Forign Rsrv Managmn in an Oil Economy: Macroconomic Risk as a Ral Opion. Vrsión prliminar Sri Documnos d Trabajo [N o. 164] Mayo, 17 Pasqual Scandizzo Carolina Pagliacci
Banco Cnral d Vnzula, Caracas, 17 Grncia d Invsigacions Económicas Producción diorial Grncia d Comunicacions Insiucionals, BCV Dparamno d Publicacions Torr Financira, piso 14, ala sur Avnida Urdana, squina d Las Carmlias Caracas 11 Tléfonos: 81.875 / 863 Fax: 536.9357 publicacionsbcv@bcv.org.v www.bcv.org.v Las opinions y análisis qu aparcn n la Sri Documnos d Trabajo son rsponsabilidad d los auors y no ncsariamn coincidn con las dl Banco Cnral d Vnzula. S prmi la rproducción parcial o oal simpr qu s mncion la fun y no s modifiqu la información.
Forign Rsrv Managmn in an Oil Economy: Macroconomic Risk as a Ral Opion Pasqual Scandizzo & Carolina Pagliacci ** Absrac This papr asssss rsrv managmn for drmining opimal or minimal rsrvs for an oil producing conomy undr dynamic uncrainy. Rsrv bnchmarks ar formulad aking ino considraion h amoun of coningn liabiliis in forign xchang ha ariss during currncy criss. Ths coningn liabiliis ar drivd basd on h analogy bwn holding domsic mony and possssing a financial opion whos payoff dpnds on h xpcd bhavior of oil procds. Whn rsrv accumulaion has an opporuniy cos in rms of capial goods, an opimum lvl of rsrvs can b sablishd, givn h capabiliy of rsrvs o dlay and miiga currncy criss. Alrnaivly, whn rsrvs consiu h bs mans o accumula counry walh, an appropria minimal rsrv lvl may b calculad. In his cas, rsrvs ac as an insrumn of slf-insuranc ha guarans honoring a slcd amoun of forign xchang claims a h im of a crisis. Economric simas for Vnzula show rasonabl numrical valus for counrfacual opimal and minimal rsrvs. Kywords: uncrainy and risk, opimal rsrvs, currncy crisis, ral opions. JEL Classificaion Numbrs: D81, G13, F31. Opinions xprssd in his aricl ar hos of h auhors and do no rflc h viws of h Board of Dircors of h Cnral Bank of Vnzula. & Profssor of h Univrsiy Tor Vrgaa, mail:scandizzoniroma.i. ** Snior Rsarchr of h Economic Rsarch Offic, Cnral Bank of Vnzula, -mail: cpagliac@bcv.org.v.
Manjo d Rsrvas Inrnacionals n una Economía Prolra: El risgo Macroconómico como una Opción Ral Pasqual Scandizzo & Carolina Pagliacci Rsumn Es rabajo analiza la l manjo d rsrvas para drminar rsrvas ópimas o mínimas para una conomía prolra n un conxo con incridumbr dinámica. Esos nivls rfrncials d rsrvas son formulados omando n considración los pasivos coningns n monda xranjra qu mrgn duran las crisis cambiarias. Esos pasivos coningns son drivados basados n la analogía nr mannr monda domésica y posr una opción financira cuyo payoff dpnd dl comporamino sprado d los ingrsos prolros. Cuando la acumulación d rsrvas in un coso d oporunidad n érminos d bins d capial, un nivl d rsrvas ópimo pud dr drminado, dada la capacidad d las rsrvas para rardar y miigar las crisis cambiarias. Alrnaivamn, cuando las rsrvas son l mjor mdio para acumular la riquza d un país, un nivl mínimo d rsrvas pud sr calculado. En s caso, las rsrvas acúan como un insrumno d auo-asguramino qu garaniza honrar un mono slccionado d obligacions n monda xranjra al momno d una crisis. Las simacions para Vnzula musran valors numéricos razonabls para rsrvas ópimas y mínimas conrafacuals. Palabras Clavs: Incridumbr y risgo, rsrvas ópimas, crisis cambiarias, opción ral Clasificación Jl: D81, G13, F31. Las opinions miidas n s arículo son rsponsabilidad d los auors y no compromn la visión qu l Banco Cnral d Vnzula puda nr sobr l ma. & Profssor of h Univrsiy Tor Vrgaa, mail:scandizzoniroma.i. Invsigador Snior d la Oficina d Invsigacions Económicas dl Banco Cnral d Vnzula. Corro lcrónico: cpagliac@bcv.org.v
3 1. Inroducion Wih hir spcacular ris o mor han 3 rillion dollars in h pas yars, forign rsrvs hav bcom a worldwid mblm of global imbalancs in rad and financ flows. On on hand, hy may b considrd h mirror imag of h rcord xpansion of U.S. forign dfici and is corrsponding db. On h ohr hand, hy may b akn o rflc h growing concrn of govrnmns and cnral banks on currncy insabiliy and currncy criss. So far, as mos of h liraur on h subjc noics, forign rsrv accumulaion has bn mosly h rsul of passiv policis, i.. prudn, bu rsidual accumulaion of forign xchang surpluss o proc h counry from a rainy day. Nihr from h poin of viw of financial rurns, nor from ha of risk managmn, h choic of forign currncy accumulaion or is allocaion o financial asss appars o hav followd a raional policy modl. Th prsn papr addrsss h policy qusion of forign rsrv accumulaion in an oil conomy as a cas sudy of dvlopmn planning undr macroconomic risk. Risk, in his papr, rlas o h hra of currncy criss, which ar drivn by h condiions of dynamic uncrainy ha characriz forign xchang marks. Th approach proposd is basd on h ida ha an adqua lvl of forign rsrvs can b dfind ihr as an opimal lvl for miigaing currncy crisis or as a minimal slf-insuranc lvl. Opimaliy ariss bcaus forign rsrvs can b sn as an ass ha comps wih h allocaion of h counry s incom flow in capial goods, bu also as an ass ha has h propry o counrbalanc lan liabiliis ha rsul from agns financial valuaion of wo alrnaiv asss -domsic and forign currncy-. In his cas, h ssnial rol assignd o rsrvs is ha of discouraging ponial forign xchang claims agains h Cnral Bank. For h cas of a minimal lvl, rsrvs ar xclusivly usd o rduc h xposur o risk according o h xplici prfrncs of policymakrs. Th drminaion of hs forign xchang coningn liabiliis a an aggrga lvl builds h conncion of his papr wih ral opion hory, gnraing also furhr implicaions for macroconomic planning. According o Dixi and Pyndick (1991), h opion valu of any commodiy drmins h spculaiv componn ha conribus o xplaining is coningn valu. In h cas of domsic mony, his opion valu rflcs h diffrnc bwn h opporuniy of buying forign xchang oday and h dcision of kping domsic currncy. Tha is, holding liquid balancs dnominad in domsic currncy mbds a righ o convr hm ino forign currncy or ohr asss dnominad in forign mony, craing h analogy wih possssing a financial opion. In his conx, coningn liabiliis agains h Cnral Bank aris from considring h inrmporal valuaion of h opion o convr domsic ino forign asss. Bcaus domsic and forign mony ar rlad hrough h concp of a financial opion, a crucial rol is playd by dprciaion xpcaions on h domsic currncy. A h sam im, hs dprciaion xpcaions will dpnd on h soundnss of h fundamnals of an oil conomy, which can b ulimaly dscribd by h xpcaions formd around h bhavior of h counry s forign arnings (oil
rvnus). Ths wo lmns lad o assr ha h xpcd dprciaion of h domsic currncy and coningn forign liabiliis rly on h uncrainy abou h fuur prformanc of hs arnings. Howvr, h chancs of xprincing currncy criss, and hir ffc on h counry walh can b miigad and dlayd by h accumulaion of inrnaional rsrvs, which ac as an insrumn of drrnc for spculaors aacks by rducing any dprciaion xpcaions hld by priva agns. In h liraur, Hllr (1966) was h firs o cas h analysis of rsrv dmand in h conx of prcauionary bhavior. Frnkl and Jovanovic (1981) also drivd opimal rsrvs undr h noion ha rsrvs srv as a buffr ha smoohs ou h sochasic flucuaions of xrnal ransacions. Th ida ha rsrvs ac as an insrumn of slf-insuranc was mainly dvlopd by h liraur ha followd h financial criss of h 199 s, wih paprs such as, Fldsin (1999), and Klzr and Mody (). Mor rcnly, Aiznman and L (5) and Jann and Rancièr (6) focus on h ida ha rsrvs ac as slf-insuranc bcaus hy minimiz h coss of adjusmns rlad o h occurrnc of suddn sops. García and Soo (4), insad, cnr h discussion on xploiing h ponial of rsrvs o rduc h liklihood of a suddn sop, and no o diminish h cos of adjusmn islf. L (4) aks a diffrn approach and drmins h opimal covrag for slfinsuranc by compuing h insuranc valu of rsrvs using ral opion hory. W cnr our anion on h ida ha rsrvs can dlay h occurrnc of currncy criss as in García and Soo (4), bu w us h ral opion hory o driv h link bwn criss and h uncrainy xhibid by forign xchang procds of h counry. Implicily, our modl can also b sn as a way o analyz h susainabiliy of monary policis in a condiion whr no fiscal bas is availabl xcp for a primary scor (Ghaak and Sánchz-Fung, 7). Th srucur of h papr is h following. Firs, in scion, w xplain h analogy of holding domsic currncy wih possssing a financial opion, and includ, as a paricular cas, h valu of an opion in h prsnc of a dual xchang ra. Thn w driv h amoun of coningn liabiliis for h gnral cas, and in scion 4 w provid h dfiniion of walh for an oil conomy. In scion 5, w addrss h problm of rsrv managmn by driving h xprssions for compuing opimal and minimal rsrvs. Finally, in scion 6, w giv paramrs simas and show h numrical calculaions for h Vnzulan conomy. 4
5. Domsic mony as a financial opion.1. Th gnral cas Considr h cas of a counry whos domsic currncy is subjc o a loss of xrnal purchasing powr. From h poin of viw of individuals, holding liquid balancs dnominad in domsic currncy mbds h righ, bu no h obligaion, o convr hm ino forign currncy or ohr asss dnominad in forign mony. Mor prcisly, a any givn im, individuals hav h possibiliy of swiching hir holdings of domsic mony ino forign currncy a h currn xchang ra or waiing up o a fuur im, l h purchasing powr of domsic mony driora, and mak h convrsion a a diffrn (probably highr) xchang ra. Bcaus agns ar consanly facd wih such choic, w can say ha holding domsic mony is quivaln o possssing a call opion on forign asss, or analogously, o possssing a pu opion on domsic currncy, i.. an opion o xi from domsic currncy by acquiring forign asss a h ongoing xchang ra. Thrfor, h dcision o buy forign currncy is quivaln o dciding whn o xrcis such an opion. Dfin F i as h currn valu of h call (pu) opion, i.. h valu assignd by a singl individual o mainaining opn h possibiliy of buying forign currncy in h fuur (or slling long posiions of domsic currncy). If w rul ou arbirag opporuniis, h maximum valu for F i is h gain ha h individual would obain by slling h domsic currncy a h currn xchang ra wih rspc o h (lowr) valu ha h would obain by slling h sam amoun a a ra fully rflcing h dprciaion of h currncy. Lik wih any financial opion, as F i gs largr, h incnivs for individuals o xrcis hir opion ar grar. Idally, h individual would wan o xrcis his opion whn h diffrnc bwn h valu of forign asss a h currn xchang ra and h on a h xpcd xchang ra is so larg ha i would no b jusifiabl o wai for a rvrsal ***. Considr ha ach individual (h i h opraor) holds a fracion w i of h sock of high powrd mony in Bs (M ) ha can vnually b convrd ino forign currncy. Th currn valu assignd by h opraor o h implici opion is givn by: (1) F i wi M wi M = max, D ε ε Th xchang ra is dfind as h pric of h forign currncy in rms of domsic currncy,.g. Bs/$. Bcaus convrsion can happn a any im wihou any givn xpiraion da, his ral opion would b quivaln o an Amrican prpual opion. *** Nvrhlss, on h basis of h good nws principl of Brnank (1983), h pu opion can b xpcd o b xrcisd whn h opraors bliv ha h bs possibl oucom has alrady occurrd and no improvmn of h siuaion can b xpcd.
6 whr ε rprsns h currn xchang ra (unis of domsic currncy pr uni of forign currncy), and D is h xpcd annual ra of variaion of h xchang ra in a yar, i.. h xpcd ra of dprciaion of h domsic currncy. In his w M xprssion, i rprsns h currn valu of asss in forign currncy ha ε could b bough a h currn xchang ra wih an amoun w i M of domsic mony. Th scond rm indicas h valu of h asss in forign xchang ha would b obaind, by convring an amoun w i M of domsic mony using h D xpcd xchang ra ( ε ) a h xrcis im. This diffrnc rprsns h gain ha h individual would obain by convring hr domsic currncy long D posiions a h currn ra, rahr han a h dprciad ra ε. Givn ha all individuals in h conomy hold domsic mony, h aggrga payoff of h opion is simply F =, providd ha w = 1. A linarizaion of quaion (1) can b sad as: () F ( D ) ( D ) $ M for > D = ohrwis i F i $ M whr M = is h high powrd mony of h conomy in forign currncy ε (dollars) a h currn xchang ra. Exprssion () indicas ha h currn valu of h implici opion is qual o h xpcd loss of purchasing powr (in rms of forign xchang) ha holdrs of domsic mony fac. Thrfor, an incras in h xpcd dprciaion of h domsic currncy will incras h valu of h opion, and h incnivs o xrcis i. Also noic ha, h inrinsic valu of his opion is diffrn han zro, only for xpcaions of dprciaion, sinc apprciaion xpcaions induc agns o kp hir holdings of domsic mony and driv h valu of h opion o zro. For a highr lvl of h high powrd mony, h valu of h opion incrass as wll du o h grar bas ovr which h xpcd loss is compud. In any conomy, h xpcd dprciaion ra of h domsic currncy ypically dpnds on fundamnals, which can b hough as fiscal or financial indicaors ha signal h dgr of soundnss of h conomy. In an conomy whos forign rcips dpnd ssnially on h sa oil xpors, fundamnals ulimaly rly on h xpcd oil rvnus, which affc h prformanc of h fiscal variabls and also drmin h sa of ral conomy and h financial sysm. This dscripion is spcially accura, if h conomy dos no uiliz any saving mchanism o buffr oil shocks, as i is h cas for Vnzula. On h ohr hand, an xpcd accumulaion of rsrvs can play an imporan rol in his yp of conomy by signaling lowr vulnrabiliy o currncy criss. Modls such as Sachs, Tornll and Vlasco (1996) and Sims (1) provid horical background o xplain h ngaiv rlaionship bwn h occurrnc of i i
7 xrnal criss and h accumulaion of inrnaional rsrvs. For insanc, in Sachs, Tornll and Vlasco (1996) agns obsrv h lvl of inrnaional rsrvs o drmin whhr capial ouflows can occur wihou causing a balanc of paymn crisis. Th sory from his modl is ha whn a counry facs wak fundamnals, h probabiliy of occurrnc of a crisis du o slf-fulfilling prophcis is highr if rsrvs ar low. In h sam lin of rasoning, Sims (1) in a sylizd modl of a small conomy, shows ha xplosivs pahs of prics (i.., h xchang ra) can b ruld ou if h Cnral Bank commis o mainain nough rsrvs o back up h quaniy of mony in h conomy. Basd on hs lmns, and acknowldging h rol of im in forming xpcaions, h gnral form of h xpcd dprciaion ra of h domsic currncy for an oil conomy can b wrin as: (3) D = D g y h r whr D is h xpcd dprciaion ra of h domsic currncy (no rflcd in h currn xchang ra) formd wih h informaion s availabl a im -1, D is an auonomus annual ra of dprciaion, y E(y - y -1 ) is h xpcd chang in oil rvnus for h yar and r is h xpcd accumulaion of rsrvs for h sam priod. For g, h>, his funcion indicas ha as xpcd oil arnings and rsrvs incras, h xpcd dprciaion diminishs bcaus agns prciv a mor robus conomy. I also implis ha h ffc of ngaiv oil shocks on h xchang ra can b counrbalancd by hoarding largr rsrvs. Alrnaivly, on could argu ha oil booms incras govrnmn profligacy o ovr-xpand is xpndiur causing a grar dmand of forign asss and a largr dprciaion of h currncy. In his cas g<, bu an xpcd incras in inrnaional rsrvs could sill b sabilizing for h conomy by rducing dprciaion xpcaions (h>). Incorporaing h paricular form of h xchang ra dprciaion in (3), h aggrga currn valu of an opion varis in im according o: $ (4) F( y, r ) = M ( D g y h r ) Assuming ha g, h>, his xprssion shows ha for an oil conomy, an incras in xpcd oil rcips and rsrv accumulaion will rduc h incnivs for individuals o xrcis h xising call opion on forign asss, by rducing is currn payoff. I also shows ha accumulaing rsrvs can b sn as a way o dr forign xchang claims ha com from h convrsion of domsic mony liabiliis whn a hug dprciaion of h domsic currncy is xpcd. If rsrv accumulaion wr also dsabilizing (h<), hn h accumulaion of rsrvs could no b undrsood as a man o proc h conomy from xrnal shocks, making any considraion rgarding rsrv managmn uslss.
8.1. Th dual xchang ra cas Oil conomis ha hav no implmnd saving mchanisms o buffr oil shocks ar ypically subjc o cycls of accumulaion/dsaccumulaion of rsrvs ha rflc h rollrcoasr bhavior of oil prics in combinaion wih policis of fixing h nominal xchang ra. I can also b common ha, in h downward phas of rsrvs, xchang ra conrols ar sablishd as a way o vad an xplici dprciaion of h domsic currncy ha would r-balanc h ongoing currn accoun dfici and ha would sop capial flighs. In ohr words, on can inrpr xchang ra conrols as an amp a insulaing rsrvs from a ransiory ngaiv shock in h supply of forign xchang ha dos no wan o b rsolvd wih a mporary dprciaion. In his scion, w driv h paricular form of h abov opion assuming ha financial ransacions ar acivly rsricd by xchang ra conrols. Ths yps of conrols ypically imply a form of a dual xchang ra sysm in which par of commrcial ransacions (impors) ar pricd a h official xchang ra (ε ), whil h rs of ransacions (mosly financial) ak plac in a paralll mark a h xchang ra (η ). Providd always ha η > ε, an xchang ra prmium ( p η 1) ariss o rflc h fac ha h sa cnralizs h allocaion η = ε of forign currncy and hr is raioning in h official supply of forign xchang for imporrs hrough licnsing. Th official xchang ra is fixd by h auhoriis and w assum ha dos no chang whil h dual sysm is in plac. Th currn lvl of h paralll xchang ra is basically drmind by h supply and dmand of forign xchang for financial ransacions. In paricular, h xpcd dprciaion ra in his mark can hav h sam drminans as in h cas of a floaing or smi-fixd xchang ra dscribd in quaion (3). On could argu ha in h official xchang ra mark, by ovr invoicing impors, a fracion of oil procds dvod o impors will b divrd o h paralll mark, spcially as h prmium bwn h official and h paralll mark grows. As in Guidoi (1988), his divrsion of rsourcs implis ha hr is an imprfc sparaion bwn h official and h paralll mark ha allows a crain dgr of lakags in h sysm. Taking ino considraion all h abov lmns, h currn valu of h opion on forign asss can b wrin as: wi M wi M wi M (5) F max q + ( 1 q) [ 1 D ] i =, ε η v All xchang ras ar xprssd as quaniis of domsic currncy pr uni of forign currncy, for insanc Bs/$.
9 wi M wi M In his xprssion, q + ( 1 q) rprsns h avrag currn valu ε η of asss in forign currncy ha could b bough wih an amoun w i M of domsic mony, considring h xisnc of a dual sysm. Sinc in his sysm hr is an imprfc sparaion bwn h official and h paralll mark, q rprsns h probabiliy of obaining a dollar a h official xchang ra (ε ) if agns dcidd o liquida hir Bs long posiions. Symmrically, 1-q rprsns h probabiliy of obaining a dollar a h paralll xchang ra (η ). In ohr words, q can b dscribd as h rlaiv amoun of financial ransacions whos supply of forign xchang is divrd from h official mark. Inuiivly, as h dgr of financial lakags in h sysm incrass, his fracion q should nd o ris. I will also ris, for insanc, if h govrnmn inrvns in h paralll mark rying o avoid an xcssiv gap bwn h official and h paralll ra by slling dollars a a pric xrmly clos o h official ra. wi M Th rm ( 1 D ) v of xprssion (5) indicas h valu of asss in forign xchang ha would b obaind, by convring an amoun w i M of domsic mony using h xpcd xchang ra a h xrcis im. This xpcd xchang ra would b h on rsuling from incrasing h currn avrag xchang ra prvailing in h conomy ( v ) by h xpcd dprciaion ra ( D ). This xpcd xchang ra is also h uniqu xchang ra ha would aris from h abandonmn of h dual sysm, which collapss as all h opraors (or, in pracic, a sufficinly larg numbr of hm) xrcis hir righ and ry o convr h sock of domsic asss ino forign xchang. Sinc v is dfind as h currn avrag xchang ra prvailing in h conomy, w could assum ha v = q ε + ( 1 q)η, or i could also b xprssd as a proporion of h currn official xchang ra ( v f ε ), whr f = q + ( 1 q)( 1+ p η ) is a scalar ncssarily grar han 1. Th aggrga payoff of h opion, providd ha wi = 1, can b wrin as: i $ (6) F( D ) = M [ D + Ρ] M for D > $ whr M = is h high powrd mony of h conomy in dollars a h currn v 1 avrag xchang ra, and q P = f q + 1 1 is a rm ha can b inrprd as + p η an indicaor of h sa of h dual sysm a h crisis poin, corrcd by h xchang ra prmium. In xprssion (6), no ha if q=1 and f=1, or quivalnly ρ η = and f=1, his would corrspond in pracic o h liminaion of h dual sysm, or a dual sysm wih almos no rsricions on financial ransacions. In his cas, all ransacions ar
1 undrakn a h official xchang ra, P is qual o zro, and h formula rducs o h original cas shown in quaion (). Alrnaivly, for h cas of a dual sysm wih no lakags, q= and f = η, h valu of P bcoms also zro, bu h ε quaniy of high powrd mony is xprssd in rms of dollars convrd a h paralll xchang ra (η ). In his las insanc, h currn valu of h opion can also b wrin as: M (7) F( D ) 1 = ( D ) p for D > ε 1 + η which indicas ha highr currn valus of h paralll xchang ra (η ), and hrfor of h xchang ra prmium ( p ), dissuad individuals o xrcis hir η opion of buying forign asss oday. This is h cas bcaus, par of h dvaluaion xpcaions for h official xchang ra hav alrady marializd in h paralll mark, and h acual dvaluaion ra is h diffrnc bwn h currn paralll xchang ra and h uniqu xpcd xchang ra whn h dual sysm will b abandond. Noic ha in boh xrm cass, an liminaion of h dual sysm (q=1) or a dual sysm wih no lakags (q=), h rm P drops o zro, bu for < q < 1, P is posiiv and maximizs h incnivs o xrcis h implici opion as q 1. This non-linariy of P on q sms o show ha h mr xisnc of a dual sysm wih wo simulanous maningful prics would xacrba dprciaion xpcaions. On h ohr hand, h ffc of h xchang ra prmium ( p η ) on P is sricly posiiv ( P / p = (1 ) ( + )/(1 + ) η q q pη pη pη > ). This suggss ha a grar prmium will induc a largr insananous gain ha will push individuals o xrcis hir opion, spcially as q 1. Wih rspc o govrnmn inrvnions in h paralll mark, which can b hough as incrasing h valu of q by slling dollars a h official xchang ra, hs inrvnions migh b counrproduciv, if h iniial valu of q < 1, ha is, if mos ransacions ar alrady pricd a h paralll xchang ra. Nonhlss, bcaus h sal of forign xchang by h govrnmn can also b undrsood as an incras in h supply of dollars, an apprciaion in h paralll xchang ra should occur as wll, for insanc as D q <. Thrfor, w find ha a govrnmn inrvnion in h paralll mark migh b succssful, vn for an iniial q < 1, if h apprciaion of paralll xchang ra is grar han h incras in P du o h incras in q, or quivalnly: D q P q (8) + < P has a maximum in a q=.5, sinc P q > for q<.5 and P q < for q>.5.
11 3. Coningn liabiliis on rsrvs So far, w hav compard holding domsic currncy wih acquiring a financial opion, and w hav providd an xplici xprssion for h currn payoff of such opion. Sinc hs payoffs ar id o h fuur prformanc of oil rcips, in h conx of sochasic uncrainy for oil procds, agns dcision o xrcis hir opion will dpnd on h inr-mporal valuaion of h payoffs ha could b gnrad upon. This mans ha w can find an xprssion ha compus h pric of h opion, and drmins is xi valu, in rms of oil procds. W sar by assuming ha dvlopmn of h oil aciviy occurs undr dynamic uncrainy. This implis ha, as a consqunc of a pluraliy of concurring facors, boh h avrag valu and h varianc of oil rvnu nds o incras ovr im. Adoping h convnin assumpion of a gomric Brownian procss, w hus assum ha oil producion yilds a n cash flow formd by a sysmaic par, which is normalizd o uniy, and a sochasic par, dnod by y, obsrvabl in vry priod, volving according o h xprssion: (9) dy = α y d + σ y dz whr α rprsns h drif (consan rnd componn) of oil arnings, σ hir (consan insananous) varianc, and dz is a normally disribud random variabl ha saisfis E(dz)= and E(dz ) = d. W also dfin δ = ρ α, and assum ha ρ > α, bing ρ h discoun ra in quaion (1). From h poin of viw of is holdrs, h pric of h opion is h on ha solvs h dynamic valuaion of h payoff of buying forign currncy (or xiing domsic currncy): (1) V ρ τ = sup E τ ρ ( s τ ) F( y, s) s ds y = y whr E [ y = y] is h opraor ha aks xpcaions condiional on h availabl informaion a im zro rgarding h oil incom, and V is h pric of h opion rprsnd by h maximum xpcd prsn worh of h opion valu hld by all individuals a any im. A h im h opion is xrcisd, V rprsns h aggrga valu of forign asss claimd agains h forign xchang (rsrvs) hld by h Cnral Bank. This is h cas bcaus, whn individuals xrcis hir opion, h Cnral Bank provids h forign currncy in xchang for domsic mony. A any ohr im, V is inrprd as h aggrga coningn forign xchang liabiliis ha could marializ agains inrnaional rsrvs. To solv his gnral class of valuaions, h following sandard dynamic programming condiions nd o b saisfid (Dixi and Pyndick, 1994):
1 = ρ τ ρ (11) ( ) ( s τ ) ρ V * y d E df( y, s) ds y = y (1) V * ( y *) = F( y*) τ s (13) dv * ( y *) df( y*) = dy dy whr ( y) V * is h soluion o h opimizaion problm, y* is h lvl of forign xchang arnings a which opraors abandon h domsic currncy, F ( y ) is h xpcd prsn valu of h opion, and (11) and (1) rprsn h valu maching and h smooh pasing condiion rspcivly. If arbirag possibiliis ar xhausd, all opraors ar idnical, xcp for h fac ha hy hold diffrn shars of domsic mony, so ha hy all xrcis hir opion a y*. Whn his happns, a currncy crisis occurs. Using h aggrga currn valu of h opion drivd in xprssion (4), w hav ha: whr F = E τ = y = M ρ τ ρ (14) ( ) ( s τ ) $ ( ) y F y, s s ds y D y G h r δ $ $ M M = rprsns h currn sock of high powrd mony dividd by ρ, ρ D and D = sands for h prsn valu of h auonomous annual dprciaion, and ρ r r = rprsns h prsn valu of h annual xpcd (consan) accumulaion ρ of rsrvs, or quivalnly, a onc and for all chang in h currn sock of α α inrnaional rsrvs. Sinc [ ] ( 1) α α ( ) α hn w can dfin = g ( )( ρ δ ) E y y = y = y y = y, 1 G 1 and l y δ rfr o h prsn valu of a consan annual oil incom. β Condiion (11) is saisfid by h gnral class of soluions V * ( y) = A y. Assuming ( ) β V * y = A y and manipulaing rminal condiions (1) and (13), h valu y* is givn by: (15) y * = δ G β ( ) [ D h r ] β 1
13 Implicily, h valu of y* drmins h probabiliy of occurrnc of a crisis, i.. h probabiliy ha y falls undr y*, and hrfor, h avrag waiing im for individuals o xrcis hir opion. For any β< or β>1, if G>, his xprssion suggss ha a largr auonomous xpcd dprciaion will incras h xi valu y*, and hrfor, on avrag, ris h probabiliy of a crisis and dcras h waiing im for individuals o xrcis hir opion. Also, sinc h>, an accumulaion of forign rsrvs will dcras h xi valu, and imply on avrag, a smallr probabiliy of a currncy crisis ****. Thrfor, bcaus rsrv accumulaion simulanously incrass h waiing im for individuals o xrcis hir opion and rducs h probabiliy of a currncy crisis, i can b undrsood as a mchanism o dlay currncy criss by discouraging spculaors aacks. Subsiuing y* back ino h smooh pasing condiion, w find ha h soluion for h oal valu of coningn claims is: (16) (17) $ β β M G ( β 1) β y V = [ ] ( β ) β D h 1 r 1 δ for y>y* $ y V = M D h r G δ for y y* whr β has wo roos: β > 1 and 1 β < ha saisfy h characrisic quaion 1 σ β ( β 1) + ( ρ δ ) β ρ =. Noic ha V > only for β <, which consrains our soluion o using β = β. For his cas, and h, G>, h valu of oal coningn claims agains h Cnral Bank is a dcrasing funcion of h prsn valu of oil procds and rsrv accumulaion, and an incrasing funcion of h auonomous xpcd dprciaion D. This shows ha rsrv accumulaion also acs as an insrumn o miiga h ffc of currncy crisis by rducing h amoun of forign xchang liabiliis ha can marializ. To undrsand soluions (16)-(17), considr h cas in which h accumulaion of rsrvs hav alrady bn dcidd by h auhoriis o an arbirary lvl. Givn hs rsrvs and h ohr condiions of h conomy ( D ), w can know h lvl of incom y* ha riggrs a currncy crisis (whn opraors dcid o convr domsic currncy ino forign xchang). A his poin, only h bhavior of incom drmins h occurrnc of such crisis. If incom falls undr y*, h crisis insanly aks plac wih h amoun of liabiliis drmind by (17). If incom is highr han y*, opraors do no xrcis hir opion, bu hr is a hra ovr rsrvs idnical o h amoun of coningn liabiliis poind ou by (16). **** If G <, xprssion (15) will b grar han zro, only if, for h >, h r > D, i.. only if h bnficial ffc of accumulaing rsrvs is sufficinly larg wih rspc o h auonomous dprciaion xpcaions. In ohr words, sinc oil procds hav a dsabilizing ffc, h accumulaion of rsrvs nds o b sufficinly high o caus apprciaion xpcaions. Howvr, if hs apprciaion xpcaions ar oo srong, paradoxically h probabiliy of a crisis incrass.
14 Th xplici xprssion for h ngaiv roo and is drivaiv wih rspc o h varianc of oil procds ar corrspondingly: 1 ( ρ δ ) ( ρ δ ) 1 ρ (18) β = + σ σ σ dβ ( ρ δ ) ρ δ 1 ρ ρ δ 1 ρ δ ρ (19) = + > 4 + 4 4 + dσ σ σ σ σ σ σ Exprssion (19) is posiiv for ρ > δ, a condiion ha always holds for α, sinc by dfiniion δ = ρ α. Thrfor, as volailiy incrass, h absolu valu of h roo gs smallr and h amoun of liabiliis incrass. Likwis, a smallr absolu valu of h roo rducs h xi valu y*, indicaing a smallr probabiliy of a currncy crisis. Saisically his happns bcaus, as uncrainy incrass, h probabiliy of ging an insananous posiiv jump (drif) in incom also incrass, which is quivaln o saying ha h probabiliy of a crisis dcrass. Nonhlss, if a crisis aks plac, h amoun of forign xchang claims would b highr. 1 4. Walh in an oil conomy In his scion, w modl h walh of an conomy ha obains mos of is forign xchang arnings from h xracion of oil. Th rsourc is dvlopd by h sa, which can dcid o kp inrnaional rsrvs or o impor capial goods in ordr o accumula produciv asss. Individuals can also claim par of hs oil arnings as savings in forign xchang or as consumpion of forign goods. Sinc hr ar only wo asss in h conomy, h inrmporal counry walh dpnds on h fuur accumulaion and rurns of hs asss: = 1 d ρ () W W + E [( + ϕ) I + ( + θ ) r ] 1 whr W is h iniial walh, ϕ is h rurn of h domsic invsmn in capial goods pr yar, and θ is h annual ra of rurn of rsrvs. Tha is, h xpcd counry walh is dfind as h xpcd prsn valu of h ass accumulaion in h conomy. Bcaus capial goods ar no producd domsically and oil procds ar h only sourc of forign xchang, h inr-mporal budg consrain of h conomy is givn by h prsn valu of h balanc of paymn:
15 ρ ρ (1) E y ( 1 ) = = [ + + + ] ω d y y E C I O r d () y ( 1 ω) = C + I + O + r δ whr ω y is h opporuniy cos of dpling h naural rsourc, O = O ρ, C = C ρ and I = I ρ ar h prsn valu of h xpcd (consan) annual financial ouflows and impors of consumpion and capial goods rspcivly. This xprssion poins ou ha h prsn valu of uss of forign xchang (impors of consumpion and capial goods, capial ouflows and rsrv accumulaion) canno xcd h prsn valu of h xpcd oil procds. Coningn liabiliis drivd in h prcding scion rprsn, during currncy criss, capial flighs dfind as h massiv xchang of domsic mony claims for forign currncy. Th rs of h im, coningn liabiliis characriz a hra ovr rsrvs ha can b parially marializd dpnding on h xchang ra policy followd by h auhoriis. In his sns, w can dfin h prsn valu of xpcd capial ouflows (O ) as a fracion k of h coningn liabiliis. Also, h rm kv can b hough as a masur of h disrupiv ffcs ha a crisis can ngndr on h ral conomy. Subsiuing ou h prsn valu of capial goods in xprssion (1), h xpcd walh of h conomy is: y y = W + + C + r + k V, 1 ϕ (1 ω) θ ϕ 1 ϕ r δ δ (3) ( ) ( ) ( ) W Th firs addndum o h iniial walh W rprsns h gains on walh obaind by h ransformaion of oils procds ino h sock of capial goods of h conomy. This gain is posiivly rlad o h sock of naural rsourcs and ngaivly rlad o h accumulad consumpion of impord goods. Th scond addndum indicas h dirc n xpcd conribuion of rsrvs of forign xchang o h counry walh. This conribuion is proporional o h diffrnc bwn h financial rurn arnd by rsrvs and h ra of rurn ha can b obaind by imporing invsmn goods or by invsing abroad. Th hird rm on h righ hand sid rprsns h ponial dplion of walh (i.. h coningn liabiliy) ha may com from h financial dcisions of priva agns, should hy choos o convr hir claims of domsic currncy ono forign xchang. This coningn rducion in walh also accouns for h opporuniy cos in rms of capial invsmns. Noic ha rsrv accumulaion will hav an ovrall posiiv impac on walh if h drivaiv dw dr >, ha is if: Th rm ω can b hough as h ra ha capurs h implici wdg bwn is prsn pric and is suprior long rm pric.
16 $ (4) M ( 1 + ϕ) k h G β δ r ( β 1) y ( D h ) > ϕ θ $ As a mar of fac, considring h ordr of magniud of M, his xprssion can b saisfid indpndnly of ϕ θ, if h r < D, givn G, h>. This condiion is h sam ha nsurs ha y*> and ha V lis in h lin of ral numbrs. Alrnaivly, if h>, bu G <, hn i is sill sufficin ha h r > D, which implis ha, for compnsaing h dsabilizing ffc of oil incom, h accumulaion of rsrvs nds o b sufficinly larg o caus apprciaion xpcaions grar han h xpcd auonomous dprciaion. β 5. Rsrv managmn According o h prcding scions, forign rsrvs hav a bnficial ffc on coningn liabiliis by acing as a mchanism o dlay and miiga currncy criss. In his conx, risk is characrizd by h probabiliy assignd o a currncy crisis, which occurs if oil rvnus fall blow h hrshold a which ass holdrs will massivly xrcis hir xi opion from h domsic currncy. Howvr, forign rsrvs migh caus a parial drimn on h xpcd walh, if h rurn arnd in inrnaional marks falls blow h ra of rproducion of capial goods in h conomy. In his cas, opporuniy coss ar givn by h invsmn opporuniis forgon whn holding financial rsourcs in h form of a coningn ass rahr han commiing hm o spcific invsmns and/or dvlopmn policis. Thrfor, dpnding on n rurn arnd by rsrvs, h sragy of rsrv accumulaion should b dsignd according o on of hs wo valus: opimal or minimal rsrvs. 5.1. Opimal rsrvs Assum also ha counry walh is incrasing in h ovrall valu of rsrvs accumulad, bu θ < ϕ. If h rurn of capial invsmns is highr han h rurn of rsrvs, h accumulaion of rsrvs has mbddd an imporan opporuniy cos. On h ohr hand, accumulaing rsrvs sill rducs h amoun of ponial forign liabiliis and rducs h probabiliy of a crisis, all of which ncourags is hoarding. This radoff allows arguing ha h sock of rsrvs can b drmind opimally by sing: (5) * r = arg max W ( r )
17 Th FOC of his maximizaion problm is givn by: (6) θ ϕ dv ( r ) = k ϕ ( 1+ ) dr ( ) whr ) β β dv ( r $ G β 1 [ β y = M D h r ] ( h) <. This condiion, as dr β δ mos maximizaion condiions, quas h marginal cos of accumulaing rsrvs ( ϕ θ ) o h marginal bnfi (h absolu valu of h righ hand sid rm) in rms of smallr forign xchang liabiliis. Solving h FOC for h sock of rsrvs: (7) r * = 1 D h G ( β 1) β h h ϕ θ k M ( 1+ ϕ) $ 1 β y δ This xprssion conains wo balancing rms. Th firs on shows h amoun of rsrv accumulaion rlad o h xisnc of auonomous dprciaion xpcaions. This whol rm dos no dpnd of h uncrainy of h oil procds, and h highr hs xpcaions, h grar h nd o accumula forign rsrvs as an ass o counrbalanc h corrsponding liabiliy. Th scond rm conains h variabls ha induc a lowr accumulaion of rsrvs, providd ha ϕ θ > : a grar xpcd oil incom and smallr ousanding liabiliis in h form of high powrd mony rduc h nd o accumula rsrvs, and so i dos a rducion in volailiy of oil incom. This scond rm rndrs rsrvs dpndn on uncrainy and ransforms, hrfor, h maximum amoun of asss ha would b ndd o offs a sur liabiliy ino a form of coningn ass. To valua h impac of incom volailiy on opimal rsrvs, rcall ha as volailiy incrass, h absolu valu of h roo ( β ) gs smallr. Sinc opimal rsrvs ar highr whn h β approachs o zro, his implis ha incrasing volailiy will incras h amoun of opimal rsrvs. This occurs bcaus, as uncrainy incrass, h probabiliy of a crisis dcrass, bu h amoun of coningn liabiliis incrass. Th SOC of h maximizaion problm rquirs ha ( d W r ) d V ( ) ( r ) = 1 + ϕ k <. Sinc: dr dr As a mar of fac, * d r dβ >, if ln ϕ θ < 1, which is auomaically saisfid for a sufficinly $ ( 1 ) h + ϕ k M larg magniud of h prsn valu of h high powrd mony in h conomy.
18 d V ( (8) r ) dr = M $ G ( β 1) β β y δ β β 1 ( h) [ D hr ] ( β ) > givn β <, hn h SOC of h maximizaion problm is always saisfid. 5.. Minimal rsrvs as a slf insuranc Whn h diffrnc bwn h rurn of rsrvs and h rurn of capial invsmn is posiiv, ha is θ ϕ >, accumulaing rsrvs only has bnficial ffcs. On on hand, hr is an accumulaion of oil procds in h form of h mos produciv ass availabl ha incrass walh, and on h ohr hand, hr is a gain associad o h rducion of forign liabiliis and h probabiliy of a crisis, all of which ncourags h hoarding of rsrvs. In his cas, h radoff ha calld for an opimizaion procdur disappars, and h amoun of rsrvs accumulad can b arbirarily larg. In his cas, sinc hr is no an uppr bound o h accumulaion of rsrvs, i would sm dsirabl o poin ou a lowr bound or a minimal amoun of rsrvs. This minimal amoun could b sablishd in rms of answring wha lvl of rsrvs covrs h xpcd forign xchang liabiliis ha would aris a h im of a currncy crisis whn priva agns xrcis hir claims. Mor gnrally, considr a ra of covrag (φ) applid on h xpcd amoun of liabiliis, h prsn valu of his minimum amoun of rsrvs should xacly mach h slcd valu of shildd liabiliis, such ha: (9) m m m r = φ V [ y *( r ), r ] $ (3) φ M r m = D $ 1 β + h φ M According o his xprssion, h minimal rsrvs should b dircly proporional o h siz of auonomous dprciaion xpcaions, h sock of ousanding liabiliis of domsic currncy and h ra of covrag (φ) dcidd by auhoriis. Nonhlss, noic ha changing h amoun of minimal rsrvs, for insanc by varying h dsird siz of h covrag, modifis boh, h siz of xpcd forign liabiliis during a crisis and h implici probabiliy of a crisis. In paricular, as h siz of covrag gs largr, coningn claims ar rducd, and h probabiliy of a crisis gs smallr as y* diminishs. In fac, h closd form soluion for h criical incom lvl whn accumulaing minimal rsrvs is y * β = D $, which is invrsly proporional o φ. δ G( β 1 φ h M )
19 Thrfor, slcing h siz of h covrag agains xpcd forign claims during a crisis is idnical o choosing h probabiliy of a crisis ha auhoriis will fac and h amoun of claims ha ffcivly could b honord by h Cnral Bank. Bcaus his amoun of minimal rsrvs limis h xposur o risk according o h prfrncs rvald by auhoriis, hy rprsn a form of slf insuranc mchanism agains a currncy crisis. This form of slf insuranc is in lin wih h approach followd by García y Soo (4). Diffrnly han h approach prsnd by L (5), w do no addrss h possibiliy ha par of h insuranc agains criss can b obaind hrough markbasd mchanisms (such as a pu opion) and nihr can w rfr o h opimal siz of his insuranc. Nvrhlss, in our approach, auhoriis can discrionally dcid h qualiy of h slf insuranc by valuaing is covrag in rms of h xpcd xposur o currncy crisis. 6. Esimaion of rsrvs for Vnzula 6.1. Paramrs simaion. Opimal or minimal rsrvs can b compud hrough his modl, if paramrs for h xpcd dprciaion (g and h in quaion 3) ar simad. Howvr, o obain simas of hs paramrs for Vnzula, w nd o considr ha h dynamic of h nominal xchang ra has varid ovr im du o svral modificaions applid o h xchang ra rgim. To ovrcom his difficuly, insad of modling h nominal xchang ra, w modl h xchang ra mark prssur (EMP), which allows using a sufficinly long daa s on h mark, indpndnly of h yp of xchang ra rgim in plac. Empirical grounds for h simaion of h xchang mark prssur ar found in h liraur of currncy criss, in paricular, in h works of Sachs, Tornll and Vlasco (1996), García and Soo (4) and Edwards (4). Inspird in Giron and Ropr (1977), h xchang ra mark prssur is a masur ha linarly combins h growh ra of h nominal xchang ra D and h raio of Cnral Bank n forign xchang sals o inrnaional rsrvs (Sl/R), such ha: (31) EMP f D, Sl R whr f(.) dnos a linar funcion, whos cofficins ar h invrs of h sandard dviaion of h variabl. As i is dfind, ihr a dprciaion of h domsic currncy or in an incras of h amoun of dollars sold by h Cnral Bank incrass h mark prssur, capuring any chang in h xcss dmand of forign currncy. During priods of xchang ra conrols (dual sysms), D rfrs o h growh ra
of h paralll xchang ra, whil Sl rprsns h amoun of dollars supplid by auhoriis for commrcial ransacions. In priods of fixd xchang ra, h mark prssur is complly capurd by h forign xchang sals of h Cnral Bank. Th simaion of h xchang ra mark prssur is carrid ou wih a GARCH modl o conrol for im hroskdasiciy. Th mpirical xplanaory variabls for h mark prssur ar h annual chang in h valu of yarly oil xpors ( y), h annual accumulaion of rsrvs ( r). Esimaion rsuls ar shown in h appndix. W rriv h cofficins of quaion (3) by a wo sp procdur: firs, by compuing h annual (insad of h quarrly) chang in h mark prssur pr uni of chang in oil xpors and rsrv accumulaion using h dynamic srucur of h quaion, and scond, by ransforming hs mark prssur cofficins in unis of nominal xchang ra dprciaion (using h sandard dviaion of h xchang ra dprciaion). Finally, o rriv h drif paramr (α ) for quaion (9), w us h fac ha h man of h chang of h logarihm of h annual oil xpors (μ) can b xprssd as funcion of h sandard dviaion and h drif paramr ( µ = α.5 σ ). Sinc h sampl availabl for h oil xpors includs h oil boom rgisrd from 5 o 8, h hisorical valu of µ is qual o.1, which sms a vry larg valu o us as a forcas for h xpcd bhavior of h oil rvnus. W s µ =.5, σ aks is hisorical valu of.5, and compu h roos of h characrisic quaion according o h formulas providd. Th discoun ra ρ is s a.15, o saisfy ha ρ > α. Esimad cofficins ar summarizd in h following abl: 6.. Numrical calculaions Tabl 1. Esimad cofficins Paramr Esima g*.93 h*.85 G*.16 D.169 σ.5 α.81 β 1 1.53 β -3.13 *Cofficins ar xprssd in p.p. of currncy dprciaion pr n billions of US dollars In his scion, w provid numrical valus for opimal and minimal rsrvs o assss h adquacy of h modl for h cas of Vnzula. Th closd form xprssions ha w us incorpora h xisnc of an xchang ra conrol implmnd in Vnzula sinc 3. For his rason, w nd o sima h probabiliy of obaining a dollar a h official xchang ra whn undraking financial ransacions (h paramr q), which is pinnd down o
1.5 *****. This paramr affcs h avrag xchang ra prvailing in h conomy (v), h amoun of h high powrd mony in dollars valud a v, and h rm P, inrprd as an indicaor of h sa of h xchang ra conrol. Th xchang ra prmium is compud as h wdg bwn h official xchang ra (Bs/$.15) and h valu of h paralll xchang ra s a Bs/$ 5.5 (an avrag valu obsrvd during 9 in h paralll mark). In gnral, opimal rsrvs ar highly dpndn on h assumpions mad rgarding h currn lvl of oil rvnus (y) and h rurns of capial goods and rsrvs. In his xrcis, w considr svral valus for h annual oil incom, and compu h xprssion y/δ, which is inrprd as h xpcd prsn valu of rciving a consan annual oil incom. Howvr, providing a good sima of h yild of capial invsmns gos byond h scop of his papr. Insad, w provid possibl valus for h opporuniy cos of rsrvs ( ϕ θ ), considring diffrn lvls of h capial invsmn rurn. Rsuls ar shown in Tabl. Tabl. Opimal rsrvs* Opimal Rsrvs Opporuniy Coss y ϕ θ 4, 65, 9,. 35,91 8,443 1,794.5.5 37,3 31,874 6,545.49 4,678 4,771 38,864. 3,65 4,479 16,36.1.5 35,48 8,697,147.99 4,73 4,844 38,965. 31,55 1,883 1,71.15.75 33,968 6,617 19,66.149 4,765 4,913 39,6 Man 37,43 31,613 6,184 Sandard dviaion 4,588 7,456 1,33 *Monary figurs ar in MM of US $ According o Tabl, and o h formulas providd, h opimal rsrvs will dcras as h valu of h xpcd oil incom gs largr. Noic ha, for any lvl of h rurn of invsmns, as ϕ θ, h opimal socks of rsrvs nd o modsly vary around U.S.$ 4,8 MM, vn for larg variaions in h xpcd oil incom. In his cas, h opimal lvl of rsrvs mosly rflcs h sa of h auonomous dprciaion xpcaions (D ), which ar paramrizd around 17% pr yar. Whn opporuniy coss ar diffrn from zro, opimal rsrvs, on avrag, dcras as h rurn of invsmns in capial goods is highr. Also, a grar gap ***** Esimas of his paramr can b compud marginally, givn h approxima siz of ransacions carrid ou in h paralll mark and h amoun of ovr-invoicd impors. Rcn simas of q rang bwn. and.3, bu hy could b subjc o imporan changs.
bwn ϕ and θ will rduc h nd for rsrvs, as capial goods bcom a br opion of invsmn han rsrvs. To illusra h bhavior of minimal rsrvs, w giv svral xampls for diffrn lvls of h ra of covrag φ and h annual auonomous dprciaion xpcaions D. Esimas ar providd in abl 3. Tabl 3. Minimal rsrvs* Minimal Rsrvs / Criical Oil Incom φ variabl D =.35 D =.17 D =.85.5 r m 7,85 14,143 8,31 y* 57,366 9,954 17,9 1. r m 41,437 1,636 1,86 y* 43,881,913 13,11 1.5 r m 5,35 6,78 14,9 y* 35,59 18,55 1,535 *Monary figurs ar in MM of US $ Tabl 3 shows ha as h lvl of covrag incrass, no only h amoun of coningn liabiliis ha could b honord incrass, bu h risk facd in rms of h probabiliy of a currncy crisis diminishs. On h ohr hand, largr auonomous dprciaion xpcaions incras h amoun of minimal rsrvs ndd o saisfy a givn ra of covrag. I is imporan o poin ou ha hs valus of opimal and minimal rsrvs rprsn avrag valus, givn a sylizd xpcd bhavior of h conomy. In his sns, his xrcis nihr capurs h changing bhavior of h conomy nor dos i considr h impac ha sochasic shocks could imping on h diffrn variabls involvd in calculaions. From h poin of viw of policymakrs, hs valus should b inrprd as mrly rfrnial and canno b undrsood as h xac amoun of rsrvs ha h Cnral Bank should hold a all ims. Indd, many oil conomis mainain par of hir forign xchang procds in h form of saving or invsmn funds, which nd o gain highr rurns han h rsrvs managd by h Cnral Bank. Bcaus hs alrnaiv forms of savings also consiu a sock of forign asss ha can dr spculaors from riggring a currncy crisis, on could inrpr hs amouns of opimal or minimal rsrvs simply as h sum of forign asss ha should b mainaind aloghr a h Cnral Bank and a h invsmn fund. Th allocaion of forign asss bwn hs wo forms of accumulaion can b ulimaly a dcision of policymakrs basd on h dsirabl dgr of liquidiy o b achivd. In comparison o h managmn of rsrvs a h Cnral Bank, h grar rurn of hs invsmn funds is gnrally aribud o h lss consrvaiv porfolio allocaion pursud. Such financial sragy ypically nails a grar financial divrsificaion a h xpns of a lowr dgr of immdia availabiliy of rsourcs (liquidiy).
3 7. Conclusions In his papr w hav lookd a h problm of rsrvs from h poin of viw of hir funcion as an insrumn o conrol h coningn liabiliy consiud by h accumulaion of individual claims agains h Cnral bank. Ths claims corrspond o h issuanc of high powrd mony dnominad in domsic currncy and o h consqun risk of massiv amp a convrsion on h par of h claimholdrs. In his papr, rsrvs ar on insrumn o counrac h coningn liabiliy wih a corrspondn coningn ass bcaus hy rduc h xpcaions of dprciaion of h domsic currncy and discourag coningn capial fligh. In an oil dpndn conomy, hs coningn valus dpnd on h dynamic uncrainy of oil rvnu, whos man valu and varianc boh nd o vary ovr im as a consqunc of h myriad of facors affcing inrnaional dmand and domsic supply. Undr hs condiions, rsrv accumulaion can b raionally plannd according o wo possibl parns. If h rurn on rsrvs is lowr han h rurn obainabl on h alrnaiv us for h sam funds, a rad off mrgs bwn h us of forign xchang o obain maximum rurns and is us o dr holdrs of domsic balancs o convr hir claims. In his cas, opimal rsrvs can b s a a lvl rflcing wo spara componns: a posiiv on ha prfcly counrbalancs h xpcd (non coningn) dvaluaion for h ousanding claims, and a ngaiv on, rflcing h coningn naur of oil rvnu and of is alrnaiv uss. As h common wisdom would indica, a grar volailiy of oil procds should b compnsad wih a highr accumulaion of rsrvs, in ordr o adqualy fac h marializaion of largr coningn claims. Whn h rurn on rsrvs is sufficinly high wih rspc o is alrnaiv us, opimal lvls canno b spcifid, and rsrvs can b accumulad in arbirarily hug amouns. In his cas, h accumulaion of rsrvs can sill b usd as an insuranc o limi h xposur o h risk of a currncy crisis. In paricular, minimal rsrvs can b s o guaran honoring a slcd amoun of forign xchang claims a h im of a crisis. Th simas dvlopd for Vnzula show ha h n ffc of rsrvs on rducing xpcd dprciaions is boh significan and subsanial. As a consqunc, combind wih h simas of h ohr paramrs of h modl, h compud lvls of opimal and minimal rsrvs appar o b rasonabl wih rspc o h siz and condiions of h conomy.
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6 Appndix 1. Esimaion of Mark Prssur Dpndn Variabl: EMP Mhod: ML - ARCH Sampl (adjusd): 1991Q1 8Q4 Includd obsrvaions: 7 afr adjusmns Convrgnc achivd afr 18 iraions Prsampl varianc: backcas (paramr =.7) GARCH = C(6) + C(7)*RESID(-1)^ + C(8)*GARCH(-1) Cofficin Sd. Error z-saisic Prob. C.59536.63355 4.96511. EMP(-1) 1.1471.1548 11.911. EMP(-) -.39484.1141-3.51481.4 y -1.43E-5 8.48E-6-1.688596.913 r (-1) -4.39E-5 1.68E-5 -.61375.9 Varianc Equaion C.859.6688 1.7173.84 RESID(-1)^.3744.4643 1.38734.1839 GARCH(-1).49478.3569.9957.71 R-squard.95534 Man dpndn var.774564 Adjusd R-squard.91739 S.D. dpndn var 1.49578 S.E. of rgrssion.45141 Akaik info cririon 1.35834 Sum squard rsid 1.549 Schwarz cririon 1.88796 Log liklihood -9.91 Hannan-Quinn crir. 1.136539 F-saisic 113.6367 Durbin-Wason sa 1.7743 Prob(F-saisic). EMP: mark prssur (in sandardizd unis) y: h annual chang of h valu of yarly oil xpors (in millions of US $) r: h annual accumulaion of inrnaional rsrvs (in millions of US $)