The Formaion of he Deposi Porfolio in Macroeconomic Insabiliy Anriy Skrypnyk, Maryna Nehrey Naional Universiy of Life an Environmenal Sciences of Ukraine avskripnik@ukr.ne, Marina.Nehrey@gmail.com Absrac. In 04 he main enency of Ukrainian economy was he losing of grea eposi value. In his aricle we wish o explore a eposi porfolio srucure in macroeconomic insabiliy. We applie wo approaches o he sanar opimizaion porfolio: risk minimizaion for a given maximum reurn an reurn maximizaion for a given maximum risk. Of he wo approaches o he sanar opimizaion problem of porfolio: risk minimizaion a a given minimum reurn an reurn maximizaion for a given maximum risk he avanage was given he laer. The exchange rae risks are he main facors ha have a significan impac on he en resul. The opimum srucures eposi porfolio was calculae for six ifferen siuaions in naional an worl financial markes. Comparison of he opimal porfolio srucure wih real hisorical aa showe ha cusomers of he banking sysem over evaluae he reliabiliy of he financial sysem. Keywors. eposi, evaluaion, porfolio, opimizaion, reurn, revaluaion, risk. Key Terms. Daa, DecisionSuppor, Developmen, FormalMeho, Managemen, MahemaicalMoel. Inroucion The unsable macroeconomic siuaion in Ukraine an he crisis of he banking sysem cause isrus in he banking insiuions. Accoring o he opinion of expers, he Ukrainian populaion kep a home cash equivalen o 0 billion USA. In recen years was observe he following enency: in 04 banks los eposis in he amoun of 6 billion UAH, an aroun 8 billion UAH uring firs wo monhs of he curren year []. However, sorage of money a home has several isavanages: for example lack of income from capial an high risks, which lea o aiional coss for he implemenaion of he safey of heir own homes an significanly ecrease he level of living. Banking expers usually avise o ivie money ino hree equal pars, wo of which are nominae ino euros an US ollars accoring o he curren exchange rae, an pu on eposi accouns in ifferen banks which can be consiere reliable
(i is avisable o choose banks which are inclue in he eposi insurance program NBU) an wai for ineress uring his perio (simple iversificaion). Unforunaely, his meho is connece wih ifficulies. I is almos impossibile o conver legally he accumulae funs ino any reliable currency, besies i is raher ifficul o fin a reliable bank. This suy is limie o wo currencies - US ollars an euros, however, presene meho can be use o form a eposi porfolio using oher currencies. There are wo approaches o he porfolio opimizaion problem: risk minimizaion a a given minimum reurn an reurn maximizaion for a given maximum risk. For porfolio opimizaion you nee o eermine in which currency o evaluae he resul. We can ask a quesion: Why o we save money? The answer can be he following: In orer o increase consumpion uring our life (real esae, househol appliances, auomobiles, raveling) []. The vas majoriy of consume goos in Ukraine are prouce ousie he counry an herefore i is beer o measure he cos by he mos sable currency, which is now can be consiere he US ollar. Alan Greenspan evoe aenion o keeping a low ollar inflaion level han in he pas since such a policy, combine wih he larger preicabiliy of moneary policy, conribue o making ollar capial enominaion mos aracive []. Markowiz Problem uner Devaluaion Coniion The Markowiz s porfolio opimizaion problem can be solve using he wellknown erm of reurn an risk (variance of reurn) componens porfolio. If reurn is measure as he eposi ineres, he rae of risk is measure by is ispersion [4]. Linear moel was propose for crei risks in orer o maximize bank profi [6, 0]. However, here is a facor ha has a significan impac on he en resul - an exchange rae risks, which is more imporan for unsable economics []. Of course ineress on eposi an crei accouns for exchange rae risks, as he ineres on UAH eposi wice as much han he ollar eposi [, ]. The imporance of foreign exchange componen in he susainabiliy of he banking sysem was emphasize in a number of research [5, ]. In his suy we wish o evaluae he opimal srucure of he eposi porfolio uring economic urbulence an make a comparison beween real an opimal srucure eposi porfolio. Exchange rae risks can be aken ino accoun, if a evaluaion marix is specifie. We will consier he case-suy of placing eposis for one year. We assume ha hree macroeconomic siuaions, which eermine he evaluaion processes in he counry ; ;, which are efine probabiliies p ; p; p( p i ). Each siuaion correspons o a cerain evaluaion facor relaive o USD efine as he raio of he exchange rae in a curren momen o exchange rae wha will be in a year. We will enoe evaluaion muliplier for each economic siuaions (i,, ). If i i we know he value of a ranom variable an he corresponing probabiliies, we can esimae he expece value of epreciaion facor an is variance:
ii ; ф i i i i p p () Laer we will consier he case of uniform isribuion of evaluaion muliplier. If hen ominae evaluaion expecaions, if hen ominae revaluaion expecaions. There were shor perios of revaluaion of UAH, bu we observe he enency of evaluaion accoring o resuls of any year. I is suppose o use he share enominae in euro for eposi porfolio, which has currency insabiliy relaive o leaing worl currencies an he objecive funcion is enominae in USD, we nee o specify he expece evaluaion an is variance in EUR agains he USD for he nex year. We will enoe hese parameers: ;. In his formulaion ollar eposis is compleely risk-free, which is raher opimisic assumpion. During he year, he ineres on ollar eposis was changeable, which can be use as a risk assessmen. We enoe he variance of ineress on USD eposis. We assume ha he curren ineres on USD eposis is in he inerval 9-% [8] an is characerize by a uniform isribuion, he ispersion ineres is approximaely 5 equal, 0. We consier he sanar formulaion of he Markowiz problem aking ino accoun he expece evaluaion (revaluaion) processes. We presen he paricles eposi porfolio in UAH, EUR an USD: ; ; ( ), percenage ineress r ;r ; r ( r r r ) are range uner level of risk of eflaionary expecaions. If an iniial invesmen is S han in a year he expece amoun of he eposi porfolio an is ispersion will be: S П S ( r ) S ( r ) S ( r ), S S S. () There are no members in porfolio variance ha appear as a resul of presence of he connecion beween reurn componens of porfolio. The reason is ha in his case inepenen evaluaion processes influence on he profiabiliy: euro an US ollar an he processes of evaluaion of he naional currency because of macroeconomic insabiliy in he counry. Therefore, we can asser absence of connecion beween reurn of he porfolio shares enominae in ifferen currencies in he propose formulaion. If he level of evaluaion is high, he eposior will have loses S S ), ha is ( why we will limi he possible risk-free profi accoring o he ineres which is equal o r (he reurn of ollar eposis): S ( r ) S ( r ) S ( r ) S ( r ) ()
From he las expression we can ge maximum porfolio share of eposis enominae in UAH : ( r r ) r ( r ) We esimae he maximum share of UAH eposis in erms of caasrophic evaluaion in 04. The ifference in ineress enominae in euros an ollars is less han %, he maximum value of he numeraor is less han 0.0. Devaluaion muliplier for he previous year is approximaely equal o 0.4 (8 USD / UAH 0 = 0.4). Ineress on eposis are r 5%; r 0%. Therefore, he share of UAH eposis in erms of lanslie evaluaion shoul no excee %. (4) Opimal Porfolio Srucure We esimae he porfolio srucure wih maximum profiabiliy an limie risks for ifferen combinaions of UAH/USD an EUR/USD evaluaion muliplier facors. Evaluaion of evaluaion muliplier facors is base on monhly ime series of UAH/USD (0.997-0.05) an EUR/USD (0.007-0.05) exchange raes. Fig.. Dynamics of evaluaion muliplier UAH/USD Devaluaion muliplier measure wih one year inerval (eposi ime in opimizaion problem) an currency pairs we calculae every monh from March 997 o February 04 (0 observaions UAH/USD) an form February 007 o February 04 (98 observaions EUR/USD). (Fig., ).
Fig.. Dynamics of evaluaion muliplier EUR/USD r The perio (997-04 for UAH/USD) consiss of perios of economic growh wih fixe course an perios crisis when moneary sysem ens o new equilibrium. Devaluaion muliplier facor UAH/USD uner 55 observaions (minor revaluaion probabiliy p 76 ), uner 55 observaions (evaluaion probabiliy p 64 ). Devaluaion muliplier facor EUR/USD uner 44 observa- ions (revaluaion probabiliy p 449 ), uner 54 observaions (evaluaion r probabiliy p 55). Devaluaion muliplier EUR/USD has more naural characer, when he equilibrium is se uner he influence of many non-inerrelae reasons an a sable enency is missing. The saionary hypohesis of he exchange rae of EUR/USD can be prove if we explore a long ime perio. The same hypohesis for exchange rae of UAH/USD mus be rejece because of a full asymmery of evaluaion muliplier relaively o uniy level. We consier he opimal porfolio srucure in hree cases: lanslie evaluaion from 4% o 50% - ( 7 ); moerae evaluaion of % o 4% - ( 7 9); an a evaluaion less han % - ( 9,0 ). We regar he isribuion of evaluaion muliplier a each of he inervals being uniform. We consier wo possible saes in he global financial marke for evaluaion muliplier for EUR/USD: ( 8, 0) an revaluaion muliplier: (, 0, ). We presen six possible siuaions ha correspon o wo siuaions of he worl finance marke (he euro-ollar) an hree siuaions of evaluaion in he omesic marke (Table ).
We have use ineress of one-year eposis in banks of firs group (he mos reliable) o buil opimizaion moels. Of course, oher banks ineress can be significanly higher, bu in his case i is necessary o increase he risk measures of bankrupcy probabiliy ue o he growh (receiving conribuions uner he insurance program of NBU connece wih he loss of ime an ineres an primary conribuion for more han 00 housans UAH). We use he curren annual eposi ineress February 05: r ru %; r re %; r r %. Table. Expece value evaluaion facors for ifferen classes of naional an worl economies in 05 ( 7 ); 55; 7, 50 ( 8, 0) 9;, 0 ( 7 9); 8; 9;, 0, 0 ( 9,0) 95; 9; 80, 0 55; 7, 50 (, 0, ) 05, ; 80 8; 05, ;, 0 80 95; 05, ; 80 80 We consier he problem of calculaion of he share of cerain currencies in eposi porfolio ha maximizes he reurn of he porfolio for a given maximum risk level, which is equal o variance of ineress on USD eposis: max min ( r r ). (5) max min 5 For r r 0, 0. We obain he following problem o be resolve for fining ( ; ; ) :, S S ( r ) S ( r ) S ( r ) max S ( r r ), r ( r ) j n j j S, j,. S, (6) We analyze he resuls of he calculaion of he srucure of eposi porfolio wih maximum reurn, epening on he siuaion in he global an omesic foreign currency markes (Table ).
There are six siuaions accoring o he number of componens in Table : (, ) - moerae evaluaion of he euro an he significan UAH epreciaion; (, ) - moerae evaluaion of he euro an he moerae evaluaion of he UAH (, ) - moerae evaluaion of he euro an sligh currency epreciaion; (, ) - moerae appreciaion of he euro an he significan currency epreciaion; (, ) - moerae appreciaion of he euro an moerae currency epreciaion; (, ) - moerae appreciaion of he euro an he sligh epreciaion of he UAH. Table. Opimizaion of eposi porfolio accoring o he crierion of profi maximizaion ( 8, 0) (, 0, ) ( 7 ); ( 7 9); ( 9,0) ( ) S, ( ) S, ( ; 0 ) S, 685 ( 7; 7 ) ( 7; 7 ) ( ; 0 ) S 685, S, 685 S, 865 In cases (, ) an (, ) opimal porfolio conains only ollar eposis wih cerain reurn. In he case (, ) porfolio consiss only of UAH eposis (he reurn is correce o he expece epreciaion up o.%). In cases (, ) an (, ) he same reurn is efine by 7% share of eposis nominae in euros an 7% of eposis nominae in ollars. In he case (, ) he reurn which is equal o 8.65% is efine by 00% share of euro eposi. However, i is beer o base he assumpions on mahemaical forecas abou he srucure of porfolio ha epens on he probabiliies of he exernal environmen: p he probabiliy of evaluaion i sae (i =,,..., k) cross currency exchange rae UAH/USD, q he probabiliy of he epreciaion of he j-h sae (j =,,..., n) cross currency j exchange rae EUR/USD, of he i an j evaluaion saes, p ij p i q j he probabiliy of simulaneous occurrence ij he opimal porfolio srucure accoring o i evaluaion sae of he UAH/USD an j sae pair EUR/USD. Expece porfolio srucure is efine as: k n i j p ij ij. (7) We calculae he expece porfolio srucure, assuming ha he evaluaion an revaluaion expecaions of he euro-ollar are equal. ( p p 0 5 ), he firs basic varian is calculae accoring o he assumpion, ha all hree evaluaion saes have he same evaluaion probabiliy (i is a siuaion i
of absolue uncerainy). Tha is why p ij / 6. This is basic srucure of he porfolio an is expece reurn: Б (67;4;4)... r Б 5,5%; 4 7,4 0. We consier pessimisic opion in which he probabiliy of a significan evaluaion is wice higher han he probabiliy of low, moerae evaluaion an probabiliies moerae evaluaion is equal o he sum of probabiliies of large an small evaluaion: /... /... / p ij (8) /... /... / In his case we obain he following srucure an reurn of he porfolio: 4 П (08;88;59)... r П 4,98%; 6,4 0.. We consier opimisic opion in which he probabiliy of a significan evaluaion is wice lower han he probabiliy of moerae evaluaion bu he probabiliy of moerae evaluaion is equal o he sum of probabiliies of significan an moerae evaluaion: Б П pij /... /... / /... /... / (9) In his case we obain he following srucure an reurn of he porfolio: О (67;4;4)... r О 5,5%; 7,4 0 4 О The las opion is no ifferen from he basic one. In macroeconomic environmen an exchange rae insabiliy, he banking sysem an is cliens replace he unsable asses wih sable, an his leas o an increase in ollarizaion of economy in general an he banking sysem in paricular (his quaniaive crieria is measure as he share of ollar eposis o he oal amoun of eposis [5]).. 4 Hisorical Daa Moel Verificaion Moel verificaion can be mae on he base of currency exchange rae (UAH/USD) measure for a long perio of ime an enencies of he exchange rae of wo main worl currencies (EUR/USD). For moel verificaion we use perio of sable growh of Ukrainian economy from 00 o 007 year, which coincies wih perio exchange rae sabiliy. We calculae he opimal porfolio srucure for wo perios: afer-shock perio 00-005 an pre-shock perio 006-007 on he base of NBU aa. Average
annual eposi ineress for his perio is 0%; 5%; 6% an 4%; 9%; 9% (UAH, EUR, USD). Maximum ispersion magniue has increase in four imes in comparison wih previous calculaions because of possibiliy of subsanial changes in eposi ineress for long perio. Opimal porfolio srucure has no UAH componen in all six possible siuaion (able ) for 00-005. Table. Opimizaion of eposi porfolio accoring o he crierion of profi maximizaion for 00-005 eposi ineress: r 0 %; r 5%; r 6% U Є ( 8, 0) (, 0, ) ( 7 ); ( 7 9); ( 9,0) ( ) S 06, ( ) S, 06 ( ) S, 06 ( ; 8 ) ( ; 8 ) ( ; 8 ) S 0685, S, 0685 S, 0685 Devaluaion muliplier UAH/USD probabiliies for Tabl. ranges calculae from aa analisis: p ) 077; p( ) 87; p( ) 76. For EUR/USD evaluaion ( ( с с muliplier probabiliies: p ) 449; p( ) 55. Nex sep probabiliy evaluaion of simulaneous occurrence of all 6 possible evaluaion saes on long ime inerval: 05... 084... pij piq j (0) 04... 00,... 406 The expece porfolio srucure, for his probabiliy marix an opimal srucure porfolio for each of six siuaion: 004 (;89)... r 004 6,47%, 004,5 0 This resul iffers from previously obaine for perio of crisis. Firs of all, i concerns he full absence of UAH componen, an seconly, much smaller proporion of he conribuions in EUR. Boh feaures are explaine by raio of key ineress. Difference in ineress in UAH was no enough o compensae evaluaion risk of naional currency, aiional ineress on USD eposis for EUR provie a small share of EUR eposis. Opimal porfolio srucure for pre-crisis perio 006-007 iffers in increasing share of EUR conribuion because ineress on USD EUR eposis were equal, UAH share is sill equal o zero (Table 4). The expece porfolio srucure for 006-007 years:. 5
4 006 (449;55)... r 006,4%, 006 5, 0 Table 4. Opimizaion of eposi porfolio accoring o he crierion of profi maximizaion for 006-007 eposi ineress: r 4 %; r 9%; r 9% U Є ( 8, 0) (, 0, ) ( 7 ); ( ) ( 7 9); ( ) ( 9,0) ( ) S 09, S, 09 S, 09 ( 8; ) ( 8; ) ( 8; ) S 6, S, 6 S 6, Bu real srucure of bank eposis a ha perio i no correspon o opimal ecision, populaion prefere UAH eposis because of fixe ineress an higher reurn. I was hough ha he sraegy of he fixe exchange rae provie a ecrease in he level of ollarizaion of economy, which is efine as a raio of foreign currency eposis o all eposis. A his enire inerval opimal sraegy wihou risk accouning consiss of wo key poins: borrowing in foreign currency an placing of savings in he naional currency. A ha ime, noboy knew when he perio macroeconomic sabiliy woul be over, bu now i has become clear ha he financial crisis was only a rigger for he sysem ha was reay o collapse. UAH savers an currency borrowers who were unable o complee heir operaions before 008 crisis ha losses. Banking cusomer behavior on he inerval of economic growh can be consiere on he basis of he heory of focusing illusion [9] when banker cliens exaggerae he imporance of one facor (fixe course), neglecing he influence of oher facors, he effec of which may lea o opposie resuls. 5 Conclusion In his research we calculae maximum profiabiliy hree componens UAH, EUR, USD eposi porfolio srucure (argee funcion is enominae in US ollars) wih risk egree limiaions in he economic growh perio an perios of macroeconomic insabiliy. The exchange rae insabiliy is regare as main cause of eposi risks an formalize by he relaionship of curren currency price o currency price which will be in a year (evaluaion muliplier). Long ime evaluaion muliplier facor analysis gave possibiliy o evaluae probabiliies of six possible ifferen evaluaion (revaluaion) siuaion for pairs UAH/USD an EUR/USD. The opimal soluions were obaine for each of he six possible ifferen siuaions an for hree ineres opions (wo opions uring economic growh an one uring he perio of economic urbulence). Expece eposi porfolio was eermine in coniions of macroeconomic insabiliy for hree possible choices: basic (probabiliies of all saes are equal), pessimisic (probabiliy of a
significan UAH evaluaion is wice higher han he probabiliy of minor evaluaion) an opimisic (probabiliy of a significan evaluaion is wice less han he probabiliy minor evaluaion). For opimisic opion he par of UAH eposi mus be no more han 7%, in oher siuaion expece UAH par mus be no more han 8%. Opimal porfolio srucure in a perio of economic grows has no UAH componen because of a small ifference in he ineress of UAH eposis an EUR, USD eposis. Bu his ifference was enough o provie preferre growh UAH enominae eposis. The reasons of his phenomenon is overconfience of he cliens of banking sysem in UAH sabiliy cause by fixe exchange rae accoring o NBU sraegy. References. Annual repor NBU - 007, online bank.gov.ua/occaalog/ocumen? i=5855 (007). Akinson, A. B., Sigliz, Joseph E.: Lecciones sobre economía pública. Miniserio e Economía y Haciena. Insiuo e Esuios Fiscales (988). Bershisky, L.: Ukraine's Economy Is Worse Than I Looks. online bloombergview.com/aricles/05-0-06/ukraine-s-economy-is-worse-han-i-looks (05) 4. Boie, Zvi, Kane, Alex an Marcus, Alan J.: Invesmens. 7h eiion. New York: McGraw Hill/Irwin (008) 5. Dzyublyuk, O., Vlaymyr, O. Foreign capial in he banking sysem of Ukraine: an impac on he currency marke evelopmen an banks aciviy. Visnyk Nasionalnoho banku Ukrainy 5, 6 (04) 6. Elon, Ewin J., an Gruber, Marin J.: Moern Porfolio Theory & Invesmen Analysis. John Wiley&Sons, Inc. (987) 7. Grushko, V., Ivanenko, T.: Opimizaion of he srucure of he loan porfolio of a commercial bank. Visnyk Nasionalnoho banku Ukrainy,, 8 (04) 8. Invesfuns.ua. Informaion poral. online invesfuns.ua/markes/inicaors /usuah- nbu/ (05) 9. Kahneman, D.; Tversky, A.: On he realiy of cogniive illusions. Psychological Review, 0 (), 58 59 (996) 0. Kaminsky, A.B.: Moeling of financial risks. Publishing cener "Kyiv Universiy", (006). Cerrao, Mario, Kim, Hyunsok, MacDonal, Ronal: Nominal ineres raes an saionariy. Working Papers Business School - Economics, Universiy of Glasgow, online gla.ac.uk/meia/ meia_50448_en (00). Moneary an financial saisics, online bank.gov.ua/conrol/en/publish/aricle? ar_i=67604&ca_i=780 (05). Plasun, O., Makarenko, I.: Moeling of he financial markes behavior uring he financial crisis wih he use of he fracal marke hypohesis Visnyk Nasionalnoho banku Ukrainy, 4, 8 45 (04)