FX Derivatives.ppt

fxderivatives,1.fxfuturesandforwards,fxrisk,example:abyz,au.s.company,importswinefromfrance.abyzhastopayeur5,000,000onmay2.today,february2,theexchangerateis1.15usd/eur.situation:paymentdueonmayy2:eur5,000,000.ssep2=1.15usd/eur.problem:stisdifficulttoforecastuncertainty.uncertaintyrisk.example:onjanuary2,storthisisaperfecthedge!,note:inthepreviousexample,wehadaperfecthedge.wewerelucky!vsep12=voct29=gbp1,000,000(fsep12,dec-ssep12)=(foct29,decsoct29)=usd.05anequalpositionhedgeisnotaperfecthedgeif:(1)vtchanges.(2)thebasis(ft-st)changes.,changesinvtifvtchanges,thevalueofopwillalsochange.example:reconsiderpreviousexample.onoctober29:foct29,dec=1.45usd/gbp.soct29=1.50usd/gbp.voct29increases2%.sizeofup(long):gbp1,020,000.sizeofhp(short):gbp1,000,000.usdchangeinup(longgbpbond)isvoct29*(long)=gbp1.02mx1.50usd/gbp=usd1,530,000vsep12*(long)=gbp1.0mx1.60usd/gbp=usd1,600,000usdchangeinvt*(long)=usd-70,000,usdchangeinhp(shortgbpfutures)=usd100,000.netchangeontheoverallportfolio=usd-70,000+usd100,000=usd30,000.=notaperfecthedge:onlytheprincipal(gpb1million)washedged!,basischangedefinition:basis=futuresprice-spotprice=ft,t-st.basisriskarisesifft,t-stdeviatesfromaconstantbasisperperiod.ifthereisnobasisriskcompletelyhedgetheunderlyingposition(includingchangesinvt).ifthebasischangesequalhedgeisnotperfect.ingeneral,if(ft,t-st)(orweakens),theshorthedgerloses.if(ft,t-st)(orstrengthens),theshorthedgerwins.,example(continuation):now,onoctober29,themarketdatais:foct29,dec=1.50usd/gbp.soct29=1.50usd/gbp.basissep12=fsep12,dec-ssep12=1.55-1.60=-.05(5points)basisoct29=foct29,dec-soct29=1.50-1.50=0.comparedtopreviousexample,basisincreasedfrom-5pointsto0points.(thebasishasweakenedfromusd.05tousd0.)datelongposition(buy)decfutures(sell)september121,600,0001,550,000october291,500,0001,500,000gain-100,00050,000note:(ft-st)shorthedgersprofitsloses(usd-50,000).equalhedgeisnotperfect!,basisriskrecallirpt.fortheusd/gbpexchangerate,wehave:assumet=360.aftersomealgebra,wehave:thebasisisproportionaltotheinterestratedifferential.asinterestrateschange,thebasischangestoo.,derivationoftheoptimalhedgeratioadditionalnotation:ns:numberofunitsofforeigncurrencyheld.nf:numberoffuturesforeignexchangeunitsheld.(numberofcontracts=nf/sizeofthecontract)h,t:uncertainprofitofthehedgerattimet.h=hedgeratio=(nf/ns)=numberoffuturesperspotinup.wewanttocalculateh*(optimalh).forthat,weminimizethevariabilityofh,t.h,t=stns+ft,tnf(or,h,t/ns=st+hft,t.)wewanttoselecthtominimize:var(h,t/ns)=var(st)+h2var(ft,t)+2hcovar(st,ft,t)h*=-sf/f2.,optimalhedgeratio:h*=-sf/f2.(acovarianceoveravariance=a(ols)regressionestimate!)remarks:(1)h*isthe(negative)slopeofanolsregressionofstagainstft:st=+ft,t+t=h*=-b(olsestimateof)(2)recallirpt:ft,t=st(1+id)/(1+if)=st.calculatingchanges:ft,t=st=st=(1/)ft,tthen,h*=-bestimates(1/)intheirptequation:=1/h*.(3)twocasesregardinghedgeratios:-whenft,tisdenominatedinthesamecurrencyastheassetbeinghedged,wecanuseirpttogetthehedgeratio,h*.-whenft,tisdenominatedinadifferentcurrencythantheassetbeinghedged(cross-hedging),olsprovidesanestimateofh*.,olsestimationoftheoptimalhedgeratioconsiderthefollowingregressionequation:st=+ft,t+t.=olsproducesb=sf/f2=-h*ahedgeisperfectonlyifstandft,tareperfectlycorrelated:tohaveaperfecthedgeweneedttobealwayszero.therofregressionmeasurestheefficiencyofahedge.,example:weestimateahedgeratiousingols:weusefiveyearsofmonthlydataforatotalof60observations.st=.001+.92ft,t,r2=.95.h=-.92.nf/sizeofthecontract=hns/sizeofthecontract=-.92x1,000,000/62,500=-14.715contractssold!thehighr2pointsouttheefficiencyofthehedge:changesinfuturesusd/gbppricesarehighlycorrelatedwithchangesinusd/gbpspotprices.note:adifferentinterpretationofther2:hedgingreducesthevarianceofthecfbyanestimated95%.remark:olsestimatesofthehedgeratioarebasedonhistoricaldata.thehedgeweconstructisforafutureperiod.problem!,time-varyinghedgeratios:ht*=-sf,t/f,t2garchmodels:thevariancechangeswiththearrivalofnews.agarch(1,1)specificationisagoodapproximation:2s,t=s0+s12s,t-1+s12s,t-1s,t-1=forecastingerroratt-1.(underrwm,s,t-1isthechangeinst-1.)recallthatgarchmodelsaccommodatetwofeaturesoffinancialdata:-largechangestendtobefollowedbylargechangesofeithersign.-distributionisleptokurtici.e.,fattertailsthananormal.statisticalpackagesthatestimategarchmodels:sas,e-views.toestimateatime-varyinghedgeratio,youneedamodelforthebivariatedistributionofstandft,t(togetcovariances).,hedgingstrategies,threeproblemsassociatedwithhedginginthefuturesmarket:-contractsizeisfixed.-expirationdatesarealsofixed.-choiceofunderlyingassetsinthefuturesmarketislimited.imperfecthedges:-delta-hedgewhenthematuritiesdonotmatch-cross-hedgewhenthecurrenciesdonotmatch.anotherimportantconsideration:liquidity.,contractterms(deltahedging)majordecision:choiceofcontractterms.advantagesofashort-termhedging:-short-termft,tcloselyfollowsst.recalllinearizedirpt:ft,tst1+(id-if)xt/360ast0,ft,tst(upandhpwillmoveclosely)-short-termft,thasgreatertradingvolume(moreliquid).disadvantagesofashort-termhedging:-short-termhedgesneedtoberolledover:cost!,contractterms(deltahedging)short-termhedgesareusuallydonewithshort-termcontracts.longer-termhedgesaredoneusingthreebasiccontractterms:-short-termcontracts,whichmustberolledoveratmaturity;-contractswithamatchingmaturity(usuallydonewithaforward);-longer-termcontractswithamaturitybeyondthehedgingperiod.,threehedgingstrategiesforanexpectedhedgeperiodof6months,differentcurrencies(cross-hedging)q:underwhatcircumstancesdoinvestorsusecross-hedging?aninvestormaypreferacross-hedgeif:(1)thereisnoavailablecontractforthecurrencyshewishestohedge.futurescontractsareactivelytradedforthemajorcurrencies(atthecme:gbp,jpy,eur,chf,mxn,cad,brr).example:wanttohedgeanokpositionusingcmefutures:youmustcross-hedge.(2)cheaperandeasiertouseadifferentcontract.banksofferforwardcontractsformanycurrencies.thesecontractsmightnotbeliquid(andexpensive!).empiricalresults:(i)optimalsame-currency-hedgeratiosareveryef