security defaults on coupon or interest payments.In the case of a loan made to a counterparty, the whole principalamount of the loan is potentially at risk. The same is true of a longposition in a security if the issuer defaults.In many cases, however, counterparty risk is rather smaller. Forexample, if the counterparty is bankrupted before a forward foreignexchange outright matures, our bank knows that it will not receive
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anything from the counterparty and therefore deliberately does notdeliver its side of the deal either. In this case, how much will ourbank lose? If the deal is showing a loss from our point of view, we willnot lose anything. In practice, in this case the administrators of thebankrupt counterparty should insist on consummation of the dealanyway, so that there would be no effect on our bank.Suppose, however, that the deal is showing a mark-to-market proﬁtto our bank. That is, the deal would show a loss to the counterpartyif it were closed out now. In this case, the deal will simply not beconsummated. Our loss is therefore limited to the proﬁt on the deal.This loss can be seen as how much it will cost our bank to replacethe deal with a similar deal with another counterparty. The risk istherefore called replacement risk.For a short period during the settlement cycle when a FX deal isdelivered, the risk does involve the entire principal amount of thedeal. After our bank has already committed itself to making paymenton its part, but before it can be certain that its counterparty has donethe same, the whole amount of the trade is at risk. This is knownas settlement risk (also Herstatt risk in the case of foreign exchangeafter Bank Herstatt, which defaulted in 1974). This risk is removedwhen securities are delivered against payment through a clearingorganization.
Example 5On 15 August, the bank sells USD 10 million against CHF to acounterparty for value 17 September at 1.7324. By 22 August,the forward rate has moved to 1.7188. The bank has a potentialproﬁt of CHF 136,000 on 17 September, which it would lose ifthe counterparty goes bankrupt. The size of the replacement riskis therefore the present value of CHF 136,000.10,000,000 × (1.7324 − 1.7188) = 136,000Settlement risk in foreign exchange should be rather short-termbecause payment instructions should be revocable (able to be cancelled) until settlement date. In practice, however, the cut-off time forirrevocable instructions is sometimes earlier.The clearing houses for futures exchanges are generally consideredto be free of credit risk because of their arrangements for margin.This is a combination of collateral placed with the clearing house incase of default (initial margin) and the requirement to pay losses asthey arise daily (variation margin) rather than on ﬁnal settlement.
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Exchanges do not all have the same rules, however, and, in extremecircumstances, could possibly still fail.Credit risk can increase during the life of a deal for two reasons.Firstly, the credit rating of a counterparty, or of the issuer of asecurity in the bank’s portfolio, might weaken after a deal has beentransacted or a security purchased. Secondly, credit risk will changeas the market moves. For example, the bank has no counterpartyrisk when a forward foreign exchange deal is ﬁrst transacted. If thecounterparty goes bankrupt immediately, there is no mark-to-marketproﬁt or loss, so that our bank can replace the deal with anothercounterparty at the same rate. If the market then moves so that ourbank is in proﬁt however, this creates a replacement risk. Credit riskand market risk are in this way interlinked.Credit risk includes both issuer default risk and counterparty risk.Counterparty risk is credit risk arising from default of a counterparty at any time.Where a deal can be replaced, counterparty risk is calledreplacement risk and is limited to the cost of replacement – i.e.any mark-to-market proﬁt.After irrevocable payment instructions have been given, counterparty risk is called settlement risk and is potentially the entireamount of the deal.
ControlsThe essential ﬁrst step in reducing credit risk is rigorous creditassessment of counterparties and issuers. If there are no defaults,there is no credit risk. In practice, however, there will always becredit risk.• As with market risk, there must be limits set on the size ofoutstanding transactions with any one counterparty together withthe value of securities held which have been issued by that counterparty. Within the limit, the amount of business allowed willdepend on the nature of the transaction. A USD 1 million loan to acounterparty is much riskier (because the whole principal amountis at risk) than a USD 1 million FRA transacted with the samecounterparty.• Limits are set not only on individual counterparties, but also, forexample, on each sector of industry and each country.• Monitoring of credit risk must take account of the fact that creditrisk can depend on market movements, as described earlier.
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• The value of any collateral taken from counterparties must be carefully monitored and additional collateral called for when appropriate.• All settlements expected from counterparties must be reconciledpromptly, as a warning system for potential default.• Operations staff should be trained in what constitutes a default.• The bank should negotiate the latest possible cut-off times formaking payments.• Wherever possible, the bank should set up legally enforceabledocumentation with each counterparty which incorporates obligation netting and close-out netting. The bank should also use nettingsystems, and DvP and PvP systems where possible. These variousareas are outlined in the next section.
NettingNetting cash payments means transferring net amounts rather thangross amounts between parties. Transfers of a particular security canbe netted in the same way.
Example 6Bank A is due to make a payment of USD 5 million to Bank Bon 15 June in settlement of one transaction and Bank B isdue to make a payment of USD 4 million to Bank A on thesame date in settlement of a different transaction. Instead ofmaking both these payments gross, Banks A and B couldagree that Bank A pays Bank B an amount of USD 1 million(=USD 5 million – USD 4 million) as full net settlement of thetwo transactions.The purposes of netting are to reduce credit risk, improve liquidityand reduce operational risks and costs. In the above Example, if thetwo gross payments are made separately, Bank A must normally giveirrevocable instructions to pay away USD 5 million before it knowswhether it has received the USD 4 million from Bank B. If Bank Bsubsequently proves unable to pay the USD 4 million, Bank A mighthave a USD 4 million loss. Bank B is similarly exposed to the creditrisk of Bank A. This risk reduction also enables an increase in thevolume of business transactions between the two parties, because ofthe reduction in capital requirements allowed by supervisors wherethere is appropriate netting – see ‘Capital adequacy requirements’later in this chapter. The bank’s credit risk monitoring system shouldaccurately reﬂect the effect of netting.
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In the same Example, the net settlement improves liquidity. IfBank A only has to pay the net USD 1 million, its available fundsare reduced by that amount. If, however, it must pay USD 5 million,its available funds are reduced by USD 5 million until it has ﬁnallyreceived the USD 4 million from Bank B. The net settlement in theexample should also reduce the operational cost and risk of error, asthere is only one payment rather than two.An arrangement to net should always be supported by a writtenmaster agreement between the parties to that effect. A master agreement is one which covers all deals of a particular type between thetwo parties, except those which are speciﬁcally agreed at the timeof the deal to be treated separately. There are two netting aspectsto a master agreement. The ﬁrst is netting of settlements in thenormal course of business as described in the example above; this isknown as obligation netting. The second is close-out netting, whichoccurs when one of the parties is in default of the agreement for anyreason; close-out netting allows the non-defaulting party to close-outall existing transactions – i.e., terminate them early. Agreement toclose-out netting provides that, in these circumstances, a single netsettlement is made for all outstanding transactions. This removesthe possibility of cherry-picking, a term used to describe the way inwhich an administrator for a counterparty in liquidation might beable to insist on consummating proﬁtable deals with a particularcounterparty, while defaulting on unproﬁtable ones.Netting in a master agreement is effective only if it will prove tobe legally binding in the event of dispute. Whether this is so mightdepend on the various legal jurisdictions of the agreement itself, theparties and any correspondent banks or custodians involved in thesettlements. It is therefore always important for legal opinions to besought. Legal opinions in the UK and USA, for example, supportthe use of netting domestically, but there are still concerns over theenforceability of cross-border netting.Netting in master agreements is often netting by novation. Thisinvolves legally substituting a new single contract between the twoparties to combine and replace all existing similar contracts betweenthem for a given settlement date. The major master agreementsused internationally which cover the instruments described in thisbook are:• IFEMA (International Foreign Exchange Master Agreement) forforeign exchange spot and forward deals.• ISDA (International Swaps and Derivatives Association) masteragreement for FRAs (also used for swaps, options and other
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transactions). FRABBA (The BBA’s documentation for FRAs) isalso used, but less frequently.• GMRA (Global Master Repo Agreement) for repos and buy/sellbacks.• SAFEBBA (The BBA’s documentation for SAFEs)Netting systemsThe example above involves bilateral netting – netting between twoparties. It is possible to organize such netting through a third-partybilateral netting system. FXNET is such an organization, which runsa bilateral netting system for banks involved in foreign exchangedeals.A multilateral netting system nets payments between more thantwo banks. Transactions between all the banks involved are nettedso that, in each currency, each bank only receives one net amount orpays one net amount or does neither.Example 7Suppose the following gross amounts are due, all on the samedate:Bank A owes Bank B USD 5 millionBank B owes Bank A USD 4 millionBank A owes Bank C USD 3 millionBank C owes Bank A USD 5 millionBank B owes Bank C USD 10 millionBank C owes Bank B USD 8 millionThe net result for Bank A is that it is owed USD 1 million(=−USD 5 million + USD 4 million − USD 3 million + USD 5million). The net result for Bank B is that it owes USD 1 million(=−USD 5 million + USD 4 million + USD 10 million − USD 8million). The net result for Bank C is zero (= −USD 3 million +USD 5 million − USD 10 million + USD 8 million). In this case,multilateral settlement could be achieved by a simple paymentof USD 1 million from Bank B to Bank A, instead of six grossbilateral payments.PvP and DvPBilateral and multilateral netting systems operate by netting andsettling the payments due on a particular date at certain times onthat day – often at the end of the day. An alternative is a paymentversus payment (PvP) system. In this, a payment from Bank A to
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Bank B is made only if, and at the same time as, the correspondingpayment from Bank B to Bank A is made. The payments are madeduring the day on a real-time basis and, once made, are ﬁnal. Sucha system – continuous real-time linked settlement (CLS) – has beendeveloped for FX settlements by CLS Bank, starting in 2002 withsettlements for USD, CAD, EUR, GBP, CHF, AUD and JPY, andextending to SEK, NOK, DKK and SGD in 2003. Settlement is available during a 5-hour window from 07:00 to 12:00 Central EuropeanTime. Members of CLS need to maintain collateral in the system tocover the net risk they represent to other members. A danger of PvP isthat there can be non-credit-related reasons for non-payment, suchas systems failures, strikes, severe weather problems, human erroretc. Non-settlement could cause the whole system to fail, causing aliquidity crisis. A systemic failure in one country, for example, couldbring the system down.Delivery versus payment (DvP) is the corresponding settlementmechanism, used widely both domestically and internationally, forsettlement of securities transactions. In this, a payment from Bank Ato Bank B is made only if, and at the same time as, the correspondingsecurity is delivered from Bank B to Bank A.Contracts for differencesA contract for differences is a transaction where only the net differencebetween two amounts is settled, and the principal amount involved isnot transferred. This reduces credit risk very signiﬁcantly. Generallythe settlement is the difference between the rate or price dealt atthe outset and a reference rate or price at maturity, calculated on anotional principal amount.FRAs, Futures and SAFEs, covered earlier in this book, arecontracts for differences.Forward outrights are available as non-deliverable forwards (NDFs),also covered earlier. These contracts for differences are largely usedin emerging currencies for exchange control reasons rather than riskcontrol, but the concept can be extended to major currencies.
Operational riskThe risksOperational risk is a wide term, covering the risk of losses due tofailures in the bank’s operations generally. This includes the activitiesof the operations department itself (deal input, conﬁrmation, netting,payments and reconciliation) but also covers other areas such asthe bank’s computer systems (system risk), accounting, personnel
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problems and even third-party organizations such as custodians andcorrespondent banks. The problems might arise from staff mistakes,management weaknesses or system errors. Many of the risks canhave knock-on effects on market risk or credit risk.Example 8Operational risk can arise in many ways. The following are justsome examples:A deal ticket for the purchase of USD 10 million from Bank Aagainst CHF at 1.7324 is entered incorrectly in the bank’s systemas a sale of USD 10 million. A dealer covers the short USD exposure which the system is showing, by buying USD 10 millionfrom Bank B. In fact this has doubled the size of the long position, rather than reducing the exposure to zero. The dollar nowfalls to 1.7188 and the bank makes a loss of CHF 272,000.If in fact the dollar had risen instead, there would have been aproﬁt on the original deal with bank A, giving rise to a credit riskfrom bank A. The system, however, would show no such creditrisk because the deal would appear to show a loss.The error could thus give rise to market risk or credit risk, bymis-stating the position in both.A deal conﬁrmation sent to a counterparty is incorrect, or anincorrect incoming conﬁrmation is not checked properly. Thiscould similarly give rise to market and/or credit risk, as well asharm the bank’s reputation (reputational risk).The payment in settlement of a deal is sent incorrectly, so thatthe counterparty, which does not receive the funds on time,makes a claim for interest.A power cut causes the computer systems to crash and there isno adequate back-up power system.The bank relies on a few key staff members for processingcertain complex transactions and this whole team of staff leavesthe bank to join a competitor. Errors are made as further dealsof this type are processed, leading to market risk, credit risk andreputational risk.A bomb or a natural disaster makes it impossible for the bankto carry on its business at its usual premises and there areno adequate back-up facilities. This could lead to the loss ofa considerable volume of business, as well as creating market,credit and reputational risks.
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ControlsThe task of controlling operational risk is as broad as operational riskitself. It is paramount that staff are competent and well trained andthat systems are thoroughly tested. An approach to reducing humanerror is the introduction of straight-through processing (STP). This isa general term for the computerization of tasks in such a way thateach process feeds automatically to the next. Other points include:• No deal should be undertaken unless operations staff, riskmanagers, accounting staff and IT staff all understand themechanics of the transaction. Existing systems might not beadequate, or input might be required to several incompatiblesystems for position recording, risk management, settlement etc.• It is important that conﬁrmations are sent, and incoming conﬁrmations checked, as quickly as possible. Speed is particularlyimportant in areas where a loss could increase very quickly.• It is important to have a team approach, as the individual processes relating to a trade are completed by different people. Eachperson should know how his role ﬁts into the whole process.
Other risksFraudIt is possible for the bank to try to address the risks mentioned sofar – even though risk is rarely reduced to zero. The perpetrator of afraud, however, is presumably circumventing exactly those controlswhich have been put in place to protect the bank. This could perhapsbe seen as yet another type of operational risk. For example, it couldbe difﬁcult to prevent fraud if there were sufﬁcient collusion betweendealers and operations staff in two counterparty banks.Segregation of responsibilitiesAn important principle – particularly in seeking to avoid fraud butalso to help control operational risks – is the segregation of responsibilities between the front ofﬁce (the dealers) and the back ofﬁce (theoperational staff). It is essential that the two areas be totally separatein terms of both staff and management reporting. Ideally, they shouldbe physically separate also, although this might not always be practicable. It is important also that computer access by dealing staff tothe back-ofﬁce systems is not possible. Operational errors or odditiesare less likely to be noticed – or remedial action taken – if the sameperson is responsible for more than one of these areas. The internalaudit function should also be totally separate.
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Systemic riskThis is the risk of failure in the entire system of which the bank itselfis only a part – for example, a failure of the entire payment clearingsystem or the entire banking system. This could, for example, bebecause of mechanical difﬁculties (a computer failure) or because amajor payment default by another bank, which might be one withwhom our bank has no dealings, has caused a chain reaction ofdefaults, seizing up the payment clearing.
Legal and regulatory riskThis is the risk that the bank’s business is affected by changes inlaws and regulations, or by existing laws and regulations which ithad not properly taken into account. Again, this may be seen as atype of operational risk, but some of the risks here arise from changesoutside the bank’s control and which it might not reasonably be likelyto anticipate.
Example 9The bank expects to receive an FRA settlement from a counterparty. Although ﬁnancially healthy, the counterparty refuses topay the settlement and the bank is unable to enforce settlementbecause the counterparty is in a legal jurisdiction which doesnot support the transaction. Alternatively, the counterparty didnot have the authorization for the transaction, which is thenconsidered legally void.A corporate customer refuses to consummate a particulartransaction, because it claims that it was misadvised by thebank in undertaking it, and the courts support the customer.Some of the bank’s outstanding transactions are adverselyaffected by changes in taxation or changes in the requirementsfor capital adequacy (see later in this chapter).The bank permits transactions, knowingly or unknowingly,which involve money laundering, and the bank is subsequentlypenalized by the authorities for doing so.
Business riskThe bank is at risk to general business conditions in the same wayas any other business, although this can possibly be magniﬁed. Asevere recession, for example, as well as possibly reducing demandfor the bank’s services, could result in a fall in creditworthiness of the
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bank’s existing business across the board. The bank also faces othercommercial risks, such as the commercial value of its buildings.A fall in the bank’s own credit rating for any reason will also resultin higher funding costs compared with its competitors.
Value at risk (VaR)A full treatment of VaR is mathematically complex and outside thescope of this book. This is therefore an overview only, aimed at givingthe reader an understanding of the process. The details of the ﬁrstsection on basic statistics are not essential to understanding theVaR section which follows it, but they might be helpful if you areinterested.
Basic statisticsMean, variance and standard deviationThe arithmetic mean of a series of numbers is the average of thenumbers as we normally understand it. If we have the following ﬁvenumbers:52, 53, 57, 58, 60then their mean is:(52 + 53 + 57 + 58 + 60)= 565The mean is useful, because it gives us an idea of the how big thenumbers are – about 56. However, if we knew only this mean, 56, itwould not give us any idea of how spread out all the numbers arearound 56; perhaps they are all very close to 56, or perhaps they arevery spread out.The standard deviation of the same numbers is a measure of howspread out the numbers are around this mean. If all the numberswere exactly the same, the standard deviation would be zero. If thenumbers were very spread out, the standard deviation would be veryhigh. Effectively, the standard deviation gives an idea of the answerto the question: On average, how far away are the numbers from theirmean?The mean is the average of a set of numbers.Standard deviation is a measure of how spread out the numbersare around the mean.
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The standard deviation is deﬁned as the square root of the variance.The variance in turn is deﬁned as the average of the squared differencebetween each number and their average.Consider the two sets of numbers in Figures 12.1 and 12.2. Theyalso each have a mean of 56, but in Figure 12.1 the ﬁrst set is closelypacked together and the second set in Figure 12.2 is very spread out.In fact, the ﬁrst set has a standard deviation of 1.4 and the second sethas a standard deviation of 4.3. If the standard deviation or varianceis lower, the histogram is compressed horizontally – it looks taller andthinner – and there is a lower probability that any particular numberis a long way from the mean. If the standard deviation or varianceis greater, the histogram is more stretched out horizontally – it lookslower and fatter – and more numbers are further from the mean.52545555565656575758
53555555565656575758
53555555565656575758
54555555565656575758
54555556565657575758
54555556565657575759
54555556565657575759
54555556565657575860
25242322212019181716151413121110987654321046 47 48 49 50 51 52 53 54 55
56 57 58 59 60 61 62 63 64 65
Figure 12.1 The set of numbers is closely packed together.
46505254555657586062
47515354555657586062
48515354555657596063
48515354555658596063
49525354565758596164
49525355565758596164
50525455565758596165
50525455565758606266
25242322212019181716151413121110987654321046 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
Figure 12.2 Here the set of numbers is very spread out.
Mean (μ) = sum of all the values divided by thenumber of valuesVariance (σ 2 ) = mean of (difference from mean)2=
sum of all the (difference from the mean)2the number of values
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This gives the variance of a set of numbers, given that all thenumbers are known. Very often, however, a sample only of thenumbers is used. For example, a representative sample of pricesfor a particular instrument might be the daily closing prices over aperiod of only one year, rather than over the entire history of thatinstrument since it began trading. In this case, a better estimate ofthe variance of all the numbers is:Estimated variance =
sum of all the (difference from the mean)2(the number of values − 1)
Whichever formula is used,Standard deviation =
√
variance
Example 10What are the variance and standard deviation of the followingnumbers?52, 53, 57, 58, 60As above, their mean is:(52 + 53 + 57 + 58 + 60)= 565Numbers
Difference betweenthe numbers and 56
(Difference)2
5253575860
−4−3+1+2+4
1691416
Mean = 56
Total = 4646= 9.2 and the standard deviation isThe variance is therefore5√9.2 = 3.03.Correlation and covarianceCorrelation and covariance are measures of the extent to whichtwo things do, or do not, move together. The precise mathematicaldeﬁnitions are given below.
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Consider, for example, the USD/DKK exchange rate and the USD/EUR exchange rate. Generally, one rate will rise and fall in line withthe other. The two rates are therefore very closely correlated. On theother hand, the USD/DKK exchange rate will fall as the EUR/USDexchange rate rises, so that there is a close negative correlationbetween these two rates. There is probably very little relationship atall between Mexican interest rates and the HUF/JPY exchange rate,so these 2 numbers have no correlation – the price of one moving upor down suggests no information about whether the other is movingup or down.A correlation coefﬁcient lies between +1 and −1. If two series ofnumbers are perfectly correlated – they move exactly in line – theircorrelation coefﬁcient is +1. if they move exactly in line but in oppositedirections, their correlation coefﬁcient is −1. If there is no link at allbetween the two series, their correlation coefﬁcient is 0.A correlation coefﬁcient lies between −1 and +1 and measuresthe extent to which two things do, or do not, move together.Covariance quantiﬁes this in terms of the magnitudes of the twothings.
Example 11First Second Correlationseries seriescoefﬁcient⎫12⎪⎪⎪⎪24⎬+136⎪⎪48⎪⎪⎭510
First Second Correlationseries seriescoefﬁcient⎫1−2⎪⎪⎪⎪2−4⎬−13−6⎪⎪4−8⎪⎪⎭5−10
First Second Correlationseries seriescoefﬁcient⎫110⎪⎪⎪⎪22⎬034⎪⎪46⎪⎪⎭59
Covariance is a concept linking correlation and variance. Whereasvariance quantiﬁes how much the value of one particular thing varies,covariance measures how much two things vary, relative to eachother.Correlation coefﬁcientsum of (x × y) − (n × (mean of x) × (mean of y))=((sum of (x 2 ) − (n × (mean of x)2 ))×(sum of (y2 ) − (n × (mean of y)2 )))Covariance = correlation coefﬁcient× (standard deviation of x) × (standard deviation of y)
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215
correlation coefﬁcientn×
(sum of (x-mean of x)2 × sum of (y-mean of y)2 )
where n is the number of pairs of data.
Example 12What are the correlation coefﬁcient and covariance of the following price series x and y?First Secondprice pricex
y
x ×y
x2
y2
Day 1:Day 2:Day 3:Day 4:Day 5:
9495939192
7574737271
7,0507,0306,7896,5526,532
8,8369,0258,6498,2818,464
5,6255,4765,3295,1845,041
14041
41014
Totals:
465
365
33,953 43,255
26,655
10
10
365= 73510variance of y == 2.54
465= 93510variance of x == 2.54
average of y =
average of x =
standard deviation of x =standard deviation of x =
(x-ave of x)2 (y-ave of y)2
√√
2.5 = 1.58112.5 = 1.5811
correlation coefﬁcient33,953 − (5 × 93 × 73)=   = 0.8043,255 − 5 × (93)2 × 26,655 − 5 × (73)2covariance = 0.80 × 1.5811 × 1.5811 = 2.00.80 is a reasonably high level of correlation, indicating that theprice of x and the price of y move together to some extent (seeFigure 12.3).
Probability densityThe probability density of a series of numbers is a description ofhow likely any one of them is to occur. Thus the probability density
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100908070601
2
3
4
5
Figure 12.3 Correlation.
of the results of throwing a die is 16 for each possible result. Theprobability density of the heights of 100 adult men chosen at randomwill be relatively high for around 170 cm to 180 cm, and very low forless than 150 cm or more than 200 cm. The shape of the probabilitydensity therefore varies with the type of results being considered.One particular probability density which is used as an approximatedescription of many circumstances in life is known as the normalprobability function.If the probabilities are as shown in Figure 12.4, for example, anumber less than −3 or more than +3 is extremely unlikely, while anumber between say −1 and +1 is rather likely.