BASIS RISK IN FINNISH STOCK INDEX FUTURES

Transcription

1 Lappeenrana Universiy of Technology School of Business Finance BASIS RISK IN FINNISH STOCK INDEX FUTURES Esa Koponen Bachelor s hesis Suden number

2 TABLE OF CONTENTS 1 INTRODUCTION THEORETICAL BACKROUND Pricing of he fuures conracs Index Arbirage Basis Risk Price paerns of fuures Feaures of fuures prices Saisical mehods DATA OMX25 fuures series OMX25 Index RESEARCH METHODOLOGY AND RESULTS Cos of carry Basis risk Explaining basis CONCLUSION REFERENCES

3 1 INTRODUCTION One of he growing produc groups in he field of finance are differen derivaive insrumens. Sock index fuures are par of he group of equiy fuures. For an invesor holding a porfolio of Finnish socks, one way he hedge he posiion is o use sock index fuures. If invesor prefers o hedge he porfolio wih fuures, obained fuures posiion ofen requires a cross hedge, where fuures conrac doesn mach he underlying porfolio. Anoher difficuly is o adjus he iming of he hedge; using fuures his means aking shor/long posiions and closing he hedge before he delivery monh of he conrac. These difficulies expose invesor o basis risk. This variey beween fuures and cash price is deermined by fuures marke price minus curren spo price (which should be he expeced fuures price). Increase in volailiy of he underlying index, increases invesors demand for hedge. Rise in volailiy should increase open ineres in fuures conracs and herefore reflec ino fuures prices. Several papers have sudied relaionships beween sock and fuures markes. Chen e al. (1995) sudied effec of sock volailiy o basis risk and open ineres in S&P 500 fuures conracs. Figlewski (1984) examined basis and differen sources of basis risk also wih S&P 500 daa. The presence of basis risk where esed agains hedging performance of fuures conracs. Chan (1992) esed he lead-lag relaionship beween cash and fuures marke and how lead-lag paerns vary wih changing condiions. General resuls of earlier sudy have shown ha, fuures lead cash marke, unsysemaic risk(basis) affecs hedging performance, main sources of basis risk arises from duraion of he hedge and ime-o-expiraion, basis decreases when volailiy of underlying index increases whereas open ineres increases wih he volailiy of cash index. 3

4 However, esing basis risk wih Finnish daa enables updaed field of research. Hieala e al. (1994), (2000) sudied Finnish sock index fuures, offering explain o coninuous under pricing of Finnish index fuures compared o heoreical pricing. Differen approaches have been used when explaining he differences like marke resricions and informaion lags. Puonen (1992) esed pu-call-spo pariy and pucall-fuures pariy and he possibiliy of index arbirage. In general, previous esing has been carried ou wih relaively old daa. The daa of previous esing have usually obained from he end of he 1980 s o beginning of 1990 s. Regulaions of Finnish capial markes have changed, making shor sales possible compared o earlier sudies. Basis risk is esed wih newer daa and more opical resuls are ried o obain. Main resuls wih Finnish daa show ha shor sale consrain cause deviaion in fuures pricing and make sock prices less informaive In his paper, he behavior of he basis risk is sudied in Finnish sock index fuures. I s also examined how changes in volailiy of he underlying index affec he basis risk. Magniude of basis risk is esed as funcion of i s deviaion from is own heoreical value and index change. Oher esing measures he how basis risk is affeced by index reurns and possible lead-lag effec beween fuures and cash marke. Thesis is srucured as follows, Secion 2 covers heoreical background of fuures pricing, explaining pricing models, index arbirage, basis risk, price paerns and feaures of fuures prices. In Secion 3 we begin he empirical par of his hesis by presening he daa for esing basis risk. In Secion 4 research mehodology and resuls are inroduced. Finally, Secion 5 summarizes he differen pars of his hesis. 4

5 2 THEORETICAL BACKROUND To undersand aspecs behind basis risk, i s necessary o clarify heoreical fuures pricing. This secion covers he heoreical background of pricing of he fuures conracs. Pricing of he conracs are illusraed by presening he cos of carry model. Oher perspecive is considering fuures price rough expeced fuures spo price meaning he fuures price oday. In case of mispricing or marke failure we define he possibiliy of index arbirage. The basis risk gives an explanaion of he deviaion beween fuures and cash prices when he difference is no caused by mispricing. 2.1 Pricing of he fuures conracs The basic model for implemening he relaionship beween fuures prices and spo prices is he cos of carry. The cos of carry model assumes no ransacion coss, same ax rae for all invesors, lending and borrowing can be done wih he same risk free ineres and invesors ake he opporuniies for arbirage profis as hey occur. Using he model i is possible o define he heoreical price of he fuures conracs. Model measures he sorage cos of holding he asse and he ineres for financing he asse wih also he income earned during he holding of he asse (dividends ec.). For an asse ha pays no dividend he cos of carry is simply r because here are eiher no coss of holding he asse or income earned. The cos of carry model for an invesmen asse can be modeled as follows (Hull, 2006): (1) F0 S0 ct e Where F 0 is he fuures price when i s been purchased, S 0 is he spo price of he underlying asse a he same momen (=0), c presens he cos of carry, and T is he fuures mauriy. Sock indices can be considered as an asse ha pays dividends 5

6 (excep cross currency index derivaives, quanos 1 ) so he cos of carry for sock index fuures is r q, where q is he dividend yield. The equaion can be rewrien as:(hull, 2006) (2) F 0 S 0 e ( r q) T The dividend yield q in he equaion varies in pracice wihin differen mauriies. Dividends are usually paid in cerain daes of he year so he chosen value for q should be annualized dividend yield for he mauriy of he conrac. (Hull, 2006) One approach which explains he relaionship beween fuures prices and spo prices are he expecaions concenraed on he fuures spo price (S ), in oher words he fuures price oday (F 0 ). If he expeced fuures spo price diverges from fuures price i creaes opporuniies for speculaive invesors. The connecion beween expeced fuures spo price and fuures price can be wrien: (Kolb e al., 2006) (3) F E S ) ( 0, 0 Where E 0 (S ) is he expecaion a =0 of he fuures spo price a ime. If he relaionship beween prices doesn hold rue, wo reasons can be expressed if he reason isn mispricing of he fuures conracs. Transacion coss and invesors risk aversion. For invesor enering he fuures conrac does always cause ransacion coss and because of hese coss fuures price can diverge from expeced fuures spo price. Fuures marke paricipans can be caegorized ino hedgers and speculaors. Hedgers ener he fuures conracs o reduce risk of heir posiion, while speculaors ener he conracs for a hope of profi. Invesors who are risk averse are 1 For more informaion see Hull (2006) 6

7 willing o be exposed o he invesmen risk only if he expeced profi of aking he posiion compensaes he risk. Mos of he invesors can be considered as a risk averse invesors. (Kolb e al., 2006) 2.2 Index Arbirage If he cos of carry model doesn hold, mispricing gives a possibiliy for an index arbirage. Before index arbirage is conceivable, markes mus conain cerain liquidiy. In heory, i mus be possible for invesor o rade boh he index fuures and he asse porfolio of he underlying index simulaneously wih rading volume which maches he invesor s posiion. (Hull, 2006) Replicaing he index wih seleced porfolio is also a condiion for successful arbirage. In pracice, his kind of a porfolio can be formed bu changing he porfolio srucure by buying and selling he securiies can be difficul o carry ou when i is necessary. Considering he siuaion ha invesor has a long posiion in socks of he underlying index. If F 0 > S 0 e (r-q)t invesor should shor fuures conracs and remain he obained long posiion on socks. If F 0 < S 0 e (r-q)t arbirage profis can be made in his case selling (or shoring) he socks from he porfolio and aking he long posiion in fuures conracs. For he porfolio ha consis of a sample of socks of he underlying index ha has relaively large amouns of securiies, index arbirage can be made by rading relaively small porions of socks whose reurns replicaes he mos of he index reurns. (Hull, 2006) Puonen(1991,1992) sudied in index arbirage wih Finnish sock index derivaives. Tess were commied as ex-pos ess and several deviaions from heoreical fuures value were repored. Lack of shor sale possibiliy caused a possibiliy for arbirage profis even afer ransacion coss. 7

8 2.3 Basis Risk When invesor akes a posiion in fuures conrac, few aspecs of using fuures make hedging in pracice more complex han i seems. I may no be possible for hedger o obain such a posiion in fuures which maches exacly he underlying asse o be hedged. Timing of buy/sell decisions cause uncerainy and he posiion in fuures may have o be closed before is expiraion dae. Basis risk is defined o be he risk ha arises because of maching and iming problems in hedging wih fuures. The basis risk is difference beween spo price of he hedged asse and he price of he fuures conrac. (Hull, 2006) (4) Basis = Fuures price Spo price Equaion 4 is he basic definiion of he basis risk of a financial asse. When fuures conrac maches he underlying asse and he conrac is closed in delivery dae, basis risk should be equal o zero. Before he delivery dae basis can flucuae wih he asse price movemens and have negaive and posiive values. The longer he mauriy lef o ime-o-expiraion is, he more flucuaions is caused by he basis risk. Basis srenghens when spo price rises faser han fuures price and on he opposie basis weakens when fuures price rises faser han spo price. (Hull, 2006) According o Figlewski (1984) basis risk is a resul of mislinkage beween spo and fuures markes. The longer he holding period is he less basis risk should affec hedging performance. Also dividend risk has small meaning in hedging performance and basis risk. Figlewski also found ha, basis risk had a remarkable effec in hedging performance 8

9 2.4 Price paerns of fuures I is imporan o undersand he differen operaion models for differen invesors in conex of fuures pricing. Le us assume ha speculaive invesors are raional. Speculaors make assumpions on expeced fuure price using he informaion available. Because of hese expecaions, speculaors make infrequen misakes in forecasing fuure spo price. If he prevailing fuure price would always equal price for expeced fuure spo price, here would be no reason for invesor o speculae in fuures marke. When fuures price would equal he expeced spo price, speculaor wouldn achieve any addiional profi wih increased risk by enering fuures marke wih he possibiliy of expecaion error. When comparing hedgers and speculaors as a group, for every hedged posiion here mus be an opposie posiion. This scene happens when fuures price differs from spo price, raionalizing posiions for hedgers and speculaors. So if hedgers are on he shor side of he conracs, speculaors on he whole mus hold he long side. (Kolb e al., 2006) 9

10 W Y Fuures price E Expeced fuure spo price Hedgers (ne) A B Speculaors (ne) C Z X Shor conracs 0 Long conracs Figure 1 Hypoheical Ne Posiions ( Kolb e al., 2006 ) Figure 1 shows he relaionship beween hedgers and speculaors ne posiions due o changes in fuures price. Price changes in fuures leads o changes in he posiions held by wo groups. For hedger i s assumed ha for reducing risk hey hold ne shor posiions. Hedger s posiion is shown in WX line. A rise in fuures price leads o increase in shor posiion and he lower he fuures price he less hedgers hold shor posiions. Speculaors on he oher hand, hold long or shor posiions dependen of he siuaion. If fuures price equals expeced spo price, speculaors on he whole hold neural posiions because expecaions differences on average lead o neural holdings. Speculaors ne posiions are indicaed in line YZ. When expeced fuures spo price is below fuures price speculaors are also ne shor(in line YE) and on he oher hand speculaors are ne long when expeced fuures spo price exceeds curren fuures price. (Kolb e al., 2006) 10

11 Ye, all of he posiions in Figure 1 are no possible because he number of shor and long conracs mus equal. For example, when fuures price exceeds poin E, boh sides are ne shor. This leads o siuaion ha marke can clear only wih price B. In Figure 1 disance beween AB and BC are he same. The greaer slope of hedgers line WX is due o greaer risk olerance on speculaors. This is reasonable because speculaors are acceping larger risk from he hedgers side. And, i leads o siuaion represened by Keynes and Hicks, where hedgers are ne shor and fuures price rise during he fuures mauriy, because basis mus be zero a delivery dae. (Kolb e al., 2006) Fuures price Conango Ne hedging Expeced fuure spo price Normal backwardaion Time-o-mauriy Figure 2 Price paerns of Fuures (Kolb e al., 2006) Figure 2 shows differen price paerns of fuures. Theory of normal backwardaion summarizes connecion of rise in fuures prices during ime-o-expiraion and hedgers 11

12 aspiraion of holding shor posiions as group. In case of hedgers hold long posiions, fuures price exceeds expeced fuure spo price and fuures price will decline o imeo-expiraion. This reverse price paern is called conango. However, hedger s posiions can change during conracs mauriy. In he beginning of he conrac hedgers hold ne shor posiions agains speculaors opposie ones. If he price of fuures is less han expeced fuure spo price, hedgers will adjus heir posiion o be ne long. Now, he speculaors mus adjus heir posiions o consis of shor conracs. Fuures price have o be now higher han expeced fuure spo price so ha speculaors would gain reurn for he change in risk of heir oal posiion. This Ne Hedging Hypohesis leads finally o same price paern as conango. (Kolb e al., 2006) Capial Asse Pricing Model can be involved wih fuures pricing. Sysemaic risk can be measured wih he CAPM by β. Typical regression equaion for β can be wrien: (5) r j, j jrm, j, Where r j, is he asse reurn, he consan erm of he regression equaion and r m, is presen marke reurn in he same period, j is j, is he error erm for residuals. Trading in fuures marke involves sysemaic risk, bu no invesmen. Marginal paymen requiremens can be considered as invesmen. Because lack of invesmen, risk-free rae can be earned, so if fuures have zero bea, he posiion should earn zero reurn. When fuures bea is posiive, holding long posiion should yield a posiive reurn. On he whole, differen values of beas have an effec o fuures price expecaions. Posiive bea should presen expeced rise in fuures price, zero bea should signal seady price expecaions whereas negaive beas should presen expeced fall in fuures price. Resuls of bea esing in fuures prices indicae ha fuures beas are close o zero. (Kolb e al., 2006) 12

13 2.5 Feaures of fuures prices Several facors can lead o diverge beween fuure and spo prices wihou crosshedging issues. Differences migh cause deviaions in axaion, ransacion coss and required margins. Specific relaionship beween forward and fuures prices can be defined rough ineres rae correlaion wih spo prices. If ineres raes have posiive correlaion wih spo prices, fuures prices should be higher han spo prices. If here is no correlaion wih ineres raes and spo prices, fuures price should equal spo price and negaive correlaion leads o higher spo price compared o fuures price. (Kolb e al., 2006) Fuures price disribuion is ofen assumed o be normally disribued. Ye, researchers agree ha, in real world variey in fuures prices is more lepokuric han normally disribued. If observaions don follow normal disribuion, general proposals are ha he observaions can follow Parenian disribuion or be a combinaion of differen normal disribuions. Sill, non-normaliy makes saisical inerpreaion more complex. Price changes of fuures ofen involve saisically significan auocorrelaions, especially wih firs order auocorrelaion. Ye, magniude of significan auocorrelaion isn large enough creae profiable sraegies. (Kolb e al., 2006) Fuures volailiy can be divided o wo caegories, how fuures rading affec volailiy of underlying asse and second he price changes of he fuures. Inconsisen opinions are ha fuures rading increases volailiy of underlying asse in some cases, bu on he oher hand, don affec or even decreases i. Volailiy of fuures conrac increases o ime-o-expiraion. This increasing volailiy is known as Samuelsson hypohesis. According o he hypohesis, following expeced fuures price should be he same as oday s price, so he variaion would equal zero following maringale process. (Kolb e al., 2006) 13

14 2.6 Saisical mehods All reurns in empirical esing secion are calculaed using logarihmic reurns. (Brooks, 2005) p (6) r ln( ) p 1 Regression equaions are buil o explain basis risk and mehod for ordinary-leassquares is used. As a leas squares principle, esimaed equaion should fi in a line wih daa values as bes as possible. Sum of squares of he verical disance of each o he fied line should be as small as possible. Squared disances are used o offse negaive values. As a resul, inercep and slope of his line are found. General regression equaion can be wrien (7) y b1 b2 x where values of b 1 and b 2 are coefficiens, b 1 being he inercepor and b 2 is coefficien for explanaory variable. Equaion is easily exendable by adding more explanaory variables. (Hill e al., 2001) Equaion 8 shows he verical disance from daa values o regression line called as leas squares residuals. (8) e y y y b1 b2 x Ordinary leas squares regression can be used when residuals shows no auocorrelaion. Durbin-Wason saisic measures he firs-order auocorrelaion of residuals. Durbin-Wason es is showed in equaion 9 ( e e (9) DW 2 e 2 1) 14

15 Where values of e sands for regression residuals. As a rule for inerpreaion of DWsa, if es saisic is 2, here are no posiive auocorrelaion and if is 0 here are perfec posiive auocorrelaion and if is 4 here perfec negaive auocorrelaion. (Washam e al., 2002) 15

16 3 DATA Case daa is obained from Daasream online daabase and using OMX25 (FFOX) index fuures wih he ime period of 9/ /2002. Time frame is seleced because of Finnish sock markes wen rough large decline. Period known as he echno bubble burs in he end of year 1999 and he decline of OMX25 index lased ill he middle of he year Marke condiions in Finnish sock marke could be described as a bear marke. In hese marke circumsances invesor s moives o hedge heir porfolio should have increased. 3.1 OMX25 fuures series Seleced fuures consis of 12 differen fuures conracs. OMX25 fuures are raded in Eurex exchange which is locaed in Frankfur, Germany. (Eurex-a) and conrac specificaions can be seen in Table 1; Table 1 - Conrac specificaions of OMX25 fuures Conrac specificaion s Mauriy Conrac value Minimum price change Selemen Up o 9 monhs 10 euros per index poin 0.1 poin equals 1 Euro In cash by firs rading day afer closing Daily selemen price Derived from volume-weighed average of all ransacions in las minue of rading Logarihmic reurns of fuures series were calculaed and descripive saisics are shown in Table 2. Disribuion of reurns is esed wih Bera-Jarque values. (Brooks, 2005) Saisic show ha reurns are no normally disribued as i s common 16

17 according o heory secion. Disribuions seem more fla han normal disribuion and are in some cases negaively skewed and on he oher hand posiively in some of he series. Fuures reurns also show negaive mean reurns, larges negaive mean reurn is achieved wih Sepember 2001 series and only posiive reurn wih June 2002 series. Table 2 Descripive saisic of fuures series logarihmic reurns Mean S. Error Variance Kurosis Skewness Size Conf.l.(95%) Bera-Jarque MAR00 0,0000 0,0034 0,0006 1,0330-0, , ,7050 JUN00-0,0010 0,0023 0,0007 0,4143-0, , ,3150 SEP00-0,0012 0,0017 0,0005 0,7921-0, , ,7290 DEC00-0,0017 0,0017 0,0005 0,7610 0, , ,4000 MAR00-0,0028 0,0016 0,0005 0,8438 0, , ,5960 JUN01-0,0026 0,0017 0,0005 0,5444 0, , ,7550 SEP01-0,0036 0,0015 0,0004 0,3981 0, , ,1650 DEC01-0,0004 0,0014 0,0004 0,5541 0, , ,8980 MAR00-0,0001 0,0013 0,0003 1,0050 0, , ,6610 JUN02 0,0008 0,0010 0,0002 0,6982 0, , ,3770 SEP02-0,0015 0,0010 0,0002 0,5682 0, , ,0800 DEC02-0,0013 0,0011 0,0002 0,5178 0, , , OMX25 Index OMX25 Index consis of 25 larges socks measured wih marke value in OMXHelsinki- index. Performance of he OMX25 Price index is shown in Figure 3. Index shows a large declining rend from he early of year 2000 unil o near end of Index value decreases from approximaely 3500 poins o 1100 wih a oal price drop of 68.5%. Sock markes decline sars o balance in he beginning of year

18 OMX Helsinki Index value OMX Helsinki Figure 3 Performance of OMX25 Index Table 3 shows descripive saisic from logarihmic reurns of OMX25 Price Index reurns. Mean reurn in seleced ime period has been -7.2% which is a relaively large decline. Index volailiy is 184% which concludes he oher evidence of marke crash. Again, index reurns are no normally disribued according o Bera-Jarque es saisics. Table 3 Descripive saisic OMX25 Price Index logarihmic reurns Descripive saisic - OMX25 Price Index logarihmic reurns Mean reurn -0,0723 Sandard Error 0,0006 Sandard Deviaion 1,8412 Sample Variance 0,0003 Kurosis 1,7611 Skewness -0,1396 Minimum -0,0799 Maximum 0,0723 Bera-Jarque 31,4926 Confidence Level (95,0%) 0,

19 4 RESEARCH METHODOLOGY AND RESULTS Performed ess for explaining he basis risk are aken from sudies by Figlewski (1984) and Chen e al.(1995) and a par of hese ess are replicaed wih Finnish daa. Theoreical prices are needed for o calculae heoreical basis which is needed in esing. Objecive is o es and view basis risk. 4.1 Cos of carry Theoreical cos of carry prices are calculaed for each of he series using daily observaions. Theoreical prices are needed laer on wih esing basis risk. OMX25 Price index is used as an underlying index. Price index is picked because oal reurn series are available for OMX Helsinki bu no wih his sub index. Pricing equaion includes a power componen consising of risk free rae r and dividend yield q. In calculaions, daily values of 12 monh Euribor is chosen and day couning acual/360 is used (Vaihekoski, 2004). Puonen (1992) uses closes ime-omauriy rae in his paper. Alhough, i is saed ha deviaions are minimal. In his paper calculaions are simplified by choosing 12 monh rae wih chancing day couning insead exac rae which is no available. Dividend yield is no included o calculaions. Price index is used as a spo price so dividends are excluded because of complex measuremen. Figlewski (1984) examines hedging performance and basis risk saing ha dividend risk has a small affec in overall hedging performance and basis risk. 19

20 4.2 Basis risk Basis risk is calculaed fuures price lessen he spo index price. Values of basis are calculaed daily basis o all of he colleced series. Correspondingly, heoreical basis is calculaed by deducing index value from calculaed cos of carry values. Figure 2 presens he behavior of he price differences beween fuures and cash marke. Coninuous values of basis are formed using series closes-o-expiraion.(chen e al.1995) Trading of he nex fuure conrac afer close-o-expiraion seemed o sar less han 30 days on average before delivery dae of curren conrac. Also o preven hin rading, rolled-up basis is srucured. Basis risk - whole sample period Basis Figure 4 Basis risk wih whole sample period As seen Figure 4, price difference flucuaes heavily, especially wihin firs half of sample period. Larges deviaions are around -110 index poins o approximaely +70 index poins. For example, -110 poins basis means price difference per fuures conrac. Even hough i s an oulier example, bu as seen Figure 4 hese 20

21 kinds of flucuaions happened wih very shor imeframe. In Figure 5 heoreical basis is drawn for comparison. Theoreical basis 40,00 35,00 30,00 25,00 20,00 Theoreical basis 15,00 10,00 5,00 0, Figure 5 Theoreical basis for whole sample period In Figure 5, heoreical basis deviaes oally of wha seen in Figure 4 wih real prices. Firs of all basis does no ge any negaive values, because of calculaion formula used. Index was muliplied wih e power of rae muliplied wih mauriy which leads values of fuures wih price paern of conango as seen in heoreical secion. Resuls are surprising compared o real deviaions. Wih real basis, he price difference does no equal zero even in he end of mauriy like wih heoreical prices. Of course, some simplificaions are included o calculaions bu his deviaion can be due o ransacion coss. 21

22 4.3 Explaining basis We sar building a es o explain basis by performing regression presened by Figlewski(1984). In his paper, Figlewski explains ha basis end o overreac due o changes in he cash marke. Regression is buil o es how basis is affeced by change from is heoreical value and change in he underlying index. (9) B B C e C ( B B 1) C2( I I 1) In equaion 9, B B 1represens he change in basis risk from is las value, e B B 1 is he deviaion of basis risk from is heoreical value o previous realized value and I I 1 measures he affec of index change due o basis risk. Figlewski found explanaory variables o be very significan and basis increased wih marke and oher way around. Basis changed approximaely 40% from yeserday s level. Table 4 shows he resuls of regression. e Table 4 Resuls of regression B B C C B B ) C ( I I ) 1 0 1( Variable Coefficien Sd.Error -Saisic Probabiliy Consan B e B I - I R-squared Adjused R- squared Durbin-Wason

23 Obained es resuls do no reach he same level compared o Figlewski (1984). Adjused R-squared drops o 19.8% which can be considered barely accepable. All of he variables are saisically significan wih saisfying -Saisic. Durbin-Wason shows no residual auocorrelaion. (Brooks, 2005) According o resuls, basis moved on average 29.4% from previous value o oday level. Basis seems o have negaive relaionship o index movemens, bu value of coefficien is raher small. Sill, consan erm is found o be significan which akes away crediabiliy of he resuls. Even hough quesions can be raised agains explanaory power of resuls, guidelines are in line wih Figlewski s inerpreaion. Cos of carry calculaions can be one reason causing drop wih he explanaory level. Figlewski also esed hedging performance wih differen holding periods and basis risk effec on hedging. Basis risk affeced wihin hedge duraion and ime-o-mauriy of conracs. Nex we coninue by esing relaionship wih volailiy and marke response beween cash and fuures marke. Chen e al. (1995) claims ha fuures should presen new marke informaion and lead cash marke. Because of his lagging reacion, basis should response wih marke moves. To examine his phenomenon, simulaneous index reurn and he following days reurn is included in regression. In addiion, Chen e al. find in his same paper ha increase in volailiy of underlying index depresses values of basis. Original es is made wih implied variance, bu robusness is esed wih using realized variance of cash index 5 days before ( 5 o 1) and 5 days afer ( 1 o 5). Resuls show no significan difference so he mehod of realized variance is applied in he regression excluding he day when basis is measured. Equaion is srucured (10) B C C B C B C B i C Ir C Ir C 23

24 In equaion 10 B represens basis risk, 1 lags, presen index reurn is wrien Ir and 1 B are lagged values of basis wihin hree Ir and nex days index reurn is presened by 2 i presens for implied variance. Auocorrelaion saisic show significan auocorrelaions wihin over hree lags, so hree lagged values of basis is included o regression as in Chen e al.(1995) paper. Regression resuls are shown in Table 5. Table 5 Resuls of regression B C C B C B C B C Ir C Ir i C Variable Coefficien Sd.Error -Saisic Probabiliy Consan B B B Ir Ir S R-squared Adjused R- squared Durbin-Wason sa Resuls of he second regression are saisfying. Adjused R-squared is 52.9% which is fairly larger han Chen e al. resuls. Durbin-Wason shows no problems wih residual auocorrelaions. Consan erm is no significan which suppors he equaion. Values of lagged basis seem o have srong influence o he value of measuremen day. Third lag seem o affec 12% of oday s value. Basis seems o las for few days. Index reurn have srong negaive influence in basis, coefficien is significan bu shows also large sandard error. This resul suppors coefficien of 24

25 index change in he firs regression. Noneheless, nex days index reurn is no significan indicaing ha lead-lag effec of fuures and cash marke doesn exis a leas for his ime frame. Original es were made in 1995 and resuls showed significan lead-lag effec. Reasonable explanaion could develop rading sysems, informaion efficiency due o echnological developmen. Furher lead-lag esing should be made wih inra-day daa. Realized variance shows negaive relaion o basis bu i s no found significan. This can be considered as a backlash for es resuls. Chen e al. esing were conduced wih implied variance and he same resuls were found wih realized values and Wednesday values only. In he same paper hey also esed open ineres relaion o implied volailiy and found ha open ineres is posiively correlaed wih he index. Inraday lead-lag esing was commied by Chan e.al. (1992). Fuures markes were found o be he source of marke-wide informaion. Lead-lag relaion is no explained by nonsynchronous rading. The qualiy of new marke informaion caused differen resuls. Under bad news, no lead-lag paerns were found and under good news, fuures marke end lead cash index. 25

26 5 CONCLUSION This paper has provided a heoreical background of fuures pricing and empirical esing of basis risk. This price difference is deermined by fair fuures price minus curren spo price. Basis risk was esed and modeled wih Finnish sock index fuures using series of OMX25 -index fuures and amoun of resuls were found. Basis risk has a powerful impac on price changes beween o markes. Basis seems o move heavily wih marke downswings. Tesing period was ineresing because of curren marke condiions. Marke volailiy increased in his sample period due o burs of echno - bubble in he beginning of year Changes in cash marke volailiy have negaive influence in basis, even hough es resuls using realized variance were no significan. Obviously, using implied variance would be possible o obain more accurae resuls. Ye, basis risk seemed o persis few days in he marke. Values of basis were highly auocorrelaed and i seemed ha hird lag sill had over 10% effec o oday s values. Price difference beween o markes showed negaive relaionship wih index change and index reurns. Index reurns seemed o have larges influence in basis risk. Basis end o decrease when marke rise and increase when marke dropped. However, no lead-lag effec connecion beween basis and iming differences beween wo markes were found. Fuure index reurns had no significan effec in basis. To conclude, invesor who considers enering fuures markes should adjus his porfolio accordingly o basis risk. Theoreical frame of fuures pricing gives pricing models and explanaions of behavior of fuures prices. Sill, heoreical models include several simplificaions and as resuls of his sudy show ha heoreical prices can be hardly compared o acual prices. Because of hese deviaions and hedging issues, basis risk causes problems for hedger. The price difference beween fuures and cash 26

27 markes can be parially explained by few facors as shown in his paper. Despie of given explanaions, afer presence of lagged values and index change is aken ino accoun, some causes of basis are sill lef wih uncerainy. In overall, basis risks seem o conain far more noise han facors which explain i. 27

28 REFERENCES Brooks, C.: 2005; Inroducory Economerics for Finance, Sixh reprin. Cambridge Universiy Press, Unied Kingdom. Chan, K.: 1992: A Furher Analysis of he Lead-Lag Relaionship beween he Cash Marke and Sock Index Fuures Marke. The Review of Financial Sudies, 1992, vol.5, No.1, pp Chen, N.&Cuny, C.J.&Haugen, R.A., 1995: Sock Volailiy and he Levels of he Basis and Open Ineres in Fuures Conracs. The Journal of Finance, 1995, No.1, pp Figlewski, S., 1984: Hedging Performance and Basis Risk in Sock Index Fuures, The Journal of Finance, 1984, No.3, pp Hieala, P.&Jokivuolle, E.&Koskinen,Y., 2000: Informed Trading, Shor Sales Consrains and Fuure s Pricing, Bank of Finland Discussion Papers, 2000, No. 4 Hieala, P.&Jokivuolle, E.&Koskinen, Y., 1994: Shor-Selling Resricions, Sraegic Sock Holdings and Index Fuures Markes in Finland, Bank of Finland Discussion Papers, 1994, No.19. Hill, R. C., Griffihs, W. E., Judge, G. G., Undergraduae Economerics Second Prin, New York, John Wiley&Sons Inc.,2001 Hull, J.C., 2006: Opions, Fuures and Oher Derivaives (6 h ediion). USA: New Jersey, Prenice Hall. Kolb, R.W.&Overdahl,J.A., 2006: Undersanding Fuures Markes (6 h ediion). UK: Oxford, Blackwell Publishing. 28

29 Puonen, V., 1992: Sock Index Derivaives Arbirage in Finland, Proceedings of he Universiy of Vaasa, 1992, Research No Puonen, V., 1991: Sock Index Fuures Arbirage in Finland Therory and evidence in a new marke, 1991, Proceedings of he Universiy of Vaasa, Discussion papers No.126. Vaihekoski, M., 2004, Rahoiuksen sovelluukse ja excel, WSOY, Finland, Vanaa. Washam, T.&Parramore, K., 2002, Quaniaive Economerics For Finance 1sh Ediion, Thomson Publishing, Grea Briain. Inerne references: Eurex-a, he webpage of Eurex - exchange, referred

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