The Sensitivity of the Optimal Hedge Ratio to Model Specification

Transcription

1 Face Leers Te Sesvy of e Omal Hedge Rao o Model Secfcao Imad. Moosa * La Trobe versy usrala bsrac Ts aer vesgaes e effec of e coce of e model used o esmae e edge rao o e effecveess of fuures ad cross-currecy edgg usg daa from e sock ad foreg excage markes. Four dffere models are used for s urose o esmae e edge rao. Te resuls sow a model secfcao as lle effec o e edgg effecveess. I seems a wa maers mos s e correlao bewee e rces of e uedged oso ad e edgg srume. Key words: Hedgg Effecveess Hedge Rao Cross-Currecy Hedgg JEL classfcao: G5. INTRODCTION Two mora quesos are volved facal edgg: o edge or o o edge; ad f e decso o edge s ake do we edge e full oso? Ts aer deals w e secod queso wc amous o esmag e edge rao or deermg e sze of e oso o e edgg srume a s used o edge a so cas oso. I s exercse we use daa o sock rces as well as excage raes ad ece we deal w e edgg of exosure o equy rsk ad foreg excage rsk. I as bee suggesed a e omal edge rao ca dffer sgfcaly deedg o e model a s used o esmae e edge rao Gos 993. Te coveoal model akes e form of a OLS regresso equao wc e deede varable s e rce of or e rae of reur o e uedged oso wereas e exlaaory varable s e rce of or e rae of reur o e edgg srume wc could be a forward or a fuures corac. Ts model as bee crcsed o e grouds a gores sor-ru dyamcs we s secfed levels ad e log-ru formao emboded e error correco erm we s secfed frs dffereces. Gos 993 fds e edge raos obaed from radoal models o be uderesmaed because ese models are mssecfed. Le 996 sows aalycally a e edger makes a msake f e edgg decso s based o e edge rao derved from a frs-dfferece model a does o coa a error correco erm. Tere s also e ssue of weer or o e edge rao sould be esmaed from a frs dfferece or a level model wc are mlcly ake o be equvale see for examle Gos 993; W e al d ere s e roblem of weer e edge rao sould be esmaed from e codoal or e ucodoal momes wc as bee deal w by Kroer ad Sula 993 as well as Brooks ad Cog 00. I s aer we do o deal w s ssue bu raer cocerae o weer or o makes ay dfferece for edgg effecveess f e edge rao s derved from a levels as oosed o a frs-dfferece model; ad a frs-dfferece as oosed o a error correco EC model.. MESRING THE OPTIML HEDGE RTIO Le ad be e logarms of e rces of e uedged so or cas oso ad e edgg srume resecvely suc a e raes of reur o ese osos are ad resecvely. Te level ad frs dfferece models are wre as * Emal:.moosa@larobe.edu.au ISSN Global EcoFace ll rgs reserved. 5

2 Moosa 6 α ε α ε were ad are e esmaed edge raos suc a e R of e regressos measures e edgg effecveess. Ts rocedure for calculag e edge rao s based o a alcao of e rcles of orfolo eory as demosraed by Joso 960 Se 96 Edergo 979 McEally ad Rce 979 Frackle 980 ad Hll ad Sceewes 98. Some ecoomss make soud as f e wo models rereseed by equaos ad are wo alerave meas for measurg e same g. For examle Gaccoo e al alk abou mmsg e volaly of e oal cas flow or equvalely e cage flow. Hll ad Sceewes 98 recommed e use of e frs-dfferece model oly because e model levels roduces serally correlaed resduals. Srcly seakg owever e coce would or sould deed o weer e objecve s o mmse e varace of e rce or e rae of reur. Ts s because e varaces of e edged osos corresodg o equaos ad are H 3 4 H Te mmum-rsk or e mmum-varace edge raos ca be obaed by dffereag equaos 3 ad 4 w resec o e edge raos ad solvg e frs order codos wc are wre as d d d H 0 H d Solvg e frs order codos gves 0 7 Obvously e edge raos ad are o ecessarly equal. We wll fd ou wa aes we e edge rao esmaed from a model levels s used o reduce e varace of e rae of reur o e edged oso ad vce versa. Oe roblem w equaos ad s a a equao gores sor-ru dyamcs wereas equao gores e log-ru relaos as rereseed by equao. Secfcally f ad are coegraed suc a ε ~I0 e equao would be mssecfed wc case e correcly secfed model s a error correco model of e form α β γ θ 9 Le 996 argues a e esmao of e edge rao ad e edgg effecveess may cage sarly we e ossbly of coegrao bewee rces s gored. I Le ad Luo 994 s sow a aloug GRCH may caracerse e rce beavour e coegrao relaos s e oly ruly dsesable comoe we comarg e ex os erformace of varous edgg sraeges. Gos 993 cocluded a a smaller a omal fuures oso s uderake we e coegrao relaos s uduly gored. He arbued e uder-edge resuls o model mssefcfcao. Le 996 rovdes a eorecal aalyss of s cojecure by assumg a coegrag relaos of e form. smlfed error correco model wc mles a rces adjus resose o dsequlbrum ca be wre as 5 6 8

3 Moosa 7 α 0 β If e edge rao s cose o mmse e e edge rao s calculaed as ρ were ρ s e correlao coeffce bewee ad. leravely e edge rao ca be calculaed from e regresso equao ζ γ α 3 If e coegrag relaos s gored e e edge rao s calculaed as 8. From equaos 0 ad we ave α β ρ αβ 4 ad β β 5 Hece e edge rao s measured as β ρ αβ 6 Obvously ere s a dfferece bewee e exressos equao 6 ad equao. O e bass of ese wo exressos Le 996 cocludes a a erra edger wo msakely oms e coegrag relaos by usg equao 6 always uderakes a smaller a omal oso o e edgg srume comared w a edger usg equao. Ts rooso s cofrmed emrcally by Gos 993. By usg a geeral secfcao of equaos 0 ad we ave b a 0 α 7 d c 0 β 8 wc case e edge rao calculaed o e bass of e correcly secfed model s gve by ρ 9 wereas e erra edger wo does o ake o accou e coegrao relaos wll coose a edge rao a s gve by

4 Moosa 8 ρ αβ β wc meas a e erra edger wll uderake a smaller a omal oso o e edgg srume currg losses edgg effecveess. For e urose of assessg e edgg effecveess based o varous models a edge s cosdered o be effecve we e varace of e rce or e rae of reur of e uedged oso s sgfcaly ger a a of e edged oso. Ts wll be obaed f e varace rao sasfes e codo VR > F H were s e samle sze. Te effecveess of wo edges ca be comared o e bass of varace reduco wc s calculaed as VD VR Four models are used for e urose of calculag e edge rao: e levels model equao ; e frs-dfferece model equao ; a smle error correco model equao 9 w β 0 ad γ 0; ad v a geeral error correco model equao DT ND EMPIRICL RESLTS Two ses of daa are used s emrcal exercse. Te frs s a se of moly observaos o cas ad fuures rces of usrala socks. Te cas rce s rereseed by e ll Ords dex wereas e fuures rce s rereseed by e SPI dex. Te samle wc was obaed from e usrala Sock Excage covers e erod 987:-997:. Te secod samle cosss of quarerly observaos coverg e erod 980:-000:4 o e so excage raes of e oud ad e Caada dollar agas e.s. dollar. I s case of cross-currecy edgg e base currecy s e oud e exosure currecy s e.s. dollar ad e currecy used for edgg s e Caada dollar. Tus SSD/GBP ad SSD/CD. Te daa samle was obaed from e OECD s Ma Ecoomc Idcaors. Table ad Table reor e esmaed edge raos e varaces varace raos ad varace reducos for sock rces. loug e esmaed edge raos are umercally dffere e resuls erms of varace reduco are o a dffere. I all cases edgg s effecve ad e reduco e varace s close over 97 er ce all cases. Table. Esmaed Hedge Raos: Sock Prces Model Hedge Rao R Level Frs Dfferece Smle EC Geeral EC We ow exame e resuls obaed by usg excage raes wc are reored Tables 3 ad 4. ga e esmaed edge raos are umercally dffere bu s makes lle dfferece o e resuls: o case s e edge effecve as e varace raos are sascally sgfca. Te reaso for e dfferece bewee ese resuls ad ose obaed by usg sock rce daa s arbued o e lack of correlao bewee ad s case ulke e revous case. Wa maers for e resuls seems o be o e model used o esmae e edge rao bu raer e correlao. Resuls obaed by Moosa 00 sow a for a effecve edge e correlao coeffce bewee ad mus be a leas 0.50 o roduce varace reduco of abou 5 er ce.

5 Moosa 9 Table. Hedgg Effecveess: Sock Prces Varace Model Esmaed Value VR VD Level Frs Dfferece Smle EC Geeral EC Level * Frs Dfferece * 99. * Relave o. Table 3: Esmaed Hedge Raos: Excage Raes Model Hedge Rao R Level Frs Dfferece Smle EC Geeral EC Table 4: Hedgg Effecveess: Excage Raes Varace Model Esmaed Value VR VD Level Frs Dfferece Smle EC Geeral EC Level * 6.97 Frs Dfferece * 6.97 * Relave o. 4. CONCLSION I as bee argued a e coce of e model used o esmae e edge rao makes some dfferece for e effecveess of edgg measured as e reduco e varace of e uedged oso. Ts sudy vesgaed s ssue emrcally by emloyg four dffere models o esmae e edge raos used o cover exosure o so osos socks ad curreces. loug e eorecal argumes for wy model secfcao does maer are elega e dfferece model secfcao makes for edgg erformace seems o be eglgble. Wa maers for e success or falure of a edge s e correlao bewee e rces of e uedged oso ad e edgg srume. Low correlao varably roduces sgfca resuls ad effecve edge wereas g correlao roduces effecve edge rresecve of ow e edge rao s measured.

6 Moosa 0 REFERENCES Brooks C. ad J. Cog 00 Te Cross-Currecy Hedgg Performace of Imled versus Sascal Forecasg Models Joural of Fuures Markes Edergo L.H. 979 Te Hedgg Performace of e New Fuures Markes Joural of Face Frackle C.T. 980 Te Hedgg Performace of e New Fuures Markes: Commes Joural of Face Gos. 993 Hedgg w Sock Idex Fuures: Esmao ad Forecasg w Error Correco Model Joural of Fuures Markes Gaccoo C. S.P. Hedge ad J.B. McDermo 00 Hedgg Mulle Prce ad Quay Exosures Joural of Fuures Markes Hll J. ad T. Sceewes 98 Noe o e Hedgg Effecveess of Foreg Currecy Fuures Joural of Fuures Markes Hll J. ad T. Sceewes 98 Te Hedgg Effecveess of Foreg Currecy Fuures Joural of Facal Researc Joso L. 960 Te Teory of Hedgg ad Seculao Commody Fuures Revew of Ecoomc Sudes Kroer K.F. ad J. Sula 993 Tme-Varyg Dsrbuos ad Dyamc Hedgg w Foreg Currecy Fuures Joural of Facal ad Quaave alyss Le D. 996 Te Effec of e Coegrao Relaos o Fuures Hedgg: Noe Joural of Fuures Markes Le D. ad X. Luo 994 Mulerod Hedgg e Presece of Codoal Heeroskedascy Joural of Fuures Markes McEally R.W. ad M.L. Rce 979 Hedgg Possbles e Floao of Deb Secures Facal Maageme 0-8. Moosa I.. 00 Te Effecveess of Cross-Currecy Hedgg ublsed Paer La Trobe versy usrala. Se J.L. 96 Te Smulaeous Deermao of So ad Fuures Prces merca Ecoomc Revew W H. T. Scroeder ad M. Hayega 987 Comarso of alycal roaces for Esmag Hedge Raos for grculural Commodes Joural of Fuures Markes