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CLS and Payment System Stability

With the introduction of the Danish krone in CLS, settlement risk in foreign-exchange transactions in Danish kroner can be reduced. CLS will increase the number of pay-ins over the settlement day for the settlement members, thereby increasing focus on liquidity management. In 2002 the automatic collateralisation agreement was expanded to include additional settlement purposes, in view of CLS among other factors. This has created the basis for more flexible liquidity management. The resulting degree of interdependence between the settlements is not assessed to have implications for the stability of the settlement structure. The access to sufficient liquidity at the right times is a precondition for a stable settlement structure. Stress testing and sensitivity analysis of the settlement structure show that in a situation where the automatic collateralisation agreement is not applicable, there is still access to ample liquidity. In general, there is also ample liquidity available at the level of individual banking institutions.

The significance of CLS to financial stability

CLS (Continuous Linked Settlement) is an international foreign-exchange settlement system that offers settlement of foreign-exchange transactions in seven key currencies[1]. With the introduction of CLS on 9 September 2002 credit risk in foreign-exchange transactions can be eliminated. CLS thereby entails that a significant settlement risk can be reduced considerably. It has long been possible to settle interbank payments, retail payments and securities transactions without any credit risk, while settlement of foreign-exchange transactions has traditionally been associated with a credit risk of the same magnitude as the trade[2]. Given a daily average turnover of approximately USD 1,200 billion in the foreign-exchange market[3], CLS can potentially imply a significant contribution to financial stability.

The use of CLS has increased gradually, and in March 2003 an average of almost 34,000 trades were settled for a value of more than USD 400 billion per day. If the credit risk on foreign-exchange transactions is to be reduced, the system must be widely used. Obviously, the inclusion of new currencies is an important parameter. Moreover, it is of great importance that the many participants in the foreign-exchange market that are not direct settlement members in CLS will be connected as indirect settlement members in the settlement system[4]. CLS estimates the transaction volume for the potential third party settlement members to be around three times the maximum transaction volume settled by third party settlement members via CLS.

The Danish krone is expected to be introduced in CLS during 2003, as are the Norwegian krone, the Swedish krona and the Singapore dollar.

Foreign-exchange settlement in CLS
Foreign-exchange transactions are settled in CLS when both parties to a transaction report their trading instructions to CLS. The instructions are then matched by CLS, after which the two sides of the transaction are settled simultaneously via the settlement members' accounts with CLS. In this way the traditional credit risk between the parties is eliminated.

Since foreign-exchange settlement takes place in CLS, the operational risk is concentrated. It is therefore vital that CLS cannot sustain losses and that the settlement to a great extent can take place, even if a settlement member fails to honour its pay-in obligations. CLS settlement is therefore subject to strict risk management to ensure that pay-ins to CLS always take place before pay-outs to settlement members. Hereby CLS avoids credit risk on the settlement members. The principles, including risk management in CLS settlement, are described in Box 12.

The principles of cls settlement

Box 12

Pay-ins to CLS
Each settlement member has a multi-currency account at CLS with sub-accounts for each currency. On the basis of the reported trades CLS calculates the settlement members' net positions in the various currencies. The settlement members pay in foreign-exchange amounts to CLS by transferring amounts to CLS' central-bank account via the national RTGS systems. Pay-ins to this account are automatically credited to the settlement members' (sub)account at CLS.

Settlement of trades
Foreign-exchange transactions are settled by moving the traded currency between the relevant settlement members' CLS accounts. Foreign-exchange transactions are settled on a Payment-versus-Payment basis whereby the two sides of the trade are entered to CLS' books simultaneously. The settlement of a trade is only completed if the following risk management tests are met:

  • A settlement member's net balance across currencies must always be positive or zero
  • A settlement member's short position limit in a given currency may not exceed CLS' limit for that currency
  • The sum of a settlement member 's short position limit may not exceed a limit stipulated by CLS which reflects a settlement member's credit standing.

Pay-outs from CLS
CLS pays out currency to the settlement members by transferring amounts from its own central-bank account via the national RTGS systems to the relevant participant's central-bank account. At the same time the pay-out is debited to the settlement member's (sub)account at CLS. Pay-outs are subject to compliance with the aforementioned risk management tests.


To ensure that settlements are completed, CLS has made an agreement with certain settlement members to provide extra liquidity should a settlement member fail to honour its payment obligations. In each currency CLS has concluded an agreement with at least 2-3 liquidity providers that in an emergency will assume the defaulting settlement member's pay-in obligation in CLS. In exchange, they will receive the defaulting settlement member's pay-outs. The risk assumed by the liquidity provider in this connection is limited, since all settlement members always have a positive position in CLS taken as a whole, cf. Box 12.

Since pay-in and pay-out of currency to/from CLS take place in the national RTGS systems[5], the settlement depends on all RTGS systems being open at the same time across time zones. Against this background it has been decided that CLS settlement must be completed between the hours of 7.00 a.m. and 12.00 noon CET, which is late in the evening in Japan and Australia and early in the morning in the USA and Canada. Concentrating foreign-exchange settlement in CLS within this relatively short time implies great demands of the settlement members' ability to procure liquidity. For this reason liquidity-saving measures were an important factor in the design of the CLS system. A key aspect is that the settlement members pay in funds to CLS on a net basis, in numerous small portions. Furthermore, the settlement members may trade on their positions in CLS by concluding In/Out Swaps[6] with each other. The CLS settlement cycle and the fixed pay-in schedules are described in Box 13.

CLS settlement cycle, CET

Box 13
  • 00.00: Deadline for reporting trades for settlement on the next day. CLS calculates the settlement members' net positions and a preliminary schedule of when CLS must receive the pay-ins
  • 6.00 a.m.: Deadline for conclusion of In/Out Swaps
  • 6.30 a.m.: Deadline for reporting trades for settlement on the same day (In/Out Swaps). CLS provides a revised schedule of the settlement members' net pay-ins before the deadlines at 8.00 a.m., 9.00 a.m., 10.00 a.m., 11.00 a.m. and 12.00 noon
  • 7.00 a.m.: The settlement process starts. Trades are settled as soon as there are funds in the participants' CLS accounts. It follows from the risk conditions that a trade may be settled no matter which currency the settlement member has paid in. Pay-outs to the settlement members take place on an ongoing basis subject to compliance with the risk management tests
  • 8.00 a.m.: First pay-in in all currencies
  • 9.00 a.m.: Second pay-in in all currencies. The settlement (booking) of the trades is to be completed. The pay-in schedules are calculated so as to leave sufficient funds in the participants' CLS accounts after the second pay-in for all trades to be settled in compliance with the three risk management tests. Once all trades are settled, the settlement members will have long positions in some currencies and short positions in others. As the settlement members pay in the remaining amounts, CLS will gradually be able to pay out the long positions without compromising the risk management tests
  • 10.00 a.m.: Third pay-in in European and US currencies. Last pay-in in Japanese yen and Australian dollars. The pay-out of yen and Australian dollars is to be completed
  • 11.00 a.m.: Fourth pay-in in European and US currencies
  • 12.00 noon: Last pay-in in European and US currencies. All remaining pay-outs are to be completed

CLS in the settlement day
The introduction of the Danish krone in CLS implies the inclusion of yet another settlement cycle in the Danish settlement day[7]. Besides the bilateral RTGS payments there will thus be four systems for settlement of payments in Denmark; the Sumclearing (the retail payment system), settlements in VP (VP Securities Services), FUTOP settlement[8] and CLS settlement.

Individual large-value payments (RTGS payments) are completed on an ongoing basis in Danmarks Nationalbank's RTGS system, Kronos, whenever it is convenient for the settlement members within the system's opening hours from 8.00 a.m. to 3.30 p.m.

The Sumclearing and VP settlement systems are net settlement systems for the settlement of retail payments and securities transactions, respectively. The principle of net settlement is that all payments to and from a settlement member are netted. Settlement members subject to a net pay-in obligation transfer funds to the settlement, which is then completed, and pay-outs are made to the settlement members subject to net receipt of funds in the settlement process. In both the Sumclearing and the VP settlement systems the netting process takes place several times within each settlement day. The Sumclearing normally takes place as 2-3 overnight settlements, and possibly an extra settlement before noon (Sum1, Sum2, Extra1 and Extra2 respectively). Settlement of securities transactions in VP takes place in four settlement blocks (VP10, 20, 30 and 40), of which three are run in the evening and overnight and one before noon. VP's settlement of periodical payments (VP35)[9] is also processed before noon. When the Danish krone is introduced in CLS, there will be five additional pay-in deadlines between 8.00 a.m. and 12.00 noon, cf. Box 13. Chart 51 shows the schedule for the various settlements and pay-ins during the settlement day.

Settlements of Danish kroner during the settlement day
Chart 51
Note: Kronos' opening hours will begin at 7.00 a.m. when the Danish krone is introduced in CLS. There are other VP settlements such as VP05 (disbursement of yields on government bonds) and VP14 (subscription), but they are not included in the analysis.

Several consecutive settlements with the same purpose both enhances efficiency and reduces settlement risk. The three VP settlement blocks for securities transactions run during the evening and overnight are examples, since they improve efficiency of international trading settlement by ensuring smoother traffic through the link to the international settlement system Euroclear. At the same time, the division into a number of settlements with the same purpose reduces both settlement risk and systemic risk, since processing a whole day's transactions does not depend on the completion of one particular settlement.

Stricter regime for the management of liquidity
The net amounts participants have to pay in every day for settlement purposes in Denmark are substantial. The current daily average settlement amounts to approximately kr. 17 billion, which is expected to increase to approximately kr. 23 billion when the Danish krone is introduced in CLS.

The increased pay-in obligations and the more complicated settlement day will make greater demands of the settlement members' liquidity management. The participants pay in funds to the various settlements by transferring liquidity to special accounts at Danmarks Nationalbank. The settlement members can for this purpose use their current-account balances or the Scandinavian Cash Pool[10], or avail of collateralised intra-day overdrafts on their accounts at Danmarks Nationalbank. The collateral may be securities or certificates of deposit pledged to Danmarks Nationalbank or via the VP automatic collateralisation agreement system. The automatic collateralisation agreement is described in further detail in Box 14.

The automatic collateralisation agreement

Box 14

The automatic collateralisation agreement may be used for intraday credit in Danmarks Nationalbank for settlement purposes. Settlement members requiring such loans provide collateral by pledging bonds registered at a special safekeeping account at VP to Danmarks Nationalbank. The amount pledged to Danmarks Nationalbank is for an amount equivalent to the loan. The automatic collateralisation agreement thus gives the settlement members the right to freely sell or mortgage securities in the safekeeping account for as long as there remain sufficient bonds to cover the pledge to Danmarks Nationalbank.

The automatic collateralisation agreement was originally developed for securities settlement and has the special characteristic that securities deals are to a certain degree self-collateralised since the value of the acquired assets may be used as collateral for the purchase in the very same settlement block. This ensures sufficient collateral at all times for settlement of deals via the automatic collateralisation agreement.

Since 18 November 2002 the settlement members have also been able to apply the automatic collateralisation agreement to loans for settlement of payments in the Sumclearing system and for periodical payments in VP. Once the Danish krone is introduced in CLS, the settlement members can also use the automatic collateralisation agreement as collateral for loans for settlement of foreign-exchange transactions via CLS


 Fast and reliable mobilisation of the necessary liquidity is a prerequisite for a smooth settlement process. If a settlement member in e.g. the Sumclearing has not transferred sufficient funds to its settlement account, all of the settlement member's underlying retail transactions will be taken out of the system and postponed for later processing. The participant's insufficient liquidity thus also affects the other settlement members. As another example, if a CLS participant fails to pay in funds on time this may delay pay-out of the other currencies, to the detriment of the other participants. At worst, the RTGS systems in the Asian time zone may not be able to close on time.

CLS, the extended automatic collateralisation agreement and settlement risks
CLS settlement will require liquidity to be mobilised quickly, and for this reason among others the automatic collateralisation agreement, which previously applied solely to the settlement of securities transactions in VP, has been extended to include collateral for loans for CLS settlement, Sumclearing and periodical payments in VP. Viewed in isolation there is thus more liquidity available for each settlement. This reduces the settlement risk and allows for more flexible liquidity management.

The drawback of the extended automatic collateralisation agreement is that it creates potential interdependence between the settlement systems. If a settlement is not completed on schedule, collateral subject to the automatic collateralisation agreement may be tied to that settlement, and may not be available as expected for the subsequent settlements. The system has a number of inherent measures to offset the effect of these interdependences.

If the first two VP settlements for securities transactions are delayed, the automatic collateralisation agreement will initially not be available for the Sumclearing. The payments of settlement members that for that reason have insufficient liquidity to complete the settlement will not be settled until the extra Sumclearing settlement at 9.00 a.m., cf. Chart 51. The settlement members may reduce this risk by making reservations for the Sumclearing under the automatic collateralisation agreement prior to the second settlement of securities transactions in VP.

If the Sumclearing is delayed, there is in principle a risk that the collateral in the pledged safekeeping account is unavailable when the participant is to raise liquidity for the CLS payments. This risk is eliminated by the system, as collateral reserved for the Sumclearing is released at a fixed time. In other words, the link between the two settlement systems can be broken and the provision of collateral for CLS settlement be given higher priority than provision of collateral for the Sumclearing.

Settlement members using the extended automatic collateralisation agreement may reserve parts of the value of their collateralised safekeeping accounts for various settlement purposes, thereby limiting the interdependence between the settlements. Furthermore, Danmarks Nationalbank may limit the participants' reservations, should it find that the settlement members' inappropriate use of reservations gives rise to unnecessary settlement risks. Box 15 describes the reservation system for the automatic collateralisation agreement and the participants' use of the agreement.

Application of the extended automatic collateralisation agreement

Box 15

The Chart below shows the total reservations of the collateralised safekeeping accounts and the total drawings under the automatic collateralisation agreement for the Sumclearing and periodical payments. The sums of reservations and drawings, respectively, apply to the participants who exercised the extended automatic collateralisation agreement on the day in question. In principle, the participants may reserve 100 per cent of the value of the safekeeping account for each purpose, whereby the total reservations amount to 200 per cent (100 per cent for the Sumclearing and 100 per cent for periodical payments). The participants may not make special reservations for settlement of securities transactions in VP under the automatic collateralisation agreement. For these settlements the full value of the collateralised safekeeping account at the given time is applied.

Reservations and drawings on the extended automatic collateralisation agreement

The spread between the two curves shows that the reservations of collateral normally exceed the actual collateral used. This "excess cover" is mainly found in the Sumclearing where the participants do not know the exact liquidity impact, so that a certain excess cover is appropriate. On the other hand, the participants can calculate exactly the liquidity impact of periodical payments, so their reservations for this purpose therefore generally correspond to the drawings

The sum of the reservations and sum of the drawings on the automatic collateralisation agreement account for a relatively small share of the value of the collateralised safekeeping accounts, i.e. barely 10 per cent on average in the period. With a view to the forthcoming introduction of the Danish krone in CLS this indicates that the automatic collateralisation agreement provides for ample collateral for CLS settlement. Moreover, the parallel patterns of the two curves in the Chart indicate active liquidity management by the participants.

Source: Danmarks Nationalbank.

In view of the systemic measures to contain settlement risks described above, and of the settlement members' behaviour in the system so far, the extended automatic collateralisation agreement is found to contribute to a more secure and smoother settlement process.

Stress testing of the danish settlement structure

Multiple sources of liquidity for settlement purposes will ceteris paribus enhance the stability of the settlement systems. The extension of the automatic collateralisation agreement creates a general alternative to traditional pledging of collateral. However, the stability will depend on the extent to which the participants apply the two types of collateralisation. In terms of stability it is important that the two types of collateralisation can supplement each other to a reasonable degree.

Stress testing of overall liquidity
The first stress test assumes an operational "worst case" crisis scenario whereby the automatic collateralisation agreement lapses and the settlement of overnight securities transactions in VP has to be postponed until the next morning. This eliminates one source of liquidity for the participants' settlement purposes. It is also assumed that there are delays in the Sumclearing, which must also be postponed until the next morning. The CLS pay-in schedule in five instalments from 8.00 a.m. to 12:00 noon continues to apply. The stress test thus examines whether it is possible to run these three settlements and the settlement of periodical payments before noon simultaneously in a situation where the settlement infrastructure is wholly dependent on the participants' access to current-account overdrafts[11]. The assumptions for the stress tests are described in further detail in Box 16.

Assumptions in the stress tests

Box 16

The basic assumption is that the automatic collateralisation agreement is not available, and that the settlement members cannot withdraw securities from the collateralised safekeeping account or other safekeeping accounts. Another implication of the lack of access to the automatic collateralisation agreement for settlement of securities transactions in VP is that the self-collateralisation mechanism for securities trades cannot function. The assumption is therefore that the settlement of securities transactions in VP (total net settlements from VP10, 20 and 30) cannot be completed before noon the next day. Another assumption is that the other settlements, i.e. VP's settlement of periodical payments (VP35), the Sumclearing and CLS settlement will also be processed before noon.

In the first stress test, which focuses on the banking sector's total overdraft access, the assumption is that all four settlements take place at the same time before noon. This assumption deprives the settlement members of the opportunity to use liquidity received in one settlement in other settlements.

In the second stress test that focuses on the settlement members' sensitivity to changes in the overdraft access, the above assumption is eased, and the four settlements instead take place consecutively. Some settlement members will thus receive liquidity in the early settlements for use in subsequent settlements. The assumption is that CLS pay-ins are made first. This is followed by the extra settlement in the Sumclearing system at 9.00 a.m. The settlement of periodical payments in VP takes place at 9.30 a.m., and finally the net settlement of the postponed securities deals from the night before takes place at 10.30 a.m. in VP40.

Both stress tests assume that Kronos opens at 7.00 a.m., but no interbank RTGS payments are submitted before all settlements have been completed.


The daily pay-ins for the four settlements in this period on average totalled almost kr. 23 billion, of which settlement of securities transactions in VP accounted for approximately 34 per cent, Sumclearing settlements for approximately 21 per cent, and periodical payments in VP for approximately 20 per cent, while the estimated liquidity impact from CLS accounted for approximately 25 per cent. The total net pay-ins were relatively stable, apart from 2 January, when they exceeded kr. 100 billion. However, on no day in this period would the participants' current-account overdraft access not have been sufficient to cover the current net pay-ins, as well as the estimated CLS pay-ins. The large pay-ins at the beginning of the period can be explained by the extraordinarily high number of transactions on 2 January, including periodical payments concerning mortgage-credit bonds.

Liquidity conditions at the level of individual banking institutions
Despite the ample liquidity at aggregate level it cannot be ruled out that certain individual participants may find it difficult to mobilise liquidity[12]. This is examined more closely in the second stress test, which considers whether individual participants did not have sufficient overdraft access in the period. The sensitivity to a reduction of the overdraft access is also analysed.

Access to current-account overdraft and size of settlement pay-ins
Chart 52
Note: Pay-ins to CLS are estimated on the basis of foreign-exchange transactions in January and February 2002.
Source: Danmarks Nationalbank and CLS.

The restrictive assumption in the above stress test of one simultaneous settlement before noon is eased, so that the postponed settlements are assumed to be consecutive in the following order: CLS settlement, the Sumclearing, periodical payments, and finally, the net result of the postponed settlement of securities transactions in VP. This takes into consideration that participants may be net recipients of liquidity in one settlement and net contributors of liquidity in another. Charts 53-56 show the daily average number of participants that are unable to honour their obligations in the period, assuming that the individual participants' overdraft access is reduced.

As regards the CLS settlement, based on estimated data the test shows that on no day in the period analysed will any of the participants be short of liquidity, cf. Chart 53 where there is no indication at 100 per cent. The sensitivity analysis shows that the overdraft access must be reduced to 80 per cent of the actual value before a participant becomes short of liquidity on one day. If the overdraft access is reduced to 20 per cent of the actual value, on average more than one participant per day will encounter problems.

Sensitivity analysis – CLS
Chart 53
Note: The Chart shows the average daily number of participants unable to honour their obligations given a reduction of the individual participants' overdraft access. Net pay-ins to CLS are estimated on the basis of foreign-exchange settlements in January and February 2002.
Source: Danmarks Nationalbank and CLS.

In the Sumclearing too, no participant has insufficient overdraft access on any day of the period, cf. Chart 54. The sensitivity analysis shows that if the overdraft access is reduced to 80 per cent of the actual value, two participants have insufficient overdraft access on one day in the period under consideration. If the overdraft access is reduced to 40 per cent of the actual value, on average more than one participant per day will encounter settlement problems.

Sensitivity analysis – the sumclearing (retail payments)
Chart 54
Note: The Chart shows the daily average number of participants unable to honour their obligations given a reduction of the individual participants' overdraft access.
Source: Danmarks Nationalbank and CLS.

If the settlement of periodical payments and then the VP settlement of securities transactions are also executed, cf. Charts 55 and 56, it is seen that a few participants have insufficient liquidity on one given day or another in the period under review (illustrated by the slight indication at 100 per cent). If the overdraft access falls to around 40 per cent, on average one participant per day will have insufficient liquidity.

Sensitivity analysis – periodical payments
Chart 55
Note: The Chart shows the daily average number of participants unable to honour their obligations given a reduction of the individual participants' overdraft access.
Source: Danmarks Nationalbank and CLS.

Sensitivity analysis – settlement of securities transactions in VP
Chart 56
Note: The Chart shows the daily average number of participants unable to honour their obligations given a reduction of the individual participants' overdraft access.
Source: Danmarks Nationalbank and CLS.

The very few participants with insufficient overdraft access in the last two scenarios is related to the large settlements on 2 January and the assumption that no RTGS payments are processed. Had the participants in question received the payments which they actually received on 2 January, they would have been able to honour their obligations. In a crisis scenario such as that described here it is therefore important that the participants behave as normally as possible in the interbank market, and dispatch payments at the normal time.

Conclusion
The first stress test shows that the banking sector as a whole still has ample liquidity available for settlement purposes, even if the access to liquidity is reduced considerably. The second stress test shows that in general there is ample liquidity available to the individual banking institutions, but that it cannot be ruled out that on days with extraordinarily high settlement amounts a few settlement members will be unable to settle all their obligations.

Ample liquidity is a prerequisite to a robust settlement structure. It is therefore important that the participants review their access to mobilise liquidity on an ongoing basis, including their dependence on different sources of liquidity.




[1] US dollars, Canadian dollars, Australian dollars, euro, Japanese yen, pounds sterling and Swiss francs.

[2] Foreign-exchange transactions are traditionally settled via the usual international payment channels. A trade of e.g. kroner against dollars entails a transfer of kroner from one party to the other, as well as a transfer of dollars in the opposite direction. The two legs of the trade are settled separately and independently of each other. The credit risk arises because one party to the trade may default after having received the bought currency, but not yet delivered the sold currency. Typically, exposures are significant in foreign-exchange transactions. However, the probability of losses is very small and compared to the traditional credit risk assumed by banks, where exposures are smaller, but the probability of losses greater, credit risk in settlement of foreign-exchange transactions can be seen as asymmetrical.

[3] BIS: Triennial Central Bank Survey of Foreign Exchange and Derivation Market Activity 2001.

[4] Only shareholders may participate directly in settlement via CLS. Others may participate indirectly via a direct participant.

[5] RTGS systems are Real-Time Gross Settlement Systems. Danmarks Nationalbank's RTGS system, Kronos, is described in further detail in Thomas Angelius and Astrid Henneberg Pedersen, Danmarks Nationalbank's New Payment System, Kronos, Danmarks Nationalbank, Monetary Review, 1st Quarter 2002.

[6] For example, if a settlement member has accepted inappropriately large negative dollar positions in the CLS settlement, two reciprocal transactions in dollars are concluded with another CLS settlement member. One of the transactions (buying dollars) is settled via CLS, which reduces the net position in dollars. The other transaction is settled outside CLS in the traditional manner. The use of In/Out Swaps thus reintroduces a (small) part of the credit risk associated with foreign-exchange transactions.

[7] The settlement day follows the monetary-policy day and runs from 4.00 p.m. on the day before the value date to 3.30 p.m. on the value date.

[8] The scale of FUTOP settlement is relatively limited, and is not included in the analysis in this chapter.

[9] Interest, repayments and dividend.

[10] An automatic cross-border collateral system, Scandinavian Cash Pool (SCP), has been established to facilitate settlement members' access to liquidity primarily for CLS settlement. Under SCP, collateral provided to one Scandinavian central bank can be used at short notice as collateral for a loan raised at another Scandinavian central bank. SCP can be used to procure intra-day liquidity during Kronos' opening hours until 1.30 p.m. Loans raised under SCP are not included in this chapter's analyses.

[11] The analysis considers participants holding accounts at Danmarks Nationalbank that are direct settlement members in either CLS, VP settlement and/or Sumclearing. There are 75 such settlement members all in all.

[12] Individual participants' inability to settle may generate systemic effects. Examination of systemic effects is beyond the scope of this analysis.


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