A Systemic Measure of Liquidity Risk

Transcription

1 A Sysemic Measure of Liquidiy Risk Carolina Pagliacci Jennifer Peña Absrac This paper analyzes sysemic liquidiy risk by assessing he behavior of aggregae banking variables and policies relaed o he managemen of liquid asses. The basic premise is ha liquidiy is no only relaed o he abiliy o mee inerbank deb obligaions, bu also he availabiliy of sufficien liquid asses o cover oher shor-erm liabiliies, such as hose arising from commercial banks ineracion wih he cenral bank. To measure liquidiy risk, we use he coningen claims approach of Meron (1974) and Gray, and Malone (2008). Daa produced by he model (probabiliy of defaul) explains and improves predicion of he amouns and ineres raes negoiaed in he inerbank marke. In he case of Venezuela, given he imporance of fiscal expendiure in he C. Pagliacci <carolina.pagliacci@iesa.edu.ve>, associae professor, Insiuo de Esudios Superiores de Adminisración, and J. Peña <jenpena@bcv.org.ve>, economic analys, Office of Economic Research, Banco Cenral de Venezuela. The auhors are graeful for he suggesions made by aendees a he Seminar of he Vice Presidency of Sudies, Banco Cenral de Venezuela, and he Eighh Bolivian Conference on Developmen Economics organized by he Sociey of Bolivian Economiss, he Insiue for Advanced Developmen Sudies, he Bolivian Academy of Economic Sciences and he Universidad Privada Boliviana. The opinions expressed in his paper are hose of he auhors and do no necessarily represen hose of he Banco Cenral de Venezuela. Monearia, July-December, 2017

2 primary creaion of money, fiscally induced moneary expansion ends o reduce he likelihood of illiquidiy evens. Meanwhile, an increase in reserve requiremens increases he probabiliy of defaul by raising banks shor-erm liabiliies. Keywords: coningen asse analysis, inerbank marke, sysemic risk, macroprudenial regulaion. jel classificaion: G00, G13, G INTRODUCTION This paper aims o conribue o measuring sysemic liquidiy risk and undersanding he facors influencing i. Liquidiy risk for an individual bank can be undersood as he likelihood of i no being able o mee is paymen obligaions or cash flows wih oher banks as described by Cao (2015). 1 The lieraure ypically describes sysemic risk associaed wih liquidiy issues as he conagion ha akes place among insiuions in he sysem afer closely inerconneced banks (or sysemically imporan) repor defaul problems. Given ha nework models allow analyss o undersand o wha degree a single even migh cause domino ype effecs, hey have become key o he analysis of sysemic liquidiy risk. A summary of his ype of sudies can be found in Upper (2011). Meanwhile, Smaga (2014), and Drehmann and Tarashev (2011) show ha hese esimaions of individual risk conagion represen a boom-up measure of sysemic risk. However, given he complexiy of he facors conribuing o sysemic risk, Smaga (2014) also shows how here is sill no consensus regarding is definiion. This has opened up he possibiliy for measuring sysemic risk from a boom-up poin of view, i.e., associaing sysemic risk o aggregae variables or 1 This definiion refers o he illiquid funds even, which differs from marke illiquidiy. The laer can be undersood as he risk of an insiuion no being able o buy and sell asses immediaely wihou forcing changes in heir prices due o a lack of deph or disorions in he marke. 164 Monearia, July-December, 2017

3 macroeconomic facors, which can reveal he saus of he financial sysem as a whole. This perspecive is imporan if we consider he exisence of exogenous facors ha can affec he whole banking sysem bu migh remain invisible when analysis focuses on individual insiuions jus as poined ou in Elsinger e al. (2002). Moreover, Brunnermeier e al. (2009) argue ha o properly regulae sysemic risk i is necessary o abandon he predominan view which assers ha a sysem is sound if all he insiuions wihin i are sound (macroprudenial approach). In oher words, i is essenial o adop a macroprudenial approach ha includes imporan macroeconomic daa o analyze he sabiliy of he sysem as a whole. This paper esimaes sysemic liquidiy risk based on he behavior of aggregae banking variables and policies relaed o banks liquidiy managemen. The basic premise is ha liquidiy is no only relaed o he abiliy o mee inerbank deb obligaions, bu also he availabiliy of sufficien liquid asses o cover oher shor-erm liabiliies, such as hose arising from commercial bank ineracions wih he cenral bank. To pay any of hese obligaions banks ypically reduce heir liquid asses, be hey hose ha are available immediaely (such as cash) or less liquid asses ha mus firs be sold in he marke (such as Treasury bills). Given ha he marke value of less liquid asses flucuaes hey are subjec o possible losses. Hence, oal liquid asses he sum of highly liquid and less liquid asses can be reaed as a sochasic variable. Under his conex, sysemic liquidiy risk arises due o he poenial losses involved in marke ransacions ha migh jeopardize he fulfillmen of shor-erm liabiliies. This risk becomes greaer as he need o ransform less liquid asses ino liquid ones in he marke increases. Given ha his idea of liquidiy risk is sysemic, i is also crucial o include he cenral bank s impac on commercial bank funds. To measure he risks associaed wih changes in liquidiy we apply he coningen claims approach originally developed for firms by Meron (1974) and applied o differen microfinancial C. Pagliacci, J. Peña 165

4 secors by Gray and Malone (2008). This mehodology rearranges he asses of an eniy o define he probabiliy of defaul as he likelihood ha he (sochasic) value of is asses falls below ha of he highes prioriy deb (or senior deb). The spread beween he value of he asses and he value of he senior deb is named residual liabiliy (or junior deb). Given ha he value of asses is no clearly visible in his mehodology he residual liabiliies iem is of umos imporance. In our sudy of he liquidiy problem, we define residual liabiliies as capial socks and liquid asse flows ha are available, such as cash and holdings in cenral bank policy insrumens. We also include expeced flows from new deposis relaed o he primary money creaion. One characerisic of available liquid asses is ha hey can be immediaely decumulaed o mee shor-erm senior deb obligaions if here are losses (expeced or unexpeced) in oher asses. This definiion of residual liabiliies is in line wih he fac ha, during periods of liquidiy shorage (when here are low levels of cash), adverse marke condiions exis for selling asses and, herefore, he expeced amoun of oal liquid asses ends o be low. On he oher hand, shor-erm senior deb includes paymens required by he cenral bank (such as legal capial requiremens and disbursemens for currency sales or oher loans). We also consider wihdrawals from he banking sysem as shor-erm liabiliies. The inerpreaion of defaul probabiliy proposed here is ha, if he desired accumulaion of liquid asses (such as cash) exceeds he flow of new funds enering he banking sysem i increases he likelihood of an even ha inerrups o some exen paymens beween banks or wih he cenral bank. This likelihood reflecs he risks (poenial losses) arising from a generalized ranslaion of less liquid asses ino cash. In he sric sense, defaul probabiliy calculaed in aggregae erms, more han an objecive measure of risk, can be considered an indicaor of overall banking sysem vulnerabiliy, as suggesed by Gapen e al. (2004) and Kozak e al. (2006). This is because here is no clear sysem-wide definiion of a defaul 166 Monearia, July-December, 2017

5 even. Neverheless, probabiliy as a sysemic risk concep can be useful for undersanding he accumulaion (observed) of highly liquid asses by he banking sysem as a whole. Such decisions are also linked o condiions seen in he inerbank marke, where banks seek o saisfy heir immediae liquidiy needs. We aemp o explain hese ideas based on a sylized opimizaion problem ha uses esimaed defaul probabiliy as an inpu for banks decisions. Our applicaion o he case of Venezuela shows ha he probabiliy of defaul obained from he model allows for explaining he aggregae amoun of funds raded in he inerbank marke as well as heir average agreed ineres rae. In paricular, a higher probabiliy of defaul ends o signal larger ransacion amouns due o he cenral bank s increased need for funds. Meanwhile, a higher probabiliy of defaul explains higher ineres raes, possibly reflecing larger risk premiums associaed wih he behavior of sysemic liquidiy. Furhermore, he mean squared error predicion for amouns and ineres rae improves considerably when he resuls are included in he model. According o he model presened in his paper, he vulnerabiliy associaed o changes in liquidiy can be influenced o varying degrees by moneary, exchange rae and fiscal policy decisions, depending on heir ineracions inside a counry s insiuional framework. For Venezuela s case, given he imporance of fiscal managemen in he creaion of new money, we show ha greaer fiscal influence in he money supply ends o reduce he likelihood of illiquidiy evens. Conversely, when he cenral bank inervenes o a greaer exen by selling currencies o he economy, illiquidiy evens end o become more likely. Moreover, an increase in reserve requiremens raises he probabiliy of defaul by increasing banks shor-erm obligaions. The paper is divided ino four secions. The firs corresponds o he inroducion. The second describes he applicaion of he coningen claims approach o liquidiy managemen, inerpres he probabiliy of defaul obained and oulines a sylized C. Pagliacci, J. Peña 167

6 model o undersand linkages wih he inerbank marke. The hird shows he applicaion o he case of Venezuela, and he coherence and robusness of he oucomes, as well as counerfacual exercises ha allow for undersanding how changes in major policies (fiscal and exchange rae) would affec sysemic liquidiy risk. The fourh secion presens some final remarks. 2. LIQUIDITY RISK Asses and liabiliies can be classified according o heir planned mauriy dae. These classificaions can provide cenral banks wih an esimae of heir mauriy mismach. However, referring o liquidiy managemen means comparisons are no necessarily beween oal asses and liabiliies, bu raher beween liquid asses and paymen obligaions wih hose liquid asses. Moreover, liquidiy shorages can arise as a resul of asse reallocaions semming from aemps o ransform less liquid asses ino more liquid ones. As a consequence, he ideas of senior and junior deb as radiionally applied in he liabiliies or coningen claims approach (cca) need o be reconsidered. Table 1 shows bank balance shees classified according o he sandard cca. We will now analyze how he cca should be applied o he liquidiy managemen problem and how said problem can be framed. Annex A describes he mahemaical approach relaed o implemening he coningen claims mehodology. Table 1 BANK BALANCE SHEET CLASSIFICATION ACCORDING TO THE STANDARD CONTINGENT CLAIMS APPROACH Asses Liabiliies Unobservable Senior deb: Shor-erm deposis + a fracion of longerm deposis Junior deb: Capial a marke value 168 Monearia, July-December, 2017

7 Liquidiy managemen ackles he problem of having sufficien liquid asses ready immediaely o mee shor-erm obligaions. There are wo iems ha should be considered when applying he coningen claims approach o an analysis of liquidiy. Firs, he amoun of liquid asses is somewha uncerain given ha hey are no clearly observable in he shor erm. Second, liquidiy managemen needs o include he behavior of expeced flows, which are relaed o changes in he cenral bank s balance shee (moneary base) bu are unobservable in commercial bank balance shees. Asse uncerainy. I is possible o hink of wo ypes of liquid asses. One par of hem is readily available and clearly observable: Refers o cash holdings a banks, and all deposis a he cenral bank (such as reserves more han legal requiremens and cerificaes of deposi). The oher par is represened by asses ha can be ransformed ino cash via marke ransacions, for insance, securiies negoiaed in secondary markes. The laer share is precisely he par of liquid asses whose value is uncerain. Esimaion of said asses is generally subjec o marke condiions. Thus, oal liquid asses can be reaed as a sochasic variable jus as in he sandard coningen claims approach because of possible marke losses (or gains). Expeced moneary base flows. Given ha we ry o sudy he problem of liquidiy managemen from a sysemic poin of view, i is imporan o ake ino accoun he role played by he cenral bank. For insance, banks posiions in moneary policy insrumens reflec funds len by or requesed from he cenral bank in he pas. Alhough hese balances have an impac on sysemic liquidiy, hey are already considered in bank balance shees. Expeced inflows and ouflows in a banking sysem are unobservable on bank balance shees. These flows of funds (in domesic currency) ake place hrough he primary money creaion (changes in he moneary base) and should also be considered when assessing sysemic liquidiy. Tha is o say, banks real liquidiy is increased or reduced by he creaion or desrucion of domesic currency. These changes in C. Pagliacci, J. Peña 169

8 moneary base ypically refer o exchange rae inervenions and money creaion produced by disbursemens or revenues of oher organizaions wih accouns a he cenral bank, such as he cenral governmen. Our analysis only akes ino accoun moneary base flows ha are no relaed o specific moneary policy acions aken by he cenral bank o offse oher flows. In oher words, we only wan o consider money creaion semming from currency flows or oher eniies oher han he cenral bank. This is he reason why we assume banks decisions o hold larger or smaller balances in moneary policy insrumens will depend on he evaluaion of sysemic liquidiy risk. Hence, changes in he amoun of he moneary policy insrumen canno be used as an inpu for esimaing said risk. This poin is relaed o he descripion in Secion Applying he Coningen Claims Approach o Liquidiy Managemen In he sandard cca, residual liabiliies are modeled as a European call opion because heir value increases as he esimaed value of asses wih respec o he value of a senior deb rises. Jus as in mos applicaions presened in Gray and Malone (2008), he value of residual liabiliies and senior deb are considered observable, while he implici amoun of asses has o be esimaed. In he liquidiy managemen problem, we classify as residual or junior deb all cash and liquid flows banks can use immediaely o mee shor-erm senior obligaions when here are reducions (expeced or unexpeced) in oher asses. The higher hese residual liabiliies, he greaer he oal liquid asses esimaed by he model, given a fixed number of senior claims. This implies ha he sochasic properies of residual liabiliies are ransferred o esimaed oal liquid asses. This idea is also consisen wih he fac ha during periods of liquidiy shorage cash levels are low and here are adverse marke condiions for selling asses. Hence, inadequae liquidiy is associaed wih low expeced amouns of oal liquid asses. 170 Monearia, July-December, 2017

9 Wha, herefore, are he specific componens of hose liquid residual liabiliies and major obligaions for liquidiy managemen? Table 2 shows he balances and flows ha should be considered. One imporan componen of residual deb is he balance of unlen cash deposis. Banks hold such cash deposis in heir vauls or as excess reserves (o legal capial requiremens) a he cenral bank. These wo iems represen he real amoun of cash accumulaed in he pas and, poenially, an imporan buffer for unexpeced increases in senior claims. Noneheless, his cash invenory should be adjused by he amoun of funds in he inerbank marke in order o be able o esimae he par of reserves ha are no commied during liquidiy shocks. Tha is o say if inerrupions occur in inerbank deb paymens by one or more insiuions, only he ne cash of loaned amouns can be considered as acually available. Meanwhile, subracing he oal amoun of loans due also seeks o conrol for excessive cash accumulaion during liquidiy crises. For insance, during periods of liquidiy shorage, bu subsanial banking aciviy, alhough cash reserves migh seem high, unlen cash reserves migh reflec sysemic liquidiy condiions more appropriaely. As for he moneary auhoriy, he balance of funds loaned o he cenral bank, i.e., he balance of buffer insrumens, is considered a residual liabiliy because i is generally available for banks o use. On he oher hand, he balance of funds borrowed from he cenral bank are considered a senior deb because hey mus be repaid o he moneary auhoriy in he shor-erm. 2 Likewise, flows semming from he primary money creaion (changes in he sources of he moneary base) can be considered residual liabiliies or senior claims, depending on wheher hey lead o newly available funds for banks or wheher hey represen paymens o he cenral bank (or an eniy wih an accoun a he cenral bank). 2 If here are differen mauriies for he insrumens, only he porion of he balance relaed o he shores mauriies (or mos imporan) should be considered. C. Pagliacci, J. Peña 171

10 Table 2 CLASSIFICATION OF SHORT-TERM LIABILITIES FOR LIQUIDITY MANAGEMENT Toal liquid asses Unobservable Toal liquid liabiliies Senior deb, D: Balance + ineres on moneary policy injecion insrumens Expeced desrucion of money in local currency (conracion of moneary base) Expeced change in reserve requiremens Ineres on deb in he inerbank marke Expeced cash wihdrawals Junior deb, E: Balance + ineres on moneary policy absorpion insrumens Expeced money creaion in domesic currency (expansion of moneary base) The balance of unlen cash reserves 1 1 Balance of unlen cash reserves = cash in he banks + excess reserves a he cenral bank amoun (pas) of funds negoiaed in he inerbank marke. Concerning senior claims in liquidiy managemen, ineres paymens owed in he inerbank marke represen addiional funds he banking sysem needs o generae o keep he marke funcioning. Expeced changes in legal or required reserves are considered liabiliies because, despie represening asses for he banks, he cenral bank does no allow hem o be used. This means ha an increase in reserve requiremens implies disbursemens by banks ha can increase he need for liquidiy in he shor-erm, even if hose reserves can be used as a coningency during liquidiy shorages. Anoher componen of senior deb is he number of expeced wihdrawals from he banking sysem. This amoun can be esimaed by ne cheque clearing and elecronic ransacions, which represen he amoun of deposis leaving he sysem and immediaely available deposis, respecively. 172 Monearia, July-December, 2017

11 2.2 Inerpreing Probabiliy of Defaul Due o he fac ha he cca is based on a reclassificaion of asses and liabiliies, we can rewrie a simplified version of Table 2 as follows: 1 A D = E, 2 ( ) ( ) = ( )+ O 1 O 1 abs 1 A E RR E R i Q E FBM BC + + efecivo O 1 Q ( 1 ), where A, D and E are liquid asses, senior claims and residual deb, respecively. RR, R, and FBM refer o reserve requiremens, wihdrawals and moneary base flows, respecively. BC abs and cash are credis (ne absorpion) a he cenral bank and cash, respecively, and represen available balances (highly liquid). Q O and i O are he amouns negoiaed and average ineres rae in he inerbank marke (overnigh). For any variable X, X = X X 1. Expecaions regarding he flows occurring in ime are formed wih informaion available a 1. One direc inerpreaion of he probabiliy of defaul (PrD) can be obained indifferenly from each one of he wo sides of Equaion 2: O 3 PrD = Pr( A < D )= Pr A < E( RR ) + E( R ) + i Q O 1 1, ( )= ( )+ + < 4 PrD Pr E Pr E FBM BC abs O = < 0 efecivo Q Equaion 3 suggess ha if he oal value of liquid asses is lower han senior deb flows; hen he probabiliy of sysemic defaul would increase. Equaion 4, on he oher hand, depics C. Pagliacci, J. Peña 173

12 ha if he balance of available asses (BC abs and cash) plus new funds is lower han he las amoun negoiaed in he inerbank marke, he probabiliy of defaul will increase. Anoher inerpreaion of defaul probabiliy can be obained by subracing desired (no acual) amouns of cash and he cenral bank absorpion commercial banks would wish o mainain a ime. Equaion 2 can be rewrien as follows: 5 O O 1 1 A E RR E R i Q efecivo BC = E( FBM ) BC abs abs ( ) ( ) = O 1 efecivo Q. In his case he probabiliy of defaul can be wrien as: 6 ( ) PrD = Pr A < D Pr A E RR E R i 1Q 1 efecivo BC O O a bs = ( ) ( ) < +, ( )= ( ) < + O abs 7 PrD = Pr E < 0 Pr E FBM Q BC efecivo 1. Equaion 6 suggess ha if he remaining porion of oal liquid asses once deb flows have been paid is lower han he desired amoun of available asses (BC abs and cash), hen he probabiliy of sysemic defaul increases. This is due o he fac ha reaching he desired amoun of highly liquid asses would imply ransforming less liquid asses ino cash by selling hem in he marke. A he aggregae level, such conversions would end o diminish he overall expeced value of asses and, herefore, would increase he likelihood of he asses being insufficien o cover obligaions. Meanwhile, Equaion 7 suggess ha if banks new fund flows (money creaion) are insufficien wih respec o inerbank debs, cash or absorpion should be reduced by a leas he same amoun in order o preven an increase in he probabiliy of defaul. In oher words, if he desired accumulaion of cash in highly liquid insrumens exceeds he flow of new 174 Monearia, July-December, 2017

13 funds in he sysem, he probabiliy of defaul increases due o risks semming from a generalized ransformaion of less liquid asses ino cash. Assuming he exisence of desired amouns of available asses is jus one ool o obain economic insigh ino an increase in aggregae probabiliy of defaul. However, in he saisical model, probabiliy of defaul is given by implied asse volailiy and heir disance o senior claims. In he sric sense, herefore, said probabiliy does no depend on he desired amouns of available asses. Tha said, can defaul probabiliy be linked o aggregae accumulaion (observed) of available (highly liquid) asses? Alernaively, can defaul probabiliy be relaed o marke variables, such as he amouns and raes negoiaed in he inerbank marke? Below we propose a highly sylized model o answer hese quesions. 2.3 Sylized Model for Modelling Available Asses Here we presen an opimizaion problem for a period when aggregae amouns of available liquid asses (cash and cenral bank absorpion) are deermined based on a given liquidiy risk. Tha is o say, given he (pas) informaion on asses and on expeced flows, a probabiliy for sysemic defaul is generaed. This probabiliy, in urn, defines wo possible saes of naure: one sae wih some degree of inerrupion o banks paymens (wih oher banks or he cenral bank), and anoher one of normal asse and inerbank marke funcioning. In boh saes, he coss of holding available liquid asses are differen. The oal expeced coss E(CT), for boh saes of naure, relaed o holding hese liquid asses are: 8 abs ECT ( )= PrD ( LGD efecivo BC )+ ( ) ( ) O PrD O BC i efecivo + i i BC abs, C. Pagliacci, J. Peña 175

14 where LDG is losses in asses raded in he markes in he even of an inerrupion o paymens, and i BC is he ineres rae se by he cenral bank for is absorpion insrumen. Equaion 8 reveals ha, in he case of inerrupion of paymens, expeced losses include losses in less liquid asses (sochasic) and losses relaed o he reducion of available asses. The greaer he accumulaion of available liquid asses, he lower are he oal losses associaed o he paymen inerrupion even. In he normal marke funcioning sae, he observable coss of holding liquid asses are he opporuniy coss wih respec o he inerbank rae. The aggregae opimizaion problem consiss of minimizing he oal expeced cos when choosing he amoun of cash and BC abs in, subjec o he aggregae resricion: efecivo + BC abs FBM, which denoes ha he acual accumulaion of boh available asses canno exceed inflows of new funds o he sysem. This is due o he fac ha once cash has been redisribued hrough he inerbank marke or he sale of less liquid asses by some banks, only money creaion can ranslae ino new available liquid asses. We also assume ha here is an implied posiive funcion beween i O and he aggregae amoun of cash, i O = f ( cash ). If f ( cash ) > 0, i means ha high aggregae levels of cash are associaed wih high inerbank ineres raes because banks, individually, ry o increase heir holdings of cash hrough he inerbank marke. Tha is o say, he behavior of he marke reflecs o a greaer exen he behavior of hose demanding funds. If f ( cash) < 0, i implies ha high aggregae levels of cash are consisen wih lower ineres raes in he inerbank marke given ha banks ry o channel said cash as fund supply. In his case, he behavior of fund suppliers prevails o explain he inerbank ineres rae. We also assume ha i BC is relaed o BC abs BC abs, i.e., for i f BC f BC 0. 3 = ( ), where ( ) f cash 0 and f ( BC )< 0, or alernaively f cash 0 saisfy boh second order condiions for minimizing, if f ( cash) = f ( BC )= 0. 3 Assumpions ( ) > f ( cash) < 0 and ( ) < 176 Monearia, July-December, 2017

15 Because PrD and lgd in are calculaed wih pas informaion, he firs order condiions for he opimizaion problem are given by: O + ( ) = 9 i f cash cash PrD, 1 PrD O CB 10 i i f BC BC abs + ( ) = PrD. 1 PrD Equaliy Equaion 9 shows ha for f ( cash) > 0, a higher (relaive) probabiliy of sysemic defaul implies observing a greaer demand for cash and, consequenly, higher inerbank ineres raes. In his case, because banks urn o he inerbank marke in an aemp o saisfy heir demand for cash, inerbank lenders would also be posiively relaed o he probabiliy of defaul. 4 Likewise, condiion 10 shows ha a higher probabiliy of defaul implies a greaer demand for he insrumen, if f ( BC )< 0. In his case, greaer demand for he insrumen would lead o a reducion in he cenral bank s ineres rae. Higher demand for cash, as well as for absorpion insrumens, could only maerialize a he aggregae level if new funds ener he sysem, i.e., if FBM > 0, jus as shown by he resricion of he opimizaion problem. Oherwise, an increase in he probabiliy of defaul is only associaed wih upward movemens in he inerbank ineres rae. 4 Given he consan probabiliy of defaul, he relaion beween aggregae cash and he inerbank rae is negaive, i.e., an increase in he inerbank rae reduces he demand for cash. C. Pagliacci, J. Peña 177

16 3. APPLICATION TO VENEZUELA 3.1 Esimaing Probabiliy of Defaul The applicaion we perform for Venezuela uses weekly daa from beween January 2004 and December This selecion was made in order o deal wih a homogeneous period wih regards o he exchange rae regime because Venezuela implemened exchange conrols in In Venezuela s case, due o he insiuional arrangemen of public policies, moneary base creaion and desrucion flows are subsanially condiioned by fiscal and exchange rae acions relaed o oil revenues. Tha is o say, he public secor (ax auhoriies and he oil indusry) is responsible for he amoun of money enering circulaion in he economy. On he one hand, he oil indusry convers a significan share of oil revenues ino domesic currency by selling mos of is foreign currency o he cenral bank. On he oher, he ax auhoriy, hrough domesic spending financed wih resources from he oil business, channels he money back ino he economy as ransfers or in exchange for goods and services. The cenral bank, by becoming he main holder of foreign currency, reduces he amoun of money circulaing in he economy each ime i agrees wih privae banks he sale of oil revenues. 6 These public-secor acions have heir moneary counerpary 5 A he sar of 2003 he Naional Execuive and he Banco Cenral de Venezuela adoped currency conrol measures where commercial bank ransacions are channeled a a pre-esablished exchange rae regime and capial ransacions can be financed a a parallel or unofficial exchange rae. In general erms, he implemenaion of currency conrols can be undersood as he appearance of dual foreign exchange markes, where he unofficial price of he currency represens a significan premium as compared o he official price. 6 Foreign currency sales are generally no accompanied by serilizaion operaions. During foreign exchange conrols, sales of currency are decided by he governmen. 178 Monearia, July-December, 2017

17 in wo variables (or moneary impacs): if, which is he creaion of money hrough he ax auhoriy and oil indusry, and ic, which refers o demoneizaion hrough he cenral bank s sale of currency. Whereas if represens flows ha increase residual liabiliies, ic consiues paymens (senior obligaion) banks mus make o he cenral bank in domesic currency. Wih respec o socks of cenral bank insrumens, for he period considered ( ), absorpion operaions were only carried ou hrough he cenral banks own insrumens. Thus, residual liabiliies relaed o he cenral bank only include he balance of cerificaes of deposi (cd). Expeced cash wihdrawals from he sysem are esimaed by using ne cheque clearing among banks. Table 3 presens a summary of he iems used for calculaing probabiliy of defaul. Table 3 COMPONENTS OF SHORT-TERM LIABILITIES FOR THE CASE OF VENEZUELA Toal liquid asses Unobservable Toal liquid liabiliies Senior obligaions Weekly currency sales (ic) Weekly variaion in reserve requiremens Ineres on inerbank operaions from he previous week Weekly ne cheque clearing Residual liabiliies Previous week s balance of cenral bank cerificaes of deposi + weekly ineres Weekly creaion of fiscal money (if) The balance of cash reserves from he previous week (adjused by inerbank operaions) C. Pagliacci, J. Peña 179

18 The volailiy of residual liabiliies ( σ E ) is calculaed for he weekly growh of (log) E, which has a sandard deviaion equal o 2.5%. The average value of he risk-free rae ( µ A ) is assumed o be equal o 0.3%, which corresponds o he weekly growh of (log) if. This rae is calculaed based on he annualized rae of growh of (log) if, which is 14%. We use his riskfree rae because ineres raes in Venezuela are conrolled, while he cenral bank s policy rae is also fixed mos of he ime. Meanwhile, he average rae of growh of if represens he rae a which primary money is creaed. For Venezuela his also represens he rae a which banks receive new deposis. Hence, his rae can be inerpreed as a consan growh, represening commercial bank asses. The ime horizon used o calculae defaul probabiliy is generally considered fixed and equal o T = 1, which in our case will be inerpreed as one week. Defaul probabiliy is calculaed weekly. Balance values refer o hose observed a he end of he preceding week. Flows are also measured on a weekly basis. We assume ha expeced flows are equal o hose observed. Figure 1 presens he composiion of senior claims (D). In senior deb, ne cheque clearing and currency sales are he componens mosly explaining is performance. As of 2012, he paricipaion of reserve requiremens in senior deb begins o grow in response o increases in he cash reserve raio. Figure 2 shows he composiion of junior deb or residual liabiliies (E). Beween 2004 and 2009, is performance follows he behavior of cenral bank cerificaes of deposi. During hose years, absorpion operaions were imporan because of he implemenaion of foreign exchange conrols in 2003 limied currency ransacions and allowed liquidiy in he economy o increase hrough higher governmen expendiure (increase in if). This liquidiy was channeled by banks owards cenral bank insrumens. Afer 2009, he weigh of cds drops sharply due o resricions (ceilings on he amouns) imposed on financial insiuions holdings of cds. As of 2010, he behavior of junior 180 Monearia, July-December, 2017

19 Figure 1 COMPOSITION OF SENIOR DEBT (E) 1 Percen i*q RR IC Ne CCH 1 Each componen is expressed as a percenage of he average oal (in millions of bolivars) of each year. 100 Figure 2 COMPOSITION OF JUNIOR DEBT (E) 1 80 Percen (1+r)*Cerificae of deposi balance Amoun of cash reserves wihou lending IF 1 Each componen is expressed as a percenage of he average oal (in millions of bolivars) of each year. C. Pagliacci, J. Peña 181

20 deb mainly depends on he cash balances held by banks (in vauls or in excess reserves a he cenral bank). Figure 3 depics he probabiliy of defaul calculaed, as well a breakdown of is holdings and seasonal componen. The pah of defaul probabiliy allows for idenifying he periods in which srucural changes ake place in senior and junior deb. According o Figure 3, he periods of highes liquidiy are and In 2004, economic aciviy and cenral bank currency sales began o grow subsanially afer having undergone a sharp conracion during he firs year of currency conrols (2003). Such increases in boh variables generaed significan growh in senior deb due o greaer cash wihdrawals (ne cheque clearing), as well as higher exchange rae incidence (ic). Neverheless, his increased demoneizaion in 2004, associaed o foreign currency sales, was no offse unil 2005, when higher fiscal expendiure began o maerialize. In fac, during 2006 and 2007, he significan growh of fiscal impacs allowed high levels of liquidiy ha were refleced in a subsanial growh of cds (and residual liabiliies) and a reducion in defaul probabiliy. During , senior deb levels sared o increase again, parly in response o ineres raes and larger amouns negoiaed in he inerbank marke. Alhough in his case a reducion in ne money creaion was no produced, he increase in he probabiliy of defaul appears o be relaed o redisribuion processes wihin he inerbank marke iself. Afer 2012, growh in junior deb, generaed by greaer money creaion and cash accumulaion by commercial banks, produce lower levels of defaul probabiliy in he sample. The seasonal componen has a significan weigh in he probabiliy of defaul and represens approximaely ±0.15 addiional percenage poins o he rend. Said componen exhibis he following behavior: I ends o peak around Ocober and hen decreases gradually o minimum values in April he following year. This seasonaliy is associaed o he seasonal behavior exhibied by ne cheque clearing, which in urn reflecs he 182 Monearia, July-December, 2017

21 Figure 3 PROBABILITY OF WEEKLY DEFAULT FOR THE VENEZUELAN CASE Jan 2,2004 Jun 2,2004 Nov 2,2004 Apr 2,2005 Sep 2,2005 Feb 2,2006 Jul 2,2006 Dic 2,2006 May 2,2007 Oc 2,2007 Mar 2,2008 Aug 2,2008 Jan 2,2009 Jun 2,2009 Nov 2,2009 Apr 2,2010 Sep 2,2010 Feb 2,2011 Jul 2,2011 Dic 2,2011 May 2,2012 Oc 2,2012 Mar 2,2013 Aug 2,2013 Jan 2,2014 Jun 2,2014 Nov 2,2014 PrD Tend of PrD Seasonal componen of PrD seasonal paern of economic ransacions. Tha is o say, he economy s cash requiremens grow during he hird quarer of he year, and decline subsanially during he firs, in parallel wih economic aciviy. These cash requiremens ranslae ino an increase in defaul probabiliy by raising he amoun of senior deb. 3.2 Relaion wih he Inerbank Marke According o he sylized model in Secion 2.2, he banking sysem adjuss is holdings in cash and cenral bank insrumens in order o minimize coss arising from siuaions defined by he probabiliy of defaul. Our esimaion of said probabiliy conains all he daa colleced a he sar of each period. C. Pagliacci, J. Peña 183

22 Assuming ha he demand for funds in he inerbank marke is posiively relaed o he demand for cash, i is possible o make wo predicions. Firs, ha inerbank ineres raes should be posiively relaed o he probabiliy (relaive) of defaul. Second, ha amouns negoiaed in he marke should also be posiively associaed wih a growing probabiliy of defaul. In his secion, we aemp o verify hese wo predicions empirically by esimaing models for average weekly inerbank raes and amouns negoiaed as funcions of defaul probabiliy. We hen es wheher hese models improve he predicions as compared o he reference auoregressive models. We begin by presening diagrams of he dispersion beween inerbank variables and defaul probabiliy esimaed by he model (Figures 4 and 5) Figure 4 depics a posiive relaion beween he overnigh marke ineres rae and he probabiliy of defaul. This migh reflec ha higher ineres raes include greaer risk premiums associaed o he behavior of sysem liquidiy. Meanwhile, Figure 5 shows a posiive relaion beween amouns raded in he overnigh marke and he probabiliy of defaul. A higher probabiliy of defaul migh be associaed wih a greaer need for available liquid funds by commercial banks and, herefore, increase he amouns raded in he inerbank marke. Can he probabiliy of defaul improve forecasing in models for ineres raes and real amouns negoiaed in he inerbank marke? To answer his quesion, we compare hree alernaive models for he variables: he weekly amoun raded (Q O ) and average agreed raes (i O ). Firs is he reference model ha explains he overnigh marke variables only considering an auoregressive process in he mean. The second model includes he probabiliy of defaul for modeling he mean and a garch (1,1) model for a variance. 7 The 7 Generalized auoregressive condiional heeroscedasiciy (garch) models are used because we are working wih high frequency financial series in which volailiy is an inheren characerisic and 184 Monearia, July-December, 2017

23 Figure 4 CONTEMPORARY RELATION BETWEEN THE PROBABILITY OF DEFAULT (AXIS X) AND THE INTEREST RATE OF OVERNIGHT (Y AXIS) Overnigh ineres rae (%) Probabiliy of defaul Figure 5 CONTEMPORARY RELATION BETWEEN THE PROBABILITY OF DEFAULT (AXIS X) AND THE AMOUNT AGREED ON ONE-DAY OPERATIONS (Y AXIS) 40,000 Amoun of operaions of a day (millions of bolivares) 35,000 30,000 25,000 20,000 15,000 10,000 5, Probabiliy of defaul C. Pagliacci, J. Peña 185

24 hird model expands he second one by including he probabiliy of defaul as an explanaory variable for a variance. In he case of ineres raes hose models are: Model 1. Auoregressive in he mean (reference) 11 i = i i i i 4 + ε. Model 2. Wih explanaory variables in he mean and garch for variance 12 i = i 0. 05i i i PrD + ε, 4 where ε ( ) wih variance D 0, h h = ε h. Model 3. Wih explanaory variables in he mean and in he garch: 13 i = i 0. 04i i i PrD + ε, 4 where ε ( ) wih variance D 0, h canno be considered homoscedasic. For furher informaion see Engle (1982) and Bollerslev (1986). 186 Monearia, July-December, 2017

25 h = ε h PrD. Models for amoun raded only show wo possible variaions given ha he probabiliy of defaul was only significan for modeling he mean. The regressions esimaed are: Model 1. Auoregressive in he mean (reference) 14 Q = Q 0. 01Q Q Q + ε Model 2. Wih explanaory variables in he mean and garch for variance: 15 Q = Q Q Q Q PrD + ε, 4 2 where ε D( 0, h ) wih variance h = ε h 1. Tables 4 and 5 display mean absolue percenage errors (mape) of he differen models. The forecass (dynamic) were performed for he firs hree monhs of he subperiods: 2007, 2011 and The models are esimaed using he above informaion in he predicion period, i.e., , and , respecively. Moreover, and by way of comparison, we calculae he mape using saic forecass for he subsample A comparison of he equaions forecass for he amoun raded and agreed ineres rae in he overnigh marke reveals successive improvemens in he mape wih respec o he reference forecas in he equaion for he amoun as well as ha for he ineres rae, especially when he defaul probabiliy is included for modeling he mean. To corroborae he above resuls, we apply he Diebold and Mariano (1995) es, which analyzes wheher he difference C. Pagliacci, J. Peña 187

26 Cases Table 4 EQUATION FOR OVERNIGHT RATES Comparison of forecass using he mape adjusmen indicaor o forecas: Firs hree monhs (January o March) of years Subsample Model Model Model Table 5 EQUATION FOR THE OVERNIGHT AMOUNT IN MILLION 1997 BOLIVARS Comparison of forecass using he Cases mape adjusmen indicaor o forecas: Firs hree monhs (January o March) of years Subsample Model Model beween he loss funcions (sum of absolue values) of he errors beween wo models is significanly differen from zero. Deails of his es can be found in Annex B. Tables 6, 7 and 8 show he consan of he Diebold-Mariano es and corresponding p values. The comparison is performed in pairs. When comparing Models 2 and 3 wih Model 1 we find evidence o rejec he null hypohesis of equal forecas accuracy beween he models. In boh cases, he value esimaed for he consan is negaive, i.e., forecas errors of Model 1 (auoregressive) are significanly larger han hose of Models Monearia, July-December, 2017

27 e Table 6 DIEBOLD-MARIANO TEST AND ASSOCIATED P VALUES Model 2 agains Model 1 for raes H e 1 = Model Model (0.11) 2 2 ( e ) ( e ) = Model 2 Model 1 (0.09) (0.00) (0.00) (0.00) (0.03) (0.003) (0.01) e Table 7 DIEBOLD-MARIANO TEST AND ASSOCIATED P VALUES Model 3 agains Model 1 for raes H e 1 = Model Model (0.11) 2 2 ( e ) ( e ) = Model 3 Model 1 (0.10) (0.00) (0.08) (0.00) (0.03) (0.001) (0.005) e Table 8 DIEBOLD-MARIANO TEST AND ASSOCIATED P VALUES Model 2 agains Model 3 for raes H e 2 = Model Model (0.2175) 2 2 ( e ) ( e ) = Model 3 Model 2 (0.2344) (0.00) (0.00) (0.0092) (0.042) (0.09) 0.00 (0.00) C. Pagliacci, J. Peña 189

28 e Table 9 DIEBOLD-MARIANO TEST AND ASSOCIATED P VALUES Model 2 agains Model 1 for amouns H e 1 = Model Model (0.0008) 2 2 ( e ) ( e ) = 0 3, Model 2 Model 1 (0.0234) (0.008) 17, (0.0057) (0.0000) 15, (0.0000) 4.85 (0.10) 3, (0.1244) and 3 (garch). These oucomes prove he predicive gains from incorporaing defaul probabiliy ino he mean. When we compare loss funcions of Models 2 and 3, we find, in all he forecass excep 2007, ha he null hypohesis of equal forecas accuracy beween hem is rejeced. We now perform a similar procedure for comparing he models presened in Table 5 wih respec o amouns. In he amoun equaion, we also find evidence o rejec he null hypohesis of equal forecas accuracy beween he garch model and he auoregressive one in he forecass, excep for he period Policy Exercises In his secion we perform simulaions o calculae he probabiliy of defaul, focusing on he impacs of moneary base componens (if and ic). To do his we assume ha such flows of money creaion or desrucion no only affec defaul probabiliy, bu also cash holdings in he financial sysem (equaions 20 and 21). We also include auoregressive equaions for if and ic o deermine he differing impac of changes in he mean and variance of hose variables (Equaions 22 and 23). Given ha inerbank marke amouns and raes are affeced by he probabiliy of (PrD), we also incorporae behavioral equaions for said variables (equaions 18 and 19). We do no model he behavior of cds because of he low variabiliy of moneary 190 Monearia, July-December, 2017

29 policy raes hroughou he period as a whole. All he behavioral equaions are esimaed wih daa from beween 2004 and 2007, which corresponds o he period wih greaes inerbank marke deph. The simulaion model is represened by equaions 17 o 23. The probabiliy of defaul is given by: ( E A E A) 17 PrD f A E, σ, σ E, σ, D, T, µ. = ( ) ( ) Behavioral equaions for overnigh marke amouns and raes in accordance wih risk indicaors are: 18 Q = a + aq + add , 19 i = b + bi + bprd bdd Auoregressive equaions for variaion of excess reserves RE ( ) and cash in vauls ( EB ) are: 20 RE = c + c RE + cif c IC , 21 EB = d + d EB + dif d IC , Auoregressive equaions for fiscal and exchange rae influence are given by: 22 IF = e + e IF +, IC = λ + λ IC +, C. Pagliacci, J. Peña 191

30 where aj, bj, cj, dj, e j, λ j > 0 for all j = 1, 2, 3; y 1 and 2 have a normal disribuion wih mean zero and variance one. The reserve requiremen raio is considered as a muliple of moneary base in he preceding period. Moneary base is considered as he sum of excess and required reserves. Finally, o ie he model ino he ime horizon, he iniial condiions were assumed as hose observed a he beginning of The performed simulaions are shown in Annex C. The oucomes sugges ha, on average, increases (reducions) in he uncondiional mean and persisence of fiscal evens end o reduce (increase) he probabiliy of defaul, while increases (reducions) of he ordinae and persisence in he equaion for exchange rae effecs imply an increase (reducion) in he probabiliy of defaul. Changes in he variance of fiscal evens have a greaer impac on he probabiliy of defaul han changes in he variance of exchange rae evens. Finally, if he legal capial requiremen raio increases (decreases), he probabiliy of defaul ends o rise (fall) by raising (lowering) banks shor-erm obligaions. 4. FINAL REMARKS In his paper, we use risk indicaors derived from he coningen claims approach (probabiliy and disance o defaul) o evaluae liquidiy risk in he banking sysem as a whole. These ideas are easy o calculae because hey use readily available aggregae banking and moneary policy variables, in general. The probabiliy of defaul can be a useful insrumen for cenral banks o improve predicions on he inerbank marke, as well as poenially conribue o modeling he behavior of some (or all) liquid asses available o commercial banks. In he case of Venezuela, he behavior of defaul probabiliy would seem o depend, among oher facors, on he moneary impacs of fiscal and exchange rae acions. One inerpreaion ha emerges from he counerfacual exercises performed 192 Monearia, July-December, 2017

31 on he properies of such policies is ha he vulnerabiliy of Venezuela s inerbank marke could increase subsanially in he face of greaer dynamism in currency sales and conservaive fiscal expendiure rends. This oucome is consisen wih anoher paper on he Venezuelan financial sysem: Carvallo and Pagliacci (2016). According o he laer, combinaions of said policies ha generae resricive moneary condiions will end o increase bank insabiliy. In general erms, boh oucomes poin owards he necessiy for performing a review of he framework of regulaions ha enhance he significan moneary effecs of hese policy acions. ANNEXES Annex A. Coningen Claims Approach The coningen claims approach is a mehodology ha generalizes he Black-Scholes (1973) and Meron (1974) opion pricing heory, combining marke-based daa and balance shee informaion o obain financial risk indicaors such as disance o defaul and defaul probabiliy. 8 The concepual framework can be represened mahemaically as follows. Asses A +, are assumed o follow a geomeric Brownian moion wih volailiy, σ A. Senior deb is D +. Hence, he process governing he behavior of asse prices is assumed given by: ( ) A.1 da = A µ d + σ dw. A A Equivalenly, 8 Oher financial risk indicaors obained using his mehodology are: risk-neural credi risk premia and expeced losses on senior deb. For furher informaion see Saldías (2012) and Gray e al. (2006) C. Pagliacci, J. Peña 193

32 2 σ A A.2 A = Ao A + exp µ σaε, 2 ( ) and µ A is he expeced average reurn on where ε 0, ; he asses. Wih he risk-neuraliy hypohesis, µ A means here can be no arbirage in he financial derivaive during an infinie period. W is a sandard Brownian moion, i.e.: A.3 W W 0,. + ( ) This assumpion considers ha asses and senior deb (is derivaive) follow a log-normal disribuion. However, D being he value of senior deb in, he probabiliy of defaul or sysem vulnerabiliy a ime T, condiional on known informaion in, is defined as: σ A A.4 Prob( 2 A D )= Prob Ao exp µ A ( T )+ 2 + σ A ε T D,. This probabiliy capures sysem vulnerabiliy when asses are below he hreshold represened by hard or high prioriy deb. The wo equaions used for esimaing asses and heir volailiy are as follows. The firs comes from he basic formulaion of he expeced value of junior deb (E), which is obained using Iō s lemma. This expeced value is equal o he price of a European call opion on he asses, so ha: 194 Monearia, July-December, 2017

33 µ 1 2 A A.5 E A d D e d = ( ) ( ), where A.6 d1 2 A σ A ln + µ A + T D 2 = σ T A ( ) and A.7 d2 2 A σ A ln + µ A T D 2 = σ T A ( ) = d σ T. ( ) is he value of he cumulaive sandard normal Since, x 2 disribuion in x and ( 0,σ ) is he univariae normal probabiliy densiy funcion wih mean µ and variance σ 2. Bu, Equaion 5 has wo unknown variables, A and σ A ; meaning a second equaion is necessary. The model of Meron (1974) obains an equaion ha links he volailiy of junior deb, σ E, and ha of asses using: A E A.8 σe = σa. E A As well as, 1 A A.9 E A 1. = ( d ) Hence, he volailiy of junior deb can be calculaed as: A A.10 σe = ( d 1 ) σa. E C. Pagliacci, J. Peña 195

34 Finally, using Equaions 5 and 10 we obain he following sysem of non-linear equaions, formed by wo equaions and wo unknowns. A.11 f ( ) ( ) µ A A d De d E 1 2 = A. ( d1 ) σa σe E 0 Making f 0 we can use quadraic opimizaion or similar echniques o esimae he value of asses and heir volail- iy, Â and σˆ A, respecively. Once hese values have been calculaed, he number of sandard deviaions (d ) of insolvency is precisely, d 2. A.12 d1 A ln D = + µ A + σ A 2 σ A ( T ) 2. T Tha is o say, in a single measure, disance o defaul combines he difference beween he value of asses (A ) and he disress barrier (D ), sandardizing wih asse volailiy. Using Equaions 4 and 7, we obain ha he probabiliy of defaul or sysem vulnerabiliy is, herefore, he sandard normal cumulaive disribuion of negaive disance o defaul: A.13 pd = d. ( ) Tha is, he one ha inermediaes beween disance-o-defaul and probabiliy of defaul is he normal disribuion. 196 Monearia, July-December, 2017