MEASURING THE FOREIGN EXCHANGE RISK LOSS OF THE BANK

Transcription

1 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 MEASUING THE FOEIGN EXCHANGE ISK LOSS OF THE BANK Gabrel Bstrceau Ecoomst, Ph.D. Face Natoal Bak of omaa Bucharest, Moetary Polcy Departmet, 5 Lpsca Street, Sector 3, zp code: 0404 Phoe: , Emal address: Gabrel.Bstrceau@bro.ro (or) gabrel.bstrceau@gmal.com Abstract. The preset paper obtaed a relatoshp for the Potetal Loss of the bak's portfolo of foreg curreces by usg the ormal dstrbuto assumpto of the exchage rates daly varatos. Secod, t s determed the Potetal Loss of a bak that keeps the accoutg Euro for a portfolo cossts of fve the most commoly traded curreces 03. Fally, there are metoed two ma purposes of determg the bak's Potetal Loss due to foreg exchage rsk. Keywords: foreg exchage rsk, bak's Potetal Loss, foreg exchage posto, volatlty, ormal dstrbuto.0 INTODUCTION The foreg exchage rsk (or currecy rsk) s a compoet of market rsk ad expresses the possblty that exchage rate fluctuatos egatvely affect the proft ad equty of the bak. Ths rsk occurs because the bak has operatos foreg curreces. The bak's exposure to foreg exchage rsk s the foreg exchage posto. The bak foreg exchage posto a certa foreg currecy represets the et assets of the bak that currecy. The bak's foreg exchage posto s the dfferece betwee the bak's assets ad the bak's debts expressed a foreg currecy. A certa sze of the foreg exchage posto ad the volatlty of the exchage rate of oe foreg currecy agast the atoal currecy used for accoutg records may volve the possblty of losses for the bak. The foreg exchage loss may be eve hgher as the bak has a portfolo of several foreg curreces. I may research papers, the bak's loss due to market rsk s determed by several types of socalled Value at sk methodologes. For stace, Lsmeer ad Pearso (000) explaed the cocept of Value at sk ad descrbed detal the three methods for computg t: hstorcal smulato, the deltaormal method ad Mote Carlo smulato. Amma ad ech (00) foud that the Value at sk estmates by the varace covarace approach sometmes do ot dffer greatly from other smulatos eve for some optoed portfolos. Hedrks (996) made a hstorcal examato of twelve approaches to Value at sk modelg ad showed that almost all cases the approaches cover the rsk that they are teded to cover. I terms of varablty over tme, the Value at sk approaches usg loger observato perods ted to produce less varable results tha those usg short observato perods or weghtg recet observatos more heavly. Basel Commttee o Bakg Supervso (005) has made a amedmet to the Bak Captal Accord where suggested that bak's captal charge for market rsks ca be establshed by Value at sk procedures computed o a daly bass wth a 99th percetle for a 0 day movemet market prces..0 DETEMINING THE BANK S POTENTIAL LOSS DUE TO FOEIGN EXCHANGE ISK Measurg foreg exchage rate rsk loss of the bak ca be determed by calculatg the Potetal Loss related to the foreg curreces portfolo of the bak. Further, we wll obta a IJE MAY JUNE 04 Avalable ole@

2 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 relatoshp for the Potetal Loss of the bak's portfolo of foreg curreces by usg the ormal dstrbuto assumpto of the exchage rates daly varatos. Let X be a radom varable represeted by the daly varato of the exchage rate of a currecy agast aother. The, let X has a ormal dstrbuto of mea m ad stadard devato. The probablty that the radom varable X s less tha the threshold x s gve below: x t m * P( X x) N( x m ) * e <,, dt π where: N( x,m, ) s the dstrbuto fucto (or the probablty) from the ormal dstrbuto. Ay radom varable X wth ormal dstrbuto ca be trasformed to a radom varable Z havg stadard ormal dstrbuto by chagg the varable. Thus, for a threshold z of the stadard ormal dstrbuto, there s the equalty: ( x, m, ) N( z,0,) N x z x m z * + m z * sce the data seres of daly varatos the exchage It follows that rate betwee two curreces have the average m whch teds to 0 for a sample of daly data large eough. From the defto of the probablty we have X <x ad for a foreg exchage currecy portfolo holdg for oeday tme horzo ad uder the ormal dstrbuto of the daly chages of the exchage rate t follows that the Potetal Loss s gve by z *. Let be a foreg currecy owed by a bak. The the Potetal Loss for the bak foreg exchage posto deomated currecy s gve by the followg relatoshp: PL FP * z * where: () PL s the Potetal Loss of the foreg exchage posto deomated currecy ; FP s the foreg exchage posto expressed currecy ( uts of ); z s the cofdece level from stadard ormal dstrbuto; ( t ) t s the stadard devato of the daly varatos of the exchage rate of the currecy agast the base currecy. The base currecy s the atoal currecy utlzed by the bak to keep ts accoutg; t s the daly varato of the exchage rate of oe currecy agast base currecy. St t S S t, where: t ad S t are the exchage rates betwee currecy agast base currecy the days t ad t respectvely; IJE MAY JUNE 04 Avalable ole@ 3

3 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 t s the average of the exchage rate daly varatos data sample; s the umber of observatos the sample of statstcal data. The Potetal Loss for oe day of a bak portfolo cossts of m foreg curreces ca be determed as follows: ρ ρ... ρ PL PL P where: ( PL PL... PL ) PL P PL P day; m m ρ ρ... ρm *... ρm ρm... ρ mm PL *... PLm s the Potetal Loss of the foreg exchage portfolo of the bak for oe () ρ s the correlato coeffcet betwee the daly varatos exchage rate data seres ρ * t ad t of the foreg curreces ad agast base currecy. t t ( )* ( ) ( ) * ( ) t t t t t, where are the averages of the data seres t ad t respectvely; PL are the Potetal Losses of the bak expressed base currecy;,... m. The Potetal Loss of the bak portfolo cossts of m foreg curreces for a perod of T days ca be determed as follows: PLP ( T days) PLP * T (3) Further, we determed the Potetal Loss of a bak havg Euro as the base currecy for a portfolo of other fve prmary foreg curreces the most traded 03 (as t metoed "Foreg exchage turover Aprl 03: prelmary global results" of the Bak for Iteratoal Settlemets). Besdes the Euro, other fve prmary curreces most traded 03 were the followg: the Uted States dollar (USD), the Japaese ye (JPY), the Poud Sterlg (GBP), the Australa dollar (AUD) ad the Swss frac (CHF). We set a sample of the daly varatos of the exchage rates of the fve curreces agast the Euro wth a legth umber of 54 observatos. The data source for the exchage rates USD/EU, JPY/EU, GBP/EU, AUD/EU ad CHF/EU s the Statstcal Data Warehouse of the Europea Cetral Bak. IJE MAY JUNE 04 Avalable ole@ 4

4 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 I Table are preseted the daly average volatltes of the USD, JPY, GBP, AUD ad CHF exchages rates agast EU. It ca be oted that the daly average volatltes of the fve exchage rates are betwee 0.99% (for CHF / EU the least volatle exchage rate) ad 0.863% (for JPY / EU the exchage rate wth the hghest volatlty). Table : The daly average volatltes of the USD, JPY, GBP, AUD ad CHF exchages rates agast EU Exchage rate Daly average volatlty The value of the exchage rate / EU for the last day of the year 03 ( ut of y uts of EU) ( %) S / 3/ 03 USD/EU JPY/ EU GBP/ EU AUD/ EU CHF/ EU The matrx of correlato coeffcets betwee the daly varatos seres of USD, JPY, GBP, AUD ad CHF exchages rates agast EU s preseted Table. It ca be oted that the correlato coeffcets of the fve exchage rates daly varatos are betwee (for the par of exchages rates CHF/EU USD/EU) ad 0.53 (for the par of exchages rates JPY/EU CHF/EU). Table : The matrx of correlato coeffcets betwee the daly varatos seres of USD, JPY, GBP, AUD ad CHF exchages rates agast EU USD/EU JPY/EU GBP/EU AUD/EU CHF/EU USD/EU JPY/EU GBP/EU AUD/EU CHF/EU Next, we cosder the hypothetcal example of a bak that keeps ts accoutg trasactos EU ad the foreg currecy postos USD, JPY, GBP, AUD ad CHF are each of 0,000 euro equvalet. I Table 3 there are show the foreg exchage postos ad the daly Potetal Losses of the bak from the assumed example for a threshold of z.33 correspodg to a probablty of 99% the stadard ormal dstrbuto. Therefore, the Potetal Losses are hgher for the bak exposures foreg curreces wth hgher volatlty of the exchage rates agast the base currecy EU. IJE MAY JUNE 04 Avalable ole@ 5

5 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 Table 3: The foreg exchage posstos ad Potetal Losses of the bak. Hypothetcal example Foreg exchage Daly Potetal Loss Daly Potetal Loss Currecy posto PL currecy PL EU (z.33) FP (z.33) Normal dstrbuto Normal dstrbuto USD 3,79 USD 56 USD 3 EU JPY,449,75 JPY 98 JPY 0 EU GBP 8, GBP 06 EU GBP AUD 5,43 AUD 38 AUD 54 EU CHF,76 CHF 83 CHF 68 EU 0,000 FP S Note: / 3/ 03 Usg the correlatos coeffcets from Table, the daly Potetal Losses EU from the Table 3 ad the relatoshp () we obtaed the daly Potetal Loss for the hypothetcal fve foreg exchage (USD, JPY, GBP, AUD, CHF) portfolo of the bak: PL P PL P ( ) * * 06,765, 99 3,430 EU, for oe day As suggested by the Basle Commttee o Bakg Supervso, a bak may keep captal for uexpected losses from foreg exchage rsk to a sze equal to the Potetal Loss of the portfolo of curreces for a perod of 0 days. I our example, the Potetal Loss of the foreg exchage portfolo that cossts of fve curreces, for a perod of 0 days s 0,847 EU: PL P ( 0 days) 3,430* 0 0,847 EU Aother utlty of the Potetal Loss resultg from bak's exposure to certa foreg curreces s that ths Potetal Loss ca be used as a threshold for stop the loss of the bak. Oce attaed the threshold wll mea that the bak's foreg exposure should be reduced for the foreg currecy questo, especally for those that ther exchages rates agast the base currecy whch the bak keeps the accoutg have the hghest daly average volatlty. 3.0 CONCLUSIONS The fdgs of ths paper are multple. Frst, we obtaed a relatoshp for the Potetal Loss of the bak's portfolo of foreg curreces by usg the ormal dstrbuto assumpto of the exchage rates daly varatos; we also metoed the methods of calculatg the elemets ecessary for determg the Potetal Loss of the bak. Secod, usg statstcal daly data of IJE MAY JUNE 04 Avalable ole@ 6

6 Gabrel Bstrceau, It.J.Eco. es., 04, v53, 7 ISSN: 9658 foreg exchage rates, we determed the Potetal Loss of a bak that keeps the accoutg Euro for a bak portfolo cossts of fve the most commoly traded curreces 03 besdes the euro (USD, JPY, GBP, AUD, CHF) a hypothetcal example o the bak's foreg exchage postos. Thrd, we metoed two ma purposes of determg the bak's Potetal Loss due to foreg exchage rsk: () settg up captal for uexpected losses from foreg exchage rsk; () stoppg the bak s loss comg from the mafestato of the foreg exchage rsk. EFEENCES Amma, M. ad ech. C (00), Valueatsk for Nolear Facal Istrumets Lear Approxmato or Full MoteCarlo?, Facal Markets ad Portfolo Maagemet. Bak for Iteratoal Settlemets (03), "Foreg exchage turover Aprl 03: prelmary global results", Treal Cetral Bak Survey, Bak for Iteratoal Settlemets s publcato. Basel Commttee o Bakg Supervso (005), Amedmet to the Captal Accord to corporate market rsks, Bak for Iteratoal Settlemets s publcato. Hedrks Darryll (996), Evaluato of Valueatsk Models Usg Hstorcal Data, Federal eserve Bak of New York Ecoomc Polcy evew, Aprl 996. Lsmeer Thomas J. ad Pearso Nel D. (000), Value at sk, Facal Aalysts Joural, March/Aprl 000, Vol. 56, No. : pp IJE MAY JUNE 04 Avalable ole@ 7