hedge raio and hedging eeciveness require esimaes o he variance-covariance marix o spo and uures reurns. I is now well recognized ha correlaion and volailiy o asse reurns are ime-varying. To accoun or his saisical propery, mulivaraie GARCH (MGARCH) models are widely adoped; see, e.g., Baillie and Myers (1991), Kroner and Claessens (1991), Lien and Luo (1994), and Karolyi (1995). Dieren model speciicaions and resricions on he condiional variancecovariance marix in he MGRACH model have been inroduced o overcome he compuaional diiculy, o ensure a posiive deinie variance-covariance marix, and o provide beer goodness o is o he daa. For insance, here are he VECH model o Bollerslev, Engle, and Wooldridge (1988), he CCORR model o Bollerslev (1990), he FARCH model o Engle, Ng, and Rohschild (1990), he BEKK model o Engle and Kroner (1995), he ADC model o Kroner and Ng (1998), and he DCC model o Engle (2000). Each o hese models has advanages and shorcomings, and may i ino one se o daa beer han ohers 2. In his sudy, we use he BEKK represenaion o esimae he condiional ime-varying variance-covariance marix o uures and spo reurns. This model ensures a posiive variancecovariance marix and i is our daa very well. In addiional, o accommodae he saisical properies ideniied in he previous secion, we use he error correcion model o characerize he coinegraed sysem o uures and spo prices. Thus, we propose an error correcion-bivariae GARCH (EC-BGARCH) model. The condiional mean equaions are given by 2 For he comparison o hese models, see Kroner and Ng (1998) and Engle (2000). 8

9 p q 0 1, i= 1 j= 1 (4) Rs = α s + α si Rs, i + β sj R, j + φs B + γ s D + ε s p q 0 1, i= 1 j= 1 (5) R = α + α i Rs, i + β j R, j + φ B + γ D + ε where R s and R denoe he reurns o sock and uures, which equal o ps and p, respecively. p and q are he numbers o lags in he model. D is a dummy variable a ime ha equals o zero or he cash selemen period and one or he physical delivery period. The dummy variable is included ino he sysem o gauge he eecs o he change in he selemen mehod. The coeiciens, γ s and γ, measure he impac o physical delivery on he spo and uures reurns, respecively. The basis a ime -1, B 1, serves as he error correcion erm. When he spo reurn exceeds he uures reurn a ime -1 (i.e., B > 1 0 ), he spo price ends o be decreasing whereas he uures price ends o be increasing a ime in order o mainain he long-erm relaionship beween uures and spo prices. Similarly, when he spo price alls below he uures price a ime -1 (i.e., B < 1 0 ), he spo price ends o be increasing and he uures price ends o be decreasing in he nex period. This would lead one o predic ha φ 0 and φ 0. s The condiional variance-covariance marix o residual series, E =, is denoed ' ( ε s, ε ) by hs hs Var ( ε s, ε I 1) H =, hs h where I is he inormaion se a ime. The ime-varying variance-covariance marix is generaed by 9

10 c11 c12 c11 c12 a11 a12 a11 a ' 12 (6) H = + E 1E 1 + c21 c22 c21 c22 a21 a22 a21 a22 ' ' g g g g H 1 g g g g ' s + s s D This represenaion is he bivariae case o he BEKK (1,1) model proposed by Engle and Kroner (1995). I capures he dynamic srucure o variances as well as he covariance o asse reurns. The dummy variable D is included in he variance equaion o capure he eec o he change in he selemen mehod on he condiional variance o sock reurns, he condiional variance o uures reurns, and he condiional covariance beween uures and spo reurns. The values o s,, and s measure he magniude and signiican levels o he eecs, respecively. A wo-sep esimaion mehod is used 3. We irs esimae he mean equaions o obain he residuals ε s and ε using he ordinary leas squares (OLS) mehod 4. We hen rea ε s and ε as observed daa o esimae he parameers in he condiional variance-covariance marix using he maximum likelihood mehod. Beore esimaing he mean equaions, we use he Schwarz Bayesian crierion (Schwarz, 1978) o deermine p and q, he number o lags in he mean equaions. Esimaion resuls are repored in Tables 4 and 5, respecively. A number o observaions can be made across he mean equaions in Table 4. Firs, he eecs o he lagged sock reurns on he curren sock reurns are signiicanly posiive or 8 ou o 11 socks, whereas he eecs o he lagged uures reurns on he curren sock reurns are signiican or 5 ou o 11 socks, wo wih posiive eecs and hree wih negaive eecs. The eecs o lagged 3 For he wo-sep esimaion procedure, see, or example, Pagan and Schwer (1990) and Engle and Ng (1993). 4 I is well known in he lieraure on coinegraion beween convenional I(1) processes ha he OLS esimaor o he coinegraing vecor is super-consisen (see, or insance, Sock (1987)). For he heeroskedasic coinegraion sysem, e.g., coinegraed regression model wih errors displaying nonsaionary variances, as our model speciicaion, Hansen (1992) developed an asympoic heory o esimaion and inerence and demonsraed ha he OLS esimaion would also yield consisen esimaes o he sochasically coinegraing vecor. 10

11 sock and uures reurns on he curren uures reurns are more consisen across each pair o markes. Wih he excepion o WMC, lagged sock reurns have signiicanly posiive eecs while lagged uures reurns have signiicanly negaive eecs on he curren uures reurn. The above observaions sugges ha boh sock and uures reurns ollow a mean-reversing process. In addiion, he inormaion in he spo marke is more relevan in predicing he price movemen in he uures marke when compared wih he predicion o spo price movemen using he inormaion in he uures marke. Secondly, as prediced by he basis convergence, he lagged basis has a signiican posiive eec on he curren uures reurns or 8 o 11 uures markes, suggesing ha he uures price ends o move closer o he spo price. In conras, he eecs o he lagged basis on he curren sock reurns are no signiican across each sock marke. This implies ha he uures marke ends o ollow he movemen o he spo marke in order o mainain he longerm relaionship. Finally, he resuls in Table 4 show ha he swich rom cash selemen o physical delivery has no eec on he sock reurns and a negaive eec on wo uures reurns o MIM and RIO 5. In summary, he above resuls sugges ha individual sock marke ends o lead he corresponding uures marke. This lead-lag paern diers rom wha we have observed in oher markes. For example, Chan (1992) documened ha sock index uures marke leads he cash marke. Garbade and Silber (1983) ound ha he commodiy uures markes dominae cash markes. Dieren indings o he inormaional role and price discovery uncion o a uures marke may arise rom dieren inensiies o rading aciviy in spo and uures markes. Chan (1992) argued ha lower rading aciviy means ha he securiy is less requenly raded and 5 The TEL uures conrac has been seled in cash since i was inroduced. Thereore, he swich eec analysis does no apply on i. 11

12 hereore observed prices lag rue values more. In Ausralia, he individual sock uures conracs are raded ar less requenly han heir corresponding socks. Daily average rading volume raio o he individual sock o is uures during he sample period varies rom 150 o 2,000 across each marke being analyzed. This could cause he lead-lag relaion beween spo and uures markes o avor individual socks 6. Admai and Pleiderer (1988) showed ha boh liquidiy and inormed raders preer o cluser heir rades wih each group when he marke is hick. The clusering o rades causes more inormaion o be released. Thereore, he spo marke can play he leading role in disseminaing he inormaion when rading o he sock is inensiy. Table 5 presens he esimaion resuls o he variance and covariance marix. The values o a 11, a 22, g 11, and g 22 across each pair o he spo and uures markes are posiive and saisically signiican dieren rom zero. The value o g 21 is also posiive and saisically signiicanly dieren rom zero or 8 o 11 pairs whereas he value o a 21 is negaive and saisically signiicanly dieren rom zero or all he pairs. The value o a 12 is insigniican excep or BHP and NCP. The value o g 12 is insigniican excep or BHP and PDP. These resuls sugges ha he GARCH eec dominaes he ARCH eec in boh spo and uures markes 7. Thus, he volailiies in boh markes are more persisen, i.e., a high volailiy ends o remain or a longer period. The covariance beween spo and uures markes is also persisen. 6 We use an AR process o reduce he eecs o inrequen rading in he individual share uures markes suggesed by Chan (1992), hen use he reurn innovaions derived rom he AR model o proxy or rue reurns. The resuls are similar o hose observed above. 7 The eec s o he error erm E 1 on H and H 1 on H are denoed as he ARCH and GARCH eecs, respecively. I he value o he combinaion o elemens in he E 1 and heir corresponding coeiciens is greaer han ha o he combinaion o elemens in he H 1 and heir corresponding coeiciens, hen we conclude he ARCH eec is dominae he GARCH eec, oherwise, he GARCH eec dominaes he ARCH eec. 12

13 The curren covariance o spo and uures reurns is highly correlaed wih he pas covariance o wo markes. O paricular ineres, we now discuss he esimaed coeiciens s,, and s in equaion (6), which capure he eec o he swich rom cash selemen o physical delivery on he variances o spo and uures reurns, and he covariance beween he wo reurns. To ensure he nonnegaive deinieness o H during he esimaion, we ransorm he coeicien marix o he dummy variable o he produc o wo idenical vecors, Z = ( z 1 z 2 ), i.e., s s s = Z Z. Due o he ransormaion, he values o and are always posiive even when he values o z 1 and z 2 are negaive. Thus, a posiive value o s s or does no always imply a posiive eec on he variance o each marke. To avoid oversaing he posiive eec, we base on he esimaed values o z 1 and z 2 and heir corresponding saisics o draw our conclusion. The esimaed values o z 1 and z 2 along wih heir corresponding saisics are repored in Table 5. The values o s,, and s are calculaed based on he ransormaion and also repored in Table 5 8. For 7 o 10 cases, he values o z 1 are posiive and signiicanly dieren rom zero. For he res o 3 cases, he values o z 1 are negaive and signiicanly dieren rom zero. Thus, he swich rom cash selemen o physical delivery has signiicanly posiive eecs on he sock variances in a leas 7 o 10 socks. Signiicanly posiive eecs on he uures variances prevail or a leas 5 o 10 cases. The covariance beween uures and sock reurns also increases signiicanly in 7 o 10 cases. In sum, boh uures and spo markes become more 8 The saisics or z 1 and z 2 canno be ransormed ino hose or s and s. 13

14 volaile and he covariance beween wo markes becomes larger aer physical delivery mehod is adoped. To recas, he spo reurn does no respond o selemen mehod change whereas only wo uures reurns display negaive eecs. Meanwhile, mos uures and sock markes become more volaile and he covariances beween uures and sock reurns become larger during he physical delivery period. 4. Opimal Hedge Raio and Hedging Eeciveness In his secion, we direcly es he Sydney Fuures Exchange claim o improving hedging eeciveness by swiching o he physical delivery mehod. Assume ha a hedger uses he uures marke o hedge he risk o he spo marke. The ime-varying opimal hedge raio 9 under he minimum-variance ramework a ime 1 is calculaed as he condiional covariance divided by he condiional variance o he uures reurn 10 : (7) HR Cov R, R I ) / Var( R I ). 1 = ( s 1 1 Esimaes o { HR} series can be generaed rom he esimaion resuls o equaion (6). The nonparameric es o Wilcoxon sum rank is applied o es he dierences o he mean and variance o he opimal hedge raio series beween he physical delivery period and he cash selemen period. The null hypohesis is ha he mean and variance o he opimal hedge raio series during he cash selemen period is he same as hose during he physical delivery period. The alernaive hypohesis is ha he mean and variance o he opimal hedge raio series during 9 The hedge raio is he raio o he posiion aken in he uures conracs ha ose he size o he exposure in he spo marke. 10 I uures prices ollow a maringale process, hen he minimum-variance opimal hedge raio is also he expeceduiliy-maximizing hedge raio or a hedger wih a quadraic uiliy uncion. See, or example, Anderson and Danhine (1980), Ederingon (1979), and Malliars and Urruia (1991), among ohers. 14

15 cash selemen period is less han hose during he physical delivery period. The resuls o es saisics and heir P-values are repored in Table 6 along wih he mean and variance or he complee sample period, he cash selemen period, and he physical delivery period. The resuls show ha he average opimal hedge raio becomes higher aer he swich rom cash selemen o physical delivery in every case. Wih physical delivery, he hedger receives he underlying sock direcly and applies i o ose he spo posiion. Cash selemen, on he oher hand, requires he hedger o ener he spo marke or anoher round o rading i he sock is desirable. In addiion, wih cash selemen here is likely a mismach in iming beween he liquidaion o spo and uures posiions. Thus, hedging becomes more eecive when physical delivery replaces cash selemen and he opimal hedge raio increases accordingly. Figures 1-3 show he daily hedge raios o ANZ, PDP, and WMC. The larges increase o he average opimal hedge raio is PDP (rom o 0.812) while WMC presens he smalles increase aer physical delivery is adoped. ANZ represens an inermediae case. Noe also ha he variabiliy o he opimal hedge raio has no signiican changes. The variaion o hedge raio becomes larger aer he selemen mehod changes rom cash selemen o physical delivery or 3 o 10 uures conracs bu none o hem is saisically signiican. Following Ederingon (1979), he hedging eeciveness is measured by he squared covariance divided by he produc o spo and uures reurn variances: 2 (8) HE Cov R, R I ) / Var( R I ) Var( R I ). = ( s 1 s 1 1 Esimaes o { HE } series can also be derived rom he esimaion resuls o equaions (6). Again, he nonparameric es o Wilcoxcon sum rank is applied o es or he dierence o mean and variabiliy o hedging eeciveness beween cash selemen and physical delivery periods. Summary saisics o he series are provided in Table 7. Wih he excepion o BHP, MIM, and 15

16 NCP, he hedging eeciveness improves signiicanly aer he cash selemen is replaced by physical delivery. For BHP, MIM, and NCP, hey decrease minimally on average rom o 0.825, rom o 0.750, and rom o 0.834, respecively. The larges improvemen appears in he mos recenly esablished individual share uures conracs, FBG, PDP, RIO, and WBC. For example, he average hedging eeciveness o PDP increases rom 0.45 in he cash selemen period o 0.72 in he physical delivery period a more han 100% increase. The variabiliy o hedging eeciveness is very small relaive o he mean in boh periods and some o hem are indisinguishable. The comparisons o hedging eeciveness conirm he claim made by he Sydney Fuures Exchange. Aer swiching rom cash selemen o physical delivery, he individual share uures conrac becomes a more eecive hedging insrumen. The larges improvemen is made in he mos recenly esablished conracs. 5. Eec on Basis In his secion, we adop an AR(k)-GARCH model o examine he impac o he swich rom cash selemen o physical delivery on he basis behavior. The basis is expeced o converge o zero a he mauriy. Beore he mauriy, he variaion o he basis deermines he hedging perormance o a uures conrac. To model he ime-varying basis, he condiional mean and variance equaions are given as ollows: (9) B = β + β ib i + ψd + η k 0, i= (10) σ = δ 0 + δ1σ 1 + δ 2η 1 + φd, 16

17 where B and 2 D are deined as beore. σ = var( η Ω 1). We use he Schwarz Bayesian crierion (Schwarz, 1978) o choose he number o lags, k. The quasi-maximum likelihood mehod is used o esimae he parameers o he condiional mean and variance equaions (9) and (10) joinly. The coeicien esimaes and heir -values or each basis series are repored in Table 8. The resuls rom he mean equaion show ha he lagged basis has a signiicanly posiive eec on he curren basis. Thus, a large basis ends o be ollowed by anoher large basis, displaying a srong persisence. From he esimaes o ψ, i indicaes ha he swich rom cash selemen o physical delivery has no eec on he basis, which is consisen wih Lien and Tse (2002). For he variance equaion, he GARCH eec dominaes he ARCH eec or he irs seven basis series. The mos recen wo basis series, RIO and PDP, display a much sronger ARCH eec and a much weaker GARCH eec. The swich rom physical delivery o cash selemen has a saisically signiican impac on he basis variance or ive (BHP, NCP, FGB, RIO, and PDP) ou o en series. Wih he excepion o FGB, he basis becomes more volaile aer he selemen mehod changes, which is consisen wih Lien and Tse (2002). Tha is, cash selemen provides a cheaper alernaive or arbirages and hence promoes he convergence beween spo and uures markes. 6. Conclusions We adop a bivariae GARCH model wih error correcion o invesigae he eecs o he swich rom cash selemen o he Ausralian individual share uures conracs o physical delivery on individual sock and is corresponding uures markes. We ind ha he change has no signiican eec on he level o he sock reurns and has some minimal eec on he level o 17

18 he uures reurns. Boh sock and is uures markes become more volaile, he covariance beween wo markes increases, and he variabiliy o basis becomes higher aer physical delivery is adoped. When examining he eec o selemen mehods on he dynamic opimal hedge raios, we ind ha he level o he opimal hedge raio series has been increased. The average opimal hedge raio increases in all he uures markes being analyzed. The examinaion o he hedging eeciveness shows ha all individual share uures conracs (excep BHP, MIM, and NCP) have become more eecive hedging insrumens aer he selemen mehod change. The improvemen in hedging eeciveness is paricularly impressive or he mos recenly esablished individual share uures conracs. 18

19 Table 1: Ausralian Individual Share Fuures Conracs: Names and Codes o Underlying Socks, Lising Daes, and Swiching Daes o Selemen Mehod Company Name Code Lising Dae Swiching Dae Ausralia and New Zealand Banking Group ANZ March 13, 1995 April 26, 1996 Broken Hill Proprieary, Ld. BHP May 16, 1994 March 29, 1996 Fosers Brewing Group FBG March 13, 1995 April 26, 1996 Moun Isa Mines Holdings MIM Sep. 26, 1994 April 26, 1996 Naional Ausralia Bank NAB May 16, 1994 April 26, 1996 News Corporaion NCP May 16, 1994 May 31, 1996 Paciic Dunlop PDP Oc. 18, 1995 May 31, 1996 Rio Tino RIO March 13, 1995 March 29, 1996 Wesern Banking Corporaion WBC Sep. 26, 1994 April 29, 1996 Wesern Mining Corporaion WMC Sep. 26, 1994 March 29, 1996 Telsra TLS Nov. 28,

20 Table 2. Summary o Saisics on Cash and Fuures Markes All Sample Cash Selemen Physical Delivery Reurns Spo Fuures Spo Fuures Spo Fuures ANZ Mean STD Skewness Kurosis BHP Mean STD Skewness Kurosis FBG Mean STD Skewness Kurosis MIM Mean STD Skewness Kurosis NAB Mean STD Skewness Kurosis NCP Mean STD Skewness Kurosis PDP Mean STD Skewness Kurosis RIO Mean STD Skewness Kurosis WBC Mean STD Skewness Kurosis WMC Mean STD Skewness Kurosis TLS Mean STD Skewness Kurosis

21 Table 3. Uni Roo and Coinegraion Tes Resuls Spo Price Fuures Price Spo Reurn Fuures Reurn Coinegraion Cash Selemen ANZ BHP FBG MIM NAB NCP PDP RIO WBC WMC TLS Physical Delivery ANZ BHP FBG MIM NAB NCP PDP RIO WBC WMC All Sample ANZ BHP FBG MIM NAB NCP PDP RIO WBC WMC TLS

22 Table 4: Esimaion Resuls or Mean Equaions R s α s0 α s1 α s2 α s3 β s1 β s2 β s3 φ s ANZ (1.087) (-1.196) (-2.131)** (2.70)+ (1.737)* (-2.34)** (0.294) (-0.291) BHP (0.507) (1.128) (-0.993) (0.035) (0.037) (0.094) (-0.611) (0.453) (-0.286) FBG (0.790) (-0.647) (1.263) (-2.50)+ (-0.248) (-0.286) MIM (-0.785) (0.687) (-2.97)+ (-2.47)+ (1.067) (1.496) (1.767)* (-0.401) (0.591) NAB (-0.238) (1.076) (-1.691) (1.615) (0.272) (-0.163) (1.386) NCP (0.247) (1.224) (0.174) (0.537) (0.075) (-0.752) (-1.279) (0.210) (0.380) PDP (-0.546) (-1.911)* (-2.61)+ (0.514) (1.583) (-0.861) (-0.256) RIO (0.221) (2.99)+ (0.803) (-0.850) (-2.31)** (-1.599) (-0.113) (0.093) WBC (1.235) (2.62)+ (-0.030) (-1.138) (-1.078) (-0.111) WMC (0.231) (3.01)+ (-3.58)+ (0.793) (0.133) (-0.148) TLS (0.582) (-0.864) (-1.890)* (5.74)** (1.459) (-1.190) φ R α 0 α 1 α 2 α 3 β 1 β 2 β 3 ANZ (1.535) (6.69)+ (1.581) (-4.9)+ (-1.330) (-2.55)+ (3.41)+ (-0.398) BHP (0.961) (11.4)+ (5.39)+ (3.03)+ (-10.0)+ (-6.0)+ (-3.48)+ (1.429) (-0.664) FBG (-0.418) (4.18)+ (-5.26)+ (-0.981) (2.60)+ (0.759) MIM (3.78)+ (5.73)+ (0.461) (-0.855) (-3.84)+ (-1.86)* (0.068) (6.02)** (-2.394)** NAB (-0.298) (8.28)+ (3.09)+ (-6.04)+ (-4.6)+ (3.89)+ (1.322) NCP (0.112) (10.2)+ (6.41)+ (4.40)+ (-9.06)+ (-6.9)+ (-4.8)+ (0.037) (0.615) PDP (-0.677) (5.93)+ (1.503) (-7.5)+ (-3.4)+ (2.86)+ (0.506) RIO (3.15)+ (13.5)+ (7.36)+ (3.15)+ (-13.9)+ (-9.2)+ (-4.61)+ (4.02)+ (-2.80)+ WBC (1.493) (8.43)+ (1.533) (-7.2)+ (0.842) (-0.280) WMC (3.59)+ (3.90)+ (-3.86)+ (0.287) (9.86)+ (-1.097) TLS (1.557) (4.33)+ (2.155)** (-9.3)+ (-3.4)+ (1.906)* The number wihin he parenhesis is he corresponding saisics. *, **, and + denoe signiican levels o 10%, 5%, and 1%, respecively. γ s γ 22

23 Table 5: Esimaion Resuls or Variance Equaions c c c 22 a 11 a 21 a 12 a 22 g 11 g 21 g 12 g 22 z 1 z 2 s s ANZ (6.16)+ (1.86)* (8.32)+ (4.88)+ (-2.69)+ (-0.46) (6.88)+ (12.3)+ (2.19)** (0.78) (9.53)+ (3.87)+ (1.49) BHP (3.55)+ (2.71)+ (13.5)+ (7.16)+ (-4.66)+ (-2.80)+ (8.08)+ (61.5)+ (4.42)+ (1.72)* (50.4)+ (3.97)+ (3.15)+ FBG (3.28)+ (0.62) (2.03)** (2.52)+ (-3.85)+ (-0.23) (6.30)+ (23.5)+ (3.03)+ (0.31) (24.5)+ (-1.75)* (-0.74) MIM (6.38)+ (1.70)* (4.71)+ (4.71)+ (-5.89)+ (-0.15) (10.6)+ (62.0)+ (4.97)+ (-0.17) (56.2)+ (4.02)+ (-1.63) NAB (6.76)+ (0.55) (9.30)+ (5.16)+ (-5.71)+ (-0.91) (8.78)+ (16.3)+ (4.22)+ (1.19) (10.3)+ (3.34)+ (6.89)+ NCP (7.38)+ (6.89)+ (8.76)+ (4.23)+ (-3.02)+ (-2.95)+ (5.35)+ (44.3)+ (2.75)+ (-1.21) (41.5)+ (5.30)+ (4.23)+ PDP (4.72)+ (4.05)+ (3.75)+ (4.77)+ (-4.34)+ (1.52) (8.69)+ (29.0)+ (-0.07) (-1.69) (45.2)+ (-4.66)+ (-4.18)+ RIO (3.07)+ (0.71) (0.95) (4.44)+ (-15.8)+ (-0.95) (18.2)+ (56.8)+ (15.5)+ (0.82) (22.7)+ (-4.95)+ (5.08)+ WBC (5.44)+ (3.21)+ (13.3)+ (5.54)+ (-3.77)+ (-0.89) (7.51)+ (15.0)+ (3.26)+ (-0.05) (10.8)+ (4.96)+ (3.09)+ WMC (3.12)+ (1.59) (15.4)+ (3.68)+ (-2.73)+ (-1.03) (5.02)+ (35.5)+ (2.77)+ (0.44) (29.2)+ (1.71)* (0.75) TLS (7.96)+ (5.21)+ (1.62) (5.38)+ (-5.14)+ (-0.91) (11.2)+ (10.3)+ (-0.38) (0.26) (53.5)+ The number wihin he parenhesis is he corresponding saisics. The values o s,, and s have been increased by *, **, and + denoe signiican levels o 10%, 5%, and 1%, respecively. 23

24 Table 6: Opimal Hedge Raios All Sample Cash Selemen Mean Variance Physical Delivery Tes Saisics P-Value All Sample Cash Selemen Physical Delivery Tes Saisics P-Value ANZ BHP FBG MIM NAB NCP PDP RIO WBC WMC

25 Table 7: Hedging Eeciveness All Sample Cash Selemen Mean Variance Physical Delivery Tes Saisics P-Value All Sample Cash Selemen Physical Delivery Tes Saisics P-Value ANZ BHP FBG MIM NAB NCP PDP RIO WBC WMC

26 Table 8: Esimaion Resuls or he Eec on Basis Behavior β 0 β 1 β 2 β 3 β 4 β 5 ψ δ0 δ1 δ2 φ ANZ (0.076) (9.035)+ (6.524)+ (3.276)+ (1.574) (0.058) (0.595) (0.307) (0.595) (0.112) BHP (0.876) (11.35)+ (6.126)+ (3.526)+ (4.337)+ (-0.698) (1.184) (8.508)+ (1.184) (2.551)+ FBG (1.072) (11.47)+ (7.473)+ (1.758)* (2.092)** (-1.361) (2.689)+ (4.344)+ (2.689)+ (-3.184)+ MIM (4.029)+ (8.023)+ (2.767)+ (3.189)+ (1.342) (-1.769)* (1.260) (2.786)+ (1.260) (0.879) NAB (-0.920) (8.839)+ (4.740)+ (3.753)+ (1.691) (1.172) (1.386) (0.719) (1.386) (1.055) NCP (1.881)* (3.469)+ (3.475)+ (4.518)+ (-1.220) (-1.638) (2.421)+ (6.720)+ (2.620)+ (2.620)+ RIO (0.509) (7.954)+ (3.141)+ (-1.067) (-1.810)* (4.260)+ (0.534) (2.743)+ (2.743)+ PDP (-1.428) (8.008)+ (-0.503) (2.137)** (0.988) (2.962)+ (0.674) (1.805)* (1.805)* WBC (-1.313) (2.831)+ (5.109)+ (2.145)** (1.648) (1.800)* (0.671) (0.671) (8.277)+ (2.091)** (0.985) WMC (2.365)** (11.44)+ (5.544)+ (2.896)+ (2.955)+ (-1.584) (1.773)* (7.671)+ (1.773)* (1.480) The number wihin he parenhesis is he corresponding saisics. *, **, and + denoe signiican levels o 10%, 5%, and 1%, respecively. 26

27 Figure 1: ANZ Opimal Hedge Raio /23/1995 5/23/1995 7/23/1995 9/23/ /23/1995 1/23/1996 3/23/1996 5/23/1996 7/23/1996 9/23/ /23/1996 1/23/1997 3/23/1997 5/23/1997 7/23/1997 9/23/ /23/1997 1/23/1998 3/23/1998 5/23/1998 7/23/1998 9/23/ /23/1998 1/23/1999 3/23/1999 5/23/1999 7/23/1999 9/23/ /23/1999 1/23/2000 3/23/2000 5/23/2000 7/23/2000 9/23/ /23/2000 1/23/2001 3/23/2001 Figure 2: PDP Opimal Hedge Raio /30/ /30/1995 2/29/1996 4/30/1996 6/30/1996 8/30/ /30/ /30/1996 2/28/1997 4/30/1997 6/30/1997 8/30/ /30/ /30/1997 2/28/1998 4/30/1998 6/30/1998 8/30/ /30/ /30/1998 2/28/1999 4/30/1999 6/30/1999 8/30/ /30/ /30/1999 2/29/2000 4/30/2000 6/30/2000 8/30/ /30/ /30/2000 2/28/2001 4/30/2001 Figure 3: WMC Opimal Hedge Raio /7/ /7/1994 2/7/1995 4/7/1995 6/7/1995 8/7/ /7/ /7/1995 2/7/1996 4/7/1996 6/7/1996 8/7/ /7/ /7/1996 2/7/1997 4/7/1997 6/7/1997 8/7/ /7/ /7/1997 2/7/1998 4/7/1998 6/7/1998 8/7/ /7/ /7/1998 2/7/1999 4/7/1999 6/7/1999 8/7/ /7/ /7/1999 2/7/2000 4/7/2000 6/7/2000 8/7/ /7/ /7/

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