Maturity Transformation and Interest Rate Risk
in Large European Bank Loan Portfolios
Galen Sher∗ and Giuseppe Loiacono†‡
This draft May 1, 2013
Abstract
Financial intermediaries transform assets with certain risk characteristics into assets with other
risk characteristics. We define net asset transformation from liabilities to assets in terms of the
pricing characteristics of contingent claims. Maturity transformation can be defined as a special
case, across the whole balance sheet or locally to one contract type. We present and summarise
a new rich dataset on the balance sheet asset and liability exposures of large European banks
that submitted to the European Banking Authority’s EU capital exercise. In particular, we show
that these banks transform short-term customer deposits and 1-5 year hybrid and subordinated
debt liabilities into loan assets with greater than 5 years’ maturity. The value-weighted average
maturity of the assets of these banks exceeds their liabilities by 2.07 years, with standard deviation
1.44 years. Given the importance of loan assets among these banks for determining interest rate
risk, we describe and measure the interest rate risk of their loan portfolios. We find that their loan
assets are primarily allocated to households and non-financial corporations in the Euro area. We
critically 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 major
limitations in the Basel Committee guideline method and illustrate the size of the approximations
they introduce through examples. Using these five methods, we measure the extent to which a
standardised 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, rankings
of the relative interest rate riskiness of bank loan portfolios than the Basel Committee guideline
method.
JEL Classification: E43, G21, G28
1
Introduction
Interest rate risk in financial intermediation matters because it is a source of systemic or non-diversifiable
risk 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 complexity
of financial institutions and their use of non-standard contracts for hedging and speculation makes
proper risk assessment essential.
Conceptually, one may distinguish between two major categories of interest rate risk to a financial
intermediary. 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 intermediary
to 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
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 University
of Oxford, and with Matthias Sydow at the European Central Bank, without any implication for errors or omissions
contained herein. Some of the data were collected while the authors were at the European Central Bank. The first
author 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 in
prices and quantities that affect the ‘value’ of that company’s assets and liabilities. For a detailed discussion of ‘value’
in economics, see Hicks (1939).
† Department
1
There are at least three ways that an analyst (say, a regulator) may monitor or assess the interest
rate risk of a financial intermediary. Publicly listed banks and insurers disclose measures of the
sensitivity of their balance sheets to shifts in the term structure of interest rates, so in the first
instance an analyst may refer to these disclosures. These self-reported measures have the advantage
that they may take into account the complex structure of the contracts held by an intermediary that
may not be visible in its financial statements, but such measures also rely on the willingness and
ability of the intermediary to make an accurate assessment. Furthermore, only one to two measures
are typically disclosed, which cannot be hoped to provide a complete picture of the intermediary’s
exposure to interest rate changes.
As an alternative, the analyst could use regression analysis to measure the sensitivity of the stock
return of publicly-listed intermediaries against changes in specific interest rates or against measures
reflecting 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 measured
from the nominal contracts on their balance sheets. Flannery and James (1984b) infer the effective
degree 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 returns
of other companies; they also find some evidence to suggest that universal banks would be more robust
to interest rate changes due to better diversification. Czaja, Scholz, and Wilkens (2009) measure
the sensitivity of stock returns of German banks and insurers to level, slope and curvature changes
in local yield curves, and find that bank and insurer stock returns offer a premium for those banks
and 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 Market
Committee announcements to measure the effect of interest rate level and slope changes in bank stock
returns; studying short time intervals helps to avoid the pollutive effects of unrelated news on stock
prices.
The analyst could also measure the interest rate sensitivity of each item on the balance sheet, by
asking the question “How would the unit prices of the major asset and liability categories change if
interest rates were different on the valuation date?” This is the approach taken in our paper, and
can 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 measures of 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 method
for assessing the interest rate sensitivity of banks’ economic value based on their publicly disclosed
balance 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 Thift
Supervision’s internal model. Despite the limitations of publicly-available data, the authors find that
the simple model provides useful information for measuring the sensitivity of banks’ economic value
to interest rate changes; they also find that the biggest limitation of such models are the arbitrary
assumptions that have to be made about the behaviour of depositors.
Jarrow and van Deventer (1998) offer a no-arbitrage model for determining the economic value
of deposit contract liabilities, and this pricing function could also be used in principle to measure its
sensitivity to interest rate changes. O’Brien (2000) also offers such a no-arbitrage model, and further
estimates its parameters on US bank data, providing detailed sensitivity estimates of the economic
value of bank liabilities to changes in the short term interest rate. Sierra and Yeager (2004) evaluate
the predictions of the EVM against the actual performance of US community banks, which do not
typically engage in complex derivative transactions, and find that those banks that the EVM identifies
as most sensitive to rising rates show the greatest deterioration in performance in the 1998-2000 period
of rising rates in the US. Sierra (2009) finds that the ‘prospective’ sensitivities of US bank economic
value to interest rates calculated from the EVM are consistent with the ‘retrospective’ interest rate
sensitivities of stock prices discussed above. Entrop, Memmel, Wilkens, and Zeisler (2011) try to
produce a refined EVM model calibrated to German banking data by using repeated observations of
balance sheets over time. By evaluating their model using private supervisor data, they are able to
argue that their model outperforms the EVM, which relies on data at only one point in time. The
most important paper for estimating the sensitivity of US bank balance sheet derivative exposures is
2
Gorton and Rosen (1995), who find that interest rate derivative exposures seem to be used for hedging
rather than speculation.
1.1
Basel Committee guidelines for interest rate risk assessment
The Basel Committee on Banking Supervision2
temporarily releases guidance on the principles Table 1: Basel Committee guideline method for net
of the management and supervision of interest asset revaluation sensitivity to parallel interest rate
rate risk. To the best of our knowledge, the most shocks.
recent guidance document for the assessment of
interest rate risk was released in July 2004 and
maturity
point as- duration
weighting
is entitled “Principles for the Management and
bucket
sumption (yrs)
(%)
Supervision of Interest Rate Risk”. We find that
(yrs)
(yrs)
the principles and guidance given in the docu0.083
0.042
0.040
0.080
ment are generally prudent and nuanced. How0.250
0.167
0.160
0.320
ever, the guidance provided in Annexes 3 and 4
0.500
0.375
0.360
0.720
seems to depart strongly from the sensible ad1.000
0.750
0.710
1.420
vice given in the body of the document. To the
2.000
1.500
1.380
2.760
extent that supervisors use Annexes 3 and 4 to
3.000
2.500
2.250
4.500
rank banks’ interest rate risk, these supervisors
4.000
3.500
3.070
6.140
might end up overlooking the most risky banks.
5.000
4.500
3.850
7.700
To summarise these Annexes, they argue that
7.000
6.000
5.080
10.160
a supervisor should monitor the interest rate risk
10.000
8.500
6.630
13.260
of institutions using a “standardised interest rate
15.000
12.500
8.920
17.840
shock,” which amounts to either a 2% parallel
20.000
17.500
11.210
22.420
upward or downward shift in interest rates or the
Inf
22.500
13.010
26.020
1% and 99% quantile of the distribution of yield
curves. Given that Annex 4 provides a more detailed example using the parallel interest rate shock, but does not provide guidance for implementing
a quantile-based shock, it seems likely that supervisors would find the parallel interest rate shock easier to implement. In the example implementation provided for guidance in Annex 4, which proposes
a duration-based sensitivity measure akin to that of the Federal Reserve’s Economic Value Model,
shocks have a symmetric effect on value, and hence it becomes unnecessary to consider both positive
and negative shocks. Since banks almost always draw funding at short durations to invest at longer
durations, they tend to lose only when interest rates rise. When choosing between positive or negative
shocks according to the guideline method in Annex 4, it therefore makes sense only to consider a rise
in interest rates.
To implement the standardised shock, the supervisor or bank analyst3 is referred to Table 1. This
table provides the ‘risk’ or sensitivity estimates to be used as risk-weights in a calculation of overall
portfolio sensitivity to a parallel interest rate shock. For a hypothetical security,4 the supervisor
considers the remaining contractual maturity in the case of a fixed-rate security, or the time until
the next repricing date in the case of a variable-rate security. This remaining maturity determines
the “maturity bucket” into which the security falls, given by the first column in Table 1.5 Associated
with each maturity bucket is a point-in-time assumption, where the entire cashflow from the security
is presumed to fall in the form of a zero-coupon bond. The price sensitivity of such a zero-coupon
bond, i.e. the percentage decrease in present value per unit increase in interest rates, is given by the
2 “The Basel Committee on Banking Supervision is a Committee of banking supervisory authorities which was established by the central bank Governors of the Group of Ten countries in 1975. It consists of senior representatives of
bank supervisory authorities and central banks from Belgium, Canada, France, Germany, Italy, Japan, Luxembourg,
Netherlands, Spain, Sweden, Switzerland, United Kingdom and the United States. It usually meets at the Bank for
International Settlements (BIS) in Basel, Switzerland, where its permanent Secretariat is located” (Basel Committee
Basel Committee on Banking Supervision, 2004).
3 In this discussion, we use the word ‘supervisor’ to mean any analyst that is attempting to measure the interest rate
risk of banks using the recommendations of the Basel Committee for Banking Supervision.
4 The hypothetical security could be an asset or a liability.
5 In particular, the right endpoint of the maturity bucket is determined by the smallest value in the first column of
Table 1 that is greater than or equal to the remaining maturity of the hypothetical security. The left endpoint of the
maturity bucket is the largest value in the first column of Table 1 that is smaller than the remaining maturity of the
hypothetical security.
3
‘duration’ number in the penultimate column of Table 1. Multiplying this duration number by the size
of the standardised shock, which is 2%, gives the risk-weight measure that is shown in percent in the
final column of this Table. The risk weight is an estimate of the interest rate revaluation sensitivity of
the hypothetical security under a standardised interest rate shock.
We can immediately observe several shortcomings of this guideline method for interest rate revaluation sensitivity. These shortcomings can be summarised as follows:
1. The method does not depend on the specific type of security. We might expect different securities
with 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 of
2% invariant to historical yields, but the sensitivity calculation itself is unrelated to the prevailing
interest rate environment. For example, in a high interest rate environment, we might expect
larger absolute changes in interest rates to be likely, and we might expect the price of a security
to be more sensitive to a given absolute change in interest rates in a low interest rate environment
than in a high interest rate environment.
3. The method encourages the use of a parallel upward shift in interest rates of 2%, without explicitly
requiring that the supervisor investigate other scenarios. As a scenario, there is little reason to
expect that a parallel upward shift in interest rates of 2% is commensurate with a desired level of
riskiness, or even that it is plausible, given the well-known correlation between levels and slopes
of yield curves. As a risk measurement device, a single scenario incentivises banks to reduce
their exposure to just this one scenario, while potentially remaining severely exposed to other
scenarios, 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 a
portfolio sensitivity, despite the fact that the method is recommended for measuring the interest
rate revaluation risk of the whole balance sheet.
Indeed given these four criticisms, it is difficult to see how the method improves on so-called gap
analysis, where the weighted average maturity all the assets and liabilities on the balance sheet is used
as a proxy for interest rate risk.
1.2
Structure of this paper
Our objectives of this paper are twofold. First, we offer a definition of maturity transformation in
terms of the pricing characteristics of assets and liabilities. This theory of ‘transformation’, including
maturity transformation, is presented in Section 3.1. To measure the degree of maturity transformation
of large European banks, we employ a dataset collected by the authors at the European Central Bank
that covers the asset and liability exposures in greater detail than currently available from major
data providers. All the asset and liability exposure data were collected from the consolidated annual
financial statements and Pillar III disclosures of these banks. We present and summarise the data in
Section 2 and we measure the degree of transformation in Section 4.1.
Having determined that the degree of on-balance-sheet interest rate revaluation risk6 is most substantially influenced by the loan asset portfolios of these banks, our second objective in this paper is
to measure the interest rate revaluation sensitivity of these loan assets. To do so, we employ several
methods, including conventional gap analysis,7 the Basel Committee guideline method introduced in
Section 1.1, and the simple present value formulae for amortising loan contracts of Section 3.2 combined with stylised characterisations of the yield curve in Section 3.3. We present our results in Section
4, including one ranking of banks by the (2%-) interest rate risk of their loan portfolios for each of the
sensitivity 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 maturity
of all assets and liabilities on the balance sheet. By computing the weighted average maturity of loan assets only, we
obtain 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
AT001
AT002
AT003
BE004
BE005
CY006
CY007
DE017
DE018
DE019
DE020
DE021
DE022
DE023
DE024
DE025
DE026
DE027
DE028
DK008
DK009
DK010
DK011
ES059
ES060
ES061
ES062
ES064
FI012
FR013
FR014
FR015
FR016
GB088
2
Description
Erste Bank
Raiffeisen Bank
Oesterreichische Volksbank
Dexia
KBC
Marfin Popular
Bank of Cyprus
Deutsche Bank
Commerzbank
LBBW
DZ Bank
Bayern LB
Nord LB
Hypo RE
West LB
HSH Nordbank
Helaba
Landesbank Berlin
DekaBank
Danske Group
Jyske Bank
Sydbank
Nykredit
Santander
BBVA
Bankia
La Caixa
Banco Popular
OPO-Pohjola
BNP
Credit Agricole
BPCE
Societe Generale
RBS
EBA code
GB089
GB090
GB091
GR030
GR031
GR032
GR033
HU036
IE037
IE038
IE039
IT040
IT041
IT042
IT043
IT044
LU045
MT046
NL047
NL048
NL049
NL050
NO051
PL052
PT053
PT054
PT055
PT056
SE084
SE085
SE086
SE087
SI057
SI058
Description
HSBC
Barclays
Lloyds
EFG Eurobank
National Bank of Greece
Alpha Bank
Piraeus Bank Group
OTP Bank NYRT.
Allied Irish Banks
Bank of Ireland
Irish Life
Intesa Sanpaolo
Unicredit
Banca Monte Dei Paschi Di Siena
Banco Popolare
UBI Banca
Banque Et Caisse DEpargne De LEtat
Bank of Valetta
ING
Rabobank
ABN Amro
SNS Bank
DnB NOR
PKO Bank Polski
Caixa Geral de Depositos
Banco Comercial
Espirito Santo
Banco BPI
Nordea
SEB
Svenska Handelsbanken
Swedbank
NLB Group
NKBM
Data
The sample of banks we study here is the sample of banks analysed in the European Banking Authority’s 2011 EU-wide capital exercise. They form the largest European bank holding companies and
are listed in Table 2. Balance sheet data for these banks is publicly available from data providers like
Reuters, Bloomberg and SNL, but not at the full level of detail that these institutions report in their
annual financial statements. We use data collected by the authors at the European Central Bank on
balance 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 Section
4.1,8 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 the
marginal 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 device
for 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 this
8 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 countries
The loan exposure data on which this paper is based has been gathered by the authors from the
financial statements of large European banks. In this section we provide an overview of the accounting
methods used to value these assets and liabilities. In doing so, we gain a better understanding of
the exposures underlying the summaries in Section 2, and we can compare the accounting valuation
methods to the stylised economic valuation models of Section 3.
2.1.1
Introduction to accounting rules for valuing assets and liabilities
In the life of a corporate entity, every event has to be recorded in the financial statements according to
common standards. Accounting standards can have a significant impact on the financial system, in particular via their potential influence on the behaviour of economic agents. Published financial statements
provide financial and economic signals on which decisions can be made, and on which management can
be assessed. Therefore, comparability of financial statements across countries is desirable. Pursuing
this aim, the IFRS Foundation – an independent, not-for-profit private sector organisation working
in the public interest – developed a single set understandable, enforceable and globally accepted international financial reporting standards (IFRSs) through its standard-setting body, the International
Accounting 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 companies
at the consolidated level to comply with IFRS standards, but does not make prescriptions for nonlisted European companies. Therefore subsidiary companies, like banks that are part of larger holding
companies, are still subject to national GAAP and can move voluntarily to IFRS.9 The banks that are
used for the analysis in this paper complied with IFRS standards. They were chosen based on their
participation in the European Banking Authority’s 2011 EU capital exercise, and are therefore the
largest and most systemically important banks in Europe. For the sake of our analysis, this section
focuses on IAS 39 and IFRS 9, which are the specific IFRS standards that regulate the recognition
and measurement of financial assets and liabilities.
2.1.2
Explanations of fair value and amortised cost
Financial assets and liabilities can be recorded on the balance sheet at either fair value or amortised
cost. Fair value is the amount for which an asset could be exchanged, or a liability settled, between
knowledgeable, willing parties in an arm’s length transaction [IAS 39.9]. IAS 39 provides a hierarchy
to be used in determining the fair value for a financial instrument: [IAS 39 Appendix A, paragraphs
AG69-82]
• Level 1: Quoted market prices in an active market10 are the best evidence of fair value and
should 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 by
using a model-based valuation technique that makes maximum use of market inputs, and with
reference 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 technique
incorporates all factors that market participants would consider in setting a price and is consistent
with accepted economic methodologies for pricing financial instruments. A financial instrument
falls 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 be
based 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 to
the extent possible from historical data. Continuing the above example of debt instrument
9 The “consolidated level” refers to the group holding company, which may own whole or majority stakes in subsidiary
companies. 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 take
place with sufficient frequency and volume to provide informative ongoing prices.
6
valuation, prepayment rates may be unobservable in the market, but should be calibrated to
historical prepayment rates where possible.11
According to IAS 39.46-47, financial assets and liabilities (including derivatives) should be measured
at fair value, with the following exceptions:
• Loans and receivables, held-to-maturity investments, and non-derivative financial liabilities should
be measured at amortised cost using the effective interest method.
• Investments in equity instruments should be measured at fair value, but if the range of reasonable
fair value measurements is large, then such instruments, and derivatives indexed to such equity
instruments, can be measured at cost less impairment.
• Financial assets and liabilities that are designated as a hedged item or hedging instrument are
subject 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 to
particular measurement requirements.
Amortised cost is calculated using the effective interest method. The effective interest rate is the rate
that exactly discounts estimated future cash payments or receipts through the expected life of the
financial instrument to the net carrying amount13 of the financial asset or liability. Financial assets
that are not carried at fair value though profit and loss are subject to an impairment test. If the
expected 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 is
objective evidence to do so, as a result of one or more events that occurred after the initial recognition14
of the asset. An entity is required to assess at each balance sheet date whether there is any objective
evidence of impairment. If any such evidence exists, the entity is required to do a detailed impairment
calculation to determine whether an impairment loss should be recognised [IAS 39.58]. The amount
of the loss is measured as the difference between the asset’s carrying amount and the present value of
estimated cash flows discounted at the financial asset’s original effective interest rate [IAS 39.63].
2.1.3
Accounting and valuation of financial assets
IAS 39 requires financial assets to be classified in different categories, used to determine how a particular
financial 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 into
two subcategories:
• The designated category includes any financial asset that is designated on initial recognition as
one 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. All
derivatives (except those designated hedging instruments) and financial assets acquired or held
for the purpose of selling in the short term, or for which there is a recent pattern of short-term
profit taking, fall into this category [IAS 39.9].
Available-for-sale financial assets (AFS) These are any non-derivative financial assets designated
on 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 value
11 Prepayment rates are rates at which loan debtors repay their loan contracts early. In most loan contracts, debtors
retain the option to repay their loans early. Early repayment can be a risk to the creditor, because it raises the possibility
of 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 the
financial statements.
13 The net carrying amount in the accounting standards means the original cost, less the accumulated amount of any
depreciation 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 is
recorded in the financial statements.
7
through profit or loss [IAS 39.9]. AFS assets are measured at fair value in the balance sheet. Fair
value changes on AFS assets are recorded directly in equity, through the statement of changes
in equity, except for interest on AFS assets (which is recorded in income on an effective yield
basis), impairment losses and (for interest-bearing AFS debt instruments) foreign exchange gains
or losses. The cumulative gain or loss that has been recognised in equity is recognised in profit
or 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 payments that are not quoted in an active market, other than those held at fair value through
profit or loss or as available-for-sale. Loans and receivables for which the holder may not recover
substantially all of its initial investment, other than because of credit deterioration, should be
classified 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 determinable
payments that an entity intends and is able to hold to maturity and that do not meet the definition
of loans and receivables and are not designated on initial recognition as assets at fair value through
profit or loss or as available for sale. Held-to-maturity investments are measured at amortised
cost. If an entity sells a held-to-maturity investment other than in insignificant amounts or as a
consequence of a non-recurring, isolated event beyond its control that could not be reasonably
anticipated, all of its other held-to-maturity investments must be reclassified as available-for-sale
for the current and next two financial reporting years [IAS 39.9]. Held-to-maturity investments
are measured at amortised cost [IAS 39.46(b)].
2.1.4
Accounting valuation methods for financial liabilities
IAS 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 value
through profit or loss upon initial recognition.
• Held for trading: a financial liability classified as held for trading, such as an obligation for
securities 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 category includes, for example, hybrid and subordinated debt securities.
2.2
Maturity data for all assets and liabilities
Asset 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 five
years. Although not all banks provide all the information required for our data collection exercise, the
rate of coverage on our asset and liability maturity data in 2011 is of the order 80%.15 The coverage
rate 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 closely
with the SNL Financial maturity data, where they overlap. In particular, for the banks with total
loans in 2011 appearing in both datasets, the ratio of our exposure to the exposure in SNL Financial
is on average 97%, with standard deviation 13%, across the sample of banks.16 We provide summary
information 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 the
weighted average maturity of liabilities from assets. The weights used are the total asset and liability
values in each maturity bucket, normalised to sum to one. From Figure 1 it can be seen that except
for two banks (Piraeus Bank Group GR033 and Svenska Handelsbanken SE086) the weighted average
15 By coverage of the data set, we mean the ratio of the number of non-missing observations across all banks, to the
total 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 Banking
Authority in its capital exercise, we obtain a mean of 93% and a standard deviation of 37% across all banks.
8
9
Figure 1: Average maturity gap for large European banks in 2011, based on the cashflow timing
assumptions used throughout this paper. The red line shows the sample mean (2.07 years) and the
green lines show plus/minus one standard deviation (1.44 years).
Years
-1
0
1
2
3
4
5
6
AT002
AT003
Weighted average maturity gap between assets and liabilities for large European banks in 2011
BE004
BE005
CY006
CY007
DE018
DE019
DE020
DE021
DE023
DE024
DE025
DE027
DE028
DE029
DK008
DK009
DK010
DK011
ES059
ES060
ES061
ES062
ES064
FI012
FR013
FR014
FR016
GB088
GB089
GB090
GB091
GR032
GR033
HU036
IE037
IE038
IE039
IT040
IT041
IT042
IT043
IT044
MT046
NL047
NL048
NL049
NL050
NO051
PL052
PT053
PT055
PT056
SE084
SE085
SE086
SE087
SI057
SI058
10
Figure 2: Asset and liability exposures according to the annual financial statements for large European
banks as at December 2011. The maturity transformation activitiy from short term liabilities to long
term assets is immediately evident.
Eur billions
-600
-400
-200
0
200
400
600
AT002
AT003
BE004
BE005
Asset and liability exposures by maturity for large European banks in 2011
CY006
CY007
demand
DE018
DE019
DE020
DE021
DE023
DE024
DE025
DE027
DE028
DE029
up to 3 month
DK008
DK009
DK010
DK011
ES059
ES060
ES061
ES062
ES064
FI012
3 to 12 month
FR013
FR014
FR016
GB088
GB090
GB091
GR032
GR033
HU036
1 to 5 years
IE037
IE038
IE039
IT040
IT041
IT042
IT043
IT044
more than 5 years
MT046
NL047
NL048
NL049
NL050
NO051
PL052
PT053
PT054
PT055
PT056
SE084
SE085
SE086
SE087
SI057
SI058
Loan assets by bank and country of origin in 2011
country
AT
BE
CY
750
DE
DK
Loans in EUR (billions)
ES
FI
FR
Gr
500
HU
Ir
IT
LU
MT
NL
250
NO
PL
PT
SE
SI
UK
AT001
AT002
AT003
BE004
BE005
CY006
CY007
DE017
DE018
DE019
DE020
DE021
DE022
DE023
DE024
DE025
DE026
DE027
DE028
DK008
DK009
DK010
DK011
ES059
ES060
ES061
ES062
ES064
FI012
FR013
FR014
FR015
FR016
GB088
GB089
GB090
GB091
GR030
GR031
GR032
GR033
HU036
IE037
IE038
IE039
IT040
IT041
IT042
IT043
IT044
LU045
MT046
NL047
NL048
NL049
NL050
NO051
PL052
PT053
PT054
PT055
PT056
SE084
SE085
SE086
SE087
SI057
SI058
0
Bank
Figure 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. The
sample mean is 2.07 years and the sample standard deviation is 1.44 years, as indicated on the figure by
the horizontal red and green lines. The representative bank in our sample is therefore ‘short’ the level
of interest rates, meaning that parallel upward shifts in yield curves would deteriorate the solvency
position, while downward parallel shifts in yield curves would improve the solvency position.17 We can
see that there is substantial variation between banks, even within countries, and the largest weighted
average maturity gaps appear in CY, FI, IE, MY and NL. Interest-rate sensitivity of balance sheets is
similarly 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 that
the 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. The
median bank in our sample is therefore subject to the usual risk of parallel upward shifts in the yield
curve, and to the liquidity risk associated with rolling over short-term interbank borrowings. The same
stylised facts can be observed in Figure 2, where we see that banks tend to borrow in the “up to 3
month” 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 of
the yield curve (with the average level of the curve fixed), because such increases would tend to reduce
the 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 in
this paper, although for consistency with the Basel Committee guideline method, we focus on parallel
shifts in yield curves.
2.3
Geography and sector data for loan assets
In this section, we provide some summary information of the geographical and sectoral distributions of
the loan asset exposures in the annual financial statements of large European banks for the years 20072011. This information is directly related to the location (X) dimension of net asset transformation
that 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 between
origination and target countries. The origination country is the country of domicile of the bank that
17 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 (in
millions of Euros).
category
liabilities
liabilities
liabilities
liabilities
liabilities
liabilities
liabilities
liabilities
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
assets
subcategory
interbank
interbank
interbank
interbank
customer deposits
customer deposits
customer deposits
customer deposits
interbank
interbank
interbank
interbank
loans corporate
loans corporate
loans corporate
loans corporate
loans financial institution
loans financial institution
loans financial institution
loans financial institution
loans household
loans household
loans household
loans household
loans public sector
loans public sector
loans public sector
loans public sector
available for sale debt
available for sale debt
available for sale debt
available for sale debt
available for sale equity
available for sale equity
available for sale equity
available for sale equity
held for trading debt
held for trading debt
held for trading debt
held for trading debt
held for trading equity
held for trading equity
held for trading equity
held for trading equity
maturity
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
up to 3 month
3 to 12 month
1 to 5 years
more than 5 years
12
Min.
0
0
0
0
0
0
0
0
0
17
0
0
0
117
258
0
0
22
48
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Lower Q.
1707
410
540
43
3417
1822
714
66
898
237
66
4
991
1557
4633
5521
230
321
625
947
342
1140
1688
1638
11
29
45
5
93
656
1195
631
9
14
34
25
0
4
19
2
0
1
2
0
Med.
8722
1816
3092
664
14506
5716
5556
2086
4162
947
547
152
3678
5192
15007
21343
971
1733
5194
4008
2440
3825
10103
11330
161
199
478
660
1569
1374
5848
2387
55
64
293
177
11
500
993
153
2
13
50
13
Upper Q.
20282
5699
12996
2860
55321
27616
17059
10836
17467
4110
4546
1729
13122
12533
32487
48141
5158
5023
12392
16887
10243
11527
25336
46005
1466
1808
3893
3392
4191
4972
25972
14373
297
353
936
842
1003
1397
4004
4838
71
153
358
152
Max.
280667
121359
49148
26217
537284
1453598
87785
63077
223345
204875
70322
30791
55140
199475
258139
158765
34228
116453
150700
62434
85538
170050
220060
259236
19644
6653
18177
27372
29448
205487
297715
79772
2800
3987
7950
7968
10185
25050
25251
37425
1826
1582
3780
7396
5,000
Loan asset values by sector
Ba Basic and
construction
BI Banks and
intermediation
4,000
8,000
Loan asset values by target country
6,000
Ca Capital goods
EUR billions
GV Government
MO Mortgage
MT Media and
telecommunications
NC Consumer
non−cyclical
2,000
4,000
En Energy
OF Other financial
OT Other
RC Other consumer
retail
RE Commercial real
estate
Tr Transport
0
0
1,000
2,000
EUR billions
3,000
CC Consumer cyclical
Euro
area
Other
European
countries
North
America
Latin
America
Asia
Rest
of
the
word
Ba BI Ca CC En GV MO MT NC OF OT RC RE Tr
(a) Country
(b) Sector
Figure 4: Total allocation of loan assets by (a) country and (b) sector of loan counterparty, across all
banks 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 European
banks as at December 2011 by origination country in Figure 3. The heights of the bars show total loans
of each bank, measured in Euros, and the colours on the plot group the banks and loans by country
of domicile. Banks in the sample are domiciled in 21 countries. We can see that the banks with the
largest loan exposures are in Spain, France and the UK, while those in Italy and the Netherlands are
also large. If we take a “demand-side” view of economic growth under credit constraints, then these
largest banks are the most important for growth in Europe. The figure also shows that the country
with the most banks in the sample is Germany.
We also examine the geographic distribution of loans by country of loan counterparty in Figures
4a and 5. Figure 4a shows that large European banks primarily allocate loan capital to counterparties
in 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 to
these two regions. Within these two major regions, most loans are extended to households, followed
closely by non-financial corporations. Loans to the public sector are the smallest allocation, which
may be misleading because these banks could lend substantially to national and local governments by
purchasing debt instruments. On a more detailed sector breakdown, Figure 4b shows that these large
European banks allocate most of their loan capital to household mortgages and diversify among the
other economic subsectors.
2.4
Yield curve data
We use Euro area swap curves, monthly from January 1999 to March 2013 to characterise the level
and movements in yield curves. The tickers and maturities, taken from Bloomberg, are presented in
Table 4. We present summary statistics for the yield curve data used in this paper in Table 5.
13
Loan asset exposures by destination region and sector for large European banks in 2011
3.500
3.000
Eur billions
2.500
2.000
1.500
1.000
500
0
Euro area
Other european countries
Corporate
North America
Financial Institution
Latin America
Household
Asia
Rest of the world
Public Sector
Figure 5: Total loan asset exposures in our sample of large European banks in 2011, summarised by
target country and sector.
Table 4: Yield curve tickers and maturities in years according to Bloomberg. These maturities are
used in Section 3.3 to model the level and changes of the yield curve.
series
EONIA Index
EUR001W Index
EUR001M Index
EUR002M Index
EUR003M Index
EUR004M Index
EUR005M Index
EUR006M Index
EUSWG Curncy
EUSWH Curncy
EUSWI Curncy
EUSWJ Curncy
term
0.00
0.02
0.08
0.17
0.25
0.33
0.42
0.50
0.58
0.67
0.75
0.83
series
EUSWK Curncy
EUSA1 Curncy
EUSA1F Curncy
EUSA2 Curncy
EUSA3 Curncy
EUSA4 Curncy
EUSA5 Curncy
EUSA6 Curncy
EUSA7 Curncy
EUSA8 Curncy
EUSA9 Curncy
EUSA10 Curncy
14
term
0.92
1.00
1.50
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
series
EUSA11
EUSA12
EUSA15
EUSA20
EUSA25
EUSA30
EUSA35
EUSA40
EUSA45
EUSA50
Curncy
Curncy
Curncy
Curncy
Curncy
Curncy
Curncy
Curncy
Curncy
Curncy
term
11.00
12.00
15.00
20.00
25.00
30.00
35.00
40.00
45.00
50.00
Table 5: Summary statistics for the yield curve data, in percentage points.
series
EONIA Index
EUR001M Index
EUR001W Index
EUR002M Index
EUR003M Index
EUR004M Index
EUR005M Index
EUR006M Index
EUSA1 Curncy
EUSA10 Curncy
EUSA11 Curncy
EUSA12 Curncy
EUSA15 Curncy
EUSA1F Curncy
EUSA2 Curncy
EUSA20 Curncy
EUSA25 Curncy
3
3.1
mean
2.47
2.52
2.45
2.59
2.67
2.70
2.74
2.77
2.87
4.09
4.07
4.22
4.35
2.92
3.04
4.46
4.43
sd
1.44
1.43
1.44
1.43
1.40
1.38
1.36
1.34
1.36
1.04
1.01
1.01
1.00
1.34
1.31
1.01
1.03
min
0.08
0.11
0.08
0.15
0.19
0.23
0.28
0.32
0.33
1.56
1.68
1.79
1.91
0.35
0.38
1.92
1.90
max
5.16
5.05
4.89
5.13
5.28
5.32
5.36
5.38
5.38
5.95
5.98
6.06
6.16
5.43
5.52
6.22
6.22
series
EUSA3 Curncy
EUSA30 Curncy
EUSA35 Curncy
EUSA4 Curncy
EUSA40 Curncy
EUSA45 Curncy
EUSA5 Curncy
EUSA50 Curncy
EUSA6 Curncy
EUSA7 Curncy
EUSA8 Curncy
EUSA9 Curncy
EUSWG Curncy
EUSWH Curncy
EUSWI Curncy
EUSWJ Curncy
EUSWK Curncy
mean
3.23
4.45
3.81
3.40
4.12
3.84
3.56
4.07
3.70
3.82
3.92
4.01
2.72
2.73
2.74
2.74
2.75
sd
1.26
1.05
0.80
1.21
0.92
0.82
1.16
0.90
1.13
1.10
1.08
1.06
1.53
1.52
1.49
1.52
1.52
min
0.47
1.86
1.86
0.60
1.87
1.88
0.77
1.89
0.95
1.12
1.29
1.43
0.32
0.32
0.32
0.32
0.32
max
5.59
6.22
5.05
5.65
5.99
5.14
5.71
5.74
5.76
5.82
5.86
5.89
5.35
5.30
5.31
5.33
5.34
Method
A theory of maturity transformation and its relation to interest rate
risk
Consider a financial institution that enters into contractual arrangements with other parties. These
contractual agreements bind the institution into making and receiving payments many years into
the future. Let us imagine that there are finitely many characteristics of these future cashflows
that are relevant for determining the price today of transferring these rights and obligations to
other institutions. We could call this set of characteristics Ω, and we could write Ω = X × T for
some finite sets X and T with T ⊂ R+ to record the fact that among these characteristics will be
the contractual maturity or repricing date of each cashflow
is there (T ). The financial institution
N
fore
defined
by
its
asset
and
liability
cashflow
streams
A
∈
R
:
(x,
t)
∈
X
×
T
⊂
R
×
R
and
x,t
+
Lx,t ∈ R : (x, t) ∈ X × T ⊂ RN × R+ respectively, where x ∈ X ⊂ RN is an indexing set18 and
t ∈ T ⊂ R+ is time into the future.19 We can define the net asset stream or equity stream using a
functional application of the accounting identity E , {Ex,t , Ax,t − Lx,t : (x, t) ∈ X × T }. The equity
stream can be thought of as the future profit or future net cashflow in the firm emerging over time in
every tradable claim x ∈ X.
We can say that an institution engages in net asset transformation if ∃(x, t), (x0 , t0 ) ∈ X × T such
that Ex,t 6= Ex0 ,t0 , or in words, if there are differences in its borrowing and lending across characteristics
in X × T . We give a graphical representation of transformation in Figure 6 , where an intermediary
is a net borrower of some tradable claims and a net lender of others. Maturity transformation is then
a special case of net asset transformation and could be defined local to some x ∈ X or globally in all
x ∈ X . An intermediary engages in local maturity transformation at x ∈ X if ∃t, t0 ∈ T such that
Ex,t 6= Ex,t0 , which says that the intermediary transforms assets of type x ∈ X from various maturities
into other P
maturities,P
while an intermediary engages in global maturity transformation if ∃t, t0 ∈ T
such that x Ex,t 6= x Ex,t0 . 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 to
the price of a contract. Formally, X = Ω\T . Examples are sector, geographic, and ratings-based classifications of assets
and liabilities. In the context of assessing the revaluation effect of changes in asset prices or interest rates, we assume
that 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 and
liabilities that are traded together, have similar prices (which may or may not be related to others through substitution
effects) 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 like
stocks.
15
t
At
t5
t4
+
−
t3
+
+
−
−
−
t1
−
−
+
x1
x2
x43
t
t
t
t
t
t
t
t
Lt
+
t2
t
Et
+
negative
none
positive
x
x5
Figure 6: A graphical representation of (net)
asset transformation by a financial intermediary. The intermediary is a net borrower at
some contractual maturities
(t1 , t2 , t4 ) and in
1
some markets (x1 , x2 , x4 ) while being a net
lender at other maturities and in other markets.
Figure 7: Examples of positive and negative
maturity transformation for a financial intermediary. The top, middle and bottom rows
give the values of assets, liabilities and net assets by maturity.
where positive maturity transformation refers to assets that are ‘on average’ longer in maturity than
liabilities. We don’t define these notions explicitly, but provide some examples of positive and negative
maturity transformation in Figure 7. From balance sheet data, we typically find that banks engage
in positive maturity transformation, while insurers engage in negative maturity transformation. As
a complement to maturity transformation, if we use the term sector to refer to the more abstract X
dimension 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 ⊂ RN × R+ are traded in perfectly
competitive markets populated by agents with weakly monotonic preferences, we have a unique pricing
kernel for tradable claims and hence a discount factor B : RN × R+ → R+ satisfying ∂B
∂t ≤ 0 for all
t ∈ R+ . In this case, the value of assets at time zero, which is the price that another institution would
have to pay to obtain these future cash inflows, is given by
X
B(x, t)Ax,t ,
x,t
1
with the values of liabilities andPequity at time zero similarly defined. The solvency position of the
financial institution is given by x,t B(x, t)Ex,t , and the financial institution is said to be solvent at
time zero on a market-consistent basis if and only if
X
B(x, t)Ex,t > 0.
x,t
Note that the definition of At 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 depended
on realised interest rates. The value of equity is then the value of assets
of liabilities. In
´ t less the value
the case where we can express the pricing function as B(x, t) = exp − 0 r(x, s)ds for some integrable
function r : RN × R+ → R and for all x, we can interpret r , r(x, t) : (x, t) ∈ RN × R+ as the set
of yield curves implied by the discount function B.
For the balance sheet items that are valued on a market-consistent basis, the financial institution
reports their value at the valuation date, Ex,t Bx,t . If the per-unit pricing function B were to move
16
to some B 0 , and if the quantity function Ex,t were to remain constant, then the market-consistent
0
valuation of the balance sheet item would become Ex,t Bx,t
, implying a percentage change of
0
0
0
Ex,t Bx,t
− Ex,t Bx,t
Bx,t
Bx,t
=
− 1 ≈ log
.
Ex,t Bx,t
Bx,t
Bx,t
(1)
By assuming a distribution for B 0 , either through assuming a distribution for the set of yield curves
r when this exists, or through assuming a distribution for the pricing function B 0 directly, we have
a distribution for this percentage change in (1) above. The interest rate risk or asset price risk then
arises 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 assets
across all (x, t) claims.
3.2
Interest rate risk of loan securities and portfolios
As we see in Section 4.1, the most important component of the bank balance sheet for assessing interest
rate revaluation risk,20 ignoring off-balance sheet instruments, are the loan assets, because of their long
maturity. In assessing interest rate revaluation risk of banks, we therefore focus on the interest rate
risk of these loan assets. Assessing the interest rate revaluation risk of the whole balance sheet in the
spirit of the EVM for European banks would be a useful exercise, but it is beyond the scope of this
paper.
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, since
our loan exposures by maturity are categorised by time to “next repricing date”, rather than by time
to contractual maturity, variable-rate contracts behave like fixed-rate contracts maturing on thir next
repricing date. However, to the extent that these loan exposures by maturity in fact include heterogenous contract types,21 the pricing and risk methods associated with fixed-rate amortising loans may
not be appropriate.
In Section 1.1 above we discuss the Basel Committee guidelines for assessing interest rate revaluation
risk. In this section, we offer simple alternative methods for assessing interest rate revaluation risk
based on methods for pricing such amortising loan contracts. The pricing functions we propose here are
well known present value functions.22 The simplest such pricing function is the formula for the present
value of a fixed-term annuity of 1 per year for τ years, at constant annual continuously-compounded
interest δ:
1 − e−δτ
.
δ
This 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 the
forward curve,23 the present value of the same fixed-term annuity is
ˆ τ
ˆ u
p({f (m)}, τ ) ,
exp(−
f (m)dm)du.
p(δ, τ ) ,
0
0
Using p(δ, τ ) and p({f (m)}, τ ), we have pricing functions for individual loan contracts. However, if we
would like to compare banks, we need to be able to price portfolios of loan contracts too, so that we
can compute interest rate sensitivities.
The price of a portfolio defined by a (possibly countable) set
P
of shares {φi }, where perhaps i φi = 1, is24
20 The revaluation or repricing risk that we use interchangeably throughout this paper simply means the percentage
change 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 prepayment
respectively, would be key sources of pricing heterogeneity and hence heterogeneity in interest rate risk. Prepayment
risk is defined in Footnote 11.
22 More sophisticated pricing functions like those using risk-neutral valuation would be an interesting extension to this
paper.
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 have
X
p({φi }, δ, {τi }) =
φi p(δ, τi ).
i
17
p({φi }, {f (m)}, {τi }) ,
X
φi p({f (m)}, τi ).
i
For the purposes of calculating sensitivity to interest rate revaluation, we do not require that {φi } be
normalised to sum to one. In particular, we could use Euro-denominated exposures in place of {φi },
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 change
in interest rates or yield curves. We could consider using an analytic derivative25 to compute this
sensitivity, which also motivates the Basel Committee guideline discussed in 1.1 above. However, such
a derivative would only be valid, and an accurate approximation, for infinitesimally small changes in
yield curves. If, as per the Basel Committee guidelines, we were to seek the effect of a 200 basis point
interest rate shock, which is fairly large, then we would not expect the derivative to provide a good
approximation. A more exact approach would be to compute the present value under two interest rate
scenarios – one before, and one after the shock. This exact approach would capture the non-linearities
in exposure. For example, increases and decreases in interest rates of equal magnitude would not be
expected to produce equal decreases and increases in present values, respectively. If we assume a flat
forward curve, the change in present value takes the form
log p(δ1 , τ ) − log p(δ0 , τ ),
where δ0 is the constant annual continuously compounded interest rate before the shock, and δ1 is the
same rate after the shock. This expression can be interpreted as a percentage change in the present
value of a loan contract and is directly analogous to (1) above. If we assume an arbitrary shape to the
forward curve, the change in present value takes the form
log 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 form
log p({φi }, {f (m)}1 , {τi }) − log p({φi }, {f (m)}0 , {τi }),
where the weights {φi } are assumed invariant to the interest rate change, and where the normalisation
constant for {φi } cancels.
3.3
Characterising interest rate movements
We can characterise the shape of the yield curve at any point in time by the forward curve or the
zero curve. The zero rate at any given maturity is the yield to maturity one could obtain on a zerocoupon bond 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 security
or corporate obligation that does not exist in the market at that particular maturity. Zero curves
are inferred from the yields to maturity on a set of coupon-paying bonds, the prices of which can be
observed in the market, through a process known as bootstrapping.26
The forward curve at any maturity is defined as the increase in yield to maturity one could obtain
today 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) , limh→0+ ((m + h)z(m + h) − mz(m)) /h =
d (mz(m)) /dm
´ m ∀m}, and similarly, the zero curve can be obtained from the forward curve pointwise
by z(m) = 0 f (u)du/m.
In this paper, our yield curves are given by the Euro area interbank and swap rates discussed
in Section 2.4. At every month-end, we therefore have 34 points that characterise the shape of the
25 Note that we would need a directional derivative in the case of a general forward curve. In this paper, we only
consider directional derivatives in the direction of a constant function, or in other words, we only consider parallel shifts
in the yield curve for consistency with the Basel Committee guideline method for interest rate sensitivity assessment. In
Section 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. A
Nelson-Siegel model of the yield curve takes the form
f (m)
=
β0 + β1 e−m/τ1 + β2
z(m)
=
β0 + (β1 + β2 )
m −m/τ1
e
τ1
τ1
(1 − e−m/τ1 ) − β2 e−m/τ1 ,
m
(2)
where the four parameters to be specified are β0 , β1 , β2 and τ1 (Nelson and Siegel, 1987). If we assume
for convenience that the forward curve is closely approximated by the interbank swap curve for which
we have data, then we can estimate at each month-end these four parameters by choosing them to
minimise some distance measure between the 34 observed and fitted values of f .27 We also consider
the so-called Svensson model of the yield curve, which takes the form
f (m)
= β0 + β1 e−m/τ1 + β2
z(m)
= β0 + (β1 + β2 )
m −m/τ1
m
e
+ β3 e−m/τ2
τ1
τ2
τ
τ1
2
(1 − e−m/τ1 ) − β2 e−m/τ1 + β3
(1 − e−m/τ2 ) − e−m/τ2 ,
m
m
(3)
where the six parameters to be estimated are β0 , β1 , β2 , β3 , τ1 and τ2 (Svensson, 1994). By specifying
one of these parametric forms of the yield curve, i.e. Nelson-Siegel or Svensson, one can obtain the
pricing functions and sensitivities discussed in Section 3.2 above. In particular, by varying the β0
parameter, one can obtain the effect of parallel shifts in the yield curve on the price of a loan contract
or portfolio of loan contracts. We show below that our results using Nelson-Siegel or Svensson models
are qualitatively similar.
By estimating the parameters of the Nelson-Siegel and Svensson models at each month-end under a
squared error loss function, we obtain a characterisation of the yield curve at every point in time. The
parameters 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 therefore
focus on the Nelson-Siegel model, where β0 can be interpreted as the level of the yield curve, β1
as the premium of the short term rate over the long term rate (i.e. the inverse of the slope of the
curve), and β2 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 these
beta 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 β0 in Figure 8. We can
see that in both yield curve models, changes in the level of yield curves are roughly symmetric and
clustered around zero. We explore changes in the yield curve further in Section 4.3.
4
4.1
Results
Observed maturity transformation by European banks in 2011
We provide a graphical representation of the maturity transformation undertaken by our sample of
banks in Figure 9. From the figure we can see that the median bank in 2011 obtained financing
mostly from customer deposits and instruments valued at amortised cost, while investing mostly in
loans. The maturity mismatch on bank balance sheets is also evident: within the loan category, the
median bank allocated more capital to longer-dated assets, but within the deposit category, the median
bank obtained more funding from shorter-dated liabilities. The median bank also obtained a signicant
share of funding in the amortised cost category from the 1-5 year horizon, which indicates hybrid and
subordinated debt instruments.
27 In principle, we should apply a ‘bootstrap’ procedure to determine the zero and forward curves implied by the Euro
swap curve data, and then we should fit the parametric yield curve model to this forward curve. This is a work in
progress and should not affect the results significantly, since the various parametrisations are shown in this paper not to
have a noticeable affect on the sensitivity calculation.
19
Kernel density of month−on−month
changes in beta0: Svensson
80
0
0
20
50
40
60
Density
100
Density
150
100
200
Kernel density of month−on−month
changes in beta0: Nelson−Siegel
−0.02
−0.01
0.00
0.01
0.02
−0.04
N = 166 Bandwidth = 0.0006728
−0.02
0.00
0.02
0.04
N = 166 Bandwidth = 0.001099
Figure 8: Kernel densities of month-on-month changes in β0 under the Nelson-Siegel and Svensson
models.
Net assets for the median bank in 2011
by maturity and subcategory
remaining maturity, or time to next repricing
maturity
not
disclosed
undetermined
more than
5 years
net assets (EUR)
20000
1 to 5
years
10000
0
−10000
3 to 12
month
up to 3
month
demand
amortised
cost
available
for sale
central
bank
customer
deposits
held for
trading
held to
maturity
interbank
loans
asset / liability subcategory
Figure 9: A graphical depiction of maturity transformation in the 2011 European banking data. Each
cell in the matrix gives the median net asset (asset minus liability) exposure across all banks in the
sample. 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, maturities
and methods. Subtable (a) uses the Basel Committee guideline method, (b) uses the simplest flat yield
curve loan pricing model, (c) uses a model based on Nelson-Siegel forward rates calibrated to historical
parameters, and (d) uses Svensson forward rates also calibrated to historical parameter values. In each
subtable 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.
(b) Flat rate δ = 3.2%
(a) Basel Committee guideline
-3.0%
-2.0%
-1.0%
-0.5%
0.0%
0.5%
1.0%
2.0%
3.0%
1
2.1
1.4
0.7
0.4
-0.0
-0.4
-0.7
-1.4
-2.1
3
6.8
4.5
2.2
1.1
-0.0
-1.1
-2.2
-4.5
-6.8
10
19.9
13.3
6.6
3.3
-0.0
-3.3
-6.6
-13.3
-19.9
15
26.8
17.8
8.9
4.5
-0.0
-4.5
-8.9
-17.8
-26.8
20
33.6
22.4
11.2
5.6
-0.0
-5.6
-11.2
-22.4
-33.6
30
39.0
26.0
13.0
6.5
-0.0
-6.5
-13.0
-26.0
-39.0
(c) Nelson-Siegel (β0 , β1 , β2 , τ1 ) = (3.2, −.7, 4.5, 73)%
-3.0%
-2.0%
-1.0%
-0.5%
0.0%
0.5%
1.0%
2.0%
3.0%
4.2
4.2.1
1
1.5
1.0
0.5
0.2
0.0
-0.2
-0.5
-1.0
-1.5
3
4.4
3.0
1.5
0.7
0.0
-0.7
-1.5
-2.9
-4.4
10
14.5
9.6
4.8
2.4
0.0
-2.3
-4.7
-9.3
-13.8
15
21.5
14.1
7.0
3.5
0.0
-3.4
-6.8
-13.4
-19.8
20
28.2
18.5
9.1
4.5
0.0
-4.4
-8.8
-17.2
-25.3
-3.0%
-2.0%
-1.0%
-0.5%
0.0%
0.5%
1.0%
2.0%
3.0%
1
1.5
1.0
0.5
0.2
0.0
-0.2
-0.5
-1.0
-1.5
3
4.4
2.9
1.5
0.7
0.0
-0.7
-1.5
-2.9
-4.4
10
14.1
9.3
4.6
2.3
0.0
-2.3
-4.5
-9.0
-13.4
15
20.5
13.5
6.7
3.3
0.0
-3.3
-6.5
-12.8
-18.9
20
26.5
17.4
8.5
4.2
0.0
-4.1
-8.2
-16.1
-23.7
30
37.3
24.1
11.7
5.8
0.0
-5.6
-11.1
-21.5
-31.3
(d) Svensson (β0 , β1 , β2 , β3 , τ1 , τ2 ) = (2.1, 1.1, 1.8, 5.5, 65, 855)%
30
41.1
26.7
13.0
6.4
0.0
-6.2
-12.3
-23.8
-34.7
-3.0%
-2.0%
-1.0%
-0.5%
0.0%
0.5%
1.0%
2.0%
3.0%
1
1.5
1.0
0.5
0.2
0.0
-0.2
-0.5
-1.0
-1.5
3
4.6
3.1
1.5
0.8
0.0
-0.8
-1.5
-3.1
-4.6
10
18.7
12.4
6.2
3.1
0.0
-3.1
-6.1
-12.1
-18.0
15
29.2
19.3
9.6
4.8
0.0
-4.7
-9.4
-18.7
-27.9
20
38.0
25.1
12.4
6.2
0.0
-6.1
-12.2
-24.1
-35.7
30
49.9
32.8
16.1
8.0
0.0
-7.9
-15.6
-30.8
-45.4
How good is the Basel Committee interest rate sensitivity guideline
for loans?
Effect of loan-specific pricing
The Basel Committee guidelines outlined in Section 1.1 do not take into account the type of security
for which an interest rate risk assessment is being performed. In particular, the guidelines may or may
not be suitable for typical loan contracts. We investigate the performance of the Basel Committee
guideline method for interest rate revaluation sensitivity by comparing it to our alternative simple
loan pricing models of Section 3.2 with parametric forward curves specified in 3.3. The results are
summarised in Table 6. Under all methods, positive interest rate shocks (increases in the level of the
forward curve) result in decreases in the value of a loan contract with any maturity, and decreases
in interest rates result in revaluation increases. Larger absolute interest rate shocks result in large
absolute changes in value.
The Basel Committee guideline method, like any duration-based sensitivity method28 , produces
sensitivities that are symmetric about zero: positive and negative interest rate shocks of equal absolute size have an equal absolute revaluation effect; in other words, for any given loan maturity, the
percentage decrease in loan price from an interest rate increase is the same as the percentage increase
in loan price from an interest rate decrease of equal absolute size. We can see that all the alternative
simple loan models, however, are able to capture the asymmetric revaluation effect of interest rate
changes. 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 to
decreases in interest rates. It is not surprising, therefore, that the Basel Committee guideline method
sometimes 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 Basel
28 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 flat
rate 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 we
would expect the remaining maturity of most loan contracts to be less than 30 years. However, when
compared to the Svensson model, the Basel Committee method is only prudent for loan contracts of
up 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 expect
the Basel Committee method to understate the loan price sensitivity to interest rate increases.
While prudential regulators presumably favour the conservativeness of a method, investors would
like 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 gains
from interest rate decreases at shorter maturities and understates these revaluation gains at longer
maturities. The Basel Committee method for interest rate revaluation sensitivity is therefore generally
conservative for shorter-maturity loans, and understates risk for longer-maturity loans.
4.2.2
Effect of current yield curve
The Basel Committee guideline method for assessing interest rate revaluation sensitivity does not account for the prevailing yield curve at the time of the sensitivity estimate. For example, we might
intuitively 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. We
investigate this by comparing the sensitivities from the Basel Committee guideline method to the sensitivities from our simplest flat rate loan model of Section 3.2, noting that the latter does depend on
a 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% parallel
upward 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 method
does not take into account the specific form of the loan contract, it gives a conservative assessment
of the interest rate risk for loans with remaining maturity up to 27 years. However, we note that the
prevailing 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 assesses
the risk of a 2% parallel upward shift in yield curves (forward rates) for loans with remaining maturity
up to 40 years. When yield curves are flat and low, say .1% or 1%, the Basel Committee method
understates the risk associated with 30-year loans.
From the preceding section, we know that the Basel Committee guideline method is generally
conservative for shorter-maturity loans, and understated for longer-maturity loans. In addition to
these stylised facts, we also observe for interest rate increases that the Basel Committee guideline
method is less conservative, or more understated, when interest rates are low than when interest rates
are 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 aggregation
Regardless of the type of security and the current level of the yield curve, the Basel Committee
guideline method for interest rate revaluation sensitivity does not provide a unique method for portfolio
aggregation. Suppose that a bank holds two loans of different remaining maturties, one with 1 year and
the other with 10 years. The Basel Committee method provides senstivities for each of these contracts
individually, but not uniquely for a portfolio of both. Two natural methods suggest themselves for
computing 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 maturities
and 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 drop
by more than the offsetting rise in the value of (short-term) liabilities. Off course, the regulator might anticipate that
rational market participants should rationally compensate for overstatements/understatements in the Basel Committee
guideline method, and if there are no informational obstacles to the market participants doing so, such a regulator might
be 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 , β , β , τ .
0
1
2 1
See the discussion of Figure 10.
22
Percentage change in price given
a 2% parallel upward shift in interest rates
0
−10
Method
percentage
Basel guideline
loan model 0.1%
−20
loan model 1%
loan model 3%
loan model 5%
loan model 7%
loan model 9%
−30
−40
0
10
20
30
40
50
remaining loan maturity
Figure 10: The effect of a 2% increase in interest rates at all maturities on the price of a loan contract
with remaining maturity between 1 and 50 years, according to the Basel Committee guideline and the
simple 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 the
flat yield curve before the shock.
23
−6
−8
−10
−12
% change in portfolio value
−4
−2
The first is to use a weighted average of the Basel Committee interest rate revaluation sensitivities
of each asset, based on the prevailing weights of each asset in the portfolio. We call this a weighted
average sensitivity method for assessing the interest rate revaluation sensitivity of the portfolio. The
is the approach recommended in Annex 4 of the Basel Committee guidelines (Basel Committee Basel
Committee on Banking Supervision, 2004), but it is not the only possible approach. Under this
method, the portfolio sensitivity is a linear combination of the sensitivities of the securities in the
portfolio. An alternative method, which we call the weighted average maturity method, is to compute
the Basel Committee interest rate sensitivity of a single hypothetical security with maturity equal to
the weighted average maturity of all the securities in a portfolio, again using portfolio weights.31
We examine the performance of these two
methods for applying the Basel Committee
Portfolio sensitivity to a 2% parallel increase
guideline method to portfolios of loan contracts
as we allocate less to the 10−year asset
using Figure 11. Consider the case where a bank
Sv (2.1,1.1,1.8,5.5,65,855)%
holds only two loan contracts: one with 1 year
N−S (3.2,−.7,4.5,73)%
flat yield curve 3.2%
and the other with 10 years remaining maturity.
basel w.a.m.
basel w.a.s.
The horizonal axis in Figure 11 represents the
weight placed on the 1-year loan, and the various
lines show the sensitivity of the portfolio value
to a 2% increase in the level of the yield curve
under the various methods, including those discussed in Sections 1.1 and 3.2. We see that all
methods are able to capture the greater price sensitivity of the 10-year loan than the 1-year loan.
We have already analysed above the sensitivites
at the left and right endpoints of Figure 11, where
we found for individual loan contracts with maturities less than 10 years that the Basel Committee method is relatively conservative. The Basel
0.0
0.2
0.4
0.6
0.8
1.0
Committee method performs aggregation by linear interpolation between these two sensitivities,
weight in 1 year loan (= 1 − weight in 10 year loan)
while all other methods display some convexity.
In particular, although the two Basel Commit- Figure 11: Effect of portfolio aggregation under the
tee portfolio methods agree exactly at the left Basel Committee guideline method for interest rate
and right endpoints, the weighted average matu- revaluation senstivity as compared to the alternarity method is more conservative everywhere in tive models. The labels in the legend correspond,
between, which shows that the Basel Committee from top to bottom, to Svensson, Nelson-Siegel
guideline sensitivity for individual loan contracts and flat forward curve models calibrated to historis convex in the remaining maturity of the loan. ical parameters; following these, we have the Basel
This convexity is borne out by the other loan- Committee weighted average maturity method and
pricing methods too. Perhaps surprisingly, while the weighted average sensitivity method.
the two Basel Committee methods for portfolio
sensitivity overstate the sensitivity for individual
loans, they understate the sensitivity for some portfolios of loans. Even the weighted average maturity
method, which is more conservative than the weighted average sensitivity method, understates the risk
for portfolios with greater weight in the 1-year loan than in the 10-year loan. Portfolios of the 1- and
10-year loans that place just a small weight in the 10-year loan are much more price-sensitive to parallel
upward shifts in yield curves than the Basel Committee methods indicate. For supervisory purposes or
for risk self-assessment, we would therefore be most worried about using the Basel Committee method
for banks whose loan portfolios have a short weighted average maturity, but a non-negligible allocation
at long maturities.
31 To make these definitions more formal, consider the case where we have a portfolio consisting of 1 − φ in the 1 year
loan and φ in the 10 year loan. Let the Basel Committee interest-rate sensitivity of a loan with remaining maturity τ
be ∆(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 for
most securities other than zero-coupon bonds, we would expect the latter method to produce lower portfolio sensitivities
than the former.
24
Table 7: Frequency of ≥ 2% increase in the level of historical (forward or zero) yield curves over an
l−month period for various values of l. Subtables (a) and (b) are computed by estimating Nelson-Siegel
and Svensson parametric forms respectively at each month-end in the sample, and by then examining
the longitudinal distribution of β0 . In each subtable, the first row shows the number of times where
an l−month change in β0 meet or exceeds 2%, the middle row shows the number of longitudinal
observations on which this count is based, and the final row shows the frequency obtained by dividing
the first row by the second.
(a) Nelson-Siegel
number ≥ 2%
number observations
frequency (%)
1
1
166
0.60
3
3
164
1.83
6
5
161
3.11
9
5
158
3.16
12
6
155
3.87
15
6
152
3.95
18
2
149
1.34
24
6
143
4.20
(b) Svensson
number ≥ 2%
number observations
frequency (%)
4.3
1
4
166
2.41
3
6
164
3.66
6
14
161
8.70
9
19
158
12.03
12
22
155
14.19
15
29
152
19.08
18
36
149
24.16
24
33
143
23.08
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-Siegel
and Svensson models, over various time horizons. Under the Nelson-Siegel model, such large moves
in the yield curve are rare even over 24 months, while under the Svensson model they are much more
frequent. The most relevant time horizons for our purposes are up to 3 months, in which time we
may expect a bank to be relatively unable to make major portfolio adjustments in response to sharp
yield curve changes. Based on time horizons of up to 3 months, we might estimate that a 2% parallel
upward shift in yield curve occurs with probability between 0.6% and 3.7% in any one month, which
corresponds to something between a 1 in 14 year event and a 1 in 2 year event. This gives an idea of
the ‘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 of
yield curves without also varying other shape parameters of the yield curve. In particular if slope and
level changes tend to occur together, then the revaluation effect of a level shock only may under- or
overstate the revaluation effect of a shock to both levels and slope. We present an initial investigation
of these relationships between changing parameters in Table 8, where the subtables correspond to
different time horizons over which we might measure the change in parameters. The correlations are
stable between tables. They show that changes in the level and slope of the yield curve, as parametrised
by β0 and −β1 , exhibit a strong positive contemporaneous correlation over 1, 3, 6, 9 and 12 months.32
Increases in the level of the Euro yield curve are associated with simultaneous increases in the slope
of the yield curve over all of these time horizons, and the absolute size of the correlation decreases
with the time horizon. Similary, level and curvature show a strong negative association, suggesting
that yield curves flatten when they shift upward, and the absolute size of this association increases
with the time horizon. We therefore note, that regardless of the severity of the interest rate shock one
would like to apply (for example a 2% level change), association between level, slope and curvature
are highly prevalent historically. We regard these relationships as evidence against the plausibility of
a parallel yield curve shock. These relationships should be used in a proper assessment of interest rate
risk.
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 scatterplots
of the levels and month-on-month (l = 1) changes in the β parameters of the Nelson-Siegel model in
32 β and β are negatively associated, so that β and −β are positively associated, and hence increases in level are
0
1
0
1
positively correlated with increases in slope.
25
Table 8: Correlations between l−month changes in Nelson-Siegel parameters. Of particular interest in
this paper are the correlations between the β parameters, because these parameters can be interpreted
as level, slope and curvature.
(a) l = 1
β0
β1
β2
τ1
β0
1.00
-0.82
-0.59
0.28
β1
-0.82
1.00
0.34
-0.39
(b) l = 3
β2
-0.59
0.34
1.00
-0.23
τ1
0.28
-0.39
-0.23
1.00
β0
β1
β2
τ1
β0
1.00
-0.75
-0.63
0.24
(c) l = 6
β0
β1
β2
τ1
β0
1.00
-0.64
-0.69
0.32
β1
-0.64
1.00
0.29
-0.55
β1
-0.75
1.00
0.33
-0.46
β2
-0.63
0.33
1.00
-0.18
τ1
0.24
-0.46
-0.18
1.00
β2
-0.76
0.29
1.00
-0.28
τ1
0.31
-0.55
-0.28
1.00
(d) l = 9
β2
-0.69
0.29
1.00
-0.33
τ1
0.32
-0.55
-0.33
1.00
β0
β1
β2
τ1
β0
1.00
-0.54
-0.76
0.31
β1
-0.54
1.00
0.29
-0.55
(e) l = 12
β0
β1
β2
τ1
β0
1.00
-0.48
-0.81
0.35
β1
-0.48
1.00
0.27
-0.57
β2
-0.81
0.27
1.00
-0.29
τ1
0.35
-0.57
-0.29
1.00
Figure 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 τ1 .34 From the two upper plots in Figure 12, we note the negative
associations between shape parameters, saying that high levels are associated with high slopes and high
curvatures, not to be confused with the correlations in Table 8. We also note the clustering of points
given by the two or three modes of the kernel density contours and the clustering of low and high
values of τ1 . The lower two panels give the scatterplots for month-on-month changes (l = 1) in the
beta parameters. From the lower-left panel we note that the strong linear dependence, measured in
Table 8 by the strong correlation between β0 and β1 , captures virtually all of the bivariate relationship
between the changes in these two parameters. Thus the positive correlation observed between the level
and slope of the yield curve sufficiently characterises the general statistical relationship between them.
4.4
Rankings of European banks by loan portfolio riskiness in 2011
From Table 9 we see that the method by which we measure the interest rate risk of banks affects which
banks emerge as most risky. We see that the ranking of the banks is not sensitive to the three forms of
the yield curve, although the percentage change in portfolio value under a Svensson yield curve (and
hence pricing) model produces higher sensitivities than under a Nelson-Siegel model. The two methods
for calculating the portfolio riskiness under Basel Committee guidelines give different rankings of the
banks, and the weighted average sensitivity guideline method agrees very strongly with the weighted
average maturity from “gap analysis”. Given our reservations about the Basel Committee guideline
methods for portfolios of assets, and given the lack of additional information they provide over simple
gap 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 error
loss function.
34 For the scatterplots of month-on-month changes in betas, the value of τ used to size the points on the scatterplot
1
is the second and later value corresponding to the pair of betas used for differencing.
26
0.08
0.00
0.25
0.50
−0.01
tau1
beta2
beta1
tau1
0.25
0.04
0.50
0.75
0.75
0.00
−0.02
0.00
0.02
0.04
0.06
0.00
0.02
beta0
0.04
0.06
beta0
0.02
0.03
0.00
tau1
0.25
0.50
0.75
−0.01
month−on−month change in beta2
month−on−month change in beta1
0.01
tau1
0.00
0.25
0.50
0.75
−0.03
−0.02
−0.06
−0.03
−0.01
0.00
0.01
0.02
−0.01
month−on−month change in beta0
0.00
0.01
0.02
month−on−month change in beta0
Figure 12: Relationships between level, slope and curvature parameters, and their month-to-month
changes, 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 their
loan portfolio, and in Columns 2-7 by the percentage decrease in the value of their loan portfolios due
to a 2% parallel upward shift in yield curves. Columns 2-3 give the Basel Committee guideline method
under weighted-average sensitivity and sensitivity of weighted-average maturity, defined in Section
4.2.3. Column 4 uses the simple loan formula with flat yield curve. Columns 5-6 use the Nelson-Siegel
parametric form of the yield curve, which agrees analytically although not computationally with the
simple loan formula when β1 = β2 = 0. Column 7 uses the Svensson parametric yield curve with
parameters calibrated to historical averages. The methods for Columns 4-7 are defined in Section 3.2.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
Loans
weighted avg
maturity
(yrs)
DK011 9.39
NL050 9.28
PT055 8.30
NL049 7.93
GB091 7.72
BE004 7.65
IE037 7.64
SE087 7.47
NO051 7.21
NL047 7.06
CY006 6.99
ES061 6.81
MT046 6.72
PT054 6.70
IE038 6.66
ES059 6.24
DE025 6.10
FI012 5.97
PT053 5.94
DE021 5.74
ES062 5.73
GB090 5.54
PT056 5.54
CY007 5.52
IT044 5.50
SE084 5.32
ES064 5.31
DE019 5.23
IT043 5.22
DE020 5.08
ES060 5.06
IT042 4.93
FR014 4.87
FR013 4.75
IT041 4.72
DE018 4.63
HU036 4.61
IT040 4.57
DE024 4.46
AT003 4.32
DE023 4.25
DE029 3.90
DE027 3.83
SI057 3.76
FR016 3.76
SI058 3.72
GB088 3.71
AT002 3.48
DE028 3.45
SE085 3.14
IE039 2.78
GR032 2.65
DK010 2.49
NL048 2.43
PL052 2.40
DK008 2.18
BE005 2.17
GB089 1.96
GR033 1.13
DK009 1.05
SE086 0.36
Basel
guideline
w.a.s. (%)
Basel
guideline
w.a.m. (%)
Simple
δ = 3.2%
(%)
N-S
β0 = 3.2%
(%)
DK011 -12.48
NL050 -12.34
PT055 -11.08
NL049 -10.62
GB091 -10.39
BE004 -10.29
IE037 -10.28
SE087 -10.04
NO051 -9.70
NL047 -9.56
CY006 -9.47
ES061 -9.22
PT054 -9.11
MT046 -9.05
IE038 -9.03
ES059 -8.48
DE025 -8.34
FI012 -8.17
PT053 -8.13
DE021 -7.84
ES062 -7.82
CY007 -7.61
PT056 -7.56
GB090 -7.56
IT044 -7.54
ES064 -7.29
SE084 -7.25
IT043 -7.20
DE019 -7.17
DE020 -7.06
ES060 -6.95
IT042 -6.81
FR014 -6.70
FR013 -6.57
IT041 -6.53
HU036 -6.42
DE018 -6.42
IT040 -6.36
DE024 -6.27
AT003 -6.09
DE023 -5.85
DE029 -5.53
DE027 -5.45
SI057 -5.36
SI058 -5.33
FR016 -5.25
GB088 -5.24
AT002 -4.96
DE028 -4.95
SE085 -4.54
IE039 -4.20
GR032 -4.01
NL048 -3.77
PL052 -3.72
DK010 -3.71
DK008 -3.44
BE005 -3.42
GB089 -3.16
GR033 -1.78
DK009 -1.77
SE086 -0.67
BE004 -13.26
DK011 -13.26
GB091 -13.26
IE037 -13.26
NL047 -13.26
NL049 -13.26
NL050 -13.26
NO051 -13.26
PT055 -13.26
SE087 -13.26
CY006 -10.16
CY007 -10.16
DE019 -10.16
DE020 -10.16
DE021 -10.16
DE025 -10.16
ES059 -10.16
ES060 -10.16
ES061 -10.16
ES062 -10.16
ES064 -10.16
FI012 -10.16
GB090 -10.16
IE038 -10.16
IT043 -10.16
IT044 -10.16
MT046 -10.16
PT053 -10.16
PT054 -10.16
PT056 -10.16
SE084 -10.16
AT003 -7.70
DE018 -7.70
DE023 -7.70
DE024 -7.70
FR013 -7.70
FR014 -7.70
HU036 -7.70
IT040 -7.70
IT041 -7.70
IT042 -7.70
AT002 -6.14
DE027 -6.14
DE028 -6.14
DE029 -6.14
FR016 -6.14
GB088 -6.14
SE085 -6.14
SI057 -6.14
SI058 -6.14
BE005 -4.50
DK008 -4.50
DK010 -4.50
GR032 -4.50
IE039 -4.50
NL048 -4.50
PL052 -4.50
DK009 -2.76
GB089 -2.76
GR033 -2.76
SE086 -0.72
DK011 -9.24
NL050 -9.18
PT055 -9.11
NL049 -8.87
SE087 -8.79
MT046 -8.77
NO051 -8.75
IE037 -8.74
BE004 -8.65
GB091 -8.65
ES061 -8.48
NL047 -8.36
CY006 -8.36
ES059 -8.33
IE038 -8.32
SE084 -8.20
ES062 -8.20
PT056 -8.15
GB090 -8.15
DE021 -8.12
DE019 -8.03
ES064 -8.00
PT053 -8.00
DE025 -7.95
DE023 -7.95
ES060 -7.93
IT044 -7.92
FI012 -7.88
IT042 -7.81
FR014 -7.77
CY007 -7.76
IT043 -7.72
IT041 -7.69
FR013 -7.64
DE018 -7.48
FR016 -7.41
IT040 -7.38
HU036 -7.36
DE020 -7.22
GB088 -6.94
DE024 -6.87
AT003 -6.78
SI057 -6.66
DE029 -6.62
AT002 -6.61
SI058 -6.54
DE028 -6.44
DE027 -6.34
DK010 -6.27
SE085 -6.09
GR033 -6.05
SE086 -3.36
PL052 -2.78
DK008 -2.70
GB089 -2.60
DK009 -2.41
BE005 NA
GR032 NA
IE039 NA
NL048 NA
PT054 NA
DK011 -9.24
NL050 -9.18
PT055 -9.11
NL049 -8.87
SE087 -8.79
MT046 -8.77
NO051 -8.75
IE037 -8.74
BE004 -8.65
GB091 -8.65
ES061 -8.48
NL047 -8.36
CY006 -8.36
ES059 -8.33
IE038 -8.32
SE084 -8.20
ES062 -8.20
PT056 -8.15
GB090 -8.15
DE021 -8.12
DE019 -8.03
ES064 -8.00
PT053 -8.00
DE025 -7.95
DE023 -7.95
ES060 -7.93
IT044 -7.92
FI012 -7.88
IT042 -7.81
FR014 -7.77
CY007 -7.76
IT043 -7.72
IT041 -7.69
FR013 -7.64
DE018 -7.48
FR016 -7.41
IT040 -7.38
HU036 -7.36
DE020 -7.22
GB088 -6.94
DE024 -6.87
AT003 -6.78
SI057 -6.66
DE029 -6.62
AT002 -6.61
SI058 -6.54
DE028 -6.44
DE027 -6.34
DK010 -6.27
SE085 -6.09
GR033 -6.05
SE086 -3.36
PL052 -2.78
DK008 -2.70
GB089 -2.60
DK009 -2.41
BE005 NA
GR032 NA
IE039 NA
NL048 NA
PT054 NA
28
N-S (β0 , β1 , β2 , τ1 ) =
(3.2, −.7, 4.5, 73)%
(%)
DK011 -9.21
NL050 -9.15
PT055 -9.07
NL049 -8.84
SE087 -8.75
MT046 -8.73
NO051 -8.71
IE037 -8.70
BE004 -8.61
GB091 -8.61
ES061 -8.44
NL047 -8.32
CY006 -8.31
ES059 -8.29
IE038 -8.28
SE084 -8.16
ES062 -8.16
PT056 -8.11
GB090 -8.10
DE021 -8.07
DE019 -7.98
ES064 -7.95
PT053 -7.95
DE025 -7.91
DE023 -7.91
ES060 -7.89
IT044 -7.87
FI012 -7.84
IT042 -7.76
FR014 -7.73
CY007 -7.71
IT043 -7.67
IT041 -7.64
FR013 -7.59
DE018 -7.44
FR016 -7.37
IT040 -7.34
HU036 -7.32
DE020 -7.18
GB088 -6.89
DE024 -6.82
AT003 -6.73
SI057 -6.62
DE029 -6.57
AT002 -6.57
SI058 -6.49
DE028 -6.39
DE027 -6.30
DK010 -6.22
SE085 -6.05
GR033 -5.99
SE086 -3.32
PL052 -2.76
DK008 -2.68
GB089 -2.59
DK009 -2.40
BE005 NA
GR032 NA
IE039 NA
NL048 NA
PT054 NA
Sv (β0 , β1 , β2 , β3 , τ1 , τ2 ) =
(2.1, 1.1, 1.7, 5.5, 65, 855)%
(%)
DK011 -12.06
NL050 -12.02
PT055 -11.96
NL049 -11.78
SE087 -11.71
MT046 -11.70
NO051 -11.68
IE037 -11.68
BE004 -11.60
GB091 -11.59
ES061 -11.46
NL047 -11.35
CY006 -11.35
ES059 -11.33
IE038 -11.32
SE084 -11.22
ES062 -11.22
PT056 -11.18
GB090 -11.17
DE021 -11.14
DE019 -11.07
ES064 -11.05
PT053 -11.04
DE023 -11.00
DE025 -10.99
ES060 -10.99
IT044 -10.96
FI012 -10.93
IT042 -10.88
FR014 -10.83
CY007 -10.82
IT043 -10.78
IT041 -10.76
FR013 -10.70
DE018 -10.55
FR016 -10.50
IT040 -10.46
HU036 -10.44
DE020 -10.28
GB088 -10.01
DE024 -9.91
AT003 -9.81
SI057 -9.71
AT002 -9.65
DE029 -9.63
SI058 -9.58
DE028 -9.46
DK010 -9.38
DE027 -9.31
GR033 -9.27
SE085 -9.03
SE086 -5.67
PL052 -2.90
DK008 -2.82
GB089 -2.72
DK009 -2.54
BE005 NA
GR032 NA
IE039 NA
NL048 NA
PT054 NA
5
Conclusion
In Section 4.1 we are able to show that large European banks tend to transform short term customer
deposits and amortised cost instruments at 1-5 year maturity like hybrid and subordinated debt into
long term loan assets, as expected. Given the earlier work discussed in Section 1, in which the effective
maturity of core deposits is estimated to be less than three years, the interest rate revaluation risk of
these banks is significantly determined by their loan asset portfolios. Examining the loan asset values
more closely, we find in Section 2.3 that the banks with the largest loan asset porfolios in 2011 are
domiciled in the UK, France and Germany, and these banks extend loans primarily into Euro-area
countries and then into non-Euro European countries. Ranking the banks by their loan asset portfolio
repricing sensitivity to a 2% parallel shift in interest rates in Section 4.4, we find that the three riskiest
banks across most methods are Nykredit (DK), SNS Bank (NL) and Espirito Santo (PT). It must
be emphasised that these rankings are independent of balance sheet size and do not account for offbalance-sheet instruments like interest rate derivatives, but they provide a useful starting point for the
bank analyst and supervisor.
In measuring the interest rate repricing risk of these banks, we employ several methods and critically evaluate the Basel Committee guideline method for interest rate sensitivity. We show how this
guideline method is simplistic and we illustrate the size of the deviation from simple alternative pricing
models through the use of examples. The guideline method is conservative for loan individual loan contracts with 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 for
individual loan contracts with longer maturities, and these understatements are exacerbated in low
interest rate environments. Further work should be done to investigate the sensitivities of the Basel
Committee 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. More
work should therefore be done to determine the appropriate shocks to apply to interest rates, especially
for supervisory purposes. In particular, it is inappropriate for supervisors to rely on monitoring only
one interest rate scenario because it is fairly easy for banks to allocate their asset and liability maturities
so that exposure to any one scenario is zero, while exposures to other scenarios might be large.
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