1. BANK-INVESTMENT FUND INTERCONNECTIONS AND SYSTEMICALLY IMPORTANT INSTITUTIONS IN LUXEMBOURG

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1 1. BANK-INVESTMENT FUND INTERCONNECTIONS AND SYSTEMICALLY IMPORTANT INSTITUTIONS IN LUXEMBOURG ABSTRACT Max Gehred 61 Recet iteratioal fiacial market volatility has reiforced the role of the Fiacial Stability Board s recommedatio to ehace moitorig of the likages betwee ivestmet fuds ad the bakig sector. Followig the global fiacial crisis, Luxembourg s ivestmet fud sector has exhibited sustaied icreases i the value of fuds total assets. This icrease combied with elevated fiacial market volatility ad risks from emergig market ecoomies suggest that the coectios betwee the ivestmet fud sector ad the bakig system warrat ehaced moitorig from a macroprudetial perspective. The results of this study show that the Luxembourg bakig sector has some itercoectios with the ivestmet fud idustry, otably o the liability side of baks balace sheets, which may be relevat from a systemic risk perspective. Exteral shocks to the ivestmet fud sector could potetially spread to the domestic bakig sector, thereby posig a threat to fiacial stability. This paper applies etwork aalysis tools to quatify the structural features of this bak-ivestmet fud etwork that are relevat from a systemic risk perspective ad to determie which baks are most sigificat withi this etwork based o cetrality measures. I a secod step, the most pertiet measure is icluded i the other systemically importat istitutios (O-SIIs) framework to assess if the compositio of idetified systemic domestic baks chages whe ivestmet fud likages are take ito accout. The results reveal that the etwork of domestic baks ad ivestmet fuds ca be characterized as havig a relatively low umber of direct coectios. Moreover, bak-ivestmet fud ad iterbak distaces are rather small ad oly a few istitutios act as pivots withi the etwork. Such a system could potetially propagate shocks very rapidly. I terms of coectivity, out of a total of five commoly used measures, betweeess ad PageRak appear the most suited for the ivestmet fud ad bak etwork i Luxembourg as the first best captures the baks that costitute pivotal poits withi the etwork ad the secod takes best accout of the direct ad idirect ivestmet fud ad bak coectios. Eve whe the etwork aalysis is ot accouted for, this study shows that the stadard O-SII assessmet is already able to idetify a large share of the baks with a high betweeess score as systemic. However, the same is ot true for baks with a high PageRak score. Whe the latter measure is icluded i the O-SII assessmet, two additioal custodia baks tur out to be systemic. 1 INTRODUCTION Liks i the form of exposures ad liabilities betwee ivestmet fuds ad Luxembourg baks are of particular iterest for domestic macroprudetial authorities give their potetial fiacial stability implicatios. I the evet of a fiacial crisis, large shocks could be propagated through the fiacial sector. Ideed, domestic credit istitutios ivestmet fud liabilities amouted to 123 billio or 16% of total assets as of 2016Q4, the majority of it provided by domestic ivestmet fuds (87%) ad i the form of demad deposits (93%). The 16% share of total assets appears elevated compared to the 2% 61 Fiacial Stability Departmet, Baque cetrale du Luxembourg 110 BANQUE CENTRALE DU LUXEMBOURG

2 1 ratio of euro area ivestmet fud deposits at euro area baks. 62 A large share of ivestmet fud deposits could, for istace, be a source of potetial risk if the fud sector were to face a sigificat redemptio shock from ivestors. A redemptio shock could potetially trigger a ru o bak deposits by these same fuds. Such a sceario could occur i market segmets where ivestmet fuds egage i activities such as liquidity trasformatio or leverage ad simultaeously offer frequet redemptios. If domestic baks suffer a ru o their deposits by fuds, this might have egative cosequeces such as fire-sales of part of their assets. Fire sales could trigger losses ad defaults o iterbak loas, or lead to a stoppage of fiacig provisios to other baks. Ultimately, this could propagate the shock withi the iterbak market. It is worth otig that a iitial shock arisig i the ivestmet fud sector is ot likely to occur i isolatio or at the atioal level, but rather i the cotext of fiacial turmoil o a Europea or global scale, for example through a broader reassessmet of risk premia. The structure ad compositio of Luxembourg s ivestmet fud sector make it sesitive to developmets ad volatility i iteratioal fiacial markets. ANNEXES 4 Beyod the liability side of the balace sheet, domestic baks exposure towards ivestmet fuds represets 13 billio or 2% of total assets. These exposures appear small but are highly cocetrated as oe sigle istitutio holds 28% ad the top-5 istitutios 54% of the 13 billio. Thus, it ca still costitute a potetial chael for cotagio as the asset holdigs are ot fully diversified across baks. The paper relies o etwork aalysis tools to evaluate fiacial sector itercoectios ad focuses o three layers. First, the overall structure of a etwork cosistig of Luxembourg baks ivestmet fud exposures ad liabilities as well as the domestic iterbak market exposures will be aalysed i order to determie structural features relevat for systemic risk. Secod, the istitutios that are most importat withi this etwork will be idetified by usig cetrality measures. Such measures quatify differet aspects of importace withi a etwork, such as the umber of liks, the distace to other etwork odes, or the importace of the coected odes. Ultimately, the goal will be to determie the most appropriate cetrality measure to iclude as a additioal idicator i the O-SII framework i order to ascertai if its explicit iclusio reveals baks to be systemic other tha those idetified i the stadard assessmet. The last poit is of particular relevace so that macroprudetial authorities are ot limited to the aalysis of existig fiacial itercoectios but have a broad toolkit of measures aimed at fosterig baks resiliece. Such a toolkit would iclude the O-SII framework, which allows authorities to assig additioal capital buffers to systemic baks as well as complemetary assessmet tools. There is a eed for additioal aalytical tools as the stadard O-SII assessmet has limitatios i the sese that it does ot etirely accout for Luxembourg s specificity regardig ivestmet fud likages with baks ad oly cosiders fiacial sector itercoectios i terms of direct exposures. 63 Reliace o direct exposures aloe igores the idirect exposures created through couterparties couterparties. This paper aims addressig these atioal specificities. 62 ESRB EU Shadow Bakig Moitor, No 1 / July The itercoectedess idicators cosidered are iter-fiacial system assets ad liabilities, as well as debt securities outstadig. See EBA/GL/2014/10 (GL o criteria for the assessmet of O-SIIs). REVUE DE STABILITÉ FINANCIÈRE

3 2 NETWORK CONSTRUCTION AND CENTRALITY MEASURES I this sectio we outlie ad describe the etwork set-up as well as the cetrality measures used i the study. The uderlyig etwork is take to be comprised of two compoets, the Luxembourg iterbak market ad the market ivolvig ivestmet fuds ad domestic baks. The iterbak etwork is costructed from baks large exposure data 64 reported accordig to regulatio (EU) No 575/2013 o prudetial requiremets for credit istitutios. 65 The bak-ivestmet fud etwork is costructed from idividual bak balace sheet data. I this case the more graular large exposure data is ot employed sice this oly icludes the asset side of the balace sheet ad therefore igores the more sigificat liability side. Withi the etwork model each bak, as well as the ivestmet fud sector as a whole, is represeted by a ode. These odes are coected via edges, which ca either be directed or o-directed. This meas that if bak A has a asset exposure towards bak B ad vice versa, the this couts as two separate edges i the directed etwork ad as oly oe edge that sums up both trasactios i the o-directed etwork. The edges ca either all have the same weight, usually equal to oe, or they ca be weighted accordig to the exposure amout or its iverse. A resultig etwork, be it directed, weighted, or ot, ca be mathematically represeted by a adjacecy matrix A. This is a ( ) matrix with elemets a ij describig the edges of the etwork, where is equal to the umber of odes. I a directed etwork, a ij represets the edge goig from ode j to ode i. Furthermore, if the etwork is weighted, a ij equals the exposure amout j has towards i. 66 If it is o-weighted, a ij equals oe if there is a lik ad zero otherwise. I a o-directed etwork, matrix A is symmetric (a ij = a ji ) because o distictio is made betwee icomig ad outgoig liks. If there is a lik betwee odes i ad j, the i the weighted etwork, a ij equals the sum of asset exposures ad liabilities ad i the o-weighted etwork, it equals oe. As baks do ot led to or borrow from themselves, the diagoal elemets of A are always equal to zero. The followig example should illustrate the differece betwee weighted ad o-weighted, as well as directed ad o-directed etworks. If we cosider a etwork where bak 1 leds a amout of 6 to bak 2, the the four adjacecy matrices ca be costructed as follows: A 1 = ( 0 1 ), 1 0 A 2 = ( 0 0 ), 1 0 A 3 = ( 0 6 ) 6 0 ad A 3 = ( 0 0 ), 6 0 Here matrix A 1 is o-directed ad o-weighted, A 2 is directed but o-weighted, A 3 is weighted but o-directed, ad A 4 is directed ad weighted. Based o the iterbak-ivestmet fud etwork, the followig five commoly used cetrality measures will be cosidered i order to assess baks importace: (i) degree cetrality, (ii) betweeess cetrality, (iii) closeess cetrality, (iv) eigevector cetrality, ad (v) PageRak. 64 Itra-group exposures withi Luxembourg are icluded. Braches that do ot report large exposure data may also be icluded i case other baks have asset exposures towards them. 65 Regulatio (EU) No 575/2013 of the Europea Parliamet ad the Coucil of 26 Jue 2013 o prudetial requiremets for credit istitutios ad ivestmet firms ad amedig Regulatio (EU) No 648/ For cetrality measures based o distaces it ca also be the iverse of the exposure amout. 112 BANQUE CENTRALE DU LUXEMBOURG

4 1 i) Degree cetrality Degree cetrality costitutes the most basic idicator to measure a ode s importace withi a etwork as it sums up the odes edges. I a directed etwork, oe ca distiguish betwee a bak s degree cetrality i terms of ledig fuds (out-degree) ad borrowig fuds (i-degree). I a o-exposure weighted etwork, out-degree equals the umber of outgoig edges ad i-degree the umber of icomig edges. I a exposure weighted etwork, out-degree equals the sum of all asset exposures ad i-degree the sum of all liabilities. Formally, out- ad i-degree ca be respectively writte as follows: a j=1 ji a j=1 ij OUT IN D i = D i = ad (1) I a directed graph, bak i s overall degree cetrality ca be obtaied as follows: ANNEXES 4 OUT D i =D i + I a o-directed etwork, overall degree cetrality, out-degree, ad i-degree are equivalet: D i IN a j=1 ji a j=1 ij D i = = (2) (3) The stadard O-SII framework itercoectedess idicators itra-fiacial system assets, itrafiacial system liabilities ad debt securities outstadig essetially costitute degree cetrality measures for a exposure-weighted directed etwork. ii) Betweeess cetrality Betweeess cetrality assigs high values to odes that act as crossroads, thereby cotrollig etwork activity. I a o-exposure weighted etwork, the edges all have the same legth while i a exposure weighted etwork, the legth of a edge equals the iverse of the exposure amout. Followig Freema (1979), the betweeess cetrality score of ode i ca be writte as follows: B i = jk (i) jk with j ad k beig odes differet from i, jk beig the umber of shortest paths coectig j ad k, ad jk (i) beig the umber of shortest paths coectig j ad k that pass through i. (4) iii) Closeess cetrality Closeess cetrality is based o the distace betwee a ode ad the other odes i the etwork. I a o-exposure weighted etwork, all edges have the same legth while i a exposure weighted etwork, the legth of the edges correspods to the iverse of their exposure amout. The closeess cetrality score of ode i is calculated as follows (Freema, 1979): ( ) C i = d (i,j) with d(i,j) beig the shortest distace betwee odes j ad i. Thus, the closeess cetrality score equals the iverse of the sum of all distaces betwee i ad the other odes i the etwork. j=1-1 (5) REVUE DE STABILITÉ FINANCIÈRE

5 iv) Eigevector cetrality Eigevector cetrality costitutes a extesio of degree cetrality. Istead of simply summig up the umber or weights of the edges of a ode, they are further weighted by the cetrality of the odes to which they coect. The eigevector cetrality score of ode i is defied as follows (Newma, 2004): with beig a costat. Thus, i a o-exposure weighted etwork, the eigevector cetrality score of ode i, amely x i equals the sum of the eigevector cetrality scores of the odes with which it has a coectio divided by. This is the case because a ij = 1 if a coectio exists ad zero otherwise. I a exposure weighted etwork, the eigevector cetrality score of i equals the sum of the eigevector cetrality scores of the eighbours weighted by the exposure amout a ij ad divided by. Hece, a ode has a higher eigevector cetrality if it is coected to other odes with a high eigevector cetrality score ad i the case of a weighted etwork if the exposure amout is large. Equatio (6) ca be rewritte i matrix otatio: (7) with A beig the adjacecy matrix, x a eigevector of A ad the correspodig eigevalue. To guaratee the o-egativity of the obtaied cetralities, the chose eigevector should be associated with the largest eigevalue of A (Newma, 2004). v) PageRak x i = 1 a ij x j j=1 PageRak is a variat of eigevector cetrality that is employed by Google to rak websites accordig to their importace. A page is cosidered to be more importat depedig o the umber liks from other importat websites that lead to it. I this study, the stadard PageRak is applied to a directed graph ad measures the cetrality i terms of icomig liks. As oted by Kaltwasser ad Spelta (2015), the PageRak score of a website idicates the probability that a radom walker who moves aroud withi the web is preset at the website i questio. Mathematically, it ca be writte as follows: i i PR i [ a ij * mi ( 1,1) + 1 out d j ] PR i + 1- (8) j=1 k=1 a kj out where it is commo to assume j equals 1 if j has o outgoig liks (i.e. a ) ad k=1 kj zero otherwise. I our cotext, equatio (8) describes the importace of a ode i terms of the fuds it borrowed. Relative to eigevector cetrality there are three major differeces. First, sice a directed etwork is cosidered, the term -1 out d j is added to assure that a radom walker that arrives at a ode j without outgoig liks (i.e. a ij ad a ) will ot get stuck but ca leave the ode. Secod, the term k=1 kj (1- -1 prevets the same radom walker from gettig stuck i a sub-graph which might have icomig liks but o outgoig liks. Third, if ode j has outgoig liks, the cetrality PR j i will ot get fully assiged to ode i. Istead ode i has to share it with the other eighbours of ode j ad gets oly assiged the fractio a ij a of PR i. k=1 kj j (6) 114 BANQUE CENTRALE DU LUXEMBOURG

6 1 Although less commo i stadard PageRak applicatios, a equatio similar to (8) ca also be writte for outgoig liks (Kaltwasser ad Spelta, 2015): PR i out out [ a ji * mi ( 1,1) + 1 i d j ] PR j + j=1 k=1 a jk i where d j equals 1 if j has o icomig liks (i.e. a ) ad zero otherwise. Equatio (9) gives k=1 jk the PageRak score of ode i i terms of the fuds it leds out. Equatio (8) will be referred to as I- PageRak ad equatio (9) as Out-PageRak. 1- (9) ANNEXES 4 vi) Cetralisatio measures Based o cetrality measures, the structure of a etwork as a whole ca be characterised via cetralisatio measures. These measures were developed by Freema (1977) ad are calculated from the degree, betweeess ad closeess cetrality scores of the idividual odes, based o the oweighted ad o-directed etwork. They describe the tedecy of a sigle ode to be more cetral tha all other odes ad are expressed i per cet. A example of a etwork with 0% cetralisatio is a fully coected etwork, i.e. oe that has the maximum umber of possible edges. A etwork with 100% cetralisatio is a star, i.e. a graph i which the oly existig edges coect oe cetral ode to all other odes. Cetralisatio measures ca geerally be writte as follows: C = i = 1[ x*-x i] max i = 1[ x*-x i] where x* correspods to the highest cetrality score of all odes, the umerator equals the sum of the differeces betwee x* ad all other cetrality scores ad the deomiator equals the highest possible value of the umerator. As show i Freema (1977), the cetralisatio measures for degree, betweeess ad closeess ca be writte as follows: C D = i = 1[ D*- D i] ( ) C B = i = 1[ B*- B i] ( ) C C = i = 1[ C*- C i] ( - 2) / (2-3) (10) (11) (12) (13) 3 THE OVERALL NETWORK STRUCTURE Table 1 provides summary statistics of the measures regardig the amouts of fiacig exchaged withi the etwork. Over the period 2015Q4-2016Q4, asset exposures ad liabilities of baks towards ivestmet fuds have o average icreased by 15% ad 11% respectively. The average iterbak trasactio volume also wet up by 50%. The highest ivestmet fud exposure ad liability also icreased ad the highest iterbak trasactio volume wet up by more tha 3 billio This high amout is due to a itra-group trasactio. The highest o itra-group trasactio equals 1.4 billio. REVUE DE STABILITÉ FINANCIÈRE

7 Table 1: Volume measures at etwork level (i millio EUR) AVERAGE MAXIMUM 2015Q4 2016Q4 2015Q4 2016Q4 Ivestmet fud asset exposure of baks Ivestmet fud liabilities of baks Iterbak trasactios Source: BCL. Figure 1 The iterbak etwork ad bak-ivestmet fud liks, 2016Q4 Figure 1 provides a graphical represetatio of the etwork for 2016Q4. The size of the odes is proportioal to the PageRak score for icomig fuds calculated usig equatio (8). The first observatio that ca be made from the etwork visualisatio is that the most importat baks i the etwork appear to be custodia baks 68, O-SIIs ad oe bak pursuig other activities liked to ivestmet fuds. 69 The secod observatio that ca be made is that the etwork is highly cetralised o the ivestmet fud sector. Ideed, from the 117 baks active i the etwork, 92 have a direct coectio to the ivestmet fud sector. Table 2 presets differet metrics for quatifyig the geeral etwork structure i figure 1. The visual depictio of a high grade of etwork cetralisatio o the ivestmet fud ode is cofirmed by the quatitative measures sice all three metrics score aroud 70%. This idicates that the etwork s shape is closer to a star, with the ivestmet fud ode as cetre, tha to a etwork where most odes are equally well coected. This result is worth metioig as the cetralisatio measures are calculated from a etwork that does ot iclude exposureweighted edges, thereby potetially Source: BCL Notes: Custodia baks are marked i red, baks with other ivestmet fud activities i orage, other baks i gree ad O-SIIs are depicted with a blue boarder. The size of the bak odes is proportioal to their PageRak score for borrowed fuds, based o a exposure weighted etwork. The highest scorig bak is placed at the bottom ad scores decrease clockwise. The directio of the arrows goes from asset holder (leder) to liability issuer (borrower). The thickess of the arrows represets the size of the trasferred amout. 68 Custodia baks are defied as the 14 baks with the most assets uder custody as of 2015Q4. The defiitio does ot exclude that custodias pursue other lies of busiess i parallel. Oe of the 14 baks is ot icluded i the etwork because it has o iterbak or ivestmet fud lik. 69 The iformatio is provided from a iteral busiess model classificatio scheme of the CSSF. 116 BANQUE CENTRALE DU LUXEMBOURG

8 1 uderestimatig the importace of the ivestmet fud ode sice the amouts ivolved are usually larger tha i the iterbak market. ANNEXES 4 Table 2: Metrics at the etwork level 2015Q4 Degree cetralisatio (%) Betweeess cetralisatio (%) Closeess cetralisatio (%) Diameter Average distace Diameter (oly iterbak) Average distace (oly iterbak) Desity (%) Average umber of iterbak coectios Q4 Source: BCL Notes: Degree, betweeess ad closeess cetralisatio, as well as the diameter, the average distace ad the average umber of iterbak coectios are calculated from a o-weighted udirected etwork. The desity is calculated from a o-weighted directed etwork. Distaces betwee odes withi the etwork appear to be very limited sice the etwork diameter, i.e. the logest distace 70 betwee ay pair of odes, comprises oly four edges. The average distace of 2.3 edges betwee two odes is also very short. Give the high level of betweeess cetralisatio, the short average distace ca be to a sigificat extet explaied by the fact that the ivestmet fud ode acts as bridge betwee bak ode pairs. However, the 11 percetage poit drop i betweeess cetralisatio over the period 2015Q4-2016Q4, combied with a low ad decreasig average distace i the iterbak sub-graph suggests that bak odes may be icreasigly actig as bridges withi the etwork istead of the ivestmet fud ode. Geerally, the short distaces betwee odes ca potetially traslate ito a heighteed threat of cotagio followig a iitial shock i the etwork, for istace from the ivestmet fud sector. The etwork also appears to be rather sparse sice the desity 71 of the etwork equals 2.6% with four iterbak edges per bak. Cosequetly, a low umber of existig edges combied with short distaces withi the etwork idicates that several well coected odes, amog which otably the ivestmet fud sector, must act as pivots ad could be cosidered as systemic i the etwork. 4 RESULTS AT THE NODE LEVEL To determie the most systemic odes, the aforemetioed cetrality measures are calculated. Table 3 summarises the results. Except for i- ad out-degree, the score for each ode is divided by the sum of the scores of all odes ad multiplied by i order to make the idicators more comparable. Hece idividual scores are expressed i basis poits, the sum of the scores equals ad all measures have a mea value of Distace refers to the shortest path betwee two odes. 71 The desity equals the ratio of the effective umber of existig edges to the maximum umber of possible edges for a directed etwork. REVUE DE STABILITÉ FINANCIÈRE

9 Table 3: Cetrality results for the odes STD. DEV. MIN. MEDIAN 90 TH PERC. MAX. I-degree Out-degree Betweeess Closeess Degree Eigevector cetrality I-PageRak Out-PageRak Source: BCL Notes: 2016Q4 data. Std. dev. stads for stadard deviatio, 90th perc. for 90th percetile. Except for i- ad out-degree, the sum of the scores per measure equals ad the mea 85. I- ad out-degree are calculated from the directed o-weighted etwork. Betweeess, closeess, degree ad eigevector cetrality are calculated from the udirected exposure-weighted etwork. I- ad Out-PageRak refer to the measures for icomig ad outgoig fuds respectively ad are calculated from the directed exposureweighted etwork. For each measure the highest score is obtaied by the ivestmet fud ode, i lie with the previous etwork cetralisatio results. The media ad 90 th percetile values for i- ad out-degree respectively also led support to the fidig that oly a small umber of odes withi the etwork are very well coected. The betweeess scores are widely dispersed, as idicated by the highest stadard deviatio of all idicators, ad cocetrated o oly a few odes sice the ivestmet fud sector scores 68% of all poits, 12 baks score betwee 1% ad 5% of all poits, ad 94 baks score 0 poits. This illustrates that, apart from the ivestmet fud ode, there are oly a couple of baks that fuctio as pivots withi the etwork. The very low stadard deviatio of the closeess idicator further demostrates that distaces betwee odes are ot oly o average very short but that they are distributed almost uiformly. This suggests that the etwork ca be cosidered as compact. Degree ad eigevector cetrality produce scores that are more evely distributed tha betweeess o the right side of the distributio, with the former havig a higher stadard deviatio due to the much higher score of the ivestmet fud ode. Nevertheless, the scores of both measures are still very much cocetrated, with the top-10 odes scorig more tha 70% of all poits. This is mostly due to the sigificat ivestmet fud liks of a sample cosistig maily of custodia baks. As a cosequece, the top-12 most systemic baks idetified by degree cetrality iclude 9 custodia baks ad the top- 12 idetified by eigevector cetrality 10 custodia baks, ofte without sigificat iterbak ties. I additio, despite the fact that degree cosiders oly first-order exposures ad eigevector cetrality also higher-order exposures, both measures ted to yield similar results for the sample i questio. Ideed, if the ivestmet fud ode s score is excluded, the correlatio betwee both measures is This idicates that, for this paper s dataset, eigevector cetrality does ot add much iformatio to the scores produced by the basic degree measure. This is likely due to the fact that for the etwork uder cosideratio, eigevector cetrality, ulike PageRak, has the drawback that it assigs the full cetrality of the domiat ivestmet fud ode to all eighbourig odes. This meas that a bak with a large ivestmet fud coectio, but o iterbak liks, might get a higher cetrality score tha a bak with a somewhat lower ivestmet fud coectio but cosiderable iterbak ties. However, from a systemic risk perspective the latter bak should be more importat tha the former. Thus, i the cotext of this aalysis, the more sophisticated PageRak measure is better suited for idetifyig systemic baks. Ideed, both PageRak measures idetify a set of baks cosistig ot oly of 118 BANQUE CENTRALE DU LUXEMBOURG

10 1 custodias but also of baks with sigificat iterbak activity as the most systemic baks. Like i- ad out-degree, they also make it possible to assess if baks ted to be specialised i either borrowig or ledig fuds. Correlatios 72 betwee the degree measures ad betwee the PageRak measures are equal to 0.56 ad 0.66 respectively, which idicates that baks that are active i ledig out fuds to the ivestmet fud sector or domestic baks also ted to receive more fuds from these etities. Hece, baks that are systemic i terms of their itercoectedess are likely to simultaeously have asset exposures ad liabilities towards other odes i the etwork. ANNEXES 4 The ultimate goal of determiig the most importat baks withi the iterbak-ivestmet fud etwork is to iclude the fidigs withi the O-SII framework i order to assess if the compositio of the list of idetified systemic baks should be altered. The two measures that are best suited for this purpose are betweeess ad PageRak. The former because it idetifies a small set of baks that act as likely pivots for spreadig shocks towards the rest of the bakig sector, the latter because it takes ito accout first-order ad higher-order exposures of baks while givig more weight to iterbak coectios tha eigevector cetrality. I-PageRak, which measures etities importace i terms of receivig fuds, should be particularly pertiet as baks liabilities towards the ivestmet sector are otably higher tha their exposures. Degree cetrality has the clear drawback vis-à-vis PageRak that it oly cosiders first-order exposures while the closeess measure is ot a useful idicator to be icluded i the O-SII framework as the quatitative differece betwee most scores is margial. 5 THE O-SII ASSESSMENT INCLUDING CENTRALITY MEASURES Table 4 idetifies the types of baks that are most importat accordig to PageRak ad betweeess. The shares are calculated relative to the sum of all bak scores while excludig the ivestmet fud ode. The categories are ot mutually exclusive, except for custodia ad other ivestmet fud activities. Regardig betweeess, domestically orieted commercial baks (DOCBs) 73 accout for 58% of total bakig sector scores. Hece, baks with strog liks towards the real sector of the Luxembourg ecoomy are also those which are highly active i the iterbak market ad are positioed as crossroads withi the ivestmet fud-iterbak etwork. Table 4: Share of total bak cetrality scores by type (i %) CUSTODIAN OTHER IF ACTIVITIES DOCB O-SII Betweeess I-PageRak Out-PageRak Average PageRak No. of baks Source: BCL Notes: 2016Q4 data. Other IF activities refers to baks that pursue ivestmet fud activities differet from custody services. DOCB refers to domestically orieted commercial bak. Apart from custodia ad other IF activities, the categories are ot mutually exclusive. 72 Correlatios are calculated oly from bak scores, i.e. excludig the ivestmet fud ode which costitutes a large outlier. If the latter is icluded, PageRak correlatio equals 0.97 ad degree correlatio DOCBs are defied as the seve baks with the highest amout of liabilities from domestic o-fiacial corporatios ad households. They accout for 85% of the total. REVUE DE STABILITÉ FINANCIÈRE

11 O-SIIs, which iclude several DOCBs, score almost half of the betweeess poits available for the whole bakig sector. This idicates that the O-SII framework already accouts to a large extet for the iformatio cotet of the betweeess idicator. I other words, may baks with high betweeess have already bee idetified as systemic. This is to a much lesser extet true for baks with high PageRak scores ad especially for the I-PageRak, as O-SIIs score 16% of all available poits, while istitutios with strog ivestmet fud busiess liks such as custodias ad baks with other ivestmet fud activities score 46% of all poits. We caot exclude that some baks have ot bee idetified as systemic, although they evertheless might be too itercoected to fail. Hece, table 5 presets the umber of baks by type that would have bee eligible to be idetified as a O-SII 74 if some versio of PageRak had bee icluded i the 2016 assessmet. The stadard O-SII assessmet is based o four equally weighted criteria, of which oe is itercoectedess. 75 Thus, PageRak ca either be icluded as a separate fifth criterio or withi the existig itercoectedess criterio. Note that the stadard assessmet idetified six O-SIIs. If icluded as a fifth criterio, tha a 20% weightig appears the most plausible i order to have five equally weighted criteria. Other weights are also icluded to assess the sesitivity of the results. Table 5: Number of O-SIIs with the iclusio of PageRak PAGERANK INCLUDED AS/IN INDICATOR WEIGHT CURRENT O-SIIS CUSTODIANS OTHER BANKS 5% % Separate criterio Separate criterio Separate criterio Itercoectedess criterio I-PageRak 15% % % % % Out-PageRak 15% % % % % Average PageRak 15% % % I-PageRak 5% Out-PageRak 5% Source: BCL Notes: 2016 O-SII assessmet, based o 2015Q4 data. PageRak ca be icluded as a separate fifth criterio or as idicator withi the existig itercoectedess criterio. Weight refers to the share with which PageRak eters the O-SII score. Curret O-SIIs correspods to the six baks idetified i the 2016 stadard assessmet. Custodias refers to the additioal umber of custodias that were ot idetified as O-SII i the stadard framework. Curret O-SIIs already icludes two custodias. 74 I this cotext, beig eligible meas that a bak scores at least 275 basis poits i the O-SII assessmet. See EBA/GL/2014/10 (GL o criteria for the assessmet of O-SIIs). 75 The other three criteria are size, importace, ad complexity/cross-border activity. 120 BANQUE CENTRALE DU LUXEMBOURG

12 1 If the I-PageRak metric, which captures baks liabilities towards ivestmet fuds, was icorporated as a separate criterio, the six curret O-SIIs would still qualify as systemic. Note that the O-SIIs idetified to date already iclude two custodia baks. Additioally, if the weight was 10% or more, oe additioal custodia would qualify as a systemic bak ad at 20% two additioal custodias would qualify as such. At 25%, a bak that is very active i the iterbak market would also be eligible for beig a O-SII. The most plausible weight for a fifth criterio though, as previously metioed, is 20% as this would make all five criteria equally-weighted. Uder the other three scearios, ot all curret O-SIIs would qualify as systemic depedig o the weightig, without additioal custodias or other baks qualifyig as such. The oly exceptio is the 25% weightig for the average PageRak. Overall these results appear to be ituitive as may domestic baks, otably custodias, are depedet o iflows of fudig from the ivestmet fud sector. As oted previously, those baks asset exposures are comparably smaller. Give that the largest potetial risk arisig from itercoectios comes from the liability side of baks balace sheets, I-PageRak seems to be the most appropriate measure ad a 20% weightig is the most plausible choice for the O-SII assessmet. ANNEXES 4 6 CONCLUSION The etwork cosistig of iterbak exposures ad fiacial liks betwee baks ad ivestmet fuds has a rather low umber of direct coectios, the idividual odes are ot too distat from each other ad a relatively small set of baks act as pivots withi this etwork. Such a etwork structure could potetially propagate shocks very rapidly. At a more graular level, the most importat istitutios fuctioig as crossroads are domestically orieted commercial baks. Four of these baks have already bee idetified as systemic uder the EBA guidelies for O-SII assessmet. O the other had, the most importat istitutios i terms of first- ad higher-order exposures ad liabilities towards ivestmet fuds ad domestic baks are custodias. So far, oly two such baks have bee idetified as beig systemic. A modified O-SII assessmet methodology, icludig a measure to accout for this type of cetrality, reveals two further custodia baks to be systemic. The results of this study illustrate the effect of icludig a additioal itercoectedess idicator accoutig for bak-ivestmet fud likages i order to ehace the stadard O-SII framework i Luxembourg. REFERENCES Freema, L. C. (1979). Cetrality i social etworks: Coceptual clarificatio. Social etworks, 1(3), Kaltwasser, P. R., & Spelta, A. (2015). Systemic risk i the iterbak market with heterogeeous agets. Macro-Risk Assessmet ad Stabilizatio Policies with New Early Warig Sigals, SSH Newma, M. E. (2004). Aalysis of weighted etworks. Physical review E, 70(5), REVUE DE STABILITÉ FINANCIÈRE