1、contagion risk in the interbank market in china and theus#fei ziwei1, jiang xiaoquan2, zeng li1, peng jiangang1*510152025303540(1. college of finance and statistics, hunan university, 410079;2. department of finance, florida international university, 33199)abstract: in this paper, we investigate the

2、 contagion risk in the interbank market between china andthe united states. we adopt the adjusted formula of the capital adequacy ratio proposed in basel iii asthe criterion of contagion. our simulation results show that the contagion risk of individual us banksin this market when they experience a

3、single shock is relatively higher than that of china; however,when they encounter a larger shock by a specific group of banks, they perform better. a comparison ofthe two countries shows that higher financial system development does not necessarily indicate ahigher risk of contagion in the interbank

4、 market. government oversight of the financial system canfacilitate the ability of banks to resist contagion risk in the interbank market.key words: contagion risk; interbank market; commercial bank; capital adequacy ratio; basel iii0 introductionthe recent global financial crisis has had a huge imp

5、act on financial systems and the realeconomy. during the crisis, there were bank failures in the united states, european union, andelsewhere. countries like iceland and greece even faced the threat of state bankruptcy. theassessment and disposal of contagion risk has become a hot topic among regulat

6、ors, such as thebasel committee on banking supervision (bcbs), financial stability board (fsb), world bank,international monetary fund (imf), as well as academics and practitioners.as contagion risk has stood out in the financial market since the latest financial crisis, we needto know that how it s

7、preads among the financial institutions in and out of a country, and how toreduce the loss.in this paper, we examine the contagion risk of the chinese and us banking sectors in theinterbank market, and compare the contagion risk in the two countries using a simulation to 20largest commercial banks i

8、n china and the us at the end of 2012. we assume the liquidity shockcomes from two sources: single bank and specific group of banks. there are three specific groupsof banks classified by the assets level, high asset group, medium asset group and low asset group,each group contains four banks. we fin

9、d that the risk contagion for individual us banks due toliquidity shock of single bank is relatively higher than for banks in china, while the contagion riskof us banks due to specific group of banks is lower than that for banks in china. we adopt acriterion of contagion by adjusting the formula of

10、capital adequacy ratio put forth in basel iii. thisformula captures the risk of contagion before bank failure.we find that two (four) commercial banks trigger contagion risk in china (us) by due to asingle bank shock. in the case of a single bank shock, the four biggest commercial banks in chinaperf

11、orm better than those in the us. the liquidity shock due to the high asset group has a seriousimpact in the interbank market in china, but the impact by the liquidity shock from the high assetgroup in the us is relatively small. medium asset group and low asset group would not triggercontagion both

12、in china and us.foundations: the study was supported by the national natural science foundation of china (no.71073048 andno. 71373071).brief author introduction:fei ziwei(1986-), male, doctoral student, management of commercial bankcorrespondance author: peng jiangang(1955-), male, professor of fina

13、nce, management of commercial bank. pengjiangang-1-the us financial system is highly developed. it has a high degree of marketization and acomplex and diverse allocation of assets. the ratio of risk-weighted assets to total assets of the 20us banks is higher than that of the 20 banks in china at the

14、 end of 2012. the non-performing loan45505560657075ratio of the 20 us banks is higher than that of their counterparts in china at the end of 2012,which shows the quality of bank assets in the us is lower than that of chinese banks at the end of2012. however, our contagion simulation results do not s

15、how a higher contagion effect in theinterbank market in the us.we find that the risk of contagion in the interbank market depends on a banks capital level, aswell as the concentration of its interbank assets. the banks that trigger contagion in the interbankmarket are the big commercial banks in chi

16、na and the us, except for cbu in the us. big banks,which always maintain large quantities of assets and liabilities in interbank market, are moreactive in the interbank market and easier to spread risk, so they should be regulated morecarefully.a regulatory agency, whose aim is to maintain the stabi

17、lity of the entire banking system, canhelp banks reduce the loss and even avoid contagion risk in the interbank market. as losses shouldbe absorbed by bank capital, regulation is an effective way to prompt banks to maintain theircapital adequacy ratio.we find that losses-given-default (lgd) is an im

18、portant factor in estimating a contagion effect.we use lgd as a control variable. according to the simulation, there are different lgd levels atwhich commercial bank can trigger contagion, and different countries shows different triggerlevels.this paper is structured as following. in section 2, we d

19、iscuss our study methodology. in section3, we assess the contagion risk in the chinese and us banking sectors in the interbank market. insection 4, we provide simulation results on contagion risk in china and the us. in section 5, theconclusion is presented.1 methodology for contagion risk assessmen

20、tin this paper, we investigate the source of contagion risk in china and the us in terms of asingle shock and group shock, similar to the idiosyncratic shock and systematic shock defined inupper (2011)1. a single shock means that the contagion is triggered by the liquidity shock of asingle bank, lik

21、e one bank defaults in interbank market. a group shock means that the contagion istriggered by liquidity shock of a specific group of banks, like a group of banks default at the sametime in interbank market. according to the recent research, furfine(2003)2, upper(2004)3,lelyveld(2006)4, degryse(2007

22、)5, ma(2007)6 studied the contagion risk in their own countriesbanking sector using balance sheet data or settlement data.1.1network structuremodern financial systems exhibit a high degree of interdependence, with connections betweenfinancial institutions stemming from both the assets and the liabil

23、ities sides of their balance sheets.8085for instance, banks are connected through exposures to the interbank market. likewise, banks areindirectly linked by holding similar assets in their portfolios or sharing the same depositors. theinterbank network, which is broadly understood as a collection of

24、 nodes and links between nodes,is a useful representation of financial systems. usually, the typical network structure contains:complete market structure (allen, 2000)7, incomplete market structure, money centre bankstructure. in this paper, we apply a complete network structure in the interbank mar

25、ket of two-2-countries, china and the us, as in figure 1. a complete network indicates that every bank hassymmetric linkages with all other banks in the interbank market.figure 1. complete network structure of banks in the interbank market.interbankbank abank clendingbank bbank d90note: we simplify

26、the structure of interbank market to a complete network. all the counterparties in the networkhas symmetric exposures to each other.1.2estimating bilateral exposuresthe lending relationships in the interbank market can be represented by the following n nmatrix:ix11x1 jx1 na195x =xi1xijxinai(1)x n 1x

27、 njx nna njl1l jl nwhere xij is the credit exposure of bank i versus bank j, and n is the number of banks.although we cannot observe the bilateral exposures in xij directly, we know the sum of eachbanks interbank assets and liabilities: ai and li respectively. the elements of matrix x satisfy thefol

28、lowing conditions:100ai = j xij and l j = i xij .(2)in order to acquire the bilateral exposures of banks in the interbank market, we adopt anestimation methodology as in upper (2004). first, we maximize the entropy of matrix x, in whichxij = ailj, so interbank assets and liabilities can be spread ov

29、er banks equally. however, theelements on the main diagonal should be zero, as a bank would not lend to itself. second, we105construct another matrix x* in equation 3, let xij* = 0 for i=j. the other elements for xij* areunknown.i0*1 j*1na10x * =xi*10xin*ai(3)0xn*1x nj*0a njl1l jl n-3-xxlast, we min

30、imize the relative entropy of matrix x* with respect to the matrix x by solving thefollowing optimization problem1. so, x* is an approximate matrix to x under the following110restrictions:*x *x(4)n n* * *i =1 j =1equation (4) can be solved with the ras algorithm illustrated in upper (2004) and kalan

31、tari(2008)8. this method provides the interbank bilateral exposures. the element xij in matrix x*115120shows the interbank assets of bank i versus bank j, along with the liabilities of bank j versus bank i.if the ratio of xij to ai is relatively higher, then bank j holds a larger rate of interbank a

32、ssets of banki, that is, bank i will mainly be affected by the default of bank j. if the ratio of xij to ai distributesuniformly, bank i will not be affected unless a few banks default in the contagion. mistrulli(2011)9 assessed the financial contagion in the interbank market in italian with both ac

33、tualbilateral exposures and simulated bilateral exposures. the comparison indicates that, only undercertain circumstances, the maximum entropy approach may overrate the scope for contagion.1.3contagion procedurewith the help of the estimation methodology above, we can acquire the risk exposure of ea

34、chbank in the interbank market. lgd is an important factor in contagion simulation. we use lgd as125130135140a control variable that ranges from 0 to 1. lgd varies over time and over financial markets,usually concentrated at 0.1-0.7 in the interbank market (upper, 2004; bastos, 201010; memmel,201211

35、). as we are comparing the contagion effect in the interbank market between china andus, lgd is listed as a vector: lgd = 0.05, 0.1, 0.15, 0.2, 0.3, 0.4, 0.5, 0.6, 0.65, 0.7, 0.75, 0.8,0.9, 1.in a banks balance sheet, as assets equal liabilities plus owners equity in the balance sheet,once an invest

36、ment is unsuccessful, the loss of assets will be deducted from its capital. theamount of tier 1 capital and risk weighted assets will be adjusted, which will directly impact thebanks tier 1 capital adequacy ratio.when the capital adequacy ratio of a bank cannot satisfy the regulatory standards, the

37、bank mayencounter credit relegation, a bank run or other direct or indirect incidents. in order to avoid assetdeterioration and remain in operation, the bank may choose to default in the interbank market andacquire liquidity in other ways, which impacts liquidity in other banks through the creditcon

38、nection. other banks that have transactions with the bank may lose a part of their interbankassets or even default. if contagion continues, the risk will spread to the entire interbank market.at some point, a balance will be reached where there is no bank experiencing contagion.the initiation of con

39、tagion by a single bank shock can be expressed as follows:in stage 0, bank i incurs liquidity risk and defaults in the interbank market.in stage 1, the first round, which is r=1, for all the other banks, if bank j lends its money xji to1this method is usually used to complete a data table that is mi

40、ssing data. so, with this method,we can determine interbank bilateral exposures. we recognize that the simulated interbankbilateral exposures are just an approximation to the real bilateral exposures, as the real data areunobservable.-4-min x * lnxst.： xij i ij j ij 0= a x = l xbank i in the interba

41、nk market, the loss of bank j in the interbank market is lgd x ji , and the loss145should be absorbed by its tier 1 capital. if the adjusted tier 1 capital adequacy ratio in equation(5) of bank j drops below 6%212 13, bank j falls into liquidity risk and likely faces default.adjusted tier 1 capital

42、ratio j =tier 1 capital j adjustment j lgd x jirisk weighted assets j x ji100%(5)where bank j 1,i 1, i + 1, n , is the risk weight of interbank lending assets; in this3150in basel iii, and risk-weighted assetsj are the risk-weighted assets of bank j.in stage 2, the second round, r=2, bank i and bank

43、s that encounter contagion form a bank groupt, t = bankk | banks whose adjusted tier 1 capital ratio drops below 6% in contagion,k 1, , n , then the liquidity shortage of banks in t proceed to impact other healthy banks asfollows:adjusted tier 1 capital ratio j =155tier 1 capital j adjustment j lgd

44、t , k t x jkrisk weighted assets j t , kt x jk100%(6)where bank j 1， , nt , lgd t , ktx jk indicates the losses of the interbank assets ofbank j. if the adjusted tier 1 capital ratio of bank j falls below 6%, then j t .in stage r, the r round, according to the contagion rules above, we estimate the

45、adjusted tier 1capital ratio of the healthy banks one by one. in stage n, no bank has an adjusted tier 1 capital160165170ratio below 6%. the risk contagion then stops. the contagion process initiated by a group shockfollows a similar development.2 contagion simulation of china and usfor our sample,

46、we choose the 20 largest commercial banks in china and us by assets at theend of 2012. the total assets of the sample banks to total assets of all commercial banks in chinaand us are 81.85% and 70.78%, respectively. the us data are from the bankscope database. thedata for china are hand-collected fr

47、om their 2012 annual reports, which collected from theirhomepages. the total assets, total liabilities, interbank assets and interbank liabilities of thesample banks of each bank are expressed in table 1 and 2. the sample banks are listed by totalassets in china and us respectively.contagion

48、 due to a single bank shockinterbank market in chinafor the 20 banks in china, the ratio of interbank lending assets to total assets is 2.67%.2according to basel iii, the banks tier 1 capital adequacy ratio should be above 6%. this paperdoes not consider the excess reserve or hidden reserve in any b

49、ank; we assume that the losses inthe interbank market are absorbed by its tier 1 capital only.3according to basel iii, the risk weight of interbank assets is 25%.-5-paper, =0.25 , adjustmentj represents the deductions from the tier 1 capital of bank j requiredalthough the ratio is relatively small,

50、the liquidity of the interbank market reflects the liquidity of175180185the banking sector in a country. so, liquidity in the interbank market is very important whenmeasuring systemic risk.table 1 shows the assets and liabilities of the interbank lending market for the chinese sample.the interbank l

51、ending assets of cib are 6.68% of its total assets, which means cib is very activein the interbank market. boc holds the largest ratio of interbank assets to total assets and thelargest ratio of interbank liabilities to total liability in the 20 banks: 16.03% and 19.62%,respectively. icbc, cbc, abc,

52、 and boc are the most active lenders in the interbank market inchina, as their interbank assets are larger than their interbank liabilities. icbc is the largest bankin china by assets, while boc is the most internationally active bank as it has the largest volumeof international business.table1. ass

53、ets and liabilities of the interbank lending market of 20 banks in china at the end of2012 (million yuan)banksicbccbcabcbocbocomcmbcibspdbcmsbccbcebpabhxbgdbbjbegbcbhbczbnbbnjbinterbank assets24933613801522514033852515704785981214812854208008212905213597994295314342623574210858694421261866689535inte

54、rbank liabilities1902927764012730724372715008866431576793246641211159231311539068718573414720039251313481104472220312900total assets1683084913786750131971081124212052019433237644321349331246303105285283763222671681606537148789111681501117644615648472102393839373537339609ratio1.48%1.00%1.71%3.01%3.02%2.66%6.68%2.73%2.58%4.55%6.00%5.87%2.11%2.25%6.64%1.39%2.00%3.