COMMON VOLATILITY IN THE FOREIGN EXCHANGE MARKET

Transcription

1 COMMON VOLATILITY IN THE FOREIGN EXCHANGE MARKET Dr. Carol Alexander, School of Social Sciences, Universiy of Sussex, Falmer, Brighon, Sussex BN1 9QN. 1.Inroducion The adverse effec of currency volailiy on inernaional rade has promped he incepion of he European Moneary Sysem (EMS) and oher measures of inernaional policy coordinaion aimed a reducing inracurrency variabiliy. Unil "Black Wednesday" in Sepember 1992 he EMS had some sucess in his objecive, bu following pressure on he Ialian Lira, oher ERM currencies (viz. Serling, he Spanish Pesea, Porugese Escudos, Danish Kroner, Belgian Franc and he French Franc) have all experienced exremely volaile periods which culminaed in he virual break up of he EMS in Augus 1993, when all bu he German Mark and Duch Guilder moved o much wider bands. However speculaive invesmen in over-he-couner derivaives (such as ahe-money sraddles) does no help o reduce currency volailiy. Regulaion of OTC derivaives rading is now a major inernaional concern, and he Basle commiee meeings during 1993 have led o a new Capial Adequacy Direcive of he European commission, which is now being enforced by naional banks. In order o assess he exen of currency risks which are being aken in OTC derivaives rading, i is necessary o undersand any common volailiy facors in exchange raes. This is he purpose of he presen paper. We ask wheher inracurrency variabiliy is dominaed by regional facors (including associaion wih he EMS), global facors, or speculaive invesmen. An auoregressive condiionally heeroscedasic (ARCH) framework is employed for his analysis, and over limied periods a number of common condiionally heeroscedasic Applied Financial Economics 1

2 facors may exis: some of hese could be responses o global facors such as he Gulf war or evens in Easern Europe, ohers may be region specific such as he urmoil of some ERM currencies around Black Wednesday, bu neiher global nor regional facors alone can explain susained common facors wih condiional heeroscedasiciy. Following he abolishion of UK exchange conrols in 1979, London has become he cenre of he world's currency rading: in 1992 he Bank of England esimaed ha $300 billion passed hrough London dealing rooms every day - far more han in eiher Tokyo or New York. The dominaion of currency movemens by speculaive invesmen is herefore bes examined on daa from he London marke: REUTERS FX daa from January 1982 o December 1992 has been used. The plan of he paper is as follows: he nex secion reviews he common ARCH economeric mehodology; secion hree applies ARCH and common ARCH ess o daily and weekly exchange raes; generalized auoregressive condiional heeroscedasic (GARCH) models of exchange raes are esimaed and heir condiional variances used o provide some inuiion for he resuls; and secion four concludes. 2. Economeric Mehodology Common ARCH facors in exchange raes are esed using he common feaure mehodology inroduced in Engle and Kozicki (1993). This is based on he resul ha saionary, auoregressive condiionally heeroscedasic ime series x..., x have a common ARCH facor if and only if here exiss a 'no-arch' porfolio, viz., a linear combinaion n λ i x i i= 1 which displays no condiional heeroscedasiciy. This resul is simple o illusrae for wo ime series, which for our purposes will be currency reurns x and y: suppose x = w + u where w Ω x ~ D( 0, h 2 ) and y = v + u where v Ω ~ D( 0, k 2 ) y 1 n Applied Financial Economics 2

3 where Ω denoes informaion available a ime and u independen homoscedesic error componens. Consider he porfolio x x and u y are muually + λ y : V ( x + λy ) = h λ k 2 + 2λCov ( w, v ) + consan and so V ( x + λ y ) is independen of ime if and only if w = λv + consan. For in his case h = λ k and Cov ( w, v ) = λk 2 (and w and v are perfecly negaively correlaed). Thus a 'no-arch' porfolio x x = λ v + u and y = v + u x + λ y exiss if and only if y (up o a consan) in which case x and y have he common ARCH facor v. The parameer λ is a scale facor whose sign also deermines he relaionship beween he means: he common ARCH facor has he same sign in he means λ < 0. Anoher inerpreaion of λ is he relaive weigh in a risk minimizing porfolio: hus asses x and y should be combined in he proporion (1,λ) for effecive hedging of volailiy. The resul generalizes o n (saionary) ime series x1,..., xn: λ i porfolio if and only if he ARCH facors w i of each x i saisfy n i= 1 λ i w i = consan. n i= 1 x i is a 'no-arch' The Engle-Kozicki mehodology involves esing firs for univariae and mulivariae ARCH effecs in he individual currency reurn series. These Lagrange muliplier ess, which were firs derived in Engle (1982) ake he TR 2 (i.e. he produc of he sample size wih he uncenred R 2 ) from regressions of squared currency reurns on a consan and p lags, for univariae ARCH(p), adding p lags of oher squared currency reurns for he mulivariae MARCH(p) ess. The es saisics are chi- Applied Financial Economics 3

4 squared disribued wih degrees of freedom equal o he number of lagged squared reurns. The bivariae common feaure es is hen applied o hose series x, y wih significan univariae ARCH effecs, by finding he λ which minimizes he TR 2 from ARCH ess on he porfolio z (λ) = x + λy. These Lagrange muliplier ess employ lagged squares and cross producs of x and y, and if he minimum TR 2 is below he appropriae criical value, he porfolio is subjeced o oher univariae and mulivariae ARCH ess. Then if no furher evidence of ARCH is apparen we deduce ha a 'no- ARCH' porfolio exiss - and herefore ha he reurns share a common condiionally heeroscedasic componen wih scale facor λ 1. Before applying hese ess o currency reurn daa, i is necessary o sound a preliminary noe of cauion in heir inerpreaion: ARCH ess can yield a low value for series where big evens are no repeaed, and so some porfolios may pass all 'common volailiy' ess even hough volailiies are differen - provided ha large differences are only very emporary. Anoher poin o noe when employing ARCH ess on currency reurns, where GARCH models can fi beer han ARCH models wih few lags, is ha sufficien lags should be aken in he ARCH ess o capure he GARCH behaviour. 3. Daa Analysis (a) Daily Dollar Reurns Iniially he analysis was conduced using daily London closing bid dollar raes on he Ausralian Dollar (AUD), German Mark (DEM), Spanish Pesea (ESP), Briish Pound (GBP), Ialian Lira (ITL), Japanese Yen (JPY) and Duch Guilder (NLG), from 2nd January 1982 o 10h December 1992, a oal of 2768 observaions, and hese are 1 See also Engle and Susmel (1993). Applied Financial Economics 4

5 illusraed in figure 1. Firs differences of he logarihms are aken, as hese are boh saionary and approximaely equal o he daily currency reurns 2. The resuls of univariae and bivariae ARCH ess, shown in able 1, reveal several feaures, some of which will be used in subsequen analysis: firsly, he univariae ARCH(1) effecs are very weak in he Ausralian dollar 3 and so including AUD in common ARCH ess will ineviably lead o a value λ = 0 on he oher currency reurn for he minimum TR 2 ; secondly, increasing he lag used in univariae ARCH ess increases he significance of he effec, and his is o be expeced given he well-documened GARCH effecs in daily currency reurns (see Baillie and Bollerslev (1989), Hseih (1989), Alexander and Riyai (1992) and many ohers). Table 2 repors maximum likelihood esimaes of univariae generalized auoregressive condiionally heeroscedasic (GARCH) models of he form x = c + u. Here u is a GARCH(1,1) disurbance of he form u Ω ~ N ( 0, h 2 ) where h = α + α u + βh α > 0, α, β Figure 2 shows he annualized volailiies of each dollar exchange rae obained from a GARCH(1,1) model 4. Noice ha all he raes excep he Yen are paricularly volaile during he spring of 1985, when dollar depreciaion begun afer he long dollar surge. Oher evens which influence some of he raes are world evens such as he collapse of communism in 1987/88, which induced high volailiy in he German Mark, Guilder, Serling and he Yen, and he global sock marke crash of Ocober A 2 See, for example, Alexander and Johnson (1992). 3 The Ausralian dollar was ied o he US dollar during he beginning of he daa period, and before i began o floa several big changes in he exchange rae were no repeaed - hence he low ARCH value. 4 Plos are based on weekly daa.the condiional variances exhibi he same global and regional feaures as he corresponding daily series, and hese feaures are now easier o disinguish because he daa are less noisy. Applied Financial Economics 5

6 common peak in all reurn volailiies, excep he AUD, occurs during he spring of 1992, when he dollar rose on news of economic revival in he US. Regional facors also exis, such as he floaing of he Ausralian dollar in 1985, and he European currencies have been paricularly volaile during he las wo years of urbulence in he ERM: volailiy during 1991 increased as he problems of German unificaion became apparen, and in 1992 he Maasrich referendums precipiaed an ERM crisis in Sepember. The las and mos ineresing poin o noe abou able 1 is ha he Cable rae is exraordinarily efficien a deecing ARCH effecs in each oher currency. Reasons for his are no immediaely obvious, bu one possibiliy is ha speculaive dollar invesors have saic expecaions abou currency reurns. In his case Serling appreciaion could induce a swich of invesmen from foreign o UK asse markes and consequenly a downwards movemen in oher dollar exchange raes 5. If his is he case, one could expec o find condiionally heeroscedasic co-movemens in currencies which are dominaed by movemens in dollar funds, and his possibiliy will be explored by invesigaing common volailiy in boh dollar and German Mark (DM) reurns. The explanaory power of Serling in predicing he volailiy of oher currencies implies ha squared Serling/dollar reurns will be a useful insrumen for deecing ARCH in any porfolios which pass he firs sage of common feaure esing 6. Noice also he ousanding effec ha lagged Lira squared reurns has on curren Serling squared reurns - a resul which is probably dominaed by he early and dramaic response of he Lira o pressures in he ERM in Sepember 1992, before Serling fell hrough is floor and consequenly boh currencies lef he EMS. Common ARCH ess on daily daa are no repored because hey reveal no one single 'no-arch' porfolio for any exchange rae pair! This absence of common feaures holds even when he daa are resriced o he las wo years of he sample, by 5 Following he resuls of able 5 we do indeed find ha movemens in foreign currencies corresponding o a common condiionally heeroscedasic facor wih serling are in he opposie direcion: he parameers in he 'no ARCH' porfolios wih GBP are all negaive bu, since he Cable rae is $/ wheras all oher raes are in dollar erms, he corresponding movemens in he currencies are in opposie direcions. 6 I also implies a marke inefficiency which has no, as ye been arbiraged away. However as he rading of currency derivaives advances, so we would expec an anomaly such as his o disappear. Applied Financial Economics 6

7 which ime Serling had joined he EMS and so independen currency variabiliy should have been minimized 7. The obvious conclusion is ha daily daa conain oo much noise for a single common feaure o emerge. (b) Weekly Dollar Reurns The analysis of weekly currency reurns, using he Wednesday raes (o avoid any weekend effecs) leads o much beer resuls. The univariae and bivariae ARCH ess in able 3 again reveal Serling reurn variabiliy o be an imporan deerminan of he variabiliy of reurns on oher currencies, bu he effec is very much weaker han in daily reurns, indeed Serling is no beer a deecing ARCH effecs in possible 'no ARCH' porfolios han any of he oher major currencies (see able 5). So he 'Cable effec' is only deecable in daily raes, and his does no conradic he idea ha i is generaed by speculaive invesmen. All currency reurns excep he Spanish Pesea have univariae ARCH, provided sufficien lags are included o capure GARCH effecs (4 lags are illusraed in he able). Is absence of 'ARCH' implies ha inclusion of he Pesea in common ARCH(4) ess would be misleading, since i will always yield a minimum TR 2 less han he 5% criical value. In conras o daily reurns, in he weekly daa a surprising number of porfolios passed he firs sage of common ARCH(4) esing 8 : 10 ou of he 15 possible porfolios yield a minimum TR 2 less han he 5% criical value for some value of he porfolio scale parameer (see able 4). Noice ha here is no evidence of common volailiy beween he Duch Guilder and he German Mark, even hough hese currencies were so closely linked (before German unificaion) as o be coinegraed! During he 1986 Duch credi conrol period, however, he Guilder/Mark rae was excessively volaile (see figure 1) and his has obviously precluded he exisence of a common ARCH feaure over he whole daa period. However, here is even no evidence of common ARCH in he Guilder/$ and Mark/$ raes over any of he 7 Resuls of common ARCH ess for daily reurns are available on reques from he auhor. 8 Tha is, finding l o minimize he TR 2 from regression of squared porfolio reurns on 4 lagged squared reurns of each currency and 4 lagged cross producs. Applied Financial Economics 7

8 consequen sub-periods. How can his fac be reconciled wih he similariy beween heir GARCH(1,1) volailiies in figure 2? A possible explanaion is ha common volailiy is induced by oher common facors, such as hose deermined by a common ineres rae policy 9. In able 5 we lis he 10 candidaes for 'no ARCH' porfolios in he firs column and he minimum TR 2 from able 4 in he second column. The hird column gives a univariae ARCH es wih 4 lags of he squared porfolio reurns, and he las five columns are bivariae ARCH(4) ess where each currency reurn is added o he informaion se in urn. An aserisk denoes a Lagrange muliplier saisic which exceeds he 5% criical value, and which herefore conradics he iniial evidence in column 2 of a common ARCH facor. All porfolios which include he Ausralian dollar fail a leas one of he ess, which is no surprising given he behaviour in is condiional variance jus before i ceased o be fixed o he dollar (see figure 2). Only he porfolio of Serling and Yen reurns passes all he common feaure ess 10, and he resuls indicae ha hese exchange raes share a single ARCH facor wih scale facor Tha is, condiionally heeroscedasic movemens in Yen reurns are approximaely 15.6% larger han he corresponding movemens in Serling reurns and, since he parameer is negaive, hese movemens are in opposie direcions (see foonoe 5). In he absence of an adequae explanaion of why no common ARCH is deeced beween he Guilder and DM dollar reurns, wheras srong evidence of common ARCH is apparen in he raher dissimilar Serling and Yen, we should, perhaps, call ino quesion he Engle-Kozicki mehodology for finding common ARCH facors. Cerainly Neil Ericsson's criique following he Engle-Koziki aricle should be aken very seriously. In paricular i may be ha we need o allow for a dynamic 9 Alexander (1994) invesigaes common ARCH facors in inernaional bond and equiy markes. Germany and The Neherlands are he only counries which display any evidence of common ARCH facors in heir bond markes. 10 Even he porfolios which include he Pesea fail MARCH ess of 'no-arch' when squared Yen/$ reurns are included in he informaion se.garch(1,1) models are again esimaed o aid he inuiion of our resuls, and he esimaed condiional variances are given in able 6. These are ploed, afer convering ino annualized volailiies, in figure 2. Applied Financial Economics 8

9 srucure in he Engle-Kozicki mehodology in order o deec a common ARCH feaure beween he Deuschmark and he Guilder 11. And wha, exacly, has been idenified by he supposed common ARCH facor in Cable and he Yen/$ raes? Whaever i is, i can only consiue a small par of he oal ARCH volailiy, given he difference in heir GARCH volailiies shown in figure 2! I is possible ha high variabiliy in he Cable and Yen/$ raes has decreased he power of he Engle-Kozicki ess o such an exen ha we do no rejec a false null hypohesis (of a common ARCH facor). On he oher hand i may be ha a single common ARCH facor does exis, bu hen oher individual ARCH facors mus also exis which dominae he volailiy plos in figure 2. (c) German Mark Reurns The univariae and bivariae ARCH ess of weekly DM reurns in able 7 reveal huge condiional heeroscedasic effecs in he Duch Guilder, as expeced from he 1986 credi conrol period. Spain joined he EMS in 1989, bu he Ialian Lira, which has been a member hroughou he daa period, has more condiional volailiy han he Pesea. The possibiliy of common ARCH facors in Serling/DM, Guilder/DM, Lira/DM and Yen/DM reurns is explored in able 8, wih no posiive resuls. (d) A behavioural explanaion? A mechanism which could give rise o a common ARCH facor in he Serling/$ and Yen/$ exchange raes is now proposed: Firs, examinaion of he signs on he porfolio parameers in able 5 indicaes ha movemens in he mean currency reurns corresponding o a common condiionally heeroscedasic facor are always in opposie direcions (recall ha GBP, being $/, should have is sign swiched). Secondly, we have found huge explanaory power from Serling squared reurns o hose of oher currencies - and he Yen is also efficien a picking up ARCH in oher European DM raes (see able 7). Finding boh of hese is consisen wih he hypohesis ha dollar funds, invesed largely in Briish and Japanese asse markes, are 11 This analysis is lef o a subsequen paper (Alexander, 1994). Applied Financial Economics 9

10 swiched o (and from) oher markes in response o saic expecaions of reurns: when Serling (or Yen) show marked depreciaion (resp. appreciaion) he expecaion is ha i should coninue, and dollar funds are swiched ino (resp. ou of) oher currencies. There is no evidence ha such speculaive behaviour is employed by DM denominaed funds, since no evidence of common condiional heeroscedasiciy has been found in DM raes. Of course, his 'dollar dominaed speculaive invesmen' refers only o common condiionally heeroscedaic facors, no o any of he oher facors which influence currency reurns, and he influence of common ARCH facors in he oal volailiy of currency reurns appears o be quie small Concluding Remarks Boh daily and weekly dollar reurns of seven currencies have been invesigaed for common ARCH facors over a period of eleven years. Daily daa were found o be oo noisy for any such common facors o be deeced, even when he daa period is resriced. For he weekly reurns, resuls were raher couner-inuiive: no evidence of common ARCH beween he Deuschmark and he Guilder, bu evidence of a common ARCH facor beween Serling and he Yen! I is possible ha he high variabiliy of boh Cable and he Yen/$ raes has in fac reduced he power of he Engle-Kozicki ess, and a ype 2 error has been made. A srong prior ha he Deuschmark and Guilder reurns DO have a common ARCH facor is explored in a laer paper which allows for a dynamic srucure in he Engle-Kozicki common feaure mehodology. However, if a common ARCH facor does exis beween Serling/$ and Yen/$ raes, he daa also offer a possible explanaion for his, in erms of dollar dominaed speculaive invesmen flows. Firsly, volailiy boh Cable and he Yen/$ rae is found o be an imporan deerminan of fuure volailiy in oher currency reurns. Secondly, 12 Because no common ARCH facors are found in NLG and DEM, which have very similar oal ARCH volailiies, wheras evidence of common ARCH is found beween he more dissimilar GBP and JPY. Applied Financial Economics 10

11 he movemens in he mean corresponding o poenial common ARCH facors are in opposie direcions. Thus invesors on he London marke, wih saic expecaions of currency reurns, migh be moving dollars beween Serling (or he Yen) and oher currencies in response o expeced changes in reurns. No evidence of common ARCH facors is found in weekly DM raes, and so i appears ha dollar dominaed speculaive invesmen could form he basis of common condiionally heeroscedasic facors in mean currency reurns. Acknowledgemens: Thanks o David Hendry, Mike Wickens, Mike Sumner and Neil Michael for useful commens, and o Sae Sree Global Advisors (UK) for providing he daa. Applied Financial Economics 11

12 REFERENCES Alexander, C.O. (1994) "Common ARCH facors in Inernaional Currency, Equiy and Bond Markes" Wrien for Applied Mahemaical Finance. Alexander, C.O. and A. Johnson (1992) "Are Foreign Exchange Markes Really Efficien?" Economics Leers Alexander, C.O. and N. Riyai (1992) "The World According o GARCH" Risk 5 No Baillie, R.T. and T. Bollerslev (1989) "The Message in Daily Exchange Raes: A Condiional Variance Tale" Jour. Business and Econ. Sas Engle, R.F. (1982) "Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of U.K. Inflaion" Economerica Engle, R.F. and S. Kozicki (1993) "Tesing for Common Feaures" Journal of Business Economics and Saisics 11 (4) pp (including discussions). Engle, R.F. and R. Susmel (1993) "Common Volailiy in Inernaional Equiy Markes" Journal of Business Economics and Saisics 11 Hseih, D.A. (1989) "Modelling Heeroscedasiciy in Daily Foreign-Exchange Raes" Jour. Business and Econ. Sas Taylor, S.J. (1992) "Modelling Sochasic Volailiy" Lancaser Universiy working paper. Applied Financial Economics 12