WORKING PAPER NO. 149 May 2006 Using Synthetic Data to Measure the Impact of RTGS on Systemic Risk in the Australian Payments System Peter Docherty ISSN: 1036-7373 http://www.business.uts.edu.au/finance/

SCHOOL OF FINANCE AND ECONOMICSUTS: BUSINESS

Using Synthetic Data to Evaluate the Impact of RTGS on Systemic Risk in the Australian Payments System

Gehong Wang and Peter Docherty*

School of Finance and Economics University of Technology, Sydney

Abstract This paper examines the possibility that financial contagion may be spread from one bank to

another via the Australian payments system. The initial study of payments system risk was

undertaken by Humphrey (1986) who found significant risk in the U.S. Fedwire system in the mid

1980s. Subsequent studies by Angelini, Maresca & Russo (1996), Kuussaari (1996), Northcott

(2002) and Furfine (2003) have found, however, little evidence of systemic risk in the payments

systems of Italy, Finland and Canada, and in the U.S. inter-bank market. Given that the

implementation of real time gross settlement (RTGS) systems in many countries, including

Australia, at significant cost, has been designed to reduce payments system risk, the finding that

this risk is small is significant. While detailed payments system data for Australia is not available

to researchers outside the Reserve Bank, this study constructs a synthetic data set based on

available information and uses this data to simulate the failure of each financial institution

operating in the Australian payments system. We find little evidence of systemic risk in the

Australian payments system using this approach and conclude that the introduction of RTGS in

the Australian system in 1996 had only a marginal effect on risk.

JEL Classification Numbers: E44, G21

Keywords: payments system, real time gross settlement (RTGS), deferred net settlement (DNS), systemic risk, contagion. Thanks to the Reserve Bank of Australia, Payments Policy Department for providing the aggregate RTGS data used in this study. Thanks also to Warren Hogan, John Veale, Greg Chugg, Chris Terry, Tony He, Gordon Menzies and Thuy To for comments and suggestions without in any way implicating them in the final product. *Correspondence to Peter Docherty, School of Finance and Economics, University of Technology, Sydney., PO Box 123, Broadway, NSW, 2007, Australia. Ph. 61 2 9514-7780; Fax 61 2 9514-7777; email: peter.docherty@uts.edu.au

1

1. Introduction: Systemic Risk and the Payments System The possibility of financial crises and the public policy objective of preventing crises have

underscored a number of significant developments in financial systems around the world

over the last twenty years. Financial crises not only result in the destruction of existing

wealth as the value of key assets declines, but they also generate losses in potential

wealth as disruptions to the saving-investment process slow the pace of economic

growth, at least temporarily. Such disruptions tend to involve bank failures. The long

Japanese recession following the crisis of the early 1990s provides an excellent example

of this possibility (Kuttner & Posen 2001, 146ff). Reductions in trade may also result if

the payments system is disrupted in the course of such crises. Since transfers of bank

deposits between individuals, and transfers of central bank deposits between banks lie

at the heart of the payments system’s operation, bank failures may also have negative

effects on the smooth functioning of this system causing reductions in trade.

Central bank lender of last resort facilities and deposit insurance are examples of

public policies designed to reduce the impact of financial crises. The principle of central

bank lending to solvent but illiquid banks was first explicitly outlined in Walter Bagehot’s

Lombard Street published in 1873. It has since become the standard central bank

response to financial crises.

The problem, of course, with public support for troubled banks is that it generates

moral hazard on the part of bank managers, owners and depositors. This problem is

worsened under conditions of asymmetric information which raises the possibility of

banks runs and financial contagion (Bernanke 1983). Reducing moral hazard is one

important objective of prudential regulation (Goodhart 1988; Mishkin 2001).

Recent moves around the world to implement real time gross settlement (RTGS)

systems for payments finalization represents a similar public policy initiative designed to

reduce the possibility of financial crisis. Humphrey (1986, 97) argues that contagion may

be transmitted between financial institutions via the payments system as well as by

depositor runs occasioned by asymmetric information. So-called “daylight credit

exposures”, he argues, characterize deferred net settlement (DNS) clearing systems and

open up the possibility that banks may default on their payments-related debts to other

banks as a result of some crisis-related shock. Since for some banks, daylight credit

exposures exceed shareholder capital, default on these exposures could threaten the

viability of the bank itself. Given the right pattern of exposures between banks, a crisis at

2

one bank could be transmitted to other banks adding to the problem of contagion and

grinding the payments system to a halt.

Humphrey (1986, 111) identifies three principal methods of limiting this kind of

payments system risk: net debit caps which limit the maximum credit exposures to other

institutions that banks are allowed to have in aggregate; receiver bilateral credit limits

which ensure that other institutions are not excessively affected due to the failure of a

participant institution; and settlement or receiver finality according to which each

transaction is immediately and individually settled so that credit exposures are

essentially eliminated. Flannery (1988, 277) adds a fourth method according to which

daylight overdrafts incur an interest charge that is priced to encourage greater

synchronization of payments, and voluntary elimination or reduction of credit exposures

which would become costly under such a proposal.

The international trend of moving payments systems over to RTGS fits within

Humphrey’s third category of risk management. In Australia, for example, large value

payments were moved over to RTGS in 1998 although small value payments continue to

be processed on a DNS basis within several components of the payments system. This

implies two things about the Australian situation. Firstly, it implies that the overall level of

systemic risk should have been substantially reduced since the introduction of RTGS in

1998. Secondly, it implies that a certain amount of residual systemic risk may remain

within the system due to the system’s DNS component.

Given that the movement to RTGS has involved considerable cost, an important

question is whether the reduction in risk has been sufficiently large to justify this cost. A

new literature has emerged which provides a framework for evaluating risk reduction

strategies in the payments system, and for measuring the risk posed by system credit

exposures. The objective of this paper is to apply this methodology to the Australian

situation in an attempt to quantify the reduction in risk that the movement to RTGS has

brought about. The remainder of the paper surveys the literature dealing with risk

measurement, describes the precise methodology and data to be used in applying this

literature to Australia, and reports the results of the study before drawing some broad

conclusions in the final section.

2. Literature Review The payments process is depicted in Figure 1 which identifies three stages. Firstly,

payment instructions are sent from retail customers to their banks by means of retail

3

payment instruments, or from wholesale financial markets by large value payments

instructions. This is the instruction stage. Secondly, instructions are collected and

collated by inter-bank systems. This is the clearing stage. Thirdly, payment is finalised

by the transfer of central bank funds. This is the settlement stage.

Risk exists at each stage of the process, with that at the settlement stage threatening

the viability of the payments system itself due to the aggregate nature of the exposures

involved. As suggested above, a range of methods has been identified for limiting

systemic risk, but each involves a combination of explicit and implicit costs.

Instruction Clearing Settlement

Central bank funds

FX market

Security

Inter-bank

system

Instrument

Figure 1 The Payments Process

Berger, Hancock and Marquardt (1996) have developed a theoretical framework within

which risk reduction−cost combinations may be analysed. Their model uses a use

capital asset pricing model (CAPM) type structure in which social performance of the

payments system is maximized over risk and cost possibilities. They identify a tradeoff

between risk reduction and cost, and highlight how this tradeoff is affected by such

factors as technology, financial innovation and regulatory developments. The major

costs identified by Berger, Hancock and Marquardt (1996, 707) are:

•

•

•

real resource costs of making, receiving and intermediating payments;

financial costs of accommodating frictions caused by holding assets other than

those that would be optimal to maximise expected utility; and

real and financial costs of settlement delays in the payments mechanism.

The model may be expressed in terms of Figure 2. The F-F curve is the social efficient

frontier for the payments system along which risk cannot be reduced further without

increasing payments system costs, and these costs cannot be reduced without

increasing risk (Berger, Hancock and Marquardt, 1996, 700). The location of the F-F

curve depends on current technology, risk control techniques and regulatory structures.

4

Technological, financial and regulatory innovations can change technically and allocative

efficiencies by moving the frontier from F-F to F’-F’.

F

Figure 2 The Risk-Cost Frontier of the Payments System

Berger, Hancock and Marquardt include in their model factors of risk control, choice of

payments instruments, portfolio management, monetary policy, adoption of new

technologies, and payments service intermediaries. The most important risks they

identify from a public policy viewpoint, are the external risks imposed on others by

participants in a large value payments system (LVPS), associated with disruptions to the

system. They define systemic risk as the risk that a credit or liquidity problem at one

financial market participant creates substantial credit or liquidity problems for participants

elsewhere in financial markets.

DNS systems may be represented in the Berger, Hancock and Marquardt framework

by points on the FF frontier, such as B, which are high and to the left. Large, unsecured

and unpriced overdrafts expose system participants and the system as a whole to high

levels of risk from participant default under this kind of system. As risk control methods

are implemented, risk is reduced but cost increases, moving us down and to the right

along the FF frontier. Costs include setting up more sophisticated computer systems to

monitor and limit exposures between institutions and between institutions and the

system, as well as the financial cost of keeping net balances in clearing accounts at the

central bank (what are called exchange settlement accounts, ESAs, in the Australian

•

•

I P

A

F’

F

F’

P

D

I

B

C*

Risk

R*

Cost

5

system). An RTGS system is represented by points to the bottom right hand side on the

FF frontier, such as point D. Policy-makers around the world have clearly demonstrated

a preference for RTGS over DNS systems, but such a preference is predicated on the

idea that significant risk attaches to DNS systems and that the cost of implementing

RTGS given this risk represents a Pareto improvement in social welfare terms.

Humphrey (1986) was one of the first studies to investigate the extent of risk within

DNS systems. He simulates the failure of a single participant (the defaulting bank) in the

CHIPS1 system for a randomly selected business day in January 1983. All payments to

and from this participant were unwound and new net multilateral settlement positions

calculated for each participant in the system. These revisions had the potential to

change the initial exposures of other institutions from net credit positions to net debit

positions, with the possibility that liabilities associated with such position deteriorations

could not be covered by the capital bases of affected institutions. Humphrey (1986, 104)

thus assumes that further failures will ensue if two conditions are met for a given

institution:

• its revised multilateral net position to the system is negative ; and

• the institution’s increased system obligation exceeds or equals its available capital.

Once these conditions are met for a given institution, that institution is assumed to fail

and system payments to and from it are unwound. Further revisions to the multilateral

positions of surviving institutions are then calculated and the above two conditions

reapplied to surviving institutions to see whether further failures ensue. Humphrey

repeats this process of default and revision to system positions until all remaining

participants can settle their net multilateral obligations.

He finds that 50 institutions failed in this simulated crisis, representing 38.6% of the

total dollar value of daily payment instructions in the system. Six sets of failure iterations

were required before no additional participant met Humphrey’s two knock-on failure

criteria. If only 10% of bank capital is assumed available to absorb losses from position

deteriorations (rather than 100%), the number of failures increases to 73 representing

76.1% of the total dollar value of daily payment instructions. Humphrey tests the

robustness of this result by repeating the failure simulation of the same large institution

on a different randomly selected day in January 1983, and by simulating the failure of a

1 Clearing House Inter-bank Payments System (CHIPS) is a privately operated 32-year-old U.S. dollar clearing system owned by banks located in New York City. CHIPS operated as a DNS system until 2001 when it was upgraded to CHIPS Finality, a continuous netting settlement (CNS) system.

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large associated participant for two randomly selected days within the same sample

period.

He concludes that a significant level of systemic risk is present in the U.S. payments

system (Humphrey 1986, 110). The precise level of risk as measured by the number of

bank failures and the percentage of the value of daily payment instructions lost, varies

from day to day, but the overall level is of the order of multiple institution failures and is

well in excess of 30% of daily payment instructions. The identity of banks affected by a

given institution’s initial failure is also highly variable, adding to the level of uncertainty

and heightening the degree of systemic risk identified by Humphrey’s study.

Angelini, Maresca and Russo (1996) extend Humphrey’s methodology in the context of

the Italian payments system but distinguish between two types of default caused by

external shocks and system-related shocks respectively. External shocks refer to an

event unrelated to the payments system, for example the default of a major bank

borrower due to adverse economic circumstances or mismanagement, while payments

system-related shocks refer to the flow-on effects arising from settlement defaults.

Angelini, Maresca and Russo assume that any payments system participant may fail

when there is a large external or system related shock. For bank i, state i1 is defined

such that bank i defaults due to such an external shock; state i2 is defined such that bank

i defaults due to a contagion-related failure in the payments system; and state i3 is

defined such that bank i does not fail. P(·) represents the probability that these specified

events will occur for a particular institution. P(i1) is exogenously given for every bank i. At

time t, bank i = B sends a payment worth X to bank i = A, which makes bank B a daylight

‘creditor’ of bank A until the transaction is settled at the end of the day (unless the

situation is modified by further payment flows). The risk carried by bank A due to this

transaction is given by the following expression:

[ ] ⎥⎦

⎤⎢⎣

⎡⋅+⋅=+⋅ ∑

≠ BAJJBPJPBPXBPBPX

,121121 )()()()()( (1)

According to this expression, the risk to bank A depends on the total possibility of bank B

failing, which includes the risk of bank B’s exogenous default P (B1) and the risk that

bank B will fail on account of a payments system crisis that affects bank B indirectly,

P (B2). This latter risk is given by the joint probability of a payments system

counterparty, bank J’s, failure and bank B’s failure conditioned on J’s failure, summed

over all J’s. This may in turn be expressed as the product of the probability of bank J’s

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failure on account of an exogenous event P (J1) and the conditional probability of B’s

failure given the exogenous failure of J. This risk is present if, for at least one bank J,

P (i.e. J is liable to default due to external factors), and P( ) 01 >J ( ) 012 >JB (that is, bank

B is at risk of default due to bank J’s failure). Angelini, Maresca and Russo then attempt

to quantify the probability of default for any bank from settlement failure using

Humphrey’s simulation methodology.

They simulate the failure of each institution in the Italian system on each of 21

business days during January 1992. This tests the likelihood of systemic crisis much

more comprehensively that Humphrey’s examination of only two institutions on two days.

They group institutions by size in an attempt to identify the characteristics of institutions

that are more likely to cause systemic crises or to be affected by systemic crises.

Thirdly, they examine the role of liquidity (rather than simply capital) in generating knock-

on effects as in Humphrey’s approach.

Angelini, Maresca and Russo’s results differ sharply from Humphrey’s. They find that

only 4% of the 288 participants in the Italian system were capable of generating a

systemic crisis when subject to an exogenously generated default. The extent of the

crises simulated was also limited. No more than 7 banks failed in any crisis and the

average monetary loss in a crisis was 2.7% of total debtor balances. Some 50% of all

crises were caused by large banks and 90% of banks affected by knock-on effects were

foreign banks. Angelini, Maresca and Russo report similar results when liquidity rather

than capital was used as a criterion for institutional failure. Thus little evidence is found

that systemic risk is significant in the Italian netting system which suggests that

continued use of the low cost DNS system represents an adequate policy choice in

terms of the Berger, Hancock and Marquardt model.

Kuussaari (1996) adjusts the methodology employed by Angelini, Maresca and Russo

(1996) in two ways and applies this approach to the payments system of Finland. Firstly,

he allows for only 50% of capital to cover deteriorations in bank payments positions.

Secondly, he introduces illiquidity into the definition of systemic risk. If the revised net

debit position of a bank exceeds the overdraft limit of current accounts at the central

bank, that bank is viewed as illiquid, and consequent iterations for illiquidity continue.

This methodology was also applied to the RTGS data set in Finland, where the test is to

identify liquidity effects due to a bank’s failure. Kuussaari finds little evidence of credit or

liquidity risk in the Finnish system.

8

Northcott (2002) also employs default simulation methodology to test for settlement

risk and contagion in Canada’s DNS system. Using bilateral settlement flows between

clearing banks for 231 days between August 2000 and June 2001, Northcott

systematically tests the exogenous failure of each institution in the system on each of

the days in the data set as do Angelini, Maresca and Russo. However, the framework

developed by Northcott to model bilateral and multilateral payment flows between

institutions allows for a range of assumptions on such variables as the extent of

unwinding from the failed institution, the proportion of lost payments eventually

recovered from the failed institution, the value of credit reversals by surviving institutions

to customer accounts, and the size of capital and liquidity stocks available to absorb

losses. She finds limited potential for contagion in the Canadian system. Under a base

reference case she defines as the normal state, there are zero knock-on effects from the

failure of any single institution in the data set. This normal state is characterized by the

ultimate loss of only 50% of unwound payments, the remaining proportion being

recovered through the legal process, 50% of credits to bank client accounts being

recovered so that some of the risk of payments system counterparty default is shared

with bank depositors, and 100% of identified capital being available to absorb losses.

Northcott distinguishes between credit risk and liquidity risk as do Angelini, Maresca

and Russo (1996) and Kuussaari (1996) but extends the analysis of these studies to test

the importance of capital and liquidity availability in a crisis. She defines two parameters:

τ (0, 1) as the proportion of Tier 1 capital2 that a bank can use to cover credit risk; and ρ

(0,1) as the proportion of liquid assets available to cover liquidity risk. The sensitivity of

Northcott’s base case results to variations in the values of these parameters is

systematically tested. A further parameter, α, captures the proportion of items received

by the defaulter that are returned to their counter-parties to reflect various degrees of

exogenous shock to the defaulting institution. Northcott finds that only under an extreme

scenario in which the above parameters take their most risky values, are limited knock-

on defaults experienced. Not surprisingly, a higher recovery rate (R), greater availability

of capital (a higher value for τ ), greater access to liquidity (a greater value for ρ), a

higher proportion of funds recovered from bank clients (ϕ), all lower systemic risk but a

higher proportion of returned payments (α ) increases the level of risk.

2 The permanent equity capital of a bank consists of equity capital and disclosed reserves. Equity capital includes cumulative preferred stock, non-cumulative perpetual preferred stock and other instruments that cannot be redeemed at the option of the holder.

9

Furfine (2003) adds an additional dimension to simulation methodology by examining

systemic risk in U.S. inter-bank markets rather than within the payments system

narrowly defined. He tests the credit exposure of banks in the federal funds market in the

U.S., focusing on bilateral credit exposures arising from U.S. federal funds transactions.

Furfine examines the degree to which the failure of one bank causes the subsequent

collapse of other banks via inter-bank commitments. Furfine also defines two types of

systemic risk: one is ‘the risk that some financial shock causes a set of markets or

institutions to simultaneously fail to function efficiently’ (Furfine, 2003, 113); the other is

‘the risk that failure of one or a small number of institutions will be transmitted to others

due to explicit financial linkage across institutions’ (Furfine, 2003, 113). Furfine points

out that these two types of systemic risk cannot be entirely separated. His methodology

is similar to Angelini, Maresca and Russo’s but he introduces a recovery rate for the

assets of failed banks. He tests recovery rates of 60% and 95%3 finding that for a

recovery rate of 60%, the system experiences few contagion or knock-on failures, with

only one case contributing to the second iteration in which the largest borrower fails. The

largest loss is 0.8% of total bank assets. When the recovery rate is 95%, contagion fails

to occur. Overall, contagion resulting from direct inter-bank linkages does not in Furfine’s

estimation present a threat to the banking system.

Upper and Worms (2002) examine credit exposures in the German inter-bank market

and model the structure of this market as a two-tiered structure using Allen and Gale’s

(2000) model of institutional linkages. They overcome the difficulties of data availability

on inter-bank lending by constructing data at the end of December of 1998 from monthly

balance sheet ratios. They demonstrate that so called “completely–connected”

structures are less vulnerable to contagion than “incomplete” ones. They also

demonstrate that safety mechanisms, like institutional guarantees, reduce the magnitude

of risk. They further test the sensitivity of these results to the loss rate (alternative to the

recovery rate in Northcott (2002) and Furfine (2003)) obtaining robust results.

McAndrews and Wasilyew (1995) also follow the methodology of Humphrey (1986),

but the purpose of their study is to identify factors which could significantly increase the

level of systemic risk. The variables identified and tested by McAndrews and Wasilyew

include the number of banks, the size of the payments, and the probability of exchange

3 The recovery rate of 60% of a defaulting bank’s total assets was estimated by James (1991). In other words, typical losses of assets when a bank fails, including the cost of resolution, are around 40%. A 95% recovery rate is consistent with Kaufman’s (1996) estimation for the Continental Illinois case.

10

payments between any two banks. Their results support the hypothesis that the higher

the values of these variables, the higher the level of systemic risk.

A well defined methodology has thus emerged in the literature for testing the extent of

systemic risk within DNS payments systems although it presents somewhat conflicting

results. This default simulation methodology examines the impact of an assumed initial

default by a given market participant and traces the transmission of this failure to other

institutions. Losses are compared against capital and liquidity stocks held at participant

institutions to determine the effect of obligation defaults and the extent of failure

transmission. Systemic risk is measured in terms of the probability of default for any

given institution within the simulation and the extent of losses that arise from a systemic

crisis. To date no study has been published for the Australian case.

3. Methodology The objective of the present study is to evaluate whether the move to an RTGS system

in 1998 significantly reduced payments system risk in Australia. This section outlines the

framework used for modeling payment flows in the Australian DNS system and the

procedure for simulating payment obligation failures within that system.

Payments within various components of the Australian system are made upon receipt

of instructions, whether in paper or electronic form. The collection of all instructions in

these systems generates gross payment flows to and from each of the institutions in the

system. We denote Pij,t as a gross payment from institution i to institution j at time t.

Payments from each institution to all other institutions at time t may be collected to form

a payment flows matrix, Mnxn,t for the entire system as follows:

(2)

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

=

tnntn

tij

ttt

tnttt

tnttt

t

PPP

PPPPPPPPPPP

M

,,1

,

,33,32,31

,2,23,22,21

,1,13,12,11

....................

..

..

where P11,t = P22,t = … Pnn,t = 0

In this matrix, the total value of payments by bank i is given by the sum of elements in

row i. This is shown in expression (3). Total receipts by bank i are given by the sum of

elements in column i of (2) which are shown in expression (4):

11

(3) ∑=

n

jtijP

1,

(4) ∑=

n

jtjiP

1,

For the entire system, the value of payouts VP,t and receipts VR,t at time t form vectors (5)

and (6) respectively:

(5)

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

=

∑

∑

∑

=

=

=

n

jtnj

n

jtj

n

jtj

tP

P

P

P

V

1,

1,2

1,1

,

...

(6) ⎟⎠

⎞⎜⎝

⎛= ∑∑∑

===

n

itin

n

iti

n

ititR PPPV

1,

1,2

1,1, ...

The total value of transactions S for the entire system at time t is:

(7) ∑∑= =

=n

i

n

jtijt PS

1 1,

Following Northcott (2002), we define the bilateral net position between banks i and j,

BNPij,t , as follows:

(8) tijtjitij PPBNP ,,, −=

where BNPij,t > 0 implies a net receipt by bank i with respect to its dealings with bank j.

The multilateral net exposure of bank i to the entire payments system, MNPi,t at time t is

defined as follows:

(9) ∑=

=n

jtijti BNPMNP

1,,

where MNPi,t > 0 implies a multilateral net receipt by bank i from the system. Each

simulation will be started with the assumption that all previous transactions have been

settled, that is:

12

(10) 01

1, =∑=

−

n

itiMNP

Once the above payment flows for each time period t throughout the day have been

calculated, the aggregate daily payments position matrix may be calculated as :

(11) ∑=

=τ

1ttMMD

where τ is the number of time intervals during the day.

For the DNS system, although payment instructions are generated at any time

throughout the day, they are not settled until the morning of the next business day. More

importantly, these payments are settled on a net multilateral basis. In practice, each

bank sums up its payments to and receipts from each of its counter-parties before

submitting instructions to the RBA at the end of the day. The RBA computes a daily

payments position matrix MD from which the bilateral and multilateral positions can be

deduced through (8) and (9). Net payments are posted to ESAs at 9.00 am on the next

business day.

Following Humphrey (1986), Angelini, Maresca and Russo (1996), and Northcott

(2002), an exogenous shock is assumed to cause the failure of bank d (d œ n) in the

DNS system at the end of the business day. This bank, therefore, fails to settle its

payments system obligations. Payments to and from the failed institution are unwound,

and the bilateral and multilateral positions of surviving participants are revised.

Deterioration in the payments positions of survivors may be sufficient to cause a second,

third or subsequent round of failures, requiring further position revisions. An iterative

process of failure, payment position revisions and further failure is set up by the initial

failure, causing a domino effect through the financial system. The iterative process

ceases when no additional institutions fail. This procedure may be described in terms of

10 steps.

Step 1

Let one institution be assumed to fail at the end of the day so that it cannot meet its

payments system obligations. This institution, designated institution d, will have the

following “failure status index”:

10, =dF (12)

13

A value of 1 for this index indicates that a bank fails and a value of 0 indicating that it

does not fail.

Step 2

All payments to and from bank d are unwound from the end of day calculations, and the

bilateral and multilateral obligations of all surviving institutions are recalculated. The first

step in this recalculation process is to generate what we will call settlement adjustments

for each surviving bank. The settlement adjustment for surviving bank i in the first round

of recalculations is given in equation (13) as the difference between bilateral payments

to and from bank d :

(13) 0,0,0,1, iddiidi BNPPPSA −=−=

where SAi,1> 0 implies an improvement in the bilateral net position of the surviving bank

i; and SAi,1< 0 implies a deterioration in bank i’s payments position. Using this variable,

we compute the adjusted multilateral net position for bank i in the system as MNPi,1* in

equation (14):

(14) 0,0,1,0,*1, idBNPiMNPiSAiMNPiMNP −=+=

where MNPi,1* > MNPi,0 implies an improvement in the multilateral net position of the

surviving bank i; and MNPi,1* < MNPi,0 implies the multilateral net position of the surviving

bank becomes worse.

Step 3

For each survivor in the system, we next compute the credit exposure caused by the

unwinding. We define the credit exposure of bank i as:

i

ii K

SACR 1,

1, = (15)

where Ki is the capital of bank i.

Step 4

We also compute the liquidity exposure of each institution in the system associated with

the unwinding. We define the liquidity exposure of bank i as:

14

i

ii LA

SALR 1,

1, = (16)

where represents the liquid assets of bank i. The liquidity exposure ratio reflects the

bank’s ability to use its liquid assets to cover its payments position deterioration.

iLA

Step 5

The credit and liquidity exposures measured in Step 4 constitute two criteria that may be

used to establish whether the unwinding of payments causes further bank failures in the

system. Capital failure after the first round of recalculations is indicated by a value of one

for a “capital failure status index” determined as follows:

11, =CiF (17)

when (18) ⎪⎩

⎪⎨⎧

−<<

10

1,

*1,

iCRMNP

i

The second failure criterion is satisfied after the first round of recalculations when a

bank’s liquidity exposure is too large to be covered by its liquid assets. This is given as

follows:

11, =LiF (19)

when (20) ⎪⎩

⎪⎨⎧

−<<

10

1,

*1,

iLRMNP

i

Credit failure and/or liquidity failure notwithstanding, a surviving bank only fails if its

revised multilateral position is negative. Even where an institution’s net multilateral

position is positive, it may struggle to avoid failure where significant net income from the

payments system is lost. Humphrey (1986, 111), therefore, argues that the double

criteria approach underestimates systemic risk because a bank with a final positive

multilateral net position may still experience a reduction in its position too big to be

absorbed by its capital or liquidity stocks. However, while Humphrey is correct, it seems

better not to over-estimate risk so that the finding of significant systemic risk indicates an

unambiguous need for a policy response.

15

Step 6

The application of Step 5 generates a further number of failures as a result of the initial

default of bank d. Let lC,1 of these failures be due to the credit criterion after the first

round of recalculations and lL,1 be those due to the liquidity criterion. These institutions

thus have the following values for the failure status index respectively:

),,1(1 1,1,1, CCCk DkF λK∈∀=

),,1(1 1,1,1, LLLk DkF λK∈∀=

The union of sets DC,1 and DL,1, denoted as D1, gives a set of l1 = lC,1 + lL,1 total failures.

With the failure of these additional institutions another iteration of settlement

adjustments, revised net multilateral positions and test applications must be performed.

Settlement adjustments and revised net multilateral settlement positions in iteration z for

bank i will be given by its settlement adjustment from the previous iteration plus the sum

of original net bilateral payments between bank i and each bank k which failed in the

previous round of recalculations:

∑−

=−− ∈∀−+=

1

110,0,1,, )(

z

kzkiikzizi DkPPSASA

λ

(21)

zizizi SAMNPMNP ,*

1,*, += − (22)

We may once again calculate the credit and liquidity exposure of each institution for

iteration z as:

i

zizi K

SACR ,

, = (23)

i

zizi LA

SALR ,

, = (24)

And institution i suffers a further knock-on credit or liquidity failure according to:

1, =ziCF (25)

when (26) ⎩⎨⎧

−<<

10

,

*,

zi

zi

CRMNP

16

The second failure criterion is satisfied when a bank’s liquidity exposure is too large to

be covered by its liquid assets. This is given as follows:

1, =ziLF (27)

When (28) ⎩⎨⎧

−<<

10

,

*,

zi

zi

LRMNP

Step 7

Additional credit failures are indicated in Step 6 where 1,, −> zCzC λλ indicating the need

for a further iteration of settlement adjustments and revised net multilateral position

recalculations, and the application of credit failure tests. Iterations cease for the credit

sub-simulation when 1,, −= zCzC λλ . A similar argument applies for the liquidity simulation

where iterations cease once 1,, −= zLzL λλ .

Step 8

Once the conditions identified in Step 7 for completion of the iterative procedure are met,

the resulting values for zC ,λ and zL,λ give the total number of institutional failures as

( zC ,λ +1) and ( zL,λ +1) respectively. The corresponding values for the FCi,z and FLi,z

variables in each simulation define two vectors FC and FL of zeros and ones. The value

of monetary losses due to the crisis can be calculated using these vectors as follows:

FMDAFMDAL ⋅⋅−⋅⋅= ' (29)

where , and MD is the day’s payments position matrix as defined in (10)

above.

)1,...,1,1,1(1 =×nA

Step 9

Steps 1 to 8 are repeated for each of the n banks acting as the initially defaulting bank d.

That is, d progressively takes values i = 1, 2,…,n.

Step 10

Steps 1 to 9 are repeated for each of the ten business days in each of the two data sets.

17

Steps 1 to 10 thus entail n × 10 simulations for both the credit failure and liquidity failure

criteria producing n × 10 × 2 tests in all. The degree of contagion is measured for each

simulation using:

the value of monetary losses;

the number of iterations required until no further knock-on effects are

experienced;

the default vector F which defines the distribution of institution failures.

These 10 steps were applied to two different data sets and the results compared. Data

Set 1 contains estimated residual DNS data for two five day periods in 2003 after the

introduction of the RTGS system in 1998. We call this the Residual DNS system. Data

Set 2 contains RTGS data from the same two five day periods in 2003, but assumes that

the payment flows represented by this series were settled at the end of the day on a

DNS basis. This second data set represents what we call the Pseudo DNS system. It

captures the payment flows that would have been settled using the DNS system at this

time had the RTGS system not been introduced in 1998. If the introduction of RTGS has

had a significant influence on the level of settlement risk in the Australian payments

system, we would expect the degree of systemic risk in the Pseudo DNS data set to be

significantly greater than that in the Residual DNS data set.

Some problems were experienced with obtaining data for these two sets. The nature of

these problems and the solutions devised to resolve them are discussed in the following

section.

4. Data Availability: Problems and Solutions The simulations described in the previous section, require three types of data. Firstly, net

bilateral payment obligations at the end of day are required for each of ten days in the

desired sample period. This corresponds to one nn× MD matrix as defined in

expression (11) for each of the ten days. Secondly, a similar set of matrices is required

for the Pseudo DNS system which will be compared to the results from the DNS

simulations to assess whether systemic risk has been reduced by the introduction of

RTGS for high value payments. Thirdly, key balance sheet items are also needed to

construct default tests including:

Capital for each bank to test for failure using the solvency criterion;

Liquid assets for each bank to test for failure using the liquidity criterion.

18

Much of this data was either not kept by the RBA for more than a few weeks or could

not be released under the commercial in-confidence provisions of the Reserve Bank Act

1959. Data was, however, available for aggregate payments at 15 minute intervals for

the RTGS system. This aggregated data across all participating banks and other

financial institutions was used to generate two synthetic data sets that reflect the

essential features of the Australian payments system. The procedure used to generate

these synthetic data sets is described later in this section. It employs aggregate data for

the first week in January and the first week in May 2003. Altogether this provided data

for 10 working days. May was selected following the methodology employed by the

Australian Payments Clearing Association (APCA), which collects payments system data

in that month because business is around its yearly average. January was selected in

addition as a quieter month to provide some feel for seasonality. This data is shown in

Table A3 in the Appendix.

The data generation process described below was, therefore, used to obtain gross

bilateral obligations at 15 minute intervals, which was then used to estimate Residual

DNS data for the sample period and to construct the Pseudo DNS data needed for

evaluating the impact of RTGS introduction. DNS positions were generated by fixing a

closing time each day and summing real time gross transactions for the day at that time.

In Australia, net amounts from the previous day’s DNS transactions are settled through

the Reverse Bank Information and Transfer System (RITS) at 9:00am. This data is,

however, unavailable. We chose, therefore, to estimate the Residual DNS system by

allocating payments between 9am and 10am each day to the Residual DNS system.

Such an approach is somewhat arbitrary and is likely to significantly overestimate the

volume of residual DNS payments. An alternative approach would have been to allocate

a smaller fraction of the day’s payments to the DNS System. However a finding of risk

reduction using this approach would only be confirmed given this bias. This is in fact

what we find, as explained below.

Data on key balance sheet items are reported by the banks to the Australian

Prudential Regulation Authority (APRA). Data relating directly to the sample weeks in

2003 had not been released at the time the study was conducted, so we chose the

nearest released statistic, dated 31 March 2003, on bank assets and liabilities from

APRA (2002). Data on institution-specific capital is not released by APRA so capital was

calculated by subtracting liabilities from assets for each institution. Although earlier

research uses only a proportion of bank capital, such as Tier 1, to conduct institution

19

failure tests, total shareholders’ funds is used in this study since we assume that all

shareholder funds are available to rescue a bank during a solvency crisis.

For some institutions, especially branches of foreign banks, this procedure generated

negative capital values. This is clearly an unacceptable assumption since parent capital

would be available for these institutions in the event of a failure. However, rather than

assuming that these banks have access to large amounts of capital from outside the

system, we decided to model these institutions as small local operations reflecting their

economic impact on the system. To overcome the problem of negative capital, the

absolute value of capital was taken. While this procedure reverses the order of

institutions likely to fail, exact institutional identity is suppressed in this study where the

focus is on systemic characteristics. Once again this is likely to over-estimate the

amount of risk in the system by increasing the likelihood that these institutions will fail.

This feature of the approach will receive further attention later in the paper.

The definition of liquid assets used includes cash, securities eligible for repurchase,

transactions with the RBA, bank bills and certificates of deposit (CD) issued by banks

(provided the issue is rated at least ‘investment grade’), deposits held with other banks

net of placements by the other banks and any other securities approved by APRA.

The data obtained for the two periods in 2003 covered 47 institutions. It was decided to

remove three institutions due to lack of data availability to calculate capital. In addition it

was decided to remove the RBA on the grounds that the objective of the study was to

test systemic risk without central bank intervention and although the RBA trades in the

foreign exchange and money markets which impact payments system aggregates, the

value of this trading is not significant. The exclusion of these institutions, therefore, left

42 banks in the data set.

The problem posed by the availability of only aggregate payments data rather than

gross bilateral payment obligations was to turn the scalar St defined in expression (7)

into the 42 by 42 matrix Mt defined in expression (2). This represented a significant

obstacle to the study. This obstacle could be over come, however, if some reliable metric

could be found that was correlated with the average share of each bank’s payments

activity. Banks do not release specific payments business information in their annual

reports but a choice of several other bank-specific statistics is available including various

relative balance sheet sizes, such as total deposits, and various off-balance sheet

business items such as derivatives trading.

20

The driving force of RTGS transactions in Australia clearly comes from financial

market transactions in wholesale amounts requiring quick settlement. The most active

markets are the foreign exchange (FX) markets, the money markets, the bond markets

and the share market. Settlement arrangements for these markets take place via the

RITS system. The statistical bulletin of the RBA (Reserve Bank of Australia, 2003)

shows that, among the systems feeding into RITS, the SWIFT PDF system is the

largest, with its FX markets settlements constituting around 68% of total RTGS

settlements.

In order to ascertain whether FX trading would constitute a reasonable proxy for

payments system involvement, total RTGS transactions were regressed against total FX

derivatives activity for the 1998 to 2003 period. Monthly RTGS transaction values were

summed to quarterly values for the September 1998 - March 2003 period, giving 19

observations. These were regressed against monthly FX derivative trading data for the

same period. The results are presented in equation (30) and Table 1.

iii FXDRTGS ε++= 1429.094550 (30)

Equation (30) indicates that on a quarterly basis, variations in RTGS activity equals

about fifteen percent of the variation in the value of turnover in the FX derivatives

market. The high t value and low standard error for the FX coefficient in this equation,

shown in Table 1, suggest that this coefficient is statistically significant.

Variable Coefficient Standard Error

t-statistic p-value R2

C 94 550 28 179 3.36 0.0038 0.82

TOTAL FX 0.1429 0.016 8.76 0.0000

Table 1 Regression of RTGS transactions value on FX trading

Other off-balance sheet variables, including total off-balance sheet business, total

interest rate contracts (IRC) and total FX contracts did not perform as well as FX

derivatives contracts. The results for the first two of these additional regressions are

shown in Tables 2 and 3 below respectively. The results for total off-balance sheet

business is not presented because, although it is significant, this statistic is not available

for individual banks and could not, therefore, be used in the disaggregation process.

21

Variable Coefficient Standard Error t-statistic p-value R2

C 183 000 16 500 11.09 0.0000 0.85

TOTAL IRC 0.0717 0.0074 9.73 0.0000

Table 2 Regression of RTGS transactions value on IRC value.

Variable Coefficient Standard

Error t-statistic p-value R2

C 131 000 25 000 5.21 0.0001 0.89

TOTAL IRC 0.0428 0.0131 3.27 0.0048

TOTAL FX 0.0674 0.0265 2.54 0.0218

Table 3 Regression of RTGS transactions on IRCs and total FX transactions.

The coefficient for interest rate contracts in Table 2 suggests that it is statistically

significant but its value is significantly lower than that for FX derivative contracts. The

same is true for both interest rate contracts and total FX contracts as shown in Table 3.

In addition, the proportion of money market transactions settled in the RTGS system is

smaller than that for FX markets. It was decided, therefore, to use the value of FX

derivatives contracts as a proxy for payments system involvement and to use bank

specific data on this variable as a basis for disaggregation of the total payments data

made available by the Reserve Bank.

The aggregate value of FX derivative contracts is released by the RBA and the four

major banks document this item in their financial reports. It is, however, difficult to obtain

this data for smaller banks. It was decided, therefore, to use a differential approach for

the big four institutions and all remaining payments system participants. For institutions

other than the big four, total liabilities were employed as an indicator of payments

system activity on an a priori basis. This data was readily available from APRA.

To generate the 42 × 42 matrix, Mt, from the scalar St, we proceed in two steps. We

first obtain individual bank proportions of payments system business using a

combination of FX derivative contracts for the big four banks and total liabilities for the

smaller banks. We secondly, apply these proportions to the aggregate payment flow

value for each 15 minute time interval in the sample period obtained from the Reserve

Bank to obtain the payment flows matrix for each 15 minute interval.

22

Step 1: Estimating the share of each bank in payments activity

The total daily value of FX derivative trading, denoted TFXD, and the value of FX

derivative trading for each of the big four banks, denoted FXDi for i = 1 to 4, was used

firstly to calculate the share of each of the big four banks in total FX derivative trading:

TFXDFXD

VS ii = (31)

Secondly, the sum of the individual shares of the big four banks in FX derivative trading

was calculated as follows:

(32) ∑=

=4

1iiFXDMFXD

The share of each of the other 38 banks in the sample in the sum of liabilities for those

38 banks was calculated:

∑=

= 42

5ii

ii

L

Lb 425 toi =∀ (33)

The shares of these 38 institutions in the total FX derivatives market was estimated as

follows:

TFXD

MFXDTFXDbVS i

i][ −×

= 425 toi =∀ (34)

Equations (31) and (34) together determine the shares of each of the 42 banks in the

total FX derivatives business such that the sum of these shares is exactly unity. The sum

of total foreign exchange derivative contracts for the four major banks was $1 523 120m.

The sum of all such contracts for the same period was $2 100 286m. The four largest

banks thus account for 73% of total FX derivatives trading. The resulting share of each

bank is shown in Table 4.

Step 2 Obtaining the RTGS payments flow matrix

Having estimated the share of each bank in payments activity, we must now transform

the scalar St in expression (7) into the 42×42 matrix Mt in expression (2). If the 42 ×1

23

Bank VSi Bank VSi Bank VSi

1 0.0898 15 0.0013 29 0.0042 2 0.1306 16 0.0029 30 0.0001 3 0.3211 17 0.0234 31 0.0025 4 0.1837 18 0.0031 32 0.0019 5 0.0073 19 0.0085 33 0.0108 6 0.0050 20 0.0182 34 0.0007 7 0.0010 21 0.0079 35 0.0018 8 0.0079 22 0.0040 36 0.0023 9 0.0537 23 0.0020 37 0.0001 10 0.0259 24 0.0098 38 0.0039 11 0.0049 25 0.0119 39 0.0034 12 0.0048 26 0.0241 40 0.0005 13 0.0008 27 0.0034 41 0.0035 14 0.0030 28 0.0010 42 0.0033

Table 4 Bank Shares in Payments Activity – VSi

vector VS determined above, is pre-multiplied by St , we interpret the result to be the 42

×1 vector of total payments by each bank defined in equation (5). Thus we have:

(35)

⎟⎟⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜⎜⎜

⎝

⎛

==⋅

∑

∑

∑

=

=

=

42

1,42

42

1,2

42

1,1

,

...

jtj

jtj

jtj

tPit

P

P

P

VVSS

The total payment by each bank must now be allocated to each of the 41 other individual

banks in the system. This is done using (35):

0=ijP for ji =

i

j

jijij VS

VSPP

−×= ∑

= 1

42

1 for all ij ≠ (36)

Equation (36) takes the scalar of payments made by bank i (the sum of row i in matrix

Mt) and allocates this across the remaining n-1 banks using the same proportions shown

24

in Table 4. Given that bank i makes no payments to itself, the proportion of bank j’s

share in the total payments made by bank i is bank j’s own proportion VSj over the sum

of proportions for banks other than i. This last variable is identical to unity minus the

proportion for bank i itself. Application of this process to each of the scalars in (35) for

each j generates matrix Mt. The Appendix contains an example of the disaggregation

procedure for a 3 × 3 case.

There are two problems with the data transformation process described above. The

first is the existence of bias in the way data is allocated. In step 1 of the process, the

scalar St, may actually be decomposed in two ways: using the proportions shown in

Table 4 to obtain total payments made by each bank (the approach we have taken

above), or using these proportions to obtain total receipts received by each bank. These

two procedures generate different versions of Mt. In addition, according to this

procedure, the bank with the smallest share in the system is always allocated a negative

multilateral net position, while the bank with the largest share is always allocated a

positive multilateral net position. If receipts are calculated at step 1, the results are

reversed. This observation is demonstrated in the Appendix to be a general result. It is

hard to justify the constant allocation of a net negative position to the same institution.

Such an outcome would lead to financial problems at both the institutional and systemic

levels. It is more realistic to assume that payments and receipts for a bank are balanced

over time. The payments position matrix was, therefore, generated following procedure

(a) but this matrix was transposed randomly in order to ensure that each institution

experienced both positive and negative net multilateral positions through the course of a

day. The second problem with the data allocation process outlined above is that the

proportions of payments activity are effectively assumed to be constant. Again this is

unrealistic. The VS proportions estimated by (31) and (34) should be interpreted as

average proportions, which vary from time period to time period in line with economic

and activity fluctuations. A random perturbation was thus applied to the ratio vector

shown in Table 4 at each time interval to vary these proportions slightly. The range of

the perturbation chosen was from 0.92 to 1.084 for each ratio with one of the major

banks perturbation determined residually to maintain the sum of ratios at unity.

4 The range is to ensure that the perturbed ratios of vector VS remains positive after adjustments.

25

The above process was thus used to transform the data supplied by the Reserve Bank

into a series of square payments flow matrices of order 42. 48 such matrices were

generated in each day of Week 1, and 40 in each day of Week 2. These payments

position matrices were used in the construction of the DNS positions required by the

simulation process.

tM

Having obtained the matrix of bilateral payment flows at each 15 minute time interval in

the sample period, the Residual DNS and Pseudo DNS data sets were constructed.

Within the Australian payments system, settlements from its DNS component are

processed via RITS on the morning of next business day. This is called the ‘9am Batch’

by the RBA (Reserve Bank of Australia, 2001). If we assume that RTGS transactions

between 9:00am to 10:00am reflect the payments relationship of the banks in the

various component systems, the netted DNS position can be generated by summing the

payments flow matrixes during that period. Thus the payments position matrix in

expression (11) would be given as follows:

(37) ∑=

=4

1ttMMD

It should be emphasised that this assumption is likely to over-estimate the volume of

payments in the Residual DNS system. But the approach of this study has been to be

conservative on the impact of RTGS on systemic risk and this assumption is consistent

with the broad approach.

The Pseudo DNS data set is obtained by summing payments flow matrices across the

entire business day as follows:

, ∑=

=τ

1ttMMD 48=τ in Week 1 (38)

40=τ in Week 2

These two data sets may be used to run the default simulations described in the

preceding section. Given the synthetic nature of the data used to run these simulations

and the assumptions underlying the data generation process, great care must be taken

when drawing conclusions from the results of these simulations. In particular, we cannot

claim that the system simulated in this study is the Australian system itself. However, the

parameters of the simulated system, its broad dimensions and its interlinkages, are

derived from the Australian system. Thus, provided care is taken interpreting the risk

26

associated with the Residual DNS system and the role of local branches of foreign

banks, inferences about the general risk characteristics of the Australian system can be

drawn from the simulations in this study.

5. Data Characteristics This section reports the key features of the data generated by the procedure outlined in

the previous section. The mean daily transaction value for the RTGS system in 2002

was $123 805m; it was $112 387m for the week in January 2003 (Week 1) and

$118 802m for the week in May 2003 (Week 2) (Reserve Bank of Australia, 2003). The

average for our two sample weeks was higher than these values at $125 551m and

$139 077m for January 2003 and May 2003 respectively. The value of daily transactions

for the two sample weeks did not vary much, ranging from a Day 6 low of around

$118 000m to a Day 9 high of $153 000m.

Table 5 gives the statistics of the 48 time periods into which each day in Week 1 was

divided and the 40 periods per day in Week 2. The mean value of trading in each time

interval in Week 1 was lower than in Week 2 because the operating hours were 20%

longer; the total value of transactions for each day did not greatly vary.

Week 1 Day 1 Day 2 Day 3 Day 4 Day 5

Mean $2688m $2560m $2708m $2551m $2571m

Week 2 Day 6 Day 7 Day 8 Day 9 Day 10

Mean $3015m $3553m $3724m $3916m $3622m

Table 5 15-minute RTGS Data in the Australian System

Figure 3 shows the distribution of transaction values in the two sample weeks. Once the

system opens at 9:00am, payments reach a peak around 9:30am. At 9:00am the net

positions of each bank for the retail systems are posted to the ESAs. The system

reopens for RTGS payments at 9:15 at which time there is already a queue of RTGS

payments waiting to be settled. The payments in the queue settled from 9:15 to 10:00

explain the first peak in value during the day. From 10:00am to 3:00pm payment values

27

0

0.02

0.04

0.06

0.08

0.1

9:00 10:30 Noon 1:30 3:00 4:30 6:00 7:30 9:00

Time

Prop

otio

n of

tota

l dai

lytr

ansa

ctio

ns

Week 1

Week 2

Figure 3 Proportion of Daily Settlement Value by RTGS

randomly walk within a fixed range. A second peak occurs around noon, and the third

and longest peak occurs between 3:00pm and 5:00pm.

An examination of Figure 3 indicates that there are great differences in the timing of

payments between the two sample weeks. Firstly, they have differently shaped peaks,

with Week 2 (May) peaks being flatter and longer than in Week 1 (January). Secondly,

transactions may be conducted until 9:00pm in summer (Week 1), two hours longer than

usual because of the arrangements for continuous linked settlements (RBA, 2001). This

may be a reason for the lower value of the afternoon peak in Week 1. The timing

pattern, however, is quite stable. It follows that they must reflect the liquidity

management strategies of the banks, together with the institutional arrangements of the

respective payments systems and financial markets.

The data generation procedure described in the previous section produced a total of

495 42 × 42 matrices. These matrices are not reported due to space constraints but the

matrix for the second time interval on Day 1 of Week 1 is shown in Table A4 in the

Appendix by way of illustration. This matrix indicates that total payments by Bank 1 at

9:30am on Day 1 of Week 1 were $237m. The largest share of these payments was

$95m to Bank 3 (representing 40% of Bank 1’s total payments). The second largest

payment was $50m (representing 21% of Bank 1’s total payments) to Bank 4, and the

smallest payment was $0.013m (representing 0.005% of Bank 1’s total payments) to

Bank 30. Total receipts for Bank 1 were $196m in this time interval, with the largest

receipt of $72.7m being from Bank 3 (representing 37% of Bank 1’s total receipts). The

28

second largest receipt was $34m (representing 17% of Bank 1’s total receipts) from

Bank 4, and the smallest receipt was $0.015m (representing 0.008% of Bank 1’s total

receipts) from Bank 30. Among all of Bank 1’s counter-parties, Bank 3 (which is the

largest bank in the system) represents that with the strongest payments linkage to Bank

1 in this particular time interval.

Net Position Total Receipts Total Payouts

Count 42 42 42

Mean $0.00 $631.9m $631.9m

Standard Deviation

$26.6m $217.2m $231.5m

Skewness -5.7 3.3 3.6

Kurtosis 36 11 14

Median $9.3m $123.0m $112.0m

Range $1293.2m $6786.7m $7839.2m

Minimum $240.7m $2.0m $2.0m

Maximum $1052.5m $6788.7m $7841.2m

Sum $0.0 $26 541.5m $26 541m

Table 6 Statistics of the Multilateral Positions of the System

The ten vectors which represent the Residual DNS system are not reported due to

space considerations but the Residual DNS position for Day 1 is reported in Table A5 in

the Appendix to illustrate the structure of the data. Table A5 indicates that the average

bank’s net payment position is $632m in payouts as well as receipts. Bank 3 had the

largest receipts of $6789m (representing 26% of the system total). The second largest

receipts of $5154m were received by Bank 4. For payouts, Bank 3 also made the largest

with $7841m (representing 30% of the system total), while the second largest were paid

by Bank 4 at $4913m. The smallest payouts and receipts were all made by and to Bank

30, at around $2m on Day 1. There were 39 banks in net positive positions, with Bank 4

holding the largest credit from the system at $241m. Banks 3, 9 and 25 held negative

positions; Bank 3’s net debit to the system being $1052m. Table 6 shows key statistics

29

for the 10-day average multilateral positions. The following section reports the results of

the default simulations applied to these two sets of data.

6. Simulation Results The simulation procedure described in Section 3 was conducted on the two data sets

described in the previous section. Each of 42 banks was assumed to exogenously fail in

turn on each of 10 days in each of these two data sets. In total, this amounted to 420

simulated failures in each set. Data Set 1 contained the synthetic series based on the

estimated Residual DNS data after RTGS was introduced while Data Set 2 contained

the synthetic Pseudo DNS series designed to represent the size of the DNS system of

RTGS had not been introduced. If the introduction of RTGS has had a significant

influence on the level of systemic risk in the Australian payments system, we would

expect the degree of systemic risk in the Pseudo DNS data set to be significantly greater

than that in the Residual DNS data set. Seven key results emerged from the default

simulations conducted on these two data sets.

Result 1 – The Australian system appears to have been subject to limited systemic risk

Tables 7 and 8 summarise the main results when bank capital was used as the failure

criterion, under which the deterioration of a surviving banks’ payments position was

compared to its capital. In the Pseudo DNS system, knock-on failures occurred on Days

1, 3, 4, 7, 8 and 10. However, these occurred in only six out of the 420 simulations, five

of which stopped after the second iteration, and one after the first iteration. These

failures were only initiated by 2 of the 42 banks and losses were relatively low; the

highest loss among the knock on cases was 1.73% of the total value transacted on the

default day or 0.26% of the total assets of the banking system. The low level of potential

losses from the failure of a single bank in the old DNS system suggests that the

Australian payments system was subject to a low level of systemic risk prior to the

introduction of RTGS.

Result 2 – Only the default of large banks trigger systemic crises

Losses triggered by failures of the four major banks are reported in Table 7. It was not

observed that failure of any other institution could trigger contagion. Table 8 shows

losses expressed as percentages of the total value of the day’s transactions and of the

total assets of all the participating banks on different days. Using the alternative failure

criterion that compared the position deterioration with liquid assets, only one simulation

30

demonstrated knock-on effects in the Pseudo DNS system with losses of $2550m. The

impact of a bank’s failure depended on the size of its transactions in the payments

system. Except for one knock-on effect caused by Bank 4, all of the other contagion

failures were triggered by Bank 3 which has the largest proportion of payments in the

system. No regional or foreign bank caused any knock-on effects within the 10 sample

days. The largest settlement adjustment (SA) figure that emerged in any of the failures

occurred on Day 3 when Bank 3 failed. The size of this adjustment was $556m. This was

less than the average stock of capital for institutions in the banking system but more

than the estimated capital of 29 individual banks. It was also greater than the absolute

average multilateral position for that day (which was $74m). It was for this reason that

revision of payments positions involving the largest settlement adjustment was able to

cause knock-on failures.

Systemic risk –Pseudo DNS Systemic Risk – Residual DNS

Trigger defaulting institution

Number of failed banks in 10 days

Value lost in the contagion ($m)

Number of failed banks in 10 days

Value lost in the contagion ($m)

Bank 1 0 0 0 0

Bank 2 0 0 0 0

Bank 3 17 6380 1 1050

Bank 4 1 808 0 0

Table 7 Losses in Simulated System Contagion Failures

Result 3 – The migration to RTGS almost completely eliminates systemic risk

For the Residual DNS system, only one of the 420 simulations showed contagion

following the initial bank failure. This represented only 0.81% of transactions value for

the day and 0.12% of capital for the failing bank. This suggests that the migration to

RTGS for large value payments virtually eliminates systemic risk. This result was

obtained despite the over-estimation of the DNS component of the system discussed

earlier in the paper.

31

Losses to day’s total transactions (%)

Losses to total banks’ assets (%)

Triggering bank Bank 3 Bank 4 Bank 3 Bank 4

Pseudo DNS System

Day 3 1.73 0.0 0.26 0.0

Day 4 0.82 0.0 0.29 0.0

Day 7 0.63 0.58 0.10 0.09

Day 8 0.66 0.0 0.11 0.0

Day 10 0.92 0.0 0.15 0.0

Residual DNS System

Day1 0.81 0.0 0.12 0.0

Table 8 Credit Losses in Simulated System Contagion Failures by Bank and Day

Result 4 – Triggering banks must be in net debit positions to generate contagion

An examination of the failure cases with significant losses indicates that the initially

defaulting banks capable of causing knock-on failures, which we may call ‘triggering

banks’, were originally all in net debit positions to the system. Bank 3, for example, was

the most important triggering bank and this institution was in a net debit position in the

Pseudo DNS system at the end of Days 3, 4, 6, 7, 8 and 10. On Day 7, when the failure

of Bank 4 caused contagion failure, its net position was also negative (see Figure 4).

This is also true for Day 1 in the Residual DNS system. Nevertheless, the negative net

position of large banks does not mean their failure will automatically cause contagion

failure if the scale of this position is not large enough. The debit position of Bank 3 on

Day 6 was even larger than on Days 7 and 8, but there is no knock-on effect from Bank

3 on that day.

Result 5 – Foreign banks are sensitive to systemic risk when using the capital criterion

In all of the simulations, the same few banks tended to be affected by the failure of one

of the major banks. The bank most frequently impacted was Bank 35. This bank failed in

6 cases involving the initial failure of Bank 3 (5 cases) and Bank 4 (1 case). Bank 18

failed 5 times, Bank 17 failed 3 times, and Banks 20, 22, and 25 only once. All the banks

32

-3000-2500-2000-1500-1000-500

0500

1000150020002500

Value of Payments

($m)

1 2 3 4 5 6 7 8 9 10

Day

Bank 1Bank 2Bank 3Bank 4

Figure 4 The Multi-lateral Net Positions of the Major Banks in the Pseudo DNS System

subject to these knock-on effects belonged to Group 3, the foreign bank branches or

subsidiaries. It was assumed that Group 3 banks (foreign bank branches and

subsidiaries) were independent entities; that is, unable to transmit funds to or from their

parent institutions. Since the values of shareholders funds were not available for these

institutions in APRA’s (2002) statistical bulletin, their capital values were estimated from the differences between their total assets and liabilities, which were available. The

assumption of independence creates, however, something of a dilemma. On the one

hand, the simulation results may over-estimate the level of systemic risk. Since branches

are not separately capitalized it could be assumed that any difficulty they experience

would be met with assistance from the parent institution. Because these are the

institutions which tend to fail in the simulations, systemic risk is over estimated by these

simulations. On the other hand, systemic risk may be under estimated because

branches of foreign banks are linked to their parent institutions and overseas branches,

and might well transmit serious problems in other financial markets into the Australian

payments system.

Result 6 – Liquidity management appears sufficient to stem systemic risk

Following Angelini, Maresca and Russo (1996), the present study employed both capital

and liquid assets as solvency criteria. Angelini, Maresca and Russo found that results for

the two criteria were largely the same, but our results contradict this finding. The number

33

of bank failures and the value of funds lost when liquid assets are used as the criterion

for institution failure are substantially lower than when capital is used as the criterion.

Results 1 to 6, therefore, suggest that systemic risk in a payments system with similar

characteristics to that of the Australian system is relatively low. Only major bank failures

appear to have the potential to jeopardize the system, and then not very often. Foreign

banks had a tendency to be the main casualties of any contagion.

7. Conclusion

This paper has undertaken an assessment of the extent of systemic risk in a DNS

system with characteristics similar to the Australian system. Using the simulation

methodology of Humphrey (1986), Angelini, Maresca and Russo (1996) and Northcott

(2002) the degree to which systemic risk has been reduced by the movement in

Australia to RTGS has been tested. Simulations were conducted on two data sets and

the results compared. Data Set 1 used a synthetic series based on Residual DNS data

for two five day periods in 2003 after the introduction of the RTGS system in 1998. Data

Set 2 used a similarly constructed synthetic series based on RTGS data from the same

two five day periods in 2003, but assumed that the payment flows represented by this

series were settled at the end of the day on a DNS basis. This second data set was

labeled the Pseudo DNS system. It captures the payment flows that would have been

settled using the DNS system at this time had the RTGS system not been introduced. If

the introduction of RTGS has had a significant influence on the level of settlement risk in

the Australian payments system, we would expect the degree of systemic risk in the

Pseudo DNS data set to be significantly greater than that in the actual DNS data set.

The results demonstrate that systemic risk in Australia appears to have been limited in

the pre-RTGS DNS system where the default of only two of the largest banks appear to

have been capable of triggering contagion failures and where mainly foreign banks bore

the brunt of systemic losses. However, systemic risk appears to have been completely

eliminated since 1998 by the implementation of RTGS. These results confirm the

findings of previous studies for the payments systems of other countries that payments

system risk appears to have been relatively small and casts doubt on the need for the

implementation of RTGS systems given the associated cost.

34

References Allen, F. and Gale, D. (2000), ‘Financial Contagion’, Journal of Political Economy, 108,

1-33.

Angelini, P., Maresca, G. and Russo, D. (1996), ‘Systemic Risk in the Netting System’, Journal of Banking & Financing, 20, 853-868.

Australian Prudential Regulation Authority (2002), Assets and Liabilities on Australian Books of Individual Banks, http://www.apra.gov.au/statistics/australian_banking_ statistics/ABSAssetLiab200203.txt

Baghot, W. (1873), Lombard Street, London: Methuen.

Berger, A., Hancock, D. and Marquardt, J. (1996), ‘A Framework for Analyzing Efficiency, Risk, Costs, and Innovations in the Payments System’, Journal of Money, Credit and Banking, 28, 696-732.

Bernanke B. (1983), 'Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression', American Economic Review, 73, 257-276.

Flannery, M. J. (1988), ‘Payments System Risk and Public Policy’, in Haraf, W. S. and Kushmeider, R. M. (eds.), Restructuring Banking and Financial Services in America, Washington D.C. : American Enterprise Institute for Public Policy Research, 261-287.

Furfine, C. H. (2003), ‘Interbank Exposures: Quantifying the Risk of Contagion, Journal of Money, Credit and Banking, 35, 111-128.

Goodhart C.A.E. (1988), The Evolution of Central Banks, Cambridge, Mass.:MIT Press.

Humphrey, D. B. (1986), 'Payments Finality and Risk of Settlement Failure', in Saunders, A. & White, L.J. (eds.), Technology and the Regulation of Financial Markets, Lexington, Mass.: Lexington Books, 97-121.

James, C. (1991), 'The Losses Realised in Bank Failures', Journal of Finance, 46, 1223-42.

Kaufman, G. G. (1996), ‘Comment on Financial Crises, Payment System Problems, and Discount Window Lending’, Journal of Money, Credit and Banking, 28, 825-31.

Kuussaari, H. (1996), 'Systemic Risk in the Finnish Payment System: An Empirical Investigation', Bank of Finland Discussion Paper 3/96.

Kuttner K.H. and Posen A.S. (2001), 'The Great Recession: Lessons for Macroeconomic Policy from Japan', Brookings Papers on Economic Activity, 2, 93-185.

McAndrews, J. and Rajan, S. (2000),'The Timing and Funding of Fedwire Funds Transfers', Federal Reserve Bank of New York Economic Policy Review, July, 17-32.

McAndrews, J. J. and Wasilyew, G. (1995), ‘Simulations of failure in a payment system’, Working Papers of Federal Reserve Bank of Philadelphia Working Paper 95-2.

Mishkin F.S. (2001), “Prudential Supervision: Why Is It Important and What Are the Issues?”, in Mishkin F.S. (ed.), Prudential Supervision: What Works and What Doesn’t, Chicago: Chicago University Press, 1-29.

Northcott C. A. (2002), 'Estimating Settlement Risk and the Potential for Contagion in Canada's Automated Clearing Settlement System', Bank of Canada Working Paper 2002-41.

35

Reserve Bank of Australia (1999),'The role of exchange settlement accounts', Reserve Bank of Australia Bulletin, March, 13-18.

Reserve Bank of Australia (2001), Payments System Board Annual Report 2001, Sydney.

Reserve Bank of Australia (2002), Australian Notes, Australian Coins, http://www.rba.gov.au/CurrencyNote/KeyFacts/ index.html

Reserve Bank of Australia (2003a), B04 Banks - Global Off-balance Sheet Business http://www.rba.gov.au/Statistics/Bulletin/B04hist.xls

Reserve Bank of Australia (2003b), C04 Real-time Gross Settlement Statistics http://www.rba.gov.au/Statistics/Bulletin/C04hist.xls

Upper C. and Worms A. (2002), ‘Estimating bilateral exposures in the German interbank market: Is there a danger of contagion?’, Economic Research Centre of the Deutsche Bundesbank, February.

36

APPENDIX The Disaggregation Process: Generating M from S The transformation procedure for generating the matrix M from the scalar S may take

one of two possible approaches:

(a) the approach described in the paper of breaking S into payments made by each

bank via the application of VS to S. The resulting amounts are interpreted as

payments made by each bank as indicated in expression (5). These amounts are

then broken down further to obtain the individual items along the corresponding

row of M in expression (2);

(b) St may be post multiplied by VS and the result interpreted as the vector of total

receipts, VR, received by each bank at each time interval defined in equation (6).

The elements of VR may then be allocated among the other 41 banks in the

system to obtain bilateral gross payment entitlements for bank i .

These procedures yield different results as indicated with the following example.

Suppose there are three banks (banks A, B, C) in the system from 9:45am to 10:00am

and that the total value of transactions for the system is S = 100. The vector of

participant ratios, VS', is given by (0.2 0.3 0.5). If we follow sequence (a) thee are

two steps:

Step 1

In order to allocate the aggregate transactions value S = 100 among the 3 participants,

we multiply S by VS to obtain:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

503020

PV

Step 2

To allocate total payments by A, B and C to their counterparts we apply (34). For

example, A to B will be 20× (0.3/(0.3+0.5)), A to C will be 20× (0.5/(0.3+0.5)).

This generates the payments flow matrix, , in Table A1. If we follow sequence (b), the results are as shown in Table A2.

tM

37

Bank A B C Total Receipts Net Position

A 0 7.5 12.5 20 -8.6 B 8.6 0 21.4 30 -7.5 C 20.0 30.0 0 50 16.1

Total Payments 28.6 37.5 33.9 100 0

Table A1 Illustration of the data allocation process (payouts allocated first)

Bank A B C Total Receipts Net Position

A 0 8.6 20 28.6 8.6 B 7.5 0.0 30 37.5 7.5 C 12.5 21.4 0 33.9 -16.1

Total Payments 20.0 30.0 50 100.0 0

Table A2 Illustration of the data allocation process (receipts allocated first)

Proof of proposition that the bank with the smallest payments share will always have a negative multilateral payments position.

Let there be only three banks in the system and let the shares of these banks in the

payments system be ),,(' χβα=VS with

;10;1<≤≤<

=++χβα

χβα (A1)

Suppose the total value of the payments transactions is S, and S = 1

Following the framework outlined in Section 3 of the paper, the payments flow matrix M is

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

333231

232221

131211

PPPPPPPPP

M where are the payments from banki to bankj realising

that = = = 0.

ijP

11P 22P 33P

38

The total payouts of bank1: (A2) ,3

11 α=∑

=jjP

The total payouts of bank2: (A3) ,3

12 β=∑

=jjP

The total payouts of bank3: (A4) ,3

13 χ=∑

=jjP

If we distribute total payments made by each bank to its counterparties using VS we

obtain:

αβα−

×=112P

αχα−

×=113P

βαβ−

×=121P ×= β23P

βχ−1

χαχ−

×=131P

χβχ−

×=132P (A5)

Thus, the total receipts of bank1 are:

χαχ

βαβ

−×+

−×=++=∑

= 11312111

3

11 PPPP

ii (A6)

while from (A2) total payments made by bank1 are . Since S = 1 α=∑=

3

11

jjP

the net payment position of bank1 (BNP1) is:

( )( ) )321(11

11

3

11

3

111

βχαχβ

α

αχ

αχβ

αβ

−−×−−

=

−−

×+−

×=−= ∑∑== j

ji

i PPBNP (A7)

,01,01,0 >−>−> χβα andQ (A8)

Therefore the sign of (A7) will be determined by

βχα 321 −− . (A9)

From (A1), we have 310 ≤< α and letting

39

,3x

=α

;)3

1(21

;)3

1(21

ux

ux

+−=

−−=

χ

β (A10)

where and 10 ≤< x210 ≤≤ u (A11)

Putting (A10) into (A9)

[ ] ( )( )[ ]222 36131213362

121321 uxxuxx −−+−=−−+−=−− βχα (A12)

Q 10 ≤< x

( )( ) 013 ≤−+∴ xx

Q 036 2 ≤− u

∴ 0321 ≥−− βχα (A13)

Thus from (A8) and (A13), we conclude that (A14) 01 ≥BNP

Similarly, the net payments position of bank3, can be proved to be negative 3BNP

( )( ) ( αβχβα

χ )

χ

32111

3323133

−−−−

=

−++= PPPBNP (A15)

the sign of (A15) is determined by αβχ 321 −− (A16)

Putting (A10) and (A11) into (A16)

[ ] ( )( )[ uxuxuxuxx 61661126

61321 2 −−+=−−+=−− αβχ ] (A17)

Q ,10 ≤< x

∴ ( )( ) 016 ≤−+ xux

06 ≥uQ

∴ 0321 ≤−− αβχ (A18)

Thus . 03 ≤BNP

TabIeA3 Aggregate IITC,S Datå at 15 minute interr¡als for ro business days in zoo3

Time 6.I¡n TateD t.t¡D 9*t¡¡ lOrtaD 5-Mry 6-M¡y 7'Dl.ty 8-M¡y 9-May

9:00 0 0003.994,552,609 5,A24,544,287 4,711,124,2315,271,818,123 5.426,184.088 4,988,747.518

10.191,94.î19 4,957,763.471 6,110,117.1753.M,154,987 3,62,397,141 2,983,155,5022.013,265,403 1,710.157.134 5.210,806,58

3,66,480.97015,807.590,375

2,3æ,90.5704,800,632.96E

3,813,517.Æ2s23,æ'7,4s9

83.118.8323,382,082,4284,41,009,650

2,947,821,1957,073,ffi,9912.ã3.312,S96,111,360,9821.E57,989,528

2651,æ5,275î,765.681,446

317,5æ,434? ,237 ,O10,7725,197,0S4,529

3,910,il6.7991614,æ7,7402,098,250,9742,013,735,4361.417.393.3295,0s,647,5962,47 ,ã13,2834,914,65,007

2,714,259,9953.32,8S,1342.539,7ø,341î.{5,99,8æ

795,341,207æ0,957,168

1,S02,848,773

1,57î,5{,6781,032,293,308

623.750.500749,119,%

2725.990,200891,439,200

1,03î,150,3501S,831,276

2.078.195,11739,928,754m,458,530

4,869.319.6037,814,483.824

2,481,198,9393,12 1,985,892

5,570,093,S{i781,762,652

6,761,760,9783,577,69.il7

871,558,5293,785,309.9383.975,E76,748

s.308.2.3205,429.700.7184,070.{9.æ1

865,469,{71.1æ.æ7.7353,ú3,27,7573.29,047.193

938,64,345I,S95,92,208{,361,109,æ54,427,rc,3734,497,242,8333.æ8.919,8184.780.S20.604,799,ü5.973,978,788,€15,36.42,9891.449,907,7152,1æ.&5,8661.833.&3.784

417,404,7s1355.871.400249,A71,769

I ,1 03,567, 1 46

932,81 1,798

681,275,48871.013.076

1.040.259.691.412.157.5682,040,9æ,316

266,558,S21.349.437,8701.æ1.333.æ7

883,211.400

16,310

1,3æ,0000

0

0

00

0

4.431 .120.42615,071.027,585

2,818,412,2391.944,109.413

3,44,071.S52,997,100,9773.811,915,5973,1P,S6.9712,314,816.5953,9A,507,242.447.æ4.6338,424.082,663,713,941,1S2,993,331.676

307,543.865

476,252,529301,356,907

2,653,081,707494,3415786,€1,433

4,310,718,981

4.894,62,847

¿041,173,5663,766.697,263

8,711.076.235

4,069,740,426

8,065,935,5682360,284.127

4OU,754,3146,S1,016.5q

2n,77A,174808,016.432

1,507,031,035

1,481,103,312

401,ßO,724

68,000,0002,710,323,194t,1 13.311,19

241,€1.090395.6æ.406

1,5æ,503,164

4O9,7f2,249541,605,132

9S,2æ,650ffi,7æ,504

1,388.65,50755,570,033

0

0

0

0

0

3,795,734.Æ112,698,328,042

4,674,99,2402,601,23,9A23.49r,ffi.5371,924,272,æ42,341,7Æ,æ12.035,S4.S9î.99,724,9E71.635,Æ,9284,943,2A,%4,837,385,914,257,279,5086,571.53,2013,æ6.803,r¡51,68.583,58S1,570.295,429

1,247 ,41 1 ,14787,æ4,358

1,256,897.423

3,051,759,2422,49S,304.318

4,472,752,671

2,733,920,SS2,909,381,{992,919,568,S51,869,309,95,æ5,881.2S98,49.1 I 0,72 E

1,395,639,272

835,727,353

850,527,æ9980.46,184328,903,6S7

2,242,718,613.379,321,003

553,897.9m1,509,36,æ8

201,173,5â28S,æ5,927428,578,O27

1.æ7.3S,597818,650,197

2,527 ,617 ,6173,141.131,',8

1.700.955

0

376,452,800

0

000

4.990,801,2655.56.120.9213.433.731.4091,896.998.391

4,ø45,Æ7 ,6181,025,26E.208

2,801,102,9633,95,8S7,307

249æ,n24,711,1S,8953,D7289,4931,337,615,742,698,178,5102,112,993,8151.527,873,479

2.548,115,9401.329,817.375

3,486,481.9744,539,320,6966,654,508,a22,818,457,W4,6e8,æ1,1725.1æ,K.944.283.587.3381,2,26,316

9?8.&3,10541,909,206

919,381,0369æ,232471667,E76,573

1.844,769,299

79.6æ,2861,880,2æ,616

613.863.434

213,151.65'f ,019,3æ,875

9.581,6191,507,860,321

0

3,250,749,881

zm,4n5573,ù23,234,1583,059.112,0122,087.595,1379,282,703,æ42,509,856,il54.952,165,7002.037,592,622.971.242.AA5

1 ,470,689,O21.137.573.435

4n,s53,4741,715.558.G62,471,734,1Æ4,659,641,762,337 ,705,7575,401.377,9072,0æ,605.8162,49,713,5113.56¿68.9824,898.73S,384

4,58A,727,4743,718,008,S44

3,919,199.150

1,629,679,691

3,æ7,541,319409,63,63

4,4%,012,2561,661,940,949

2,762,æ7,7692,093,724,72

153,45,4891.574,9€,070

178,52,m0

3.417,6{,9354,907,%,7152,2,425,9573,S9,111,7902.690,555,722,413,613,1893,514,032.711

1,494,251,471,685,023,415.84.63.1803.350,643,7ô02.E18.338.933

s1,tÆ.672,293.838,291,663.302.421,849.610,&1.765,999.858

1,49,234,263,64,267,213,691,26,9401,994,415,071

4,439.874.688,447,407.5557.286,703.7535.892,097,507

'12.12A,057 .3æ4.763,457,0493,568.785.374

5,787,294,7232,851,012.4251,633,291.400

85,î6,182æ9,678,312209,842,000

5.304,398,3194,826,394.5203,353,760.8526,485.177.0 t83,3S,470.2033,157.286,7662,524,373,S53,303,81l,æ72,æ6,833,6715.255,179.7835.383,079,9203,498,609.342,987.430.9114.165.€8.42E4,855,200.0702,055.596.132

541.780.0861,684.907.309

1,479.561,365,682,853.177

æ2,297,#2.415,177,6886.568,557,3352,9î1.970,3€14,703.509.8414,764,099,1564,111,171,5694,662,941,2019,686,æ3,9365,381.135,954.476,898.7237 ,150,401,7234,æS,612,09S

1.381.995.9197.561.172.t61

569,010,788

501,',tE5,137

0

976,696,852

0

0

0

0

0

0

0

0

00

00

0

4.566,704.5436,728,7AO,Ul7.750.06.1514,317,07?,831

2,393,25¿8862.236,161,6072.114.5æ,3372,627 ,514,1671.729,204,4774,54¿m.4S3,435,99.2701,996,057,251

4,849,i04,4253,829.454.7332.763.æ0.6031,000,814,280

749,076,3121.883,953,40

192,29,4562.43¿175,Æ61.237,616,3525,059.176,5404,695.709.4&3.172058.6m2,923,O79,2126.676,662,0081.888.927,080

10,740.309.927.510.50E.5E1

8.555.029.569,3{,254.1615.904,243,1774.219,865,5743,96,1S,9349,229.443,963,494,425.9m

210.09,4001.143.680.&0

43,4s2.0820

0

0

0

0

0

0

0

0

0

00

0

4.97{.364.4984,656,7t1.5443.684,010.6153.998,489,254.850,392,761

1.524,769,451

4,844.09't,9332,166.527,0782,838.183.0324,E79,575.356

5.511.758.5S3,417 ,124,n76,673,107.5491,39,032.6S4.667,144.8441.593,398.055

1 ,614,421 ,ß16,802,869,2071,427,260,357

1.666.35.7681.568.718.8083,160.653,E54

1,824.835,548

12,769,01 1.1M6,036,652,4233.992,312,904,553.387,28S

3.193.28.7523.91r,94,4105.538.429.3788.609,82.1483.615.116.330

805,990,231,752.443,456

2.763.673.42394,017,235347,763.598

1.019,953.218

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Table d5 Multilateral Positions of the Residual DNS System on Dayl ($m)

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