Maturity Transformation and Interest Rate Risk in Large European ...

Maturity Transformation and Interest Rate Riskin Large European Bank Loan PortfoliosGalen Sher ∗ and Giuseppe Loiacono †‡This draft May 1, 2013AbstractFinancial intermediaries transform assets with certain risk characteristics into assets with otherrisk characteristics. We define net asset transformation from liabilities to assets in terms of thepricing characteristics of contingent claims. Maturity transformation can be defined as a specialcase, across the whole balance sheet or locally to one contract type. We present and summarisea new rich dataset on the balance sheet asset and liability exposures of large European banksthat submitted to the European Banking Authority’s EU capital exercise. In particular, we showthat these banks transform short-term customer deposits and 1-5 year hybrid and subordinateddebt liabilities into loan assets with greater than 5 years’ maturity. The value-weighted averagematurity of the assets of these banks exceeds their liabilities by 2.07 years, with standard deviation1.44 years. Given the importance of loan assets among these banks for determining interest raterisk, we describe and measure the interest rate risk of their loan portfolios. We find that their loanassets are primarily allocated to households and non-financial corporations in the Euro area. Wecritically assess the interest rate repricing risk in these loan portfolios under five simple methods,including the Basel Committee guidelines on interest rate risk assessment. We identify four majorlimitations in the Basel Committee guideline method and illustrate the size of the approximationsthey introduce through examples. Using these five methods, we measure the extent to which astandardised 200 basis point parallel interest rate shock affects the values of their loan portfolios.We find that simple loan-specific pricing models provide different, and presumably better, rankingsof the relative interest rate riskiness of bank loan portfolios than the Basel Committee guidelinemethod.JEL Classification: E43, G21, G281 IntroductionInterest rate risk in financial intermediation matters because it is a source of systemic or non-diversifiablerisk to the industry, and the health of the real economy depends on a well-functioning financial system.High and unpredictable interest rates in the 1980s led to widespread failures of banks and thrift institutions(see Federal Deposit Insurance Corporation (1994)). The ever-increasing scale and complexityof financial institutions and their use of non-standard contracts for hedging and speculation makesproper risk assessment essential.Conceptually, one may distinguish between two major categories of interest rate risk to a financialintermediary. The first is the risk that unanticipated changes in interest rates cause a loss of income,in particular interest income. Secondly, unanticipated changes in interest rates affect the so-called“economic value” of the intermediary. 1 Both of these categories affect the ability of the intermediaryto fulfil its obligations as they fall due, and therefore also its liquidity and solvency.∗ Department of Economics, University of Oxford. Corresponding author: galen.sher@economics.ox.ac.uk† Department of Economics, University of Rome Tor Vergata. giuseppe.loiacono@students.uniroma2.eu‡ The authors would like to acknowledge helpful discussions with Arnaud Lionnet and Stephen Bond at the Universityof Oxford, and with Matthias Sydow at the European Central Bank, without any implication for errors or omissionscontained herein. Some of the data were collected while the authors were at the European Central Bank. The firstauthor would like to acknowledge research support from the Oxford–Man Institute of Quantitative Finance.1 The “economic value” of a company may be understood as changes in the ‘value’ of the company, or changes inprices and quantities that affect the ‘value’ of that company’s assets and liabilities. For a detailed discussion of ‘value’in economics, see Hicks (1939).1

There are at least three ways that an analyst (say, a regulator) may monitor or assess the interestrate risk of a financial intermediary. Publicly listed banks and insurers disclose measures of thesensitivity of their balance sheets to shifts in the term structure of interest rates, so in the firstinstance an analyst may refer to these disclosures. These self-reported measures have the advantagethat they may take into account the complex structure of the contracts held by an intermediary thatmay not be visible in its financial statements, but such measures also rely on the willingness andability of the intermediary to make an accurate assessment. Furthermore, only one to two measuresare typically disclosed, which cannot be hoped to provide a complete picture of the intermediary’sexposure to interest rate changes.As an alternative, the analyst could use regression analysis to measure the sensitivity of the stockreturn of publicly-listed intermediaries against changes in specific interest rates or against measuresreflecting the shape of the yield curve. The principle paper in this category is Flannery and James(1984a), where the authors find that US banks’ stock returns are sensitive to interest rate changes,and that the degree of sensitivity is correlated with the degree of maturity transformation measuredfrom the nominal contracts on their balance sheets. Flannery and James (1984b) infer the effectivedegree of maturity transformation based on these stock sensitivity measures. Saunders and Yourougou(1990) find that bank stock returns are more sensitive to interest rate changes than the stock returnsof other companies; they also find some evidence to suggest that universal banks would be more robustto interest rate changes due to better diversification. Czaja, Scholz, and Wilkens (2009) measurethe sensitivity of stock returns of German banks and insurers to level, slope and curvature changesin local yield curves, and find that bank and insurer stock returns offer a premium for those banksand insurers with greater sensitivities to the level and curvature factors. English, van den Heuvel,and Zakrajsek (2012) use high-frequency stock and interest rate data around Federal Open MarketCommittee announcements to measure the effect of interest rate level and slope changes in bank stockreturns; studying short time intervals helps to avoid the pollutive effects of unrelated news on stockprices.The analyst could also measure the interest rate sensitivity of each item on the balance sheet, byasking the question “How would the unit prices of the major asset and liability categories change ifinterest rates were different on the valuation date?” This is the approach taken in our paper, andcan be thought of as a ‘prospective’ assessment of interest rate risk, as opposed to the ‘retrospective’assessments following Flannery and James (1984a). The concepts of duration and convexity as measuresof price sensitivity to interest rate changes were introduced by Macaulay (1938), Hicks (1939),Samuelson (1945) and Redington (1952). Houpt and Embersit (1991) propose a duration-based methodfor assessing the interest rate sensitivity of banks’ economic value based on their publicly disclosedbalance sheets. This model has since become known as the Federal Reserve’s Economic Value Model(EVM). Wright and Houpt (1996) evaluate the performance of this simple model for ‘thrift institutions’against a model that uses more detailed private supervisory data, and against the Office for ThiftSupervision’s internal model. Despite the limitations of publicly-available data, the authors find thatthe simple model provides useful information for measuring the sensitivity of banks’ economic valueto interest rate changes; they also find that the biggest limitation of such models are the arbitraryassumptions that have to be made about the behaviour of depositors.Jarrow and van Deventer (1998) offer a no-arbitrage model for determining the economic valueof deposit contract liabilities, and this pricing function could also be used in principle to measure itssensitivity to interest rate changes. O’Brien (2000) also offers such a no-arbitrage model, and furtherestimates its parameters on US bank data, providing detailed sensitivity estimates of the economicvalue of bank liabilities to changes in the short term interest rate. Sierra and Yeager (2004) evaluatethe predictions of the EVM against the actual performance of US community banks, which do nottypically engage in complex derivative transactions, and find that those banks that the EVM identifiesas most sensitive to rising rates show the greatest deterioration in performance in the 1998-2000 periodof rising rates in the US. Sierra (2009) finds that the ‘prospective’ sensitivities of US bank economicvalue to interest rates calculated from the EVM are consistent with the ‘retrospective’ interest ratesensitivities of stock prices discussed above. Entrop, Memmel, Wilkens, and Zeisler (2011) try toproduce a refined EVM model calibrated to German banking data by using repeated observations ofbalance sheets over time. By evaluating their model using private supervisor data, they are able toargue that their model outperforms the EVM, which relies on data at only one point in time. Themost important paper for estimating the sensitivity of US bank balance sheet derivative exposures is2

‘duration’ number in the penultimate column of Table 1. Multiplying this duration number by the sizeof the standardised shock, which is 2%, gives the risk-weight measure that is shown in percent in thefinal column of this Table. The risk weight is an estimate of the interest rate revaluation sensitivity ofthe hypothetical security under a standardised interest rate shock.We can immediately observe several shortcomings of this guideline method for interest rate revaluationsensitivity. These shortcomings can be summarised as follows:1. The method does not depend on the specific type of security. We might expect different securitieswith the same remaining time to maturity to have different sensitivities to interest rate changes.In particular, we have no indication of how good this guideline method is for loan contracts.2. The method does not depend on the current yield curve. Not only is the standardised shock of2% invariant to historical yields, but the sensitivity calculation itself is unrelated to the prevailinginterest rate environment. For example, in a high interest rate environment, we might expectlarger absolute changes in interest rates to be likely, and we might expect the price of a securityto be more sensitive to a given absolute change in interest rates in a low interest rate environmentthan in a high interest rate environment.3. The method encourages the use of a parallel upward shift in interest rates of 2%, without explicitlyrequiring that the supervisor investigate other scenarios. As a scenario, there is little reason toexpect that a parallel upward shift in interest rates of 2% is commensurate with a desired level ofriskiness, or even that it is plausible, given the well-known correlation between levels and slopesof yield curves. As a risk measurement device, a single scenario incentivises banks to reducetheir exposure to just this one scenario, while potentially remaining severely exposed to otherscenarios, which include parallel shifts not equal to 2% and slope changes.4. The method provides only an ad hoc way to aggregate the sensitivity of many exposures into aportfolio sensitivity, despite the fact that the method is recommended for measuring the interestrate revaluation risk of the whole balance sheet.Indeed given these four criticisms, it is difficult to see how the method improves on so-called gapanalysis, where the weighted average maturity all the assets and liabilities on the balance sheet is usedas a proxy for interest rate risk.1.2 Structure of this paperOur objectives of this paper are twofold. First, we offer a definition of maturity transformation interms of the pricing characteristics of assets and liabilities. This theory of ‘transformation’, includingmaturity transformation, is presented in Section 3.1. To measure the degree of maturity transformationof large European banks, we employ a dataset collected by the authors at the European Central Bankthat covers the asset and liability exposures in greater detail than currently available from majordata providers. All the asset and liability exposure data were collected from the consolidated annualfinancial statements and Pillar III disclosures of these banks. We present and summarise the data inSection 2 and we measure the degree of transformation in Section 4.1.Having determined that the degree of on-balance-sheet interest rate revaluation risk 6 is most substantiallyinfluenced by the loan asset portfolios of these banks, our second objective in this paper isto measure the interest rate revaluation sensitivity of these loan assets. To do so, we employ severalmethods, including conventional gap analysis, 7 the Basel Committee guideline method introduced inSection 1.1, and the simple present value formulae for amortising loan contracts of Section 3.2 combinedwith stylised characterisations of the yield curve in Section 3.3. We present our results in Section4, including one ranking of banks by the (2%-) interest rate risk of their loan portfolios for each of thesensitivity methods, in Section 4.4. Section 5 concludes.6 As opposed to off-balance-sheet interest rate revaluation risk, which is discussed for example in Gorton and Rosen(1995).7 Gap analysis is a method for measuring the interest rate risk of a bank by computing the weighted average maturityof all assets and liabilities on the balance sheet. By computing the weighted average maturity of loan assets only, weobtain an analog of gap analysis applied to the interest rate risk assessment of just the loan assets of banks.4

Table 2: List of banks in the sample.EBA code Description EBA code DescriptionAT001 Erste Bank GB089 HSBCAT002 Raiffeisen Bank GB090 BarclaysAT003 Oesterreichische Volksbank GB091 LloydsBE004 Dexia GR030 EFG EurobankBE005 KBC GR031 National Bank of GreeceCY006 Marfin Popular GR032 Alpha BankCY007 Bank of Cyprus GR033 Piraeus Bank GroupDE017 Deutsche Bank HU036 OTP Bank NYRT.DE018 Commerzbank IE037 Allied Irish BanksDE019 LBBW IE038 Bank of IrelandDE020 DZ Bank IE039 Irish LifeDE021 Bayern LB IT040 Intesa SanpaoloDE022 Nord LB IT041 UnicreditDE023 Hypo RE IT042 Banca Monte Dei Paschi Di SienaDE024 West LB IT043 Banco PopolareDE025 HSH Nordbank IT044 UBI BancaDE026 Helaba LU045 Banque Et Caisse DEpargne De LEtatDE027 Landesbank Berlin MT046 Bank of ValettaDE028 DekaBank NL047 INGDK008 Danske Group NL048 RabobankDK009 Jyske Bank NL049 ABN AmroDK010 Sydbank NL050 SNS BankDK011 Nykredit NO051 DnB NORES059 Santander PL052 PKO Bank PolskiES060 BBVA PT053 Caixa Geral de DepositosES061 Bankia PT054 Banco ComercialES062 La Caixa PT055 Espirito SantoES064 Banco Popular PT056 Banco BPIFI012 OPO-Pohjola SE084 NordeaFR013 BNP SE085 SEBFR014 Credit Agricole SE086 Svenska HandelsbankenFR015 BPCE SE087 SwedbankFR016 Societe Generale SI057 NLB GroupGB088 RBS SI058 NKBM2 DataThe sample of banks we study here is the sample of banks analysed in the European Banking Authority’s2011 EU-wide capital exercise. They form the largest European bank holding companies andare listed in Table 2. Balance sheet data for these banks is publicly available from data providers likeReuters, Bloomberg and SNL, but not at the full level of detail that these institutions report in theirannual financial statements. We use data collected by the authors at the European Central Bank onbalance sheet assets and liabilities as at 31 December 2011.In particular, our data segregates loan assets into countries, sectors and remaining time to maturity,which allows us to compute detailed estimates of the interest rate sensitivity of these loans portfolios.While we use the country and sector classifications to measure “net asset transformation” in Section4.1, 8 we use only the maturity data to measure the interest rate sensitivity of these loan assets.The joint distribution of loan asset values by geography, sector and maturity is not known (only themarginal distributions are known) and the risk assessment by maturity already provides a rich analysis.We describe the cross-section of loan exposures by sector and country merely as a qualitative devicefor assessing concentration risk. In this section we summarise these loan exposures data by maturiy,geographical location and sector. In Section 2.4 we also summarise the yield curve data used in this8 We define net asset transformation as a more general notion than maturity transformation in Section 3.1.5

paper.2.1 Accounting valuation methods in European countriesThe loan exposure data on which this paper is based has been gathered by the authors from thefinancial statements of large European banks. In this section we provide an overview of the accountingmethods used to value these assets and liabilities. In doing so, we gain a better understanding ofthe exposures underlying the summaries in Section 2, and we can compare the accounting valuationmethods to the stylised economic valuation models of Section 3.2.1.1 Introduction to accounting rules for valuing assets and liabilitiesIn the life of a corporate entity, every event has to be recorded in the financial statements according tocommon standards. Accounting standards can have a significant impact on the financial system, in particularvia their potential influence on the behaviour of economic agents. Published financial statementsprovide financial and economic signals on which decisions can be made, and on which management canbe assessed. Therefore, comparability of financial statements across countries is desirable. Pursuingthis aim, the IFRS Foundation – an independent, not-for-profit private sector organisation workingin the public interest – developed a single set understandable, enforceable and globally accepted internationalfinancial reporting standards (IFRSs) through its standard-setting body, the InternationalAccounting Standards Board.In Europe, the IFRS standards have not fully substituted for the national accounting standards(Generally Accepted Accounting Principles). EU Regulation 1606/2002 requires European companiesat the consolidated level to comply with IFRS standards, but does not make prescriptions for nonlistedEuropean companies. Therefore subsidiary companies, like banks that are part of larger holdingcompanies, are still subject to national GAAP and can move voluntarily to IFRS. 9 The banks that areused for the analysis in this paper complied with IFRS standards. They were chosen based on theirparticipation in the European Banking Authority’s 2011 EU capital exercise, and are therefore thelargest and most systemically important banks in Europe. For the sake of our analysis, this sectionfocuses on IAS 39 and IFRS 9, which are the specific IFRS standards that regulate the recognitionand measurement of financial assets and liabilities.2.1.2 Explanations of fair value and amortised costFinancial assets and liabilities can be recorded on the balance sheet at either fair value or amortisedcost. Fair value is the amount for which an asset could be exchanged, or a liability settled, betweenknowledgeable, willing parties in an arm’s length transaction [IAS 39.9]. IAS 39 provides a hierarchyto be used in determining the fair value for a financial instrument: [IAS 39 Appendix A, paragraphsAG69-82]• Level 1: Quoted market prices in an active market 10 are the best evidence of fair value andshould be used, where they exist, to value the financial instrument.• Level 2: If a market for a financial instrument is not active, an entity establishes fair value byusing a model-based valuation technique that makes maximum use of market inputs, and withreference to recent arm’s length market transactions, the current fair value of similar instruments,discounted cash flow analysis, and option pricing models. An acceptable valuation techniqueincorporates all factors that market participants would consider in setting a price and is consistentwith accepted economic methodologies for pricing financial instruments. A financial instrumentfalls under Level 2 valuation if the model inputs are substantially based on market observables.For example, in pricing debt instruments with default risk, the credit spread inputs should bebased on prevailing credit spreads that are observable at the time of valuation.• Level 3: If the model inputs are not observable in the market, they should be estimated tothe extent possible from historical data. Continuing the above example of debt instrument9 The “consolidated level” refers to the group holding company, which may own whole or majority stakes in subsidiarycompanies. Accounting statements are often produced for both the group holding company and the subsidiary companies.10 An active market in the accounting standards means a market in which transactions for the asset or liability takeplace with sufficient frequency and volume to provide informative ongoing prices.6

valuation, prepayment rates may be unobservable in the market, but should be calibrated tohistorical prepayment rates where possible. 11According to IAS 39.46-47, financial assets and liabilities (including derivatives) should be measuredat fair value, with the following exceptions:• Loans and receivables, held-to-maturity investments, and non-derivative financial liabilities shouldbe measured at amortised cost using the effective interest method.• Investments in equity instruments should be measured at fair value, but if the range of reasonablefair value measurements is large, then such instruments, and derivatives indexed to such equityinstruments, can be measured at cost less impairment.• Financial assets and liabilities that are designated as a hedged item or hedging instrument aresubject to measurement under the hedge accounting requirements of the IAS 39.• Financial liabilities that arise when a transfer of a financial asset does not qualify for derecognition,12 or that are accounted for using the continuing-involvement method, are subject toparticular measurement requirements.Amortised cost is calculated using the effective interest method. The effective interest rate is the ratethat exactly discounts estimated future cash payments or receipts through the expected life of thefinancial instrument to the net carrying amount 13 of the financial asset or liability. Financial assetsthat are not carried at fair value though profit and loss are subject to an impairment test. If theexpected life cannot be determined reliably, then the contractual life is used.A financial asset or liability valued at amortised cost is subject to an impairment test when there isobjective evidence to do so, as a result of one or more events that occurred after the initial recognition 14of the asset. An entity is required to assess at each balance sheet date whether there is any objectiveevidence of impairment. If any such evidence exists, the entity is required to do a detailed impairmentcalculation to determine whether an impairment loss should be recognised [IAS 39.58]. The amountof the loss is measured as the difference between the asset’s carrying amount and the present value ofestimated cash flows discounted at the financial asset’s original effective interest rate [IAS 39.63].2.1.3 Accounting and valuation of financial assetsIAS 39 requires financial assets to be classified in different categories, used to determine how a particularfinancial asset is recognized and measured in the financial statements.Financial assets at fair value through profit or loss This category of assets can be divided intotwo subcategories:• The designated category includes any financial asset that is designated on initial recognition asone to be measured at fair value with fair value changes in profit or loss.• The held for trading category includes financial assets that are held for trading purposes. Allderivatives (except those designated hedging instruments) and financial assets acquired or heldfor the purpose of selling in the short term, or for which there is a recent pattern of short-termprofit taking, fall into this category [IAS 39.9].Available-for-sale financial assets (AFS) These are any non-derivative financial assets designatedon initial recognition as available for sale or any other instruments that are not classified as(a) loans and receivables, (b) held-to-maturity investments or (c) financial assets at fair value11 Prepayment rates are rates at which loan debtors repay their loan contracts early. In most loan contracts, debtorsretain the option to repay their loans early. Early repayment can be a risk to the creditor, because it raises the possibilityof poor reinvestment rates at the time of prepayment.12 Derecognition is a term used in the accounting standards to mean the deletion of an asset or liability from thefinancial statements.13 The net carrying amount in the accounting standards means the original cost, less the accumulated amount of anydepreciation or amortization and less any impairments.14 The term initial recognition is used in the accounting standards to mean the first time that an asset or liability isrecorded in the financial statements.7

through profit or loss [IAS 39.9]. AFS assets are measured at fair value in the balance sheet. Fairvalue changes on AFS assets are recorded directly in equity, through the statement of changesin equity, except for interest on AFS assets (which is recorded in income on an effective yieldbasis), impairment losses and (for interest-bearing AFS debt instruments) foreign exchange gainsor losses. The cumulative gain or loss that has been recognised in equity is recognised in profitor loss when an available-for-sale financial asset is derecognised [IAS 39.55(b)].Loans and receivables These are non-derivative financial assets with fixed or determinable paymentsthat are not quoted in an active market, other than those held at fair value throughprofit or loss or as available-for-sale. Loans and receivables for which the holder may not recoversubstantially all of its initial investment, other than because of credit deterioration, should beclassified as available-for-sale [IAS 39.9]. Loans and receivables are measured at amortised cost[IAS 39.46(a)].Held-to-maturity investments These are non-derivative financial assets with fixed or determinablepayments that an entity intends and is able to hold to maturity and that do not meet the definitionof loans and receivables and are not designated on initial recognition as assets at fair value throughprofit or loss or as available for sale. Held-to-maturity investments are measured at amortisedcost. If an entity sells a held-to-maturity investment other than in insignificant amounts or as aconsequence of a non-recurring, isolated event beyond its control that could not be reasonablyanticipated, all of its other held-to-maturity investments must be reclassified as available-for-salefor the current and next two financial reporting years [IAS 39.9]. Held-to-maturity investmentsare measured at amortised cost [IAS 39.46(b)].2.1.4 Accounting valuation methods for financial liabilitiesIAS 39 recognises two classes of financial liabilities: [IAS 39.47]Financial liabilities at fair value through profit or loss This category has two subcategories:• Designated: a financial liability that is designated by the entity as a liability at fair valuethrough profit or loss upon initial recognition.• Held for trading: a financial liability classified as held for trading, such as an obligation forsecurities borrowed in a short sale, which have to be returned in the future.Financial liabilities measured at amortised cost using the effective interest method This categoryincludes, for example, hybrid and subordinated debt securities.2.2 Maturity data for all assets and liabilitiesAsset and liability maturities, where available, are classified in the financial statements into four‘buckets’: on demand, up to three month, three to twelve month, one to five years and more than fiveyears. Although not all banks provide all the information required for our data collection exercise, therate of coverage on our asset and liability maturity data in 2011 is of the order 80%. 15 The coveragerate of our maturity data in 2011 for loan contracts only is 82%, which compares favourably with 70%for the standard data provider SNL Financial in the same year. Our maturity data also agree closelywith the SNL Financial maturity data, where they overlap. In particular, for the banks with totalloans in 2011 appearing in both datasets, the ratio of our exposure to the exposure in SNL Financialis on average 97%, with standard deviation 13%, across the sample of banks. 16 We provide summaryinformation about the maturity profiles of assets and liabilities in Figures 1 and 2.The weighted average maturity gap for banks, depicted in Figure 1, is calculated by subtracting theweighted average maturity of liabilities from assets. The weights used are the total asset and liabilityvalues in each maturity bucket, normalised to sum to one. From Figure 1 it can be seen that exceptfor two banks (Piraeus Bank Group GR033 and Svenska Handelsbanken SE086) the weighted average15 By coverage of the data set, we mean the ratio of the number of non-missing observations across all banks, to thetotal number of observations that would characterise a complete data set.16 When we compare our total loan exposures to the total “exposure at default” used by the European BankingAuthority in its capital exercise, we obtain a mean of 93% and a standard deviation of 37% across all banks.8

AT002AT003BE004BE005CY006CY007DE018DE019DE020DE021DE023DE024DE025DE027DE028DE029DK008DK009DK010DK011ES059ES060ES061ES062ES064FI012FR013FR014FR016GB088GB089GB090GB091GR032GR033HU036IE037IE038IE039IT040IT041IT042IT043IT044MT046NL047NL048NL049NL050NO051PL052PT053PT055PT056SE084SE085SE086SE087SI057SI058Years6543210-1Weighted average maturity gap between assets and liabilities for large European banks in 2011Figure 1: Average maturity gap for large European banks in 2011, based on the cashflow timingassumptions used throughout this paper. The red line shows the sample mean (2.07 years) and thegreen lines show plus/minus one standard deviation (1.44 years).9

AT002AT003BE004BE005CY006CY007DE018DE019DE020DE021DE023DE024DE025DE027DE028DE029DK008DK009DK010DK011ES059ES060ES061ES062ES064FI012FR013FR014FR016GB088GB090GB091GR032GR033HU036IE037IE038IE039IT040IT041IT042IT043IT044MT046NL047NL048NL049NL050NO051PL052PT053PT054PT055PT056SE084SE085SE086SE087SI057SI058Eur billions6004002000-200-400-600Asset and liability exposures by maturity for large European banks in 2011demand up to 3 month 3 to 12 month 1 to 5 years more than 5 yearsFigure 2: Asset and liability exposures according to the annual financial statements for large Europeanbanks as at December 2011. The maturity transformation activitiy from short term liabilities to longterm assets is immediately evident.10

Loan assets by bank and country of origin in 2011Loans in EUR (billions)7505002500countryATBECYDEDKESFIFRGrHUIrITLUMTNLNOPLPTSESIUKAT001AT002AT003BE004BE005CY006CY007DE017DE018DE019DE020DE021DE022DE023DE024DE025DE026DE027DE028DK008DK009DK010DK011ES059ES060ES061ES062ES064FI012FR013FR014FR015FR016GB088GB089GB090GB091GR030GR031GR032GR033HU036IE037IE038IE039IT040IT041IT042IT043IT044LU045MT046NL047NL048NL049NL050NO051PL052PT053PT054PT055PT056SE084SE085SE086SE087SI057SI058BankFigure 3: Euro loan exposures by originating bank and country as at December 2011.maturity gap (the difference between the average maturity of assets and liabilities) is positive. Thesample mean is 2.07 years and the sample standard deviation is 1.44 years, as indicated on the figure bythe horizontal red and green lines. The representative bank in our sample is therefore ‘short’ the levelof interest rates, meaning that parallel upward shifts in yield curves would deteriorate the solvencyposition, while downward parallel shifts in yield curves would improve the solvency position. 17 We cansee that there is substantial variation between banks, even within countries, and the largest weightedaverage maturity gaps appear in CY, FI, IE, MY and NL. Interest-rate sensitivity of balance sheets issimilarly heterogenous across banks in our sample.We present a summary of the bank balance sheet data in Table 3. From this table, we can see thatthe median bank tends to fund itself at short durations from customers and the interbank market,and allocates these funds to longer-dated loans, especially to corporate and household borrowers. Themedian bank in our sample is therefore subject to the usual risk of parallel upward shifts in the yieldcurve, and to the liquidity risk associated with rolling over short-term interbank borrowings. The samestylised facts can be observed in Figure 2, where we see that banks tend to borrow in the “up to 3month” and “demand” categories, and they tend to lend in the “1 to 5 years” and “more than 5 years”categories. In addition to parallel shifts, banks are therefore highly exposed to increases in slope ofthe yield curve (with the average level of the curve fixed), because such increases would tend to reducethe value of (long-dated) assets while simultaneously increasing the value of (short-dated) liabilities.Level, slope and curvature effects are all special cases of the variability we are able to simulate inthis paper, although for consistency with the Basel Committee guideline method, we focus on parallelshifts in yield curves.2.3 Geography and sector data for loan assetsIn this section, we provide some summary information of the geographical and sectoral distributions ofthe loan asset exposures in the annual financial statements of large European banks for the years 2007-2011. This information is directly related to the location (X) dimension of net asset transformationthat we define in Section 3.1 below, and which we illustrate in Section 4.1.When considering the geographic distribution of loan exposures, we must distinguish betweenorigination and target countries. The origination country is the country of domicile of the bank that17 The sensitivity of security prices to interest rates is explained for the case of loan contracts in Section 3.2.11

Table 3: Summary of the bank assets and liabilities by maturity across all banks in the sample (inmillions of Euros).category subcategory maturity Min. Lower Q. Med. Upper Q. Max.liabilities interbank up to 3 month 0 1707 8722 20282 280667liabilities interbank 3 to 12 month 0 410 1816 5699 121359liabilities interbank 1 to 5 years 0 540 3092 12996 49148liabilities interbank more than 5 years 0 43 664 2860 26217liabilities customer deposits up to 3 month 0 3417 14506 55321 537284liabilities customer deposits 3 to 12 month 0 1822 5716 27616 1453598liabilities customer deposits 1 to 5 years 0 714 5556 17059 87785liabilities customer deposits more than 5 years 0 66 2086 10836 63077assets interbank up to 3 month 0 898 4162 17467 223345assets interbank 3 to 12 month 17 237 947 4110 204875assets interbank 1 to 5 years 0 66 547 4546 70322assets interbank more than 5 years 0 4 152 1729 30791assets loans corporate up to 3 month 0 991 3678 13122 55140assets loans corporate 3 to 12 month 117 1557 5192 12533 199475assets loans corporate 1 to 5 years 258 4633 15007 32487 258139assets loans corporate more than 5 years 0 5521 21343 48141 158765assets loans financial institution up to 3 month 0 230 971 5158 34228assets loans financial institution 3 to 12 month 22 321 1733 5023 116453assets loans financial institution 1 to 5 years 48 625 5194 12392 150700assets loans financial institution more than 5 years 0 947 4008 16887 62434assets loans household up to 3 month 0 342 2440 10243 85538assets loans household 3 to 12 month 0 1140 3825 11527 170050assets loans household 1 to 5 years 0 1688 10103 25336 220060assets loans household more than 5 years 0 1638 11330 46005 259236assets loans public sector up to 3 month 0 11 161 1466 19644assets loans public sector 3 to 12 month 0 29 199 1808 6653assets loans public sector 1 to 5 years 0 45 478 3893 18177assets loans public sector more than 5 years 0 5 660 3392 27372assets available for sale debt up to 3 month 0 93 1569 4191 29448assets available for sale debt 3 to 12 month 0 656 1374 4972 205487assets available for sale debt 1 to 5 years 0 1195 5848 25972 297715assets available for sale debt more than 5 years 0 631 2387 14373 79772assets available for sale equity up to 3 month 0 9 55 297 2800assets available for sale equity 3 to 12 month 0 14 64 353 3987assets available for sale equity 1 to 5 years 0 34 293 936 7950assets available for sale equity more than 5 years 0 25 177 842 7968assets held for trading debt up to 3 month 0 0 11 1003 10185assets held for trading debt 3 to 12 month 0 4 500 1397 25050assets held for trading debt 1 to 5 years 0 19 993 4004 25251assets held for trading debt more than 5 years 0 2 153 4838 37425assets held for trading equity up to 3 month 0 0 2 71 1826assets held for trading equity 3 to 12 month 0 1 13 153 1582assets held for trading equity 1 to 5 years 0 2 50 358 3780assets held for trading equity more than 5 years 0 0 13 152 739612

EUR billions0 2,000 4,000 6,000 8,000Loan asset values by target countryEUR billions0 1,000 2,000 3,000 4,000 5,000Loan asset values by sectorBa Basic andconstructionBI Banks andintermediationCa Capital goodsCC Consumer cyclicalEn EnergyGV GovernmentMO MortgageMT Media andtelecommunicationsNC Consumernon−cyclicalOF Other financialOT OtherRC Other consumerretailRE Commercial realestateTr TransportEuroareaOtherEuropeancountriesNorthAmericaLatinAmericaAsiaRestofthewordBa BI Ca CC En GV MO MT NC OF OT RC RE Tr(a) Country(b) SectorFigure 4: Total allocation of loan assets by (a) country and (b) sector of loan counterparty, across allbanks in the sample in 2011.originated the loan contract, and the target country is the country of domicile of the loan counterparty,which may be an individual or an institution. We summarise the loan exposures of large Europeanbanks as at December 2011 by origination country in Figure 3. The heights of the bars show total loansof each bank, measured in Euros, and the colours on the plot group the banks and loans by countryof domicile. Banks in the sample are domiciled in 21 countries. We can see that the banks with thelargest loan exposures are in Spain, France and the UK, while those in Italy and the Netherlands arealso large. If we take a “demand-side” view of economic growth under credit constraints, then theselargest banks are the most important for growth in Europe. The figure also shows that the countrywith the most banks in the sample is Germany.We also examine the geographic distribution of loans by country of loan counterparty in Figures4a and 5. Figure 4a shows that large European banks primarily allocate loan capital to counterpartiesin the Euro area and secondarily to counterparties in other European countries in 2011. In Figure 5,we see that the high-level sectoral portfolio location in 2011 is similar within the loans extended tothese two regions. Within these two major regions, most loans are extended to households, followedclosely by non-financial corporations. Loans to the public sector are the smallest allocation, whichmay be misleading because these banks could lend substantially to national and local governments bypurchasing debt instruments. On a more detailed sector breakdown, Figure 4b shows that these largeEuropean banks allocate most of their loan capital to household mortgages and diversify among theother economic subsectors.2.4 Yield curve dataWe use Euro area swap curves, monthly from January 1999 to March 2013 to characterise the leveland movements in yield curves. The tickers and maturities, taken from Bloomberg, are presented inTable 4. We present summary statistics for the yield curve data used in this paper in Table 5.13

Eur billionsLoan asset exposures by destination region and sector for large European banks in 20113.5003.0002.5002.0001.5001.0005000Euro area Other european countries North America Latin America Asia Rest of the worldCorporate Financial Institution Household Public SectorFigure 5: Total loan asset exposures in our sample of large European banks in 2011, summarised bytarget country and sector.Table 4: Yield curve tickers and maturities in years according to Bloomberg. These maturities areused in Section 3.3 to model the level and changes of the yield curve.series term series term series termEONIA Index 0.00 EUSWK Curncy 0.92 EUSA11 Curncy 11.00EUR001W Index 0.02 EUSA1 Curncy 1.00 EUSA12 Curncy 12.00EUR001M Index 0.08 EUSA1F Curncy 1.50 EUSA15 Curncy 15.00EUR002M Index 0.17 EUSA2 Curncy 2.00 EUSA20 Curncy 20.00EUR003M Index 0.25 EUSA3 Curncy 3.00 EUSA25 Curncy 25.00EUR004M Index 0.33 EUSA4 Curncy 4.00 EUSA30 Curncy 30.00EUR005M Index 0.42 EUSA5 Curncy 5.00 EUSA35 Curncy 35.00EUR006M Index 0.50 EUSA6 Curncy 6.00 EUSA40 Curncy 40.00EUSWG Curncy 0.58 EUSA7 Curncy 7.00 EUSA45 Curncy 45.00EUSWH Curncy 0.67 EUSA8 Curncy 8.00 EUSA50 Curncy 50.00EUSWI Curncy 0.75 EUSA9 Curncy 9.00EUSWJ Curncy 0.83 EUSA10 Curncy 10.0014

Table 5: Summary statistics for the yield curve data, in percentage points.series mean sd min max series mean sd min maxEONIA Index 2.47 1.44 0.08 5.16 EUSA3 Curncy 3.23 1.26 0.47 5.59EUR001M Index 2.52 1.43 0.11 5.05 EUSA30 Curncy 4.45 1.05 1.86 6.22EUR001W Index 2.45 1.44 0.08 4.89 EUSA35 Curncy 3.81 0.80 1.86 5.05EUR002M Index 2.59 1.43 0.15 5.13 EUSA4 Curncy 3.40 1.21 0.60 5.65EUR003M Index 2.67 1.40 0.19 5.28 EUSA40 Curncy 4.12 0.92 1.87 5.99EUR004M Index 2.70 1.38 0.23 5.32 EUSA45 Curncy 3.84 0.82 1.88 5.14EUR005M Index 2.74 1.36 0.28 5.36 EUSA5 Curncy 3.56 1.16 0.77 5.71EUR006M Index 2.77 1.34 0.32 5.38 EUSA50 Curncy 4.07 0.90 1.89 5.74EUSA1 Curncy 2.87 1.36 0.33 5.38 EUSA6 Curncy 3.70 1.13 0.95 5.76EUSA10 Curncy 4.09 1.04 1.56 5.95 EUSA7 Curncy 3.82 1.10 1.12 5.82EUSA11 Curncy 4.07 1.01 1.68 5.98 EUSA8 Curncy 3.92 1.08 1.29 5.86EUSA12 Curncy 4.22 1.01 1.79 6.06 EUSA9 Curncy 4.01 1.06 1.43 5.89EUSA15 Curncy 4.35 1.00 1.91 6.16 EUSWG Curncy 2.72 1.53 0.32 5.35EUSA1F Curncy 2.92 1.34 0.35 5.43 EUSWH Curncy 2.73 1.52 0.32 5.30EUSA2 Curncy 3.04 1.31 0.38 5.52 EUSWI Curncy 2.74 1.49 0.32 5.31EUSA20 Curncy 4.46 1.01 1.92 6.22 EUSWJ Curncy 2.74 1.52 0.32 5.33EUSA25 Curncy 4.43 1.03 1.90 6.22 EUSWK Curncy 2.75 1.52 0.32 5.343 Method3.1 A theory of maturity transformation and its relation to interest rateriskConsider a financial institution that enters into contractual arrangements with other parties. Thesecontractual agreements bind the institution into making and receiving payments many years intothe future. Let us imagine that there are finitely many characteristics of these future cashflowsthat are relevant for determining the price today of transferring these rights and obligations toother institutions. We could call this set of characteristics Ω, and we could write Ω = X × T forsome finite sets X and T with T ⊂ R + to record the fact that among these characteristics will bethe contractual maturity or repricing date of each cashflow (T ). The financial institution is thereforedefined by its asset and liability cashflow streams { }{ }A x,t ∈ R : (x, t) ∈ X × T ⊂ R N × R + andLx,t ∈ R : (x, t) ∈ X × T ⊂ R N × R + respectively, where x ∈ X ⊂ R N is an indexing set 18 andt ∈ T ⊂ R + is time into the future. 19 We can define the net asset stream or equity stream using afunctional application of the accounting identity E {E x,t A x,t − L x,t : (x, t) ∈ X × T }. The equitystream can be thought of as the future profit or future net cashflow in the firm emerging over time inevery tradable claim x ∈ X.We can say that an institution engages in net asset transformation if ∃(x, t), (x ′ , t ′ ) ∈ X × T suchthat E x,t ≠ E x ′ ,t′, or in words, if there are differences in its borrowing and lending across characteristicsin X × T . We give a graphical representation of transformation in Figure 6 , where an intermediaryis a net borrower of some tradable claims and a net lender of others. Maturity transformation is thena special case of net asset transformation and could be defined local to some x ∈ X or globally in allx ∈ X . An intermediary engages in local maturity transformation at x ∈ X if ∃t, t ′ ∈ T such thatE x,t ≠ E x,t ′, which says that the intermediary transforms assets of type x ∈ X from various maturitiesinto other maturities, while an intermediary engages in global maturity transformation if ∃t, t ′ ∈ Tsuch that ∑ x E x,t ≠ ∑ x E x,t ′. We can further talk of positive or negative maturity transformation,18 The index x ∈ X could be thought of as measurable time-invariant classifications of assets and liabilities relevant tothe price of a contract. Formally, X = Ω\T . Examples are sector, geographic, and ratings-based classifications of assetsand liabilities. In the context of assessing the revaluation effect of changes in asset prices or interest rates, we assumethat we have a complete market so that we can treat every element x ∈ X as a tradable claim with a measurable price.We will require that X be finite, or in other words |X| < ∞. The indexing set X is relevant for grouping assets andliabilities that are traded together, have similar prices (which may or may not be related to others through substitutioneffects) and whose risk characteristics are therefore similar.19 We will require |T | < ∞, which does not in principle preclude the institution from holding non-maturing assets likestocks.15

tA tt5++t t tt4−+L tt3+t t tt2−−−+t1−−+E tnegative none positivet t tx1 x2 x3 x4x5xFigure 6: A graphical representation of (net) Figure 7: Examples of positive and negativeasset transformation by a financial intermediary.The intermediary is a net borrower at mediary. The top, middle and bottom rowsmaturity transformation for a financial inter-some contractual maturities (t1 1 , t 2 , t 4 ) and in give the values of assets, liabilities and net assetsby maturity.some markets (x 1 , x 2 , x 4 ) while being a netlender at other maturities and in other markets.where positive maturity transformation refers to assets that are ‘on average’ longer in maturity thanliabilities. We don’t define these notions explicitly, but provide some examples of positive and negativematurity transformation in Figure 7. From balance sheet data, we typically find that banks engagein positive maturity transformation, while insurers engage in negative maturity transformation. Asa complement to maturity transformation, if we use the term sector to refer to the more abstract Xdimension of future contracts, we can similarly define local and global (in t ∈ T ) sector transformation.In an economy where all claims indexed by (x, t) ∈ X × T ⊂ R N × R + are traded in perfectlycompetitive markets populated by agents with weakly monotonic preferences, we have a unique pricingkernel for tradable claims and hence a discount factor B : R N × R + → R + satisfying ∂B∂t≤ 0 for allt ∈ R + . In this case, the value of assets at time zero, which is the price that another institution wouldhave to pay to obtain these future cash inflows, is given by∑B(x, t)A x,t ,x,t1with the values of liabilities and equity at time zero similarly defined. The solvency position of thefinancial institution is given by ∑ x,t B(x, t)E x,t, and the financial institution is said to be solvent attime zero on a market-consistent basis if and only if∑B(x, t)E x,t > 0.x,tNote that the definition of A t is sufficiently general that it could depend on the pricing function B,which would arise, for example, if the firm purchased a floating-rate note, payments on which dependedon realised interest rates. The value of equity is then the value of assets less the value of liabilities. Inthe case where we can express the pricing function as B(x, t) = exp [ t−´ 0 r(x, s)ds] for some integrablefunction r : R N × R + → R and for all x, we can interpret r { }r(x, t) : (x, t) ∈ R N × R + as the setof yield curves implied by the discount function B.For the balance sheet items that are valued on a market-consistent basis, the financial institutionreports their value at the valuation date, E x,t B x,t . If the per-unit pricing function B were to move16

to some B ′ , and if the quantity function E x,t were to remain constant, then the market-consistentvaluation of the balance sheet item would become E x,t B ′ x,t, implying a percentage change ofE x,t B ′ x,t − E x,t B x,tE x,t B x,t= B′ x,tB x,t− 1 ≈ log B′ x,tB x,t. (1)By assuming a distribution for B ′ , either through assuming a distribution for the set of yield curvesr when this exists, or through assuming a distribution for the pricing function B ′ directly, we havea distribution for this percentage change in (1) above. The interest rate risk or asset price risk thenarises from the revaluation effect of unanticipated changes in interest rates or per-unit asset prices,and the intermediary’s exposure to such risk depends on the allocation of the intermediary’s net assetsacross all (x, t) claims.3.2 Interest rate risk of loan securities and portfoliosAs we see in Section 4.1, the most important component of the bank balance sheet for assessing interestrate revaluation risk, 20 ignoring off-balance sheet instruments, are the loan assets, because of their longmaturity. In assessing interest rate revaluation risk of banks, we therefore focus on the interest raterisk of these loan assets. Assessing the interest rate revaluation risk of the whole balance sheet in thespirit of the EVM for European banks would be a useful exercise, but it is beyond the scope of thispaper.In our study of these loan assets, we assume that all loan assets are fixed-rate amortising loans.Variable-rate loan contracts exist and are less price sensitive to interest rate changes. However, sinceour loan exposures by maturity are categorised by time to “next repricing date”, rather than by timeto contractual maturity, variable-rate contracts behave like fixed-rate contracts maturing on thir nextrepricing date. However, to the extent that these loan exposures by maturity in fact include heterogenouscontract types, 21 the pricing and risk methods associated with fixed-rate amortising loans maynot be appropriate.In Section 1.1 above we discuss the Basel Committee guidelines for assessing interest rate revaluationrisk. In this section, we offer simple alternative methods for assessing interest rate revaluation riskbased on methods for pricing such amortising loan contracts. The pricing functions we propose here arewell known present value functions. 22 The simplest such pricing function is the formula for the presentvalue of a fixed-term annuity of 1 per year for τ years, at constant annual continuously-compoundedinterest δ:p(δ, τ) 1 − e−δτ.δThis formula corresponds to a present value under a flat yield curve, with level δ at every maturity.We can generalise this formula to the case where yield curves are not flat. If we let {f(m)} be theforward curve, 23 the present value of the same fixed-term annuity isp({f(m)}, τ) ˆ τ0exp(−ˆ u0f(m)dm)du.Using p(δ, τ) and p({f(m)}, τ), we have pricing functions for individual loan contracts. However, if wewould like to compare banks, we need to be able to price portfolios of loan contracts too, so that wecan compute interest rate sensitivities. The price of a portfolio defined by a (possibly countable) setof shares {φ i }, where perhaps ∑ i φ i = 1, is 2420 The revaluation or repricing risk that we use interchangeably throughout this paper simply means the percentagechange in value of a contract or portfolio of contracts given a change in interest rates or yield curves.21 Heterogeneity in loan contracts in the form of collateral or embedded options, for example for default and prepaymentrespectively, would be key sources of pricing heterogeneity and hence heterogeneity in interest rate risk. Prepaymentrisk is defined in Footnote 11.22 More sophisticated pricing functions like those using risk-neutral valuation would be an interesting extension to thispaper.23 For explanations of the terms forward curve and zero curve, see Section 3.3 and Svensson (1994).24 In the case where f(m) = δ ∀m, we havep({φ i }, δ, {τ i }) = ∑ iφ i p(δ, τ i ).17

p({φ i }, {f(m)}, {τ i }) ∑ iφ i p({f(m)}, τ i ).For the purposes of calculating sensitivity to interest rate revaluation, we do not require that {φ i } benormalised to sum to one. In particular, we could use Euro-denominated exposures in place of {φ i },because the normalisation constant cancels out in the sensitivity measures below.We seek to measure the percentage change in value of a loan, or portfolio of loans, given a changein interest rates or yield curves. We could consider using an analytic derivative 25 to compute thissensitivity, which also motivates the Basel Committee guideline discussed in 1.1 above. However, sucha derivative would only be valid, and an accurate approximation, for infinitesimally small changes inyield curves. If, as per the Basel Committee guidelines, we were to seek the effect of a 200 basis pointinterest rate shock, which is fairly large, then we would not expect the derivative to provide a goodapproximation. A more exact approach would be to compute the present value under two interest ratescenarios – one before, and one after the shock. This exact approach would capture the non-linearitiesin exposure. For example, increases and decreases in interest rates of equal magnitude would not beexpected to produce equal decreases and increases in present values, respectively. If we assume a flatforward curve, the change in present value takes the formlog p(δ 1 , τ) − log p(δ 0 , τ),where δ 0 is the constant annual continuously compounded interest rate before the shock, and δ 1 is thesame rate after the shock. This expression can be interpreted as a percentage change in the presentvalue of a loan contract and is directly analogous to (1) above. If we assume an arbitrary shape to theforward curve, the change in present value takes the formlog p({f(m)} 1 , τ) − log p({f(m)} 0 , τ),and if we consider a portfolio of loan contracts, the change in present value takes the formlog p({φ i }, {f(m)} 1 , {τ i }) − log p({φ i }, {f(m)} 0 , {τ i }),where the weights {φ i } are assumed invariant to the interest rate change, and where the normalisationconstant for {φ i } cancels.3.3 Characterising interest rate movementsWe can characterise the shape of the yield curve at any point in time by the forward curve or thezero curve. The zero rate at any given maturity is the yield to maturity one could obtain on a zerocouponbond of that maturity, and the zero curve is the collection of such zero rates at all maturities.The zero-coupon bond underlying a zero rate may be hypothetical, for example a Treasury securityor corporate obligation that does not exist in the market at that particular maturity. Zero curvesare inferred from the yields to maturity on a set of coupon-paying bonds, the prices of which can beobserved in the market, through a process known as bootstrapping. 26The forward curve at any maturity is defined as the increase in yield to maturity one could obtaintoday by marginally extending one’s holding period from that maturity. If the zero curve is defined by{z(m)}, then the forward curve is defined by {f(m)|f(m) lim h→0 + ((m + h)z(m + h) − mz(m)) /h =d (mz(m)) /dm ∀m}, and similarly, the zero curve can be obtained from the forward curve pointwiseby z(m) = ´ m0 f(u)du/m.In this paper, our yield curves are given by the Euro area interbank and swap rates discussedin Section 2.4. At every month-end, we therefore have 34 points that characterise the shape of the25 Note that we would need a directional derivative in the case of a general forward curve. In this paper, we onlyconsider directional derivatives in the direction of a constant function, or in other words, we only consider parallel shiftsin the yield curve for consistency with the Basel Committee guideline method for interest rate sensitivity assessment. InSection 4.3 we show that parallel shifts are not plausible from historical data on Euro yield curves.26 The process of bootstrapping involves transformation and interpolation. For a discussion, see Svensson (1994).18

yield curve. A particular yield curve parametrisation allows use to reduce this dimensionality. ANelson-Siegel model of the yield curve takes the formf(m) = β 0 + β 1 e −m/τ1 + β 2mτ 1e −m/τ1z(m) = β 0 + (β 1 + β 2 ) τ 1m (1 − e−m/τ1 ) − β 2 e −m/τ1 , (2)where the four parameters to be specified are β 0 , β 1 , β 2 and τ 1 (Nelson and Siegel, 1987). If we assumefor convenience that the forward curve is closely approximated by the interbank swap curve for whichwe have data, then we can estimate at each month-end these four parameters by choosing them tominimise some distance measure between the 34 observed and fitted values of f. 27 We also considerthe so-called Svensson model of the yield curve, which takes the formf(m) = β 0 + β 1 e −m/τ1 + β 2mτ 1e −m/τ1 + β 3mτ 2e −m/τ2z(m) = β 0 + (β 1 + β 2 ) τ 1m (1 − e−m/τ1 ) − β 2 e −m/τ1 + β 3( τ2m (1 − e−m/τ2 ) − e −m/τ2 ), (3)where the six parameters to be estimated are β 0 , β 1 , β 2 , β 3 , τ 1 and τ 2 (Svensson, 1994). By specifyingone of these parametric forms of the yield curve, i.e. Nelson-Siegel or Svensson, one can obtain thepricing functions and sensitivities discussed in Section 3.2 above. In particular, by varying the β 0parameter, one can obtain the effect of parallel shifts in the yield curve on the price of a loan contractor portfolio of loan contracts. We show below that our results using Nelson-Siegel or Svensson modelsare qualitatively similar.By estimating the parameters of the Nelson-Siegel and Svensson models at each month-end under asquared error loss function, we obtain a characterisation of the yield curve at every point in time. Theparameters of these models can loosely be interpreted in terms of level, slope and curvature effects,although the interpretation in the Svensson model is more difficult. For interpretation, we thereforefocus on the Nelson-Siegel model, where β 0 can be interpreted as the level of the yield curve, β 1as the premium of the short term rate over the long term rate (i.e. the inverse of the slope of thecurve), and β 2 as the premium of the medium term rate over the long and short term rates (i.e. the‘humpedness’ or curvature of the yield curve). By examining also the month-to-month changes in thesebeta parameters, we can learn about shape changes in the yield curve through time.We present the kernel density estimates for month-to-month changes in β 0 in Figure 8. We cansee that in both yield curve models, changes in the level of yield curves are roughly symmetric andclustered around zero. We explore changes in the yield curve further in Section 4.3.4 Results4.1 Observed maturity transformation by European banks in 2011We provide a graphical representation of the maturity transformation undertaken by our sample ofbanks in Figure 9. From the figure we can see that the median bank in 2011 obtained financingmostly from customer deposits and instruments valued at amortised cost, while investing mostly inloans. The maturity mismatch on bank balance sheets is also evident: within the loan category, themedian bank allocated more capital to longer-dated assets, but within the deposit category, the medianbank obtained more funding from shorter-dated liabilities. The median bank also obtained a signicantshare of funding in the amortised cost category from the 1-5 year horizon, which indicates hybrid andsubordinated debt instruments.27 In principle, we should apply a ‘bootstrap’ procedure to determine the zero and forward curves implied by the Euroswap curve data, and then we should fit the parametric yield curve model to this forward curve. This is a work inprogress and should not affect the results significantly, since the various parametrisations are shown in this paper not tohave a noticeable affect on the sensitivity calculation.19

Kernel density of month−on−monthchanges in beta0: Nelson−SiegelKernel density of month−on−monthchanges in beta0: SvenssonDensity0 50 100 150 200Density0 20 40 60 80 100−0.02 −0.01 0.00 0.01 0.02N = 166 Bandwidth = 0.0006728−0.04 −0.02 0.00 0.02 0.04N = 166 Bandwidth = 0.001099Figure 8: Kernel densities of month-on-month changes in β 0 under the Nelson-Siegel and Svenssonmodels.Net assets for the median bank in 2011by maturity and subcategorymaturitynotdisclosedremaining maturity, or time to next repricingundeterminedmore than5 years1 to 5years3 to 12monthup to 3monthnet assets (EUR)20000100000−10000demandamortisedcostavailablefor salecentralbankcustomerdepositsheld fortradingheld tomaturityasset / liability subcategoryinterbankloansFigure 9: A graphical depiction of maturity transformation in the 2011 European banking data. Eachcell in the matrix gives the median net asset (asset minus liability) exposure across all banks in thesample. This figure is the empirical analog of the theoretical chart 6.20

Table 6: Percentage change in the value of an individual loan contract for various shock sizes, maturitiesand methods. Subtable (a) uses the Basel Committee guideline method, (b) uses the simplest flat yieldcurve loan pricing model, (c) uses a model based on Nelson-Siegel forward rates calibrated to historicalparameters, and (d) uses Svensson forward rates also calibrated to historical parameter values. In eachsubtable the rows give the size of the shock, which is a parallel shift in the level of the forward curve,and the columns give the remaining maturity of the loan contract.(a) Basel Committee guideline1 3 10 15 20 30-3.0% 2.1 6.8 19.9 26.8 33.6 39.0-2.0% 1.4 4.5 13.3 17.8 22.4 26.0-1.0% 0.7 2.2 6.6 8.9 11.2 13.0-0.5% 0.4 1.1 3.3 4.5 5.6 6.50.0% -0.0 -0.0 -0.0 -0.0 -0.0 -0.00.5% -0.4 -1.1 -3.3 -4.5 -5.6 -6.51.0% -0.7 -2.2 -6.6 -8.9 -11.2 -13.02.0% -1.4 -4.5 -13.3 -17.8 -22.4 -26.03.0% -2.1 -6.8 -19.9 -26.8 -33.6 -39.0(c) Nelson-Siegel (β 0 , β 1 , β 2 , τ 1 ) = (3.2, −.7, 4.5, 73)%1 3 10 15 20 30-3.0% 1.5 4.4 14.5 21.5 28.2 41.1-2.0% 1.0 3.0 9.6 14.1 18.5 26.7-1.0% 0.5 1.5 4.8 7.0 9.1 13.0-0.5% 0.2 0.7 2.4 3.5 4.5 6.40.0% 0.0 0.0 0.0 0.0 0.0 0.00.5% -0.2 -0.7 -2.3 -3.4 -4.4 -6.21.0% -0.5 -1.5 -4.7 -6.8 -8.8 -12.32.0% -1.0 -2.9 -9.3 -13.4 -17.2 -23.83.0% -1.5 -4.4 -13.8 -19.8 -25.3 -34.7(b) Flat rate δ = 3.2%1 3 10 15 20 30-3.0% 1.5 4.4 14.1 20.5 26.5 37.3-2.0% 1.0 2.9 9.3 13.5 17.4 24.1-1.0% 0.5 1.5 4.6 6.7 8.5 11.7-0.5% 0.2 0.7 2.3 3.3 4.2 5.80.0% 0.0 0.0 0.0 0.0 0.0 0.00.5% -0.2 -0.7 -2.3 -3.3 -4.1 -5.61.0% -0.5 -1.5 -4.5 -6.5 -8.2 -11.12.0% -1.0 -2.9 -9.0 -12.8 -16.1 -21.53.0% -1.5 -4.4 -13.4 -18.9 -23.7 -31.3(d) Svensson (β 0 , β 1 , β 2 , β 3 , τ 1 , τ 2 ) = (2.1, 1.1, 1.8, 5.5, 65, 855)%1 3 10 15 20 30-3.0% 1.5 4.6 18.7 29.2 38.0 49.9-2.0% 1.0 3.1 12.4 19.3 25.1 32.8-1.0% 0.5 1.5 6.2 9.6 12.4 16.1-0.5% 0.2 0.8 3.1 4.8 6.2 8.00.0% 0.0 0.0 0.0 0.0 0.0 0.00.5% -0.2 -0.8 -3.1 -4.7 -6.1 -7.91.0% -0.5 -1.5 -6.1 -9.4 -12.2 -15.62.0% -1.0 -3.1 -12.1 -18.7 -24.1 -30.83.0% -1.5 -4.6 -18.0 -27.9 -35.7 -45.44.2 How good is the Basel Committee interest rate sensitivity guidelinefor loans?4.2.1 Effect of loan-specific pricingThe Basel Committee guidelines outlined in Section 1.1 do not take into account the type of securityfor which an interest rate risk assessment is being performed. In particular, the guidelines may or maynot be suitable for typical loan contracts. We investigate the performance of the Basel Committeeguideline method for interest rate revaluation sensitivity by comparing it to our alternative simpleloan pricing models of Section 3.2 with parametric forward curves specified in 3.3. The results aresummarised in Table 6. Under all methods, positive interest rate shocks (increases in the level of theforward curve) result in decreases in the value of a loan contract with any maturity, and decreasesin interest rates result in revaluation increases. Larger absolute interest rate shocks result in largeabsolute changes in value.The Basel Committee guideline method, like any duration-based sensitivity method 28 , producessensitivities that are symmetric about zero: positive and negative interest rate shocks of equal absolutesize have an equal absolute revaluation effect; in other words, for any given loan maturity, thepercentage decrease in loan price from an interest rate increase is the same as the percentage increasein loan price from an interest rate decrease of equal absolute size. We can see that all the alternativesimple loan models, however, are able to capture the asymmetric revaluation effect of interest ratechanges. At short maturities and for small shock sizes, these asymmetric effects are negligibly small,while at longer maturities and at larger shock sizes we note that loan prices are more sensitive todecreases in interest rates. It is not surprising, therefore, that the Basel Committee guideline methodsometimes overstates, and at other times understates, the interest rate sensitivity of loan prices.From the regulator’s point of view, we might be most concerned with situations where the Basel28 For an introduction to duration-based sensitivity measurement, see Kaufman (1984).21

Committee method understates the revaluation sensitivity to interest rate increases. 29 Against the flatrate and Nelson-Siegel models, the Basel Committee method is prudent for maturities up to 30 years,in that it overstates the loan price sensitivity to interest rate increases. 30 This is comforting since wewould expect the remaining maturity of most loan contracts to be less than 30 years. However, whencompared to the Svensson model, the Basel Committee method is only prudent for loan contracts ofup to 10 year maturity, beyond which it understates the loan price sensitivity to interest rate increases.For banks with a substantial proportion of loans in the 10-30 year maturity category, we might expectthe Basel Committee method to understate the loan price sensitivity to interest rate increases.While prudential regulators presumably favour the conservativeness of a method, investors wouldlike an accurate assessment of the risk, with overstatements and understatements being equally harmful.Relative to the alternative loan models, the Basel Committee method overstates the revaluation gainsfrom interest rate decreases at shorter maturities and understates these revaluation gains at longermaturities. The Basel Committee method for interest rate revaluation sensitivity is therefore generallyconservative for shorter-maturity loans, and understates risk for longer-maturity loans.4.2.2 Effect of current yield curveThe Basel Committee guideline method for assessing interest rate revaluation sensitivity does not accountfor the prevailing yield curve at the time of the sensitivity estimate. For example, we mightintuitively expect a 2% change in interest rates to be more serious when interest rates are low; conversely,we might expect a 2% shock not to be very serious in a high interest rate environment. Weinvestigate this by comparing the sensitivities from the Basel Committee guideline method to the sensitivitiesfrom our simplest flat rate loan model of Section 3.2, noting that the latter does depend ona reference or prevailing rate of interest. We present a graphical summary in Figure 10.From the figure, we see that the Basel Committee method overstates the risk of a 2% parallelupward shift in the yield curve for loan maturities up to 27 years, relative to the simplest loan model.This observation agrees with those of the preceding section: although the Basel Committee methoddoes not take into account the specific form of the loan contract, it gives a conservative assessmentof the interest rate risk for loans with remaining maturity up to 27 years. However, we note that theprevailing level of the yield curve does noticeably affect the sensitivity of the price of a loan contract.When forward rates are flat and high, say 5%, the Basel Committee method conservatively assessesthe risk of a 2% parallel upward shift in yield curves (forward rates) for loans with remaining maturityup to 40 years. When yield curves are flat and low, say .1% or 1%, the Basel Committee methodunderstates the risk associated with 30-year loans.From the preceding section, we know that the Basel Committee guideline method is generallyconservative for shorter-maturity loans, and understated for longer-maturity loans. In addition tothese stylised facts, we also observe for interest rate increases that the Basel Committee guidelinemethod is less conservative, or more understated, when interest rates are low than when interest ratesare high. The Basel Committee method, which does not allow for the prevailing level of interest rates,is less appropriate for supervision in low interest rate environments.4.2.3 Effect of portfolio aggregationRegardless of the type of security and the current level of the yield curve, the Basel Committeeguideline method for interest rate revaluation sensitivity does not provide a unique method for portfolioaggregation. Suppose that a bank holds two loans of different remaining maturties, one with 1 year andthe other with 10 years. The Basel Committee method provides senstivities for each of these contractsindividually, but not uniquely for a portfolio of both. Two natural methods suggest themselves forcomputing the interest rate revaluation sensitivity of the portfolio with the Basel Committee method.29 We note in Section 4.1 that European banks’ on-balance-sheet positions in 2011 are net positive at long maturitiesand net negative at short maturities. This finding is very typical of banks’ role as maturity-transformers. However,it exposes them to increases in interest rates, since such increases would cause the value of (long-term) assets to dropby more than the offsetting rise in the value of (short-term) liabilities. Off course, the regulator might anticipate thatrational market participants should rationally compensate for overstatements/understatements in the Basel Committeeguideline method, and if there are no informational obstacles to the market participants doing so, such a regulator mightbe equally averse to both over- and understatements of interest rate sensitivity.30 This statement should be qualified by the specific parameter assumptions that have been made here on δ, β 0 , β 1 , β 2 , τ 1 .See the discussion of Figure 10.22

0Percentage change in price givena 2% parallel upward shift in interest rates−10percentage−20−30MethodBasel guidelineloan model 0.1%loan model 1%loan model 3%loan model 5%loan model 7%loan model 9%−400 10 20 30 40 50remaining loan maturityFigure 10: The effect of a 2% increase in interest rates at all maturities on the price of a loan contractwith remaining maturity between 1 and 50 years, according to the Basel Committee guideline and thesimple formula log p(δ + .02, τ) − log p(δ, τ) based on the present value function p(δ, τ) = (1 − e −δτ )/δ,where τ ∈ [1 : 50] is the remaining loan maturity and δ ∈ {.001, .01, .03, .05, .07, .09} is the level of theflat yield curve before the shock.23

The first is to use a weighted average of the Basel Committee interest rate revaluation sensitivitiesof each asset, based on the prevailing weights of each asset in the portfolio. We call this a weightedaverage sensitivity method for assessing the interest rate revaluation sensitivity of the portfolio. Theis the approach recommended in Annex 4 of the Basel Committee guidelines (Basel Committee BaselCommittee on Banking Supervision, 2004), but it is not the only possible approach. Under thismethod, the portfolio sensitivity is a linear combination of the sensitivities of the securities in theportfolio. An alternative method, which we call the weighted average maturity method, is to computethe Basel Committee interest rate sensitivity of a single hypothetical security with maturity equal tothe weighted average maturity of all the securities in a portfolio, again using portfolio weights. 31We examine the performance of these twomethods for applying the Basel Committeeguideline method to portfolios of loan contractsusing Figure 11. Consider the case where a bankholds only two loan contracts: one with 1 yearand the other with 10 years remaining maturity.The horizonal axis in Figure 11 represents theweight placed on the 1-year loan, and the variouslines show the sensitivity of the portfolio valueto a 2% increase in the level of the yield curveunder the various methods, including those discussedin Sections 1.1 and 3.2. We see that allmethods are able to capture the greater price sensitivityof the 10-year loan than the 1-year loan.We have already analysed above the sensitivitesat the left and right endpoints of Figure 11, wherewe found for individual loan contracts with maturitiesless than 10 years that the Basel Committeemethod is relatively conservative. The BaselCommittee method performs aggregation by linearinterpolation between these two sensitivities,while all other methods display some convexity.In particular, although the two Basel Committeeportfolio methods agree exactly at the leftand right endpoints, the weighted average maturitymethod is more conservative everywhere inbetween, which shows that the Basel Committeeguideline sensitivity for individual loan contractsis convex in the remaining maturity of the loan.This convexity is borne out by the other loanpricingmethods too. Perhaps surprisingly, whilethe two Basel Committee methods for portfoliosensitivity overstate the sensitivity for individual% change in portfolio value−12 −10 −8 −6 −4 −2Portfolio sensitivity to a 2% parallel increaseas we allocate less to the 10−year assetSv (2.1,1.1,1.8,5.5,65,855)%N−S (3.2,−.7,4.5,73)%flat yield curve 3.2%basel w.a.m.basel w.a.s.0.0 0.2 0.4 0.6 0.8 1.0weight in 1 year loan (= 1 − weight in 10 year loan)Figure 11: Effect of portfolio aggregation under theBasel Committee guideline method for interest raterevaluation senstivity as compared to the alternativemodels. The labels in the legend correspond,from top to bottom, to Svensson, Nelson-Siegeland flat forward curve models calibrated to historicalparameters; following these, we have the BaselCommittee weighted average maturity method andthe weighted average sensitivity method.loans, they understate the sensitivity for some portfolios of loans. Even the weighted average maturitymethod, which is more conservative than the weighted average sensitivity method, understates the riskfor portfolios with greater weight in the 1-year loan than in the 10-year loan. Portfolios of the 1- and10-year loans that place just a small weight in the 10-year loan are much more price-sensitive to parallelupward shifts in yield curves than the Basel Committee methods indicate. For supervisory purposes orfor risk self-assessment, we would therefore be most worried about using the Basel Committee methodfor banks whose loan portfolios have a short weighted average maturity, but a non-negligible allocationat long maturities.31 To make these definitions more formal, consider the case where we have a portfolio consisting of 1 − φ in the 1 yearloan and φ in the 10 year loan. Let the Basel Committee interest-rate sensitivity of a loan with remaining maturity τbe ∆(τ). Then the weighted average sensitivity method computes (1 − φ)∆(1) + φ∆(10) as the interest rate sensitivity,while the weighted average maturity method computes ∆ ((1 − φ) · 1 + φ · 10). Since ∆(·) will be a convex function formost securities other than zero-coupon bonds, we would expect the latter method to produce lower portfolio sensitivitiesthan the former.24

Table 7: Frequency of ≥ 2% increase in the level of historical (forward or zero) yield curves over anl−month period for various values of l. Subtables (a) and (b) are computed by estimating Nelson-Siegeland Svensson parametric forms respectively at each month-end in the sample, and by then examiningthe longitudinal distribution of β 0 . In each subtable, the first row shows the number of times wherean l−month change in β 0 meet or exceeds 2%, the middle row shows the number of longitudinalobservations on which this count is based, and the final row shows the frequency obtained by dividingthe first row by the second.(a) Nelson-Siegel1 3 6 9 12 15 18 24number ≥ 2% 1 3 5 5 6 6 2 6number observations 166 164 161 158 155 152 149 143frequency (%) 0.60 1.83 3.11 3.16 3.87 3.95 1.34 4.20(b) Svensson1 3 6 9 12 15 18 24number ≥ 2% 4 6 14 19 22 29 36 33number observations 166 164 161 158 155 152 149 143frequency (%) 2.41 3.66 8.70 12.03 14.19 19.08 24.16 23.084.3 How representative is a 2% parallel yield curve shock?In Table 7 we show the frequency of large parallel shifts in the yield curve, under the Nelson-Siegeland Svensson models, over various time horizons. Under the Nelson-Siegel model, such large movesin the yield curve are rare even over 24 months, while under the Svensson model they are much morefrequent. The most relevant time horizons for our purposes are up to 3 months, in which time wemay expect a bank to be relatively unable to make major portfolio adjustments in response to sharpyield curve changes. Based on time horizons of up to 3 months, we might estimate that a 2% parallelupward shift in yield curve occurs with probability between 0.6% and 3.7% in any one month, whichcorresponds to something between a 1 in 14 year event and a 1 in 2 year event. This gives an idea ofthe ‘severity’, or lack thereof, of a 2% shock to the level of the yield curve.In addition, we would like to investigate the extent to which it is reasonable to shock the level ofyield curves without also varying other shape parameters of the yield curve. In particular if slope andlevel changes tend to occur together, then the revaluation effect of a level shock only may under- oroverstate the revaluation effect of a shock to both levels and slope. We present an initial investigationof these relationships between changing parameters in Table 8, where the subtables correspond todifferent time horizons over which we might measure the change in parameters. The correlations arestable between tables. They show that changes in the level and slope of the yield curve, as parametrisedby β 0 and −β 1 , exhibit a strong positive contemporaneous correlation over 1, 3, 6, 9 and 12 months. 32Increases in the level of the Euro yield curve are associated with simultaneous increases in the slopeof the yield curve over all of these time horizons, and the absolute size of the correlation decreaseswith the time horizon. Similary, level and curvature show a strong negative association, suggestingthat yield curves flatten when they shift upward, and the absolute size of this association increaseswith the time horizon. We therefore note, that regardless of the severity of the interest rate shock onewould like to apply (for example a 2% level change), association between level, slope and curvatureare highly prevalent historically. We regard these relationships as evidence against the plausibility ofa parallel yield curve shock. These relationships should be used in a proper assessment of interest raterisk.It is well known that correlation is not a very satisfactory measure of dependence. In a sense,correlation only captures a type of ‘linear’ dependence, which might ignore important and measurable‘non-linear’ relationships. As a robustness check on our correlation estimates, we provide scatterplotsof the levels and month-on-month (l = 1) changes in the β parameters of the Nelson-Siegel model in32 β 0 and β 1 are negatively associated, so that β 0 and −β 1 are positively associated, and hence increases in level arepositively correlated with increases in slope.25

Table 8: Correlations between l−month changes in Nelson-Siegel parameters. Of particular interest inthis paper are the correlations between the β parameters, because these parameters can be interpretedas level, slope and curvature.(a) l = 1β 0 β 1 β 2 τ 1β 0 1.00 -0.82 -0.59 0.28β 1 -0.82 1.00 0.34 -0.39β 2 -0.59 0.34 1.00 -0.23τ 1 0.28 -0.39 -0.23 1.00(c) l = 6β 0 β 1 β 2 τ 1β 0 1.00 -0.64 -0.69 0.32β 1 -0.64 1.00 0.29 -0.55β 2 -0.69 0.29 1.00 -0.33τ 1 0.32 -0.55 -0.33 1.00(b) l = 3β 0 β 1 β 2 τ 1β 0 1.00 -0.75 -0.63 0.24β 1 -0.75 1.00 0.33 -0.46β 2 -0.63 0.33 1.00 -0.18τ 1 0.24 -0.46 -0.18 1.00(d) l = 9β 0 β 1 β 2 τ 1β 0 1.00 -0.54 -0.76 0.31β 1 -0.54 1.00 0.29 -0.55β 2 -0.76 0.29 1.00 -0.28τ 1 0.31 -0.55 -0.28 1.00(e) l = 12β 0 β 1 β 2 τ 1β 0 1.00 -0.48 -0.81 0.35β 1 -0.48 1.00 0.27 -0.57β 2 -0.81 0.27 1.00 -0.29τ 1 0.35 -0.57 -0.29 1.00Figure 12. 33 On the scatterplots, we also provide the contours of a Gaussian kernel density estimator,and we scale the points by the value of τ 1 . 34 From the two upper plots in Figure 12, we note the negativeassociations between shape parameters, saying that high levels are associated with high slopes and highcurvatures, not to be confused with the correlations in Table 8. We also note the clustering of pointsgiven by the two or three modes of the kernel density contours and the clustering of low and highvalues of τ 1 . The lower two panels give the scatterplots for month-on-month changes (l = 1) in thebeta parameters. From the lower-left panel we note that the strong linear dependence, measured inTable 8 by the strong correlation between β 0 and β 1 , captures virtually all of the bivariate relationshipbetween the changes in these two parameters. Thus the positive correlation observed between the leveland slope of the yield curve sufficiently characterises the general statistical relationship between them.4.4 Rankings of European banks by loan portfolio riskiness in 2011From Table 9 we see that the method by which we measure the interest rate risk of banks affects whichbanks emerge as most risky. We see that the ranking of the banks is not sensitive to the three forms ofthe yield curve, although the percentage change in portfolio value under a Svensson yield curve (andhence pricing) model produces higher sensitivities than under a Nelson-Siegel model. The two methodsfor calculating the portfolio riskiness under Basel Committee guidelines give different rankings of thebanks, and the weighted average sensitivity guideline method agrees very strongly with the weightedaverage maturity from “gap analysis”. Given our reservations about the Basel Committee guidelinemethods for portfolios of assets, and given the lack of additional information they provide over simplegap analysis, neither of these rankings based on guideline methods is satisfactory.33 Recall that this model has been estimated separately for each month-end yield curve by minimising a squared errorloss function.34 For the scatterplots of month-on-month changes in betas, the value of τ 1 used to size the points on the scatterplotis the second and later value corresponding to the pair of betas used for differencing.26

0.080.00beta1−0.01tau10.250.500.75beta20.04tau10.250.500.750.00−0.020.00 0.02 0.04 0.06beta00.00 0.02 0.04 0.06beta00.020.010.03month−on−month change in beta10.00−0.01tau10.250.500.75month−on−month change in beta20.00−0.03tau10.250.500.75−0.02−0.03−0.01 0.00 0.01 0.02month−on−month change in beta0−0.06−0.01 0.00 0.01 0.02month−on−month change in beta0Figure 12: Relationships between level, slope and curvature parameters, and their month-to-monthchanges, for the Nelson-Siegel model of yield curves, when applied to the Euro swap curve data.27

Table 9: Rankings of the sample banks, in Column 1 by the value-weighted average maturity of theirloan portfolio, and in Columns 2-7 by the percentage decrease in the value of their loan portfolios dueto a 2% parallel upward shift in yield curves. Columns 2-3 give the Basel Committee guideline methodunder weighted-average sensitivity and sensitivity of weighted-average maturity, defined in Section4.2.3. Column 4 uses the simple loan formula with flat yield curve. Columns 5-6 use the Nelson-Siegelparametric form of the yield curve, which agrees analytically although not computationally with thesimple loan formula when β 1 = β 2 = 0. Column 7 uses the Svensson parametric yield curve withparameters calibrated to historical averages. The methods for Columns 4-7 are defined in Section 3.2.Loansweighted avgmaturity(yrs)Baselguidelinew.a.s. (%)Baselguidelinew.a.m. (%)Simpleδ = 3.2%(%)N-Sβ 0 = 3.2%(%)N-S (β 0 , β 1 , β 2 , τ 1 ) =(3.2, −.7, 4.5, 73)%(%)Sv (β 0 , β 1 , β 2 , β 3 , τ 1 , τ 2 ) =(2.1, 1.1, 1.7, 5.5, 65, 855)%(%)1 DK011 9.39 DK011 -12.48 BE004 -13.26 DK011 -9.24 DK011 -9.24 DK011 -9.21 DK011 -12.062 NL050 9.28 NL050 -12.34 DK011 -13.26 NL050 -9.18 NL050 -9.18 NL050 -9.15 NL050 -12.023 PT055 8.30 PT055 -11.08 GB091 -13.26 PT055 -9.11 PT055 -9.11 PT055 -9.07 PT055 -11.964 NL049 7.93 NL049 -10.62 IE037 -13.26 NL049 -8.87 NL049 -8.87 NL049 -8.84 NL049 -11.785 GB091 7.72 GB091 -10.39 NL047 -13.26 SE087 -8.79 SE087 -8.79 SE087 -8.75 SE087 -11.716 BE004 7.65 BE004 -10.29 NL049 -13.26 MT046 -8.77 MT046 -8.77 MT046 -8.73 MT046 -11.707 IE037 7.64 IE037 -10.28 NL050 -13.26 NO051 -8.75 NO051 -8.75 NO051 -8.71 NO051 -11.688 SE087 7.47 SE087 -10.04 NO051 -13.26 IE037 -8.74 IE037 -8.74 IE037 -8.70 IE037 -11.689 NO051 7.21 NO051 -9.70 PT055 -13.26 BE004 -8.65 BE004 -8.65 BE004 -8.61 BE004 -11.6010 NL047 7.06 NL047 -9.56 SE087 -13.26 GB091 -8.65 GB091 -8.65 GB091 -8.61 GB091 -11.5911 CY006 6.99 CY006 -9.47 CY006 -10.16 ES061 -8.48 ES061 -8.48 ES061 -8.44 ES061 -11.4612 ES061 6.81 ES061 -9.22 CY007 -10.16 NL047 -8.36 NL047 -8.36 NL047 -8.32 NL047 -11.3513 MT046 6.72 PT054 -9.11 DE019 -10.16 CY006 -8.36 CY006 -8.36 CY006 -8.31 CY006 -11.3514 PT054 6.70 MT046 -9.05 DE020 -10.16 ES059 -8.33 ES059 -8.33 ES059 -8.29 ES059 -11.3315 IE038 6.66 IE038 -9.03 DE021 -10.16 IE038 -8.32 IE038 -8.32 IE038 -8.28 IE038 -11.3216 ES059 6.24 ES059 -8.48 DE025 -10.16 SE084 -8.20 SE084 -8.20 SE084 -8.16 SE084 -11.2217 DE025 6.10 DE025 -8.34 ES059 -10.16 ES062 -8.20 ES062 -8.20 ES062 -8.16 ES062 -11.2218 FI012 5.97 FI012 -8.17 ES060 -10.16 PT056 -8.15 PT056 -8.15 PT056 -8.11 PT056 -11.1819 PT053 5.94 PT053 -8.13 ES061 -10.16 GB090 -8.15 GB090 -8.15 GB090 -8.10 GB090 -11.1720 DE021 5.74 DE021 -7.84 ES062 -10.16 DE021 -8.12 DE021 -8.12 DE021 -8.07 DE021 -11.1421 ES062 5.73 ES062 -7.82 ES064 -10.16 DE019 -8.03 DE019 -8.03 DE019 -7.98 DE019 -11.0722 GB090 5.54 CY007 -7.61 FI012 -10.16 ES064 -8.00 ES064 -8.00 ES064 -7.95 ES064 -11.0523 PT056 5.54 PT056 -7.56 GB090 -10.16 PT053 -8.00 PT053 -8.00 PT053 -7.95 PT053 -11.0424 CY007 5.52 GB090 -7.56 IE038 -10.16 DE025 -7.95 DE025 -7.95 DE025 -7.91 DE023 -11.0025 IT044 5.50 IT044 -7.54 IT043 -10.16 DE023 -7.95 DE023 -7.95 DE023 -7.91 DE025 -10.9926 SE084 5.32 ES064 -7.29 IT044 -10.16 ES060 -7.93 ES060 -7.93 ES060 -7.89 ES060 -10.9927 ES064 5.31 SE084 -7.25 MT046 -10.16 IT044 -7.92 IT044 -7.92 IT044 -7.87 IT044 -10.9628 DE019 5.23 IT043 -7.20 PT053 -10.16 FI012 -7.88 FI012 -7.88 FI012 -7.84 FI012 -10.9329 IT043 5.22 DE019 -7.17 PT054 -10.16 IT042 -7.81 IT042 -7.81 IT042 -7.76 IT042 -10.8830 DE020 5.08 DE020 -7.06 PT056 -10.16 FR014 -7.77 FR014 -7.77 FR014 -7.73 FR014 -10.8331 ES060 5.06 ES060 -6.95 SE084 -10.16 CY007 -7.76 CY007 -7.76 CY007 -7.71 CY007 -10.8232 IT042 4.93 IT042 -6.81 AT003 -7.70 IT043 -7.72 IT043 -7.72 IT043 -7.67 IT043 -10.7833 FR014 4.87 FR014 -6.70 DE018 -7.70 IT041 -7.69 IT041 -7.69 IT041 -7.64 IT041 -10.7634 FR013 4.75 FR013 -6.57 DE023 -7.70 FR013 -7.64 FR013 -7.64 FR013 -7.59 FR013 -10.7035 IT041 4.72 IT041 -6.53 DE024 -7.70 DE018 -7.48 DE018 -7.48 DE018 -7.44 DE018 -10.5536 DE018 4.63 HU036 -6.42 FR013 -7.70 FR016 -7.41 FR016 -7.41 FR016 -7.37 FR016 -10.5037 HU036 4.61 DE018 -6.42 FR014 -7.70 IT040 -7.38 IT040 -7.38 IT040 -7.34 IT040 -10.4638 IT040 4.57 IT040 -6.36 HU036 -7.70 HU036 -7.36 HU036 -7.36 HU036 -7.32 HU036 -10.4439 DE024 4.46 DE024 -6.27 IT040 -7.70 DE020 -7.22 DE020 -7.22 DE020 -7.18 DE020 -10.2840 AT003 4.32 AT003 -6.09 IT041 -7.70 GB088 -6.94 GB088 -6.94 GB088 -6.89 GB088 -10.0141 DE023 4.25 DE023 -5.85 IT042 -7.70 DE024 -6.87 DE024 -6.87 DE024 -6.82 DE024 -9.9142 DE029 3.90 DE029 -5.53 AT002 -6.14 AT003 -6.78 AT003 -6.78 AT003 -6.73 AT003 -9.8143 DE027 3.83 DE027 -5.45 DE027 -6.14 SI057 -6.66 SI057 -6.66 SI057 -6.62 SI057 -9.7144 SI057 3.76 SI057 -5.36 DE028 -6.14 DE029 -6.62 DE029 -6.62 DE029 -6.57 AT002 -9.6545 FR016 3.76 SI058 -5.33 DE029 -6.14 AT002 -6.61 AT002 -6.61 AT002 -6.57 DE029 -9.6346 SI058 3.72 FR016 -5.25 FR016 -6.14 SI058 -6.54 SI058 -6.54 SI058 -6.49 SI058 -9.5847 GB088 3.71 GB088 -5.24 GB088 -6.14 DE028 -6.44 DE028 -6.44 DE028 -6.39 DE028 -9.4648 AT002 3.48 AT002 -4.96 SE085 -6.14 DE027 -6.34 DE027 -6.34 DE027 -6.30 DK010 -9.3849 DE028 3.45 DE028 -4.95 SI057 -6.14 DK010 -6.27 DK010 -6.27 DK010 -6.22 DE027 -9.3150 SE085 3.14 SE085 -4.54 SI058 -6.14 SE085 -6.09 SE085 -6.09 SE085 -6.05 GR033 -9.2751 IE039 2.78 IE039 -4.20 BE005 -4.50 GR033 -6.05 GR033 -6.05 GR033 -5.99 SE085 -9.0352 GR032 2.65 GR032 -4.01 DK008 -4.50 SE086 -3.36 SE086 -3.36 SE086 -3.32 SE086 -5.6753 DK010 2.49 NL048 -3.77 DK010 -4.50 PL052 -2.78 PL052 -2.78 PL052 -2.76 PL052 -2.9054 NL048 2.43 PL052 -3.72 GR032 -4.50 DK008 -2.70 DK008 -2.70 DK008 -2.68 DK008 -2.8255 PL052 2.40 DK010 -3.71 IE039 -4.50 GB089 -2.60 GB089 -2.60 GB089 -2.59 GB089 -2.7256 DK008 2.18 DK008 -3.44 NL048 -4.50 DK009 -2.41 DK009 -2.41 DK009 -2.40 DK009 -2.5457 BE005 2.17 BE005 -3.42 PL052 -4.50 BE005 NA BE005 NA BE005 NA BE005 NA58 GB089 1.96 GB089 -3.16 DK009 -2.76 GR032 NA GR032 NA GR032 NA GR032 NA59 GR033 1.13 GR033 -1.78 GB089 -2.76 IE039 NA IE039 NA IE039 NA IE039 NA60 DK009 1.05 DK009 -1.77 GR033 -2.76 NL048 NA NL048 NA NL048 NA NL048 NA61 SE086 0.36 SE086 -0.67 SE086 -0.72 PT054 NA PT054 NA PT054 NA PT054 NA28

5 ConclusionIn Section 4.1 we are able to show that large European banks tend to transform short term customerdeposits and amortised cost instruments at 1-5 year maturity like hybrid and subordinated debt intolong term loan assets, as expected. Given the earlier work discussed in Section 1, in which the effectivematurity of core deposits is estimated to be less than three years, the interest rate revaluation risk ofthese banks is significantly determined by their loan asset portfolios. Examining the loan asset valuesmore closely, we find in Section 2.3 that the banks with the largest loan asset porfolios in 2011 aredomiciled in the UK, France and Germany, and these banks extend loans primarily into Euro-areacountries and then into non-Euro European countries. Ranking the banks by their loan asset portfoliorepricing sensitivity to a 2% parallel shift in interest rates in Section 4.4, we find that the three riskiestbanks across most methods are Nykredit (DK), SNS Bank (NL) and Espirito Santo (PT). It mustbe emphasised that these rankings are independent of balance sheet size and do not account for offbalance-sheetinstruments like interest rate derivatives, but they provide a useful starting point for thebank analyst and supervisor.In measuring the interest rate repricing risk of these banks, we employ several methods and criticallyevaluate the Basel Committee guideline method for interest rate sensitivity. We show how thisguideline method is simplistic and we illustrate the size of the deviation from simple alternative pricingmodels through the use of examples. The guideline method is conservative for loan individual loan contractswith short maturities (less than 10-15 years) and in medium-to-high interest rate environments.However, the guideline method understates risk for portfolios of loans even at short maturities and forindividual loan contracts with longer maturities, and these understatements are exacerbated in lowinterest rate environments. Further work should be done to investigate the sensitivities of the BaselCommittee guideline method, and the simple alternative methods presented here for loan contracts,to the cashflow timing assumptions, and especially the timing assumption in the 5+ maturity bucket.Furthermore, we show that the 2% parallel shift in yield curves that is typically used as the socalled“standardised interest rate shock” is atypical of historical Euro yield curve movements. Morework should therefore be done to determine the appropriate shocks to apply to interest rates, especiallyfor supervisory purposes. In particular, it is inappropriate for supervisors to rely on monitoring onlyone interest rate scenario because it is fairly easy for banks to allocate their asset and liability maturitiesso that exposure to any one scenario is zero, while exposures to other scenarios might be large.ReferencesBasel Committee on Banking Supervision (2004): “Principles for the Management and Supervisionof Interest Rate Risk,” Discussion Paper July, Basel Committee on Banking Supervision, Basel,Switzerland.Czaja, M.-G., H. Scholz, and M. Wilkens (2009): “Interest rate risk of German financial institutions:the impact of level, slope, and curvature of the term structure,” Review of QuantitativeFinance and Accounting, 33(1), 1–26.English, W. B., S. J. van den Heuvel, and E. Zakrajsek (2012): “Interest Rate Risk and BankEquity Valuations,” FEDS Working Papers, (2012-26).Entrop, O., C. Memmel, M. Wilkens, and A. Zeisler (2011): “Estimating the Interest RateRisk of Banks Using Time Series of Accounting-Based Data,” Available at SSRN 982070.Federal Deposit Insurance Corporation (1994): “The Banking Crises of the 1980s and Early1990s: Summary and Implications,” Discussion paper, Federal Deposit Insurance Corporation.Flannery, M., and C. M. James (1984a): “The Effect of Interest Rate Changes on the CommonStock Returns of Financial Institutions,” The Journal of Finance, 39(4), 1141–1153.Flannery, M. J., and C. M. James (1984b): “Market Evidence on the Effective Maturity of BankAssets and Liabilities,” Journal of Money, Credit and Banking, 16(4), 435–445.Gorton, G., and R. Rosen (1995): “Banks and derivatives,” NBER Working Paper Series, 5100.29

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