Hedging Foreign Currency, Freight and Commodity Futures Portfolios: A Note

Transcription

1 Hedging Foreign Currency, Freigh and Commodiy Fuures Porfolios: A Noe by Michael S. Haigh and Mahew T. Hol WP 0-09 Deparmen of Agriculural and Resource Economics The Universiy of Maryland, College Park

2 Hedging Foreign Currency, Freigh and Commodiy Fuures Porfolios a Noe Michael S. Haigh* and Mahew T. Hol** Foreign exchange hedging raios are simulaneously esimaed alongside freigh and commodiy raios in a ime-varying porfolio framework. Foreign exchange fuures are found o be by far he mos imporan derivaive insrumen o be employed in order o reduce uncerainy for raders. Our resuls lend suppor o he decision by LIFFE o cease rading he BIFFEX freigh fuures conrac because of is low levels of rading aciviy, which likely resuled from is apparen unaraciveness as a hedging insrumen. Manuscrip Saus: The Journal of Fuures Markes, in press. Acknowledgemens: We would especially like o hank David Dickey, Barry Goodwin, Tom Grennes, and seminar paricipans a he Universiy of Arizona and Norh Carolina Sae Universiy. We would also like o hank an anonymous reviewer and he edior for commens on an earlier version of he paper. Michael S. Haigh (corresponding auhor)* Mahew T. Hol** Assisan Professor Professor Deparmen of Agriculural and Resource Economics Deparmen of Agriculural and 10 Symons Hall Resource Economics and Economics Universiy of Maryland Norh Carolina Sae Universiy College Park, MD Raleigh, NC (301) (Tel) (919) (Tel) (301) (Fax) (919) (Fax) mhaigh@arec.umd.edu Ma_Hol@ncsu.edu Copyrigh 00 by Michael S. Haigh and Mahew T. Hol All righs reserved. Readers may make verbaim copies of his documen for non-commercial purposes by any means, provided ha his copyrigh noice appears on all such copies.

3 Hedging Foreign Currency, Freigh and Commodiy Fuures Porfolios a Noe Foreign exchange hedging raios are simulaneously esimaed alongside freigh and commodiy raios in a ime-varying porfolio framework. Foreign exchange fuures are found o be by far he mos imporan derivaive insrumen o be employed in order o reduce uncerainy for raders. Our resuls lend suppor o he decision by LIFFE o cease rading he BIFFEX freigh fuures conrac because of is low levels of rading aciviy, which likely resuled from is apparen unaraciveness as a hedging insrumen. Key Words: Foreign Exchange, Freigh, Commodiy, Fuures, M-GARCH 1. Inroducion In recen years here has been an explosion in he growh and rading of fuures conracs. Despie his, very few fuures conracs ulimaely succeed (Silber, 1981, and Carlon, 1984). Reasons for failure have ranged from bad conrac design o allegaions of marke manipulaion (o name jus wo reasons). Undoubedly a marke mus saisfy mos, if no all, of he desirable characerisics needed for a fuures conrac o succeed, bu quie possibly no one characerisic may be more imporan han volailiy in he underlying marke. Simply pu, he less volailiy he less imporan he fuures conrac is order o hedge he underlying uncerainy. I is perhaps for his reason more han any oher ha researchers focus on he hedging effeciveness of a fuures conrac in reducing price uncerainy. Ineresingly, unlike mos derivaive conracs, he BIFFEX (Balic Inernaional Freigh Fuures Exchange) conrac, which began rading a he London Inernaional Financial Fuures Exchange (LIFFE) in May of 1985, was ypically used along side oher conracs in a hedging scenario. The reason is simply because freigh is jus one of several possible ypes of uncerainy (along wih foreign exchange and commodiy price) in inernaional rade. I was naural herefore for Haigh and Hol (000) o joinly evaluae he role of freigh and commodiy derivaive insrumens (bu no foreign exchange) for inernaional raders using modern ime-series echniques (specifically MGARCH models). Their research highlighed he imporance of aking ino accoun spillovers beween markes and concluded ha ignoring he use of freigh fuures conracs in a rading environmen increased risk (decreased uiliy) by approximaely 15%. However, heir work, like oher previous research, has no considered he possibiliy of hedging commodiy price, freigh rae, and foreign exchange rae risks simulaneously, in a ime-

4 varying seing. There has been a lack of work in his area even hough here is an inuiively appealing (and documened) linkage beween hese differen, ye relaed markes (e.g., Goodwin e al. (1990)). Moreover, i is hese hree markes ha may be he mos concern o inernaional raders. Accouning for all sources of risk is vial when assessing he hedging poenial of a paricular conrac, because he hedging effeciveness of a new conrac may be reduced if oher risks are accouned for especially if here is a link beween hese markes. This poin was well illusraed by Gagnon e al. (1998) who suggesed ha esimaion procedures ha measure hedge raios in isolaion end o over-esimae he number of fuures conracs required o hedge he cash posiion. Simply saed, if here is a naural linkage beween he markes a naural hedge may already in place reducing he necessiy of a paricular conrac. In his empirical applicaion, we exend previous research by providing a complee framework for a rader exposed o foreign exchange, commodiy and freigh price risk, while a he same ime allowing for ime-varying dependencies beween he prices. We do his by using MGARCH modeling echniques inroduced by Engle (198) and Bollerslev (1986) and compare hese (in a similar fashion as Haigh and Hol (000)) o he Seemingly Unrelaed Regressions (SUR) and Ordinary Leas Squares (OLS) approaches. By accouning for foreign exchange uncerainy in he rader s objecive funcion, an added layer of complexiy is inroduced, as all dollar denominaed prices become producs of joinly disribued random variables. The resuling hedge raios are hus complicaed ye racable funcions of means and cenral momens of all prices, an issue no ye addressed in he ime-varying hedging lieraure. By accouning for all ypes of uncerainy we are able o ruly isolae he role of he BIFFEX conrac afer oher ypes of uncerainy have been hedged. Therefore we es Gagnon e al. s (1998) asserion and also ask wheher he rue hedging effeciveness of a derivaive insrumen is reduced once oher criical forms of risk have been accouned for. Building on work by Kavussanos and Nomikos (1999,000) and Haigh and Hol (000) we conclude ha he BIFFEX freigh conrac is no a paricularly effecive hedging insrumen when evaluaed alongside oher relaed conracs. 1 However, we show ha omiing he foreign exchange fuures conrac for raders resuls in subsanial increase in porfolio risk, and ha he relaive imporance of he freigh conrac is even smaller (only abou 6% increases in uiliy)

5 3 han ha repored in oher sudies once all aspecs of poenial risks have been hedged. Our finding suppors he decision by LIFFE o cease rading he BIFFEX conrac in April 00 because of is low rading volume, which likely resuled from is apparen unaraciveness as a hedging insrumen.. Theoreical Framework In his applicaion we follow Haigh and Hol (000) by considering a wo-period problem for a hedger bu here we focus on a European purchaser of U.S. grain who is exposed o foreign exchange rae uncerainy. In period one, he rader plans o purchase grain a he U.S. Gulf bu is unsure of he fuure cash grain price, G i,, where i = corn (c), whea (w) or soybeans (s). The rader is also unsure of he fuure cash freigh rae for ransporing he grain on Roue 1: U.S. Gulf o Roerdam, (R1), and he fuure spo foreign exchange rae (S) necessary o conver he raders home currency ino dollars o pay for he ransacions. In he firs period (-1) all decisions regarding fuures posiions are made, while in he second period () all uncerainies are resolved and he fuures posiions are liquidaed when he spo ransacions ake place. We assume hroughou ha he quaniy shipped remains consan a 50,000 meric ons (e.g., 1,835,000 bushels in he case of soybeans). The rader has a leas hree fuures conracs a his disposal wih which o hedge price uncerainy. Firs, he fuures conrac on he underlying commodiy in quesion denoed C i ; second, he BIFFEX conrac, B, wih which o hedge he freigh price uncerainy; and finally, he foreign exchange fuures conracs, F, used o exchange he raders home currency ino U.S. dollars wih which o pay for he cash ransacions. The reurn realized on he hedged porfolio a ime for he rader is: (1) π G S R S + b ( C S C S ) + b ( B S B S ) + b ( F G F G ), = i 1 1 i 1 1 i i 1 i where π is he oal reurn (per on) on he purchase of he commodiy and b 1, b and b 3 are he commodiy, freigh and foreign exchange fuures posiions (posiive if shor, negaive if long). A ime, he rader pays G i S for grain purchased a he Gulf. Locking ino fuures conracs a ime -1 for price C i-1 and deposiing he required amoun ino a margin accoun could hedge par of ha uncerainy. The proporion hedged is b 1. As fuures conracs are denominaed in U.S. dollars, he margin value of he

6 4 fuures conracs mus be convered o U.S. dollars by muliplying he value by he curren spo rae, S -1. A ime he grain rader would liquidae he fuures conracs a price C i, conver any proceeds from he margin accoun ino he rader s home currency by muliplying by he spo exchange rae, S, and hen purchase he enire unhedged posiion a he Gulf in U.S. dollars. For ocean freigh, he rader would go long BIFFEX conracs a ime -1 and resell he conracs a ime. As BIFFEX fuures conracs are also denominaed in U.S. dollars, he value of he fuures conracs mus be also convered o U.S. dollars by muliplying by he curren spo rae, S -1. The las erm in (1) deermines he opimal number of foreign exchange fuures conracs o be used for hedging foreign exchange risk. The foreign exchange fuures prices are muliplied by he grain prices o provide an indicaion of he number of dollars needed for he expeced grain purchases (because he hedge unis mus be deermined a priori in pracice). The mean-variance framework enables one o easily incorporae ransacion coss ino he analysis (Kroner and Sulan, 1993; Gagnon e al., 1998). Assuming ha our represenaive rader maximizes a mean-variance uiliy funcion, he problem is o selec he opimal fuures posiion, b j, where j = grain (1), BIFFEX () or foreign exchange (3), for each conrac, so as o maximize secondperiod uiliy adjused for ransacion coss: λ () MaxU = Max E( -1) - - ( -1), π Ω y σ π Ω b,b,b b,b,b where E denoes he (condiional) expecaion operaor, σ denoes he variance operaor, 1 Ω is he informaion se available a ime -1, λ is he risk aversion coefficien, and π is as defined in (1) and y represens ransacion coss incurred per uni (meric on). In his analysis he coefficien of absolue risk aversion, represened by λ, was se equal o wo, which is a level ha is in line wih mos sudies incorporaing risk ino he mean variance framework (see e.g., Kroner and Sulan, 1993). The variance of he reurn in equaion () may be wrien as: (3) σ ( π ) = σ GiS + b σ + b b σ 1 + σ GiS,B S R is C is,b S + b + b σ 3 1 GiS,FG i 1 σ C is + b b σ 3 + b + b σ C is,f Gi σ 1 B S R 1S,C is + b b σ + b 3 3 σ F Gi + b σ BS,F Gi. + σ R 1S,BS GiS,R1S + b σ 3 + b σ 1 R 1S,FG i G is,c is

7 5 The expression in (3) is a funcion of variances and covariances of producs of sochasic variables ha are, moreover, joinly disribued. 3 The firs order condiions associaed wih maximizing () comprise a se of linear equaions in he hree unknowns: b 1, b, and b 3. Solving hese equaions for he hree unknowns yields he opimal hedge raios ha would be employed by he rader (he complee derivaions are excluded o conserve space). The componens of each opimal hedge raio are hus simply he variances and covariances of underlying prices, and he expeced reurns and λ. In he curren applicaion we rerieve variance-covariance esimaes and forecass of he reurns from an MGARCH model. Therefore he reurn on he porfolio is: * * * (4) π = GiS R1 S + b 1( Ci 1S 1 CiS ) + b ( B 1S 1 BS ) + b 3( F 1Gi 1 F Gi) y, or for noaional convenience: π ) y if he rader updaes, and ( b * i (5) π = G S R S + b' ( C S C S ) + b' ( B S B S ) + b' ( F G F G ) i 1 1 i 1 1 i i 1 i, or π ( ' b i ) if he grain rader decides no o updae, where b * i is he new hedge raio and b' i is he hedge raio from he mos recen updae. We assume ha one round rip coss $5 for each conrac for each marke. 4 Imporanly, care is aken in his analysis o only include he marginal cos associaed wih updaing he porfolio. Similarly, for noaional convenience, he condiional variance (i.e., equaion (3)) * of he rader s porfolio, if updaing occurs, is simply denoed by σ ( π ( b i )). Likewise, if here is no ' updaing he porfolio is denoed by σ ( π ( b i )). Therefore in he expeced uiliy framework he rader only updaes a each ime if he following condiion is saisfied: * λ * λ ' (6) π ( b i ) y σ ( π ( b i ) > π ( b' i ) σ ( π ( b i ). 3. Daa and preliminary ime -series analysis Weekly Gulf prices covering he period May 17 h 1985 Jan 15 h 1998 (where he las 73 observaions were held back for ou-of-sample forecasing) for corn (G C ), soybeans (G S ) and whea (G W ) were obained from he Inernaional Grains Council and Unied Saes Deparmen of Agriculure. The

8 6 Balic Exchange, LIFFE, and Clarkson Research Services provided daa on freigh cash (R1) and fuures prices BIFFEX (B). These daa covered he same period of ime as he Gulf daa. The BIFFEX daa sars wih he neares conrac monh, and runs unil eiher he conrac reaches is expiry dae or unil he firs day of he acual conrac monh. The raionale behind consrucing such a series is o avoid using daa ha may be affeced by hin markes (see, e.g., Cecchei e al., 1988). The daily daa were convered o a weekly price by aking he selemen prices on he same day ha he weekly grain prices were recorded (Thursday). R1 is available in boh index form and in U.S.$ per meric on. The freigh fuures price is repored in index form, bu, following Hauser and Neff (1993), is convered o a U.S. $ figure. The Chicago Board of Trade (CBOT) fuures prices were obained from Daasream Inernaional for Corn (C C ), whea (C W ), and soybean (C S ). These daa were used o consruc a series similar o ha described for B. As rading in Euro fuures is a relaively recen phenomenon, oher currencies were esed for heir correlaion wih he Euro spo rae. Accordingly, we find ha he Deuschemark (DM) rae is highly correlaed wih he Euro spo rae (ρ = 0.968), and as such, his provides reliable proxy for he Euro foreign exchange rae agains he dollar. DM fuures daa are herefore also consruced on a weekly basis along he same lines as he freigh and grain fuures conracs. Daa for DM fuures (F) and spo (S) prices were colleced from Daasream Inernaional. Each series described above was firs esed for he exisence of a uni roo by using augmened Dickey and Fuller (1981) (ADF) ess. ADF es resuls indicae ha all series are I(1). Johansen s (1988) coinegraion procedure is also used o es for coinegraion beween pairs of cash and fuures prices. Condiional variance dynamics of each individual series and resuls indicae subsanial evidence of GARCH behavior in each case. Because no subsanial deviaions from normaliy are deeced he mulivariae sysems are esimaed under he assumpion of normaliy. 4. Economeric mehodology and model specificaion In his applicaion we employ posiive definie MGARCH parameerizaion, which was inroduced by Engle and Kroner (1995) (henceforh BEKK). In order o implemen he BEKK model, i is necessary o joinly model he firs wo momens of he prices. All daa are firs differenced and if

9 7 necessary he equaions included an error correcion erm, o capure he coinegraing relaionships. All mean equaions were esimaed as an AR(6) process which was found o be suiable o render he residuals whie noise excep for he foreign exchange rae equaions, which were bes described as maringale processes. 5 An MGARCH (1,1) model is used because of he subsanial evidence ha his model adequaely characerizes he dynamics in second momens of prices (Kroner and Sulan 1993). 5. Esimaion resuls For all hree raders models (whea, soybeans and corn), resuls were obained from sysems of equaions esimaed by using a nonlinear maximum likelihood esimaion rouine. 6 Mean equaion resuls indicae ha several lagged pr ices have significan impac on curren prices. Of paricular ineres, however, are he variance-covariance parameer esimaes. The spillover erms in he condiional covariance marix for each model reveal many significan cross-equaion influences, herefore lending suppor o he less resricive BEKK srucure. 7 To highligh a few examples, here are significan linkages beween R1 (cash freigh) and he foreign exchange price innovaions in he models. This resul confirms he inuiively appealing link beween freigh prices and foreign exchange raes. Tha is, as mos ship owners are no U.S. based and as freigh raes end o be denominaed in dollars, any variabiliy in he value of he dollar may have a significan effec on he condiional volailiy of freigh raes. There are also significan spillovers beween he commodiy prices and he foreign exchange rae. The Gulf price is clearly a funcion of many variables, bu any appreciaion/depreciaion of he dollar will affec he real price of grain for a rader whose home currency is no he U.S. dollar. Moreover, as he Gulf price flucuaes, he demand for shipping (and hence price of freigh) may also be affeced. The significance of he parameer associaed wih his effec highlighs his linkage. Finally, and perhaps more inuiively, here is srong covariabiliy beween R1 and B, as illusraed by he significance of ha parameer. This resul is no surprising because R1 had a significan weigh in he BPI, which formed he basis of rading in he freigh fuures

10 8 marke. Finally, wih regards o he esimaion procedure, resuls of several diagnosic ess for each model sugges ha given he complexiy of he models, he MGARCH specificaion works very well Comparisons of hedging performance For comparaive purposes, basic OLS models and SUR models are also esimaed. The SUR framework essenially enails modeling a sysem of OLS equaions joinly bu allowing for conemporaneous correlaion beween he disurbances in he equaions. The SUR model faciliaes a deerminaion of how much advanage (if any) here is o esimaing hedge raios joinly while resricing he variances and covariances o be consan. Comparing he MGARCH model wih he SUR model allows us o deermine wheher here is any advanage of esimaing he variances and covariances joinly and allowing hem o ime-vary. Esimaing he OLS model also permis anoher useful benchmark in he sense ha i is idenical o he SUR approach when we do no allow for conemporaneous correlaion and resric he speculaive componens o zero. If here is no a saisical difference deeced beween hese approaches hen here is unlikely o be an economic difference and so he rewards o hedging using an MGARCH framework are likely o be low. Therefore Likelihood Raio (LR) ess are firs applied o compare he models. Resuls indicae ha he MGARCH approach provides significanly more explanaory power. For insance, in comparing he MGARCH wih he SUR model for all hree models (whea, soybeans and corn) LR es saisics were: 698.1, and (wih 91 degrees of freedom). Disribued as a Chi-square, hese consrained models were rejeced wih a p-value of Therefore, from a saisical sandpoin i is imperaive for rader o no only allow for ineracions beween he markes bu o allow hese ineracions o ime-vary. A rader is more likely o be ineresed in economic differences beween he compeing approaches. For his reason hedge raio simulaions are underaken for wo ime horizons: one in sample, he oher ou-of-sample. Bu as ou-of-sample forecass are designed o provide a more accurae assessmen of hedging performance, we focus on hese resuls. 9 Therefore, for each rader model and each economeric mehodology, a forecas is made of he hedge for each week using he ou-of-sample daa. The subsequen week each model is re-esimaed (wih he new observaion included) and he

11 9 experimen repeaed unil 73 forecass for each model are generaed. Table 1 provides a summary of he hedge raios. Likewise, evaluaions of hedge raio performance are repored in Table. While he variance-covariance marix esimaed from he six-equaion SUR model is consan, he hedge raios generaed for he rader are in fac ime-varying. 10 However, while he SUR hedge raios are nonconsan hey do no vary as much as do hose for he MGARCH model. Also, because new daa are added each week he OLS hedge raio, like he SUR and MGARCH mehodologies, will experience some variabiliy (albei small) in he ou-of-sample analysis. Resuls presened in Table 1 illusrae he average hedge raios generaed for all hree economeric specificaions (OLS, SUR and MGARCH) for each of hree rader models. I is clear ha he average hedge raios for he underlying commodiy generaed from he MGARCH and SUR mehodologies differ from hose generaed by OLS. The only excepion is he recommended grain hedge raio of for he MGARCH corn model, which is much closer o he recommended raio of suggesed by he OLS model. The hedge raios for each of he economeric models imply ha he rader should ake he inuiively correc posiion in each marke o hedge porfolio risk, ha is, go long in each of he fuures marke (negaive sign). Surprising is he lack of imporance of he CBOT (C i ) grain conracs for wo of he porfolios. In paricular, only 1.7% and.7% of he exposed cash posiions should be hedged wih CBOT conracs for he MGARCH framework in model I (whea) and model III (soybeans) respecively, suggesing ha for some markes he grain price uncerainy may be naurally hedged by freigh and foreign exchange conracs. This is a resul ha is no picked up by Haigh and Hol (000) as heir model focused on a rader ha is insulaed from foreign exchange rae risk. Thus, by ignoring spillovers, a rader may overhedge in a paricular marke. So in his insance we confirm Gagnon e al. s (1998) suggesion ha esimaion procedures, generaing hedge raios in isolaion (such as OLS), end o overesimae he number of fuures conracs required o hedge he cash posiion. Ineresingly however, for he case of he foreign exchange rae marke, he recommended average MGARCH hedge raio is 1.109, 1.17 and for he whea, soybean and corn rader models, respecively. This compares o a lower recommended average hedge raio of 0.93 in he OLS model.

12 10 Following Baillie and Myers (1991), and Gagnon e al. (1998), our evaluaion proceeds under he assumpion ha he MGARCH specificaion is he correc probabiliy model for he commodiy, freigh and foreign exchange prices. The full hedge model, where he represenaive imporer uilizes all available derivaive insrumens (freigh, commodiy and foreign exchange), is analyzed under he compeing mehodologies. Several parial hedge models are also examined, where he rader uilizes jus wo of he available derivaive insrumens. Calculaing he performance of he parial hedge in comparison o he full hedge hen allows one o isolae he marginal conribuion of he excluded conrac. To perform his analysis, uiliy derived from each commodiy model is calculaed over he enire period, and hen averaged. The performance of he differen hedge mehods is hen evaluaed by compuing he percenage improvemen in uiliy compared o he unhedged case. Average uiliy for each porfolio (eiher full or parial) calculaed from, respecively, he unhedged, OLS, SUR, or MGARCH models, is repored in Table. Also repored are he incremenal uiliy increases (I.U.I.) visà-vis he unhedged porfolio, and he I.U.I. vis-a-vis he OLS model. The I.U.I. agains he unhedged porfolio allows one o evaluae he marginal conribuion of a paricular derivaive insrumen across and wihin models. The I.U.I. agains he OLS model illusraes how much exra uiliy can be obained by adoping he SUR or MGARCH mehodologies. As repored in Table, if by following his sraegy over he 73 week forecas horizon he rader would sill have been beer off updaing each period wih he MGARCH model even afer accouning for ransacion coss. This resul follows because he average uiliy obained even afer aking ino accoun ransacion coss sill subsanially ouperforms he oher economeric mehods for all commodiies. Alernaively, if he rader had followed he same sraegy bu had employed he SUR mehodology o he full model, updaing would have occurred 10 imes for model I, 1 imes for model II, and 10 imes for model III. Even a ha, he porfolio performance is superior o ha obained by using he OLS framework, confirming he imporance of accouning for spillovers (albei non ime-varying). When he BIFFEX freigh fuures marke is no included in he porfolio (parial hedge A), performance does decline slighly vis-à-vis he unhedged porfolio. Specifically, he performance of he

13 11 MGARCH model in he full model implies an improvemen over he unhedged porfolio by 74.60%. This percenage declines in parial hedge A o 68.6%, implying a marginal conribuion of abou 6.3% of he freigh conrac in he MGARCH framework. Similar magniudes are found for models II and III, once again indicaing some, albei low imporance of including freigh fuures conracs in he rader s porfolio. The BIFFEX conrac seems o provide some limied help in managing price uncerainy when he OLS and SUR mehodologies are employed. When he BIFFEX marke is excluded he MGARCH model recommends less updaing; however, lower uiliy levels are obained relaive o he full hedge model. Ineresingly whereas Haigh and Hol (000) repored a marginal conrib uion of he BIFFEX conrac of abou 15%, Kavusssanos and Nomikos (000) repor reducions in variance of abou 18% (depending on he shipping roue). However, because Kavussanos and Nomikos (000) sudied he BIFFEX in isolaion, and Haigh and Hol (000) incorporaed jus one oher source of risk, we migh infer ha afer hedging all relevan elemens of risk, he BIFFEX conrac becomes less and less essenial. The conribuion of he commodiy fuures conracs varies across commodiy and across economeric specificaion. For example, excluding he CBOT conrac from he whea, soybean and corn rader s MGARCH porfolio requires a decrease of uiliy of 0.45%, 8.74% and 9.83% respecively suggesing a slighly greaer level of imporance of hedging his elemen of uncerainy for hese commodiies compared o he BIFFEX. Moreover, unlike he BIFFEX marke, hese conracs are obviously useful in oher risk managemen seings oher han inernaional rade (as suggesed by heir non-rivial rading volume a he CBOT). Ignoring he poenial usefulness of he foreign exchange conrac is he mos derimenal omission. For he whea, soybean, and corn raders, respecively, he foreign exchange conrac conribuion ranges from 9.3% o 76.% in he MGARCH seup. The comparable conribuion for he OLS model ranges from 49.94%, o 18.03% (again implying performance improves afer is omission) and 7.78% for model I, II and III, respecively. Finally, for he SUR approach he foreign exchange fuures conrac conribues 58.39%, 55.91% and 44.76% respecively.

14 1 The incremenal uiliy increase agains he OLS model confirms previous resuls suggesing he imporance of incorporaing ime-varying covariabiliy in opimal hedge raio esimaion. In he full model, he MGARCH procedure provides a furher 19.38%, 75.% and 3.90% increase in uiliy for he whea, soybean and corn raders respecively. Moreover, hese resuls once again sugges ha, alhough aking ino accoun covariabiliy and updaing forecass of cash and fuures prices has a posiive effec on reducing risk as shown in he SUR model resuls, i is he incorporaion of ime-varying covariabiliy beween cash and fuures prices ha leads o greaer gains for inernaional grain raders Conclusion In his noe we examine linkages beween freigh, commodiy, and foreign exchange prices and relax he assumpion ha cash and fuures prices are independenly disribued. Because we examine hedging for a prooypical rader purchasing grain a U.S. pors, our model includes exchange rae uncerainy in addiion o freigh rae and commodiy price uncerainy. The implicaion is ha he grain imporer s expeced uiliy funcion includes producs of joinly disribued random variables which, moreover, posses ime-varying covariabiliy. Therefore, unlike previous sudies ha have sough o capure porfolio effecs, he hedge raios derived here are complicaed albei manageable funcions of ime-varying variances and covariances of producs of random variables. These producs are hemselves funcions of means and cenral momens of he underlying cash and fuures prices. The resuls we repor here confirm ha he assumpion of independence is erroneous and incorporaing more realisic assumpions regarding he co-dependency of prices direcly ino he hedging paradigm yields rewards in erms of risk reducion for raders. This research has also confirmed Haigh and Hol s (000) finding ha despie he fac ha frequen porfolio updaing recommended by he MGARCH model may be more expensive han radiional modeling mechanisms such as OLS he rewards in erms of reduced variabiliy, and hence exra uiliy, considerably ouweigh he exra ransacion coss associaed wih doing so. This was found o be rue for each commodiy model

15 13 evaluaed. Also, he relaive imporance of each derivaive conrac in he overall porfolio for a rader was isolaed. Perhaps mos crucially, his research has illusraed ha he BIFFEX conrac is no as imporan a hedging insrumen when evaluaed alongside oher conracs for raders. While he commodiy fuures conracs are shown o be only slighly more imporan in his seing, hese conracs are obviously vial in oher risk managemen scenarios, and he volume of rade in hese conracs a he CBOT suppors his argumen. However, unlike oher conracs he BIFFEX freigh fuures conrac is only used for hedging in inernaional rade, and would likely be used alongside oher derivaive insrumens. We find ha once oher ypes of risks have been accouned for, he imporance of he BIFFEX conrac declines (because naural hedges from oher markes seems o occur) which may help explain is decline in populariy. Consequenly hese resuls may shed some ligh on why he conrac now ceases o exis afer seveneen years of rading. Imporanly, our resuls sugges ha of all hree hedging insrumens considered, omiing he foreign exchange conrac from he rader s porfolio is by far he mos derimenal in erms of risk managemen.

16 14 Table 1 Ou-of-Sample Average Hedge Raios Freigh hedge raio Model I (Whea) OLS SUR MGARCH (0.013) Model II (Soybeans) OLS SUR MGARCH (0.051) Model III (Corn) OLS SUR MGARCH (0.006) Grain hedge raio (0.015) (0.001) (0.00) (0.546) (0.310) FOREX hedge raio (0.015) (0.00) (0.63) (0.379) Figures in parenhesis are variances.

17 15 Table Ou-of-Sample Hedge Performance Model I (Whea) Model II (Soybean) Model III (Corn) I.U.I I.U.I I.U.I I.U.I I.U.I Uiliy unhedged OLS Uiliy unhedged OLS Uiliy Unhedged I.U.I OLS Full Model: Using all hree derivaive conracs freigh, commodiy and foreign exchange conracs Unhedged OLS (3) 68.50% (18) 46.7% (3) 50.05% SUR (10) 71.05% 8.10% (1) 80.93% 64.0% (10) 58.35% 16.61% MGARCH (73) 74.60% 19.38% (73) 86.80% 75.% (73) 66.49% 3.90% Parial Model (A): Using wo derivaive conracs excluding he freigh fuures conrac Unhedged OLS (4) 61.97% (0) 40.94% (3) 46.83% SUR (5) 63.15% 3.11% (31) 76.01% 59.39% (3) 5.63% 10.91% MGARCH (56) 68.6% 16.54% (57) 80.16% 66.41% (43) 59.90% 4.59% Parial Model (B): Using wo derivaive conracs excluding he commodiy fuures conrac Unhedged OLS (39) 71.61% (38) 80.74% (35) 57.7% SUR (37) 70.76% -.95% (31) 76.3% -3.39% (37) 57.5% 0.59% MGARCH (56) 74.15% -8.94% (38) 78.06% % (31) 56.55% -1.67% Parial Model (C): Using wo derivaive conracs excluding he foreign exchange fuures conrac Unhedged OLS (50) 4.66% (38) 68.77% (47) 4.7% SUR (43) 1.66% % (40) 5.0% % (39) 13.59% % MGARCH (40) 13.17% -15.4% (38) 10.59% % (39) 37.1% -8.77% This able displays he uiliy derived from he porfolio assuming ha he grain rader rebalances he porfolio only when he poenial increase in uiliy derived exceeds he ransacions coss ha would be incurred from adjusing he holdings of fuures conracs. The uiliy (aking ino ransacion coss) is compued from equaion (). Transacion coss are assumed o be $5 per round-urn. The number of porfolio rebalancings is given in parenhesis.

18 16 References Baba, Y., Engle, R.F., Kraf, D.F., and Kroner, K.F., Mulivariae Simulaneous Generalized ARCH. unpublished manuscrip, Universiy of California, San Diego, Dep of Economics. Bollerslev, T., (1986). Generalized Auoregressive Condiional Heeroskedaciy. Journal of Economerics 31, Borhrnsed, G.W., and Goldberger, A.S., (1969). On he Exac Covariance of Producs of Random Variables. Journal of he American Saisical Associaion 64, Carlon, D.W., (1984). Fuures Markes: Their Purpose, Their Hisory, Their Growh, Their Successes and Failures. The Journal of Fuures Markes. 4, Cecchei, S.G., Cumby, R.E., and Figlewski, S., (1988). Esimaion of he Opimal Fuures Hedge. The Review of Economics and Saisics 70, Dickey, D.A., and Fuller, W., (1981). Likelihood Raio Tess for Auoregressive Time Series wih a Uni Roo. Economerica 49, Engle, R.F., (198). Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of U.K. Inflaion. Economerica 50, Engle, R.F., and Kroner, K.F., (1995), Mulivariae Simulaneous Generalized ARCH. Economeric Theory 11, Gagnon, L., Lypny, G.J., and McCurdy, T.H., (1998). Hedging Foreign Currency Porfolios. Journal of Empirical Finance 5, Goodman, L.A., (1960). On he Exac Variance of Producs. Journal of he American Saisical Associaion 55, Goodwin, B.K., T. Grennes., and M.K. Wohlgenan., (1990). Tesing he Law of One Price when Trade Takes Time. Journal of Inernaional Money and Finance 9, Haigh, M.S., and M.T. Hol., (000). Hedging Muliple Price Uncerainy in Inernaional Grain Trade. American Journal of Agriculural Economics 8,

19 17 Hauser, R.J., and Neff., D., (1993). Expor/Impor Risks a Alernaive Sages of U.S. Grain Expor Trade. The Journal of Fuures Markes 13, Johansen, S., (1988). Saisical Analysis of Coinegraion Vecors. Journal of Economic Dynamics and Conrol 5, Kavussanos, M., and N.Nomikos., (1999). Fuures Hedging when he Srucure of he Underlying Asse Changes: he case of he BIFFEX conrac. The Journal of Fuures Markes 0, Kavussanos, M., and N.Nomikos., (000). Consan vs. Time-Varying Hedge Raios and Hedging Efficiency in he BIFFEX Marke. Transporaion Research: Par E: Logisics and Transporaion Review 36, Kroner, K.F., and Sulan, J., (1993). Time Varying Disribuions and Dynamic Hedging wih Foreign Currency Fuures. Journal of Financial and Quaniaive Analysis 8, Lypny, G., and Powalla, M., (1998). The Hdging Effeciveness of DAX Fuures. The European Journal of Finance 4, Silber, W.L., (1981). Innovaion, Compeiion and New Conrac Design in Fuures Markes. The Journal of Fuures Markes 1, Tong, W., (1996). An Examinaion of Dynamic Hedging. Journal of Inernaional Money and Finance 15,

20 18 Endnoes 1. As he BIFFEX conrac is based on a baske of dry-bulk shipping roues ha comprise he Balic Panamax Index (BPI) and because shipping roue prices ofen move quie independenly from one anoher, hedging a paricular roue ha is par of he BPI may no be a perfec, making he hedge less appealing, and he volume of rading lower. For insance, over he period , he average rading volume was only 146 conracs. The moneary value of hese conracs roughly corresponds o he cos of shipping 108,000 ons of grain from he U.S. o Japan. In 1995 rading began in over-he-couner (OTC) derivaives like Freigh Forward Agreemens (FFA s) and has since winessed remarkable growh since. Indeed, many praciioners sugges ha his was par of he reason ha in June 001, LIFFE, he auhoriy regulaing he BIFFEX conrac, announced ha rading in he BIFFEX conrac would cease in April 00.. Here we ignore any opporuniy gains or losses associaed wih ineres raes on he margin accoun. 3. For he general case of joinly disribued random variables x and y, Goodman (1960) derives he exac variance of a produc xy as: V(xy) = E (x)v(y) + E (y)v(x) + E(x)E(y)C(x,y) + V(x)V(y) + C (x,y), where we denoe E(x) and E(y) as he expecaions of joinly disribued random variables x and y, V(x) and V(y) as he variances of x and y, and C(x,y) as heir covariance. Bohrnsed and Goldberger (1969) exend Goodman s resuls o derive he exac covariance of wo producs xy and uv and applying asympoic approximaion procedure, yield he expression for he covariance of covariance of xy wih uv: C*(xy,uv) = E(x)E(u)C(y,v) + E(x)E(v)C(y,u) + E(y)E(u)C(x,v) + E(y)E(v)C(x,u), where C*(.,.) denoes an approximae covariance. These are he exac expressions for he produc of random variables ha are used hroughou his paper. 4. As he quaniy being shipped is assumed o be 50,000 ons (or 1,965,000 (corn) bushels) a full CBOT hedge would imply a oal of (1,965,000/5000) 393 conracs, a a cos of $9,85. The number of freigh and foreign exchange conracs required for a full hedge is more complicaed o calculae a each ime because boh are funcions of prices, unlike he CBOT commodiy conracs which are fixed in quaniy. Noneheless, assume a level of he BPI of 95, and a cash price of freigh of $7.30 per meric on. In his case he recommended full hedge would be ($7.30(50,000))/95(10) 39 conracs or $975 as he value of a BIFFEX conrac is calculaed

21 19 by aking he level of he BPI and muliplying by $10. The number of foreign exchange conracs needed by he rader is a funcion of he Gulf price. Therefore, assuming a cash price of $.67 per bushel for corn (or $105 per on), and ha 1,965,000 bushels will be purchased, he expeced dollar purchase will be $5,46,550. A a U.S./DM exchange rae of 0.33, he number of conracs required for a full hedge would be 15,898,636DM/15,000DM 17 conracs oaling abou $3179. Therefore, assuming a full hedge in each marke, he oal cos would be approximaely $13,979 (or 4,36 DM). On a per on basis his implies ha he cos of full hedging is jus $0.7 or abou 0.85 DM. If he expeced price per on is $105 ( DM), ransacion coss are approximaely percen of he oal value. 5. Following Tong (1996), he MGARCH srucure used here has an AR represenaion in he mean equaion o capure residual serial correlaion. Seasonaliy was also esed for by applying harmonic variables se a quarerly and monhly cycles o each of he commodiy and freigh equaions. Specific ally, where he harmonic variables used are SIN1 = sin(π/13), COS1= cos(π/13) and SIN = sin(π/4), COS = cos(π/4), = 1,,T o represen quarerly and monhly seasonaliy respecively. Resuls indicaed a all convenional significance levels ha here was no evidence of remaining unexplained seasonaliy. 6. Given he large number of parameers and he fac ha several versions of he models were consruced (one per commodiy), ables reporing all parameer esimaes are excluded o conserve space. These resuls are however available upon reques. 7. An MGARCH linear diagonal specificaion was also esimaed. Resuls from likelihood raio ess confirm ha for all hree models (whea, soybeans and corn) he BEKK is superior o he parsimonious alernaive. 8. Skewness and kurosis esimaes indicae some deparures from normaliy in he sandardized residuals, as confirmed by Jarque-Bera normaliy ess bu ess for remaining residual auocorrelaion in he sandardized residuals, squared sandardized residuals, and heir crossproducs, show, for he mos par (afer excluding a rivial se of ouliers), ha here are no serious misspecificaions of he condiional mean and variance dynamics in he esimaed models. 9. In-sample resuls are qualiaively similar o he ou-of-sample resuls and are also available upon reques.

22 0 10. The asympoic expressions for he variance and covariance of producs of random variables conains expressions for he variances and covariances of he prices, and expeced values of he prices (see Foonoe 3). As he expeced values are forecased values, he variance and covariance expressions for producs of random variables will ime-vary as a resul of he updaed forecass. 11. As suggesed by an anonymous reviewer, i may also be of ineres o know wheher uiliy values across models are saisically differen. To his end, following Lypny and Powalla (1998) we conduc sign ess for he difference beween expeced and realized uiliy. Resuls sugges ha he MGARCH approach significanly ouperformed alernaives when foreign exchange risk was accouned for. However, afer excluding he foreign exchange rae fuures conracs performance declined and he MGARCH approach was ouperformed by simpler alernaives. On several occasions he OLS and SUR performances were saisically similar.