Appendix VI. Remaining Issues: Provisioning, Interest Rate Risk, and Stress Testing

International Monetary Fund
Published Date:
April 2006
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1. The Guide provides guidance for the purpose of compiling and disseminating FSIs. Nonetheless, in the course of the discussions preparing the Guide, it became clear that on some issues related to the development of data for use in supporting macroprudential analysis, there was no international consensus or best practice to draw on. This appendix describes current practices and concepts on three such issues, (1) provisioning, (2) measuring interest rate risk, and (3) stress testing, with the objective of supporting national efforts to further develop this work.

Part 1. Approaches to the Classification of Assets and Provisioning


2. There is no international consensus on best provisioning practices, resulting in significant differences among countries in the reported financial statements of deposit takers. This undermines meaningful cross-country comparisons of FSI data. The BCBS and the IMF have published several papers to encourage best practices.1 In this section, various approaches to provisioning are reviewed to help indicate a possible framework within which key decisions on provisioning policy could be addressed.2 These approaches do not necessarily constitute international best practice. The Guide relies on national practice in identifying loan loss provisions.

3. In 2003, the World Bank undertook a study titled “Bank Loan Classification and Provisioning Practices in Selected Developed and Emerging Countries” (hereafter referred to as BLCP) that provides the best overall information on current practices.3 This text is largely based on that study.

Loan Classification and Review

4. The BLCP found that authorities in all 29 countries surveyed require banks to establish loan review procedures to examine the quality of individual loans or portfolios of loans for classification and provisioning purposes. However, the practices adopted are diverse as is the frequency of review.

Loan classification

5. While the BLCP found a very wide range of philosophies and practices, in almost all the countries surveyed, the supervisor has the authority to issue prudential regulations regarding classification of loans. These classifications vary across countries, but an example is provided in the loan classification scheme proposed by the Institute for International Finance (IIF).4 It has five categories:

  • Standard. Credit is sound and all principal and interest payments are current. Repayment difficulties are not foreseen under current circumstances, and full repayment is expected.
  • Watch (special mention). The credit is subject to conditions that, if left uncorrected, could raise concerns about full repayment. Such credit requires more than normal attention by credit officers.
  • Substandard. Full repayment is in doubt due to inadequate protection (for example, on account of diminished obligor net worth or collateral), and/or interest or principal or both are more than 90 days overdue. These assets show underlying, well-defined weaknesses that could lead to probable loss if not corrected.
  • Doubtful. Assets for which collection/liquidation in full is determined by bank management to be improbable due to current conditions, and/or interest or principal or both are overdue more than 180 days. Assets in this category are considered impaired5 but are not yet considered total losses because some pending factors may strengthen the asset’s quality (merger, new financing, or capital injection).
  • Loss (write-off). An asset is downgraded to loss when management considers it to be virtually uncollectible, and/or principal or interest or both are overdue more than one year.

6. As further examples, the loan classification schemes of the United States and Japan are provided in Boxes A6.1 and A6.2.

Review practices

7. Country practices differ on whether ex post or ex ante information should be used to assess loan classification. Ex post methods rely on specific observable evidence from past behavior (such as 90-day nonpayment of interest and/or principal) or from the current condition of the debtor. Ex ante methods assess future losses by considering forward-looking information and a wide range of factors that could affect the ability of the debtor to meet the loan conditions. Reliance on ex ante methods has been increasing with the shift toward more risk-focused supervision and the use of internal models to evaluate risk.

8. In addition, other differences among country practices are evident:

  • Some countries follow standard regulatory prescriptions; others allow internal bank evaluations.
  • Some countries evaluate the portfolio on an asset-by-asset basis; others require creditors to treat the entire portfolio of loans to a single borrower as impaired if any of the loans to that borrower are impaired.

Box A6.1.U.S. Loan Classification System (Commercial Bank Examination Manual)

  • Standard assets. Loans in this category are performing and have sound fundamentals. (Fundamentals include the borrower’s overall financial condition, resources and cash flow, credit history, and character. They also include the purpose of the loan and types of secondary sources of repayment.)
  • Specially mentioned loans. Loans in this category are performing but have potential weaknesses that, if not corrected, may weaken the loan and the bank’s asset quality. Examples are credit that the lending officer is unable to properly supervise, an inadequate loan agreement, uncertainty of the condition of collateral, or other deviations from prudent lending practices.
  • Substandard loans. Loans in this category have well-defined weaknesses, where the current sound worth and paying capacity of the borrower is not assured. Orderly repayment of debt is in jeopardy.
  • Doubtful loans. Doubtful loans exhibit all the characteristics of substandard loans, with the added characteristics that collection in full is highly questionable and improbable. Classification of “loss” is deferred because of specific pending factors that may strengthen the asset. Such factors include merger, acquisition, or liquidation procedures; capital injection; perfecting liens on additional collateral; and refinancing plans.
  • Loss loans. These loans are considered uncollectible and of such little value that their continuance as bankable assets is not warranted. This classification does not mean that the asset has absolutely no recovery or salvage value but rather that it is not practical or desirable to defer full provision or writing off this basically worthless loan. Partial recovery may be effected in the future.

Box A6.2.Loan Classification System of Japanese Financial Supervisory Agency

  • Category I. Assets with no problems in terms of collectability.
  • Category II. Assets with higher collectability risk than normal because of difficulties in fulfilling contracted conditions, or due to concerns about the credit risk of the borrower (15% provisioning required).
  • Category III. Assets with concerns over final collection of value. Losses are likely to be incurred, but it is difficult to make estimates of the timing and scale of losses (70% provisioning required).
  • Category IV. Assets that are assessed as uncollectible or of no value.
  • The degree to which collateral, guarantees, or other mitigating factors can be taken into consideration varies.
  • The definition of restructured troubled assets and whether they are treated as impaired varies across countries.

Standard regulatory prescriptions versus allowing internal bank evaluations

9. Some countries have prescriptive systems that specify definitions for classifying loans into different categories based on the likelihood of default. The BLCP suggests that countries with less sophisticated supervisory systems often opt for these more explicit systems because they can be easier to monitor, provide for greater comparability, create a more even playing field among banks, promote better public understanding, and facilitate the compiling of statistical measures for off-site supervision and dissemination. Although there seems to be some convergence among these prescriptive systems toward the use of the five categories of loan quality outlined above, numerous exceptions were found.

10. Some other countries have systems that stress management responsibility in classifying loans and setting the size of provisions, with supervisors and auditors focusing on the oversight of the adequacy of the banks’ own internal evaluations and procedures and how well they are implemented. Depending on the country, banks may either be required to establish a classification system or be provided with a basic definition of what constitutes impaired assets, with little or no guidance regarding the appropriate size of provisions.

Classification of multiple loans

11. The BLCP shows that although just over half of the countries in its sample require the downgrading of all loans to a common debtor if any of these loans are classified as impaired, other countries permit a debtor’s loans to be evaluated separately or leave the decision to the discretion of individual banks. Moreover, an important related issue is whether the standards apply to the specific debtor that issued the impaired asset or to broader groups of related enterprises, under the presumption that weaknesses within one part of a group suggest weakness throughout the group.

Collateral and guarantees

12. Collateral and guarantees are off-balance-sheet instruments that can reduce the ultimate loss on impaired credits; however, the BLCP found wide differences in supervisory practice. In some jurisdictions the type and amount of collateral and guarantees may be taken into consideration in determining (1) whether the credit is impaired, (2) the recoverable amount and thereby the classification of the credit, and (3) the size of provisions needed. Often, the types of acceptable collateral and their valuation are regulated, and real estate collateral often receives special attention.

13. The liquidity of collateral and the enforceability of claims on collateral and guarantees were found to sometimes affect classification and provisioning. For example, a more creditworthy classification of an asset may be permitted if liquid securities are used as collateral instead of real estate. Where real estate is used as collateral, several countries require reductions in its value (including down to zero) the longer the period of nonrepayment of the credit. Nonetheless, fewer than one-third of respondents considered the condition of collateral in classifying loans, giving weight to the view that the quality of a loan should be judged in its own right independent of collateral and guarantees. Moreover, collateral may involve different debtors, payment conditions and flows, and maturities; it may also be characterized by a different probability of payment than the original loan.6 Indeed, there is some prevalence of the practice not to consider declines in the value of loan collateral or guarantees as a basis for classifying the loan as impaired, although in such circumstances special mention status could be justified.

14. Disclosures of the treatment of collateral would permit a more ready comparison of data from countries that follow different practices regarding provisions.

Classification of restructured troubled loans

15. Restructured troubled loans are those for which the lender grants concessions it would not otherwise grant because of the debtor’s financial difficulty. Restructuring and the lending of new funds to cover the nonpayment of older debts can disguise weakness in credits, and therefore some regulators have rules to define restructured troubled loans to prevent such practices.7 Although payments on restructured troubled loans may continue, they often are treated identically with impaired assets for provisioning purposes until a record of payment is established, after which they can be upgraded.

16. The BLCP found that 15 of 23 countries define restructured troubled loans by regulation; explicit definitions were much more common outside the G-10 countries.

Frequency of review

17. The BLCP data indicate that 16 of 23 countries require loan review for classification purposes at least every quarter. Often, more frequent review is required for large exposures or for assets deemed less creditworthy.


18. Given the classification of an asset, what size of provision should be applied? Do provisions relate to specific and identifiable events resulting in loss, or to probable losses? When is specific and general provisioning used? How should collateral be treated? Are there specific levels of provisioning for each asset classification, or is this the prerogative of individual banks, or case by case? Different philosophies and practices exist on these matters.

Do provisions relate to specific and identifiable events resulting in loss, or to probable losses?

19. In practice, this issue appears to be closely related to whether classification standards are prescribed by regulation covering readily observable factors or whether they are based on more comprehensive and diffuse reviews of the condition of the borrower. The BLCP found that countries, especially emerging market economies, that prescribe classification rules also frequently prescribe provisioning levels so that they are simple, verifiable, and enforceable. In contrast, countries that emphasize general guidance on classification tend to base provisioning more on estimates of probable losses, which sometimes are based on internal models and estimates of probabilities of default (PD) and of losses given default (LGD). These latter countries might permit provisions to be set within ranges.

When are specific and general provisioning used?

20. A specific provision is a current charge reflecting the loss in value of impaired assets. In contrast, a general provision is a reserve within the capital account that reflects the amount of losses that a portfolio may experience. A dynamic provision is a form of general provision that is adjusted over the course of the economic cycle—being built up during good economic times and drawn down in down-turns—to provide for sufficient reserves over the entire life of the financial instrument. Dynamic provisioning is a new concept practiced only in Spain among the countries covered in the BLCP study.8

How should collateral be treated?

21. The discussion above on collateral and guarantees describes some of the ways in which collateral can reduce the ultimate loss on impaired credits. The BLCP found that 12 of the 23 countries permitted the use of collateral to reduce the size of provisions, with its use most common among the G-10 countries in the sample.9 Where use of collateral was permitted in setting provision levels, wide variation was found in the types of collateral permitted in different situations and its valuation.

Are there specific levels of provisioning for each asset classification, or is this the prerogative of individual banks?

22. As noted above, different countries follow different philosophies. The BLCP provided data on the level of provisions set for different asset classifications in each country based on a classification system in line with that of the IIF, as summarized in Table A6.1.

Table A6.1.Levels of Provisions for Different Loan Classifications
ClassificationNumber of Countries Specifying ProvisionsMonths of NonpaymentMost Common Level of Provisions (In percent)Typical Range of Provisions (In percent)
Special mention6/23Up to 33 or 52–5
Substandard10/23Over 3 or up to 62010–25
Doubtful12/23Over 65050–75
Write-off10/23No guidance100100
  • The column “Number of Countries Specifying Provisions” indicates the number out of the 23 countries at each classification level that requires specific levels of provisioning. It appears that only about one-half of the respondents require specific provisioning levels, which means that common international patterns have not yet been established, and that in many countries banks probably have substantial leeway in setting provisions.The column “Months of Nonpayment” provides the number of months of nonpayment of principal or interest on the loan that is considered evidence of specific levels of impairment. There appears to be some convergence on three months as evidence of basic impairment, and six months as evidence of more severe impairment among those countries that provide such guidelines.
  • The remaining columns provide information on the most common levels of provisioning for each loan category and a typical range for provisions, expressed as a percentage of the value of the asset. Although there are hints of convergence around certain values, there are too few cases among the 23 respondents to conclude that there are general international practices.

Tax Treatment of Loan Loss Provisions

23. The tax deduction of specific provisions, which the BLCP found to be nearly universal, affects the reported income, balance sheet, and the capital adequacy ratio. However, variations in tax deductibility exist; fewer than one-third of respondents permit tax deductibility of general provisions, and various caps or special conditions apply to tax deductibility in some cases. The timing of tax deductibility for provisions varies, which affects the reported income: the study showed that a small number of respondents permit tax deductions only in write-off or near write-off situations.


24. In general, deposit takers are currently not expected to provide detailed information on the classification of loans. In contrast, the BLCP found that disclosure of aggregate information on total provisions in the current period is more common. Finally, the BLCP found that in practice, most G-10 and non-G-10 supervisors do not impose penalties on banks that breach disclosure requirements. In summary, with a few exceptions, the disclosure requirements of loan classification and provisioning are not strong.


25. While there is increased awareness of the need for good classification and provisioning systems, the evidence also suggests that little convergence has occurred to date among countries. There are, however, a number of methods and approaches that are in practice in a large number of countries: carrying out loan review on a quarterly or more frequent basis, adopting a multistage classification system, and classifying loans independently of the condition of collateral and guarantees. Future movement in these areas could considerably contribute to improvements in the usefulness and comparability of FSIs, but they are the responsibility of international and regional standard setters in accounting, supervision, valuation, and auditing.

Part 2. Measuring Interest Rate Risk

26. Because of their role in financial intermediation and the nature of their assets and liabilities, deposit takers need to manage interest rate risk—that is, the exposure of capital to interest rate changes. However, standard practices do not exist for monitoring this risk at the sector level.10,11 The techniques for monitoring interest rate risk are still being developed, by the BCBS and other institutions. Drawing on those approaches used by individual institutions, this appendix describes two common approaches—the “gap” model and duration. Measuring the effects of interest rate changes on interest income and expense using the “interest rate repricing gap” model is also described.

The Gap Model

Price effects

27. One approach to assessing interest rate changes on the market price of a portfolio of assets and liabilities is to use gap analysis. Under this approach, expected payments on assets and liabilities are sorted into various time “buckets” according to the time to repricing for floating-rate instruments and the time until payments are due for fixed-rate instruments.12 As with duration, debt assets and liabilities that are market or fair valued could be covered. The net amounts (receipts minus payments) expected under single-currency interest-rate-based financial derivatives are also included. Table A6.2 provides an illustration of the time buckets that could be set.

Table A6.2.Interest Rate Risk1(In thousands of units of account, as of the end of period)
0–3 Months4–6 Months7–12 Months1–2 Years2–5 Years5–10 Years10–15 Years15–20 Years20 Years and Above
Assets Debt instruments
Liabilities Debt instruments
Interest-rate-based financial derivatives

For fixed-rate instruments to receive/pay fixed-rate-linked payments, expected amounts to be paid/received are recorded according to their remaining maturity. Thus, for a bond with just under two years to maturity and annual coupon payments, the amount of the annual coupon payment will be included in the time bucket column of 7–12 months and the remainder of the payments in the one to two years time bucket column.

For variable-rate instruments contracts to receive/pay variable-rate-linked payments, amounts expected to be paid or received are recorded in the time period at which the next repricing of interest rates is scheduled to occur. Thus, a bond on which the interest is due to be repriced every six months will include the redemption amount of the bond and the next scheduled interest payment under either the first or second time bucket columns, depending on how recently the repricing occurred.For interest-rate-based financial derivatives, the net amounts expected to be received (+) or paid (−) are to be recorded in each time period, as appropriate.

For fixed-rate instruments to receive/pay fixed-rate-linked payments, expected amounts to be paid/received are recorded according to their remaining maturity. Thus, for a bond with just under two years to maturity and annual coupon payments, the amount of the annual coupon payment will be included in the time bucket column of 7–12 months and the remainder of the payments in the one to two years time bucket column.

For variable-rate instruments contracts to receive/pay variable-rate-linked payments, amounts expected to be paid or received are recorded in the time period at which the next repricing of interest rates is scheduled to occur. Thus, a bond on which the interest is due to be repriced every six months will include the redemption amount of the bond and the next scheduled interest payment under either the first or second time bucket columns, depending on how recently the repricing occurred.For interest-rate-based financial derivatives, the net amounts expected to be received (+) or paid (−) are to be recorded in each time period, as appropriate.

28. The net difference (gap) or the gross positions in each time bucket can be multiplied by some assumed change in interest rates and discounted, to gain an indication of the interest rate sensitivity of deposit takers’ portfolio of financial assets and liabilities. For instance, one approach could be to consider the impact of the largest interest rate change observed in recent history or some multiple of the standard deviation of interest rates in recent times.

29. The gap approach has the advantage of simplicity and intuitive appeal. But by grouping different assets together under broad time buckets, it can mask mismatches in maturities among assets in the same time bucket. For example, liabilities may tend to be repriced toward the end of the range of maturities in a bucket, while assets may tend to be repriced toward the beginning. To avoid this problem, the measure of duration provides a more accurate measure of exposure to interest rate risk; it is described later in this appendix.

Implementing the gap model

30. The use of the gap model can be demonstrated with reference to the first two columns of Table A6.3 showing the annual cash flow payments on two financial instruments. If instrument 1 is assumed to be an asset and instrument 2 a liability, the gain or loss associated with a change in the shape of the yield curve can be estimated as shown in Table A6.3:

Table A6.3.Example of Gap Analysis
TimeAssetLiabilitiesGaps (Assets minus Liabilities)NPV11NPV22
0–1 years80701099
1–2 years80701089
2–3 years80701088
3–4 years80701077
4–5 years801,070−990−609−601
5–6 years1,0801,080600559

NPV1 = Net present value1 = Gap × Discount factor specified in the first row of Table A6.8.

NPV2 = Net present value2 = Gap × Discount factor specified in the second row of Table A6.8.

NPV1 = Net present value1 = Gap × Discount factor specified in the first row of Table A6.8.

NPV2 = Net present value2 = Gap × Discount factor specified in the second row of Table A6.8.

31. The difference between NPV1 and NPV2 provides the capital gain or loss associated with the assumed change in interest rates. Thus, in Table A6.3, the steepening of the yield curve results in a capital loss of 32 (= 9 + 23). For a portfolio of assets and liabilities with cash flows occurring at different times within each bucket, a weighted average discount factor for each bucket can be used, with the weights given by the proportional size of the individual cash flows occurring in each bucket.

32. Positions in financial derivatives can be incorporated into the gap analysis by estimating changes in the net present value of expected future payments/receipts as interest rates change. For instance, if the expected payment on a bond futures contract in five years’ time changed from 0 to 10, the change in the present value of the expected payment of 6.1 would partially offset (hedge) the capital loss expected when the yield curve becomes more steep.13

Net interest income effects

33. By considering the time to repricing of assets and liabilities, the effect of an interest rate change on interest income and expense can be estimated. The so-called repricing gap model allocates interest-bearing assets and liabilities into buckets according to their time to repricing, and the gap between assets and liabilities in each bucket is then used to estimate the net interest income exposure to interest rate changes.14 For example, interest-rate-sensitive assets and liabilities with a time to repricing of one year or less are shown in Table A6.4.15

Table A6.4.Interest-Rate-Sensitive Assets and Liabilities with a Time to Repricing of One Year or Less(In millions)
Time to RepricingAssetsLiabilitiesGaps (Assets Minus Liabilities)Cumulative Gap
1 day2030−10−10
More than 1 day to 3 months3040−10−20
More than 3 months to 6 months7085−15−35
More than 6 months to 12 months907020−15

34. The one-day gap indicates a difference of minus 10 million between assets and liabilities being repriced in one day. A proportionate rise in interest rates on these assets and liabilities would therefore lower net interest income because there are more interest-rate-sensitive liabilities than assets in this bucket.

35. More generally, for a given change in interest rates (ΔRi), the repricing gap can be used to calculate the changes in income in each bucket i:

Δ Net interest incomei = GAPi × Δ Ri.16

36. For the first bucket, the impact of a 1 percent rate increase (ΔRi = 0.01) on future income is −100,000.17 By repeating the calculation for each bucket, the overall effect on net interest income for a one-year horizon (if annualized interest rates are applied to each time bucket) can be estimated. Depending on the time horizon used, it may be necessary to discount the impact on the gaps to the current period.

37. Positions in interest-rate-based financial derivatives can be incorporated into this analysis by recalculating the expected future receipts and payments as interest rates change. For instance, if following the interest rate shock the change in expected net receipts/payments on an interest rate swap contract maturing in 12 months is +150,000, this partially offsets (hedges) the net interest income loss on nonderivative positions associated with the rate change.


38. Duration18 measures the maturity of an instrument by taking account of the size and timing of payments between now and maturity. Even if the maturities of financial assets and liabilities are matched, a difference in the timing of the cash flows on those assets and liabilities can expose institutions to gains (or losses) as interest rates change. Thus, the longer the duration of the portfolio of assets or liabilities, the greater the gains (or losses) for any given change in interest rates.19

39. A simple measure of duration (Macaulay Duration) can be calculated for any fixed-income security by using the general formula set out below:


Di=Duration measured in years for instrument i;
CFt=Cash flow to be received on the financial instrument at end of period t;
N=Last period in which the cash flow is received (maturity of instrument);
DFt=Discount factor = 1/(1 + R)t, where R is the yield or current level of interest rates in the market (the discount rates on government bonds are commonly used as the discount factor, R, to reflect the time value of money);
Σt=1N=Summation sign for addition of all terms for t = 1 to t = N; and
PVt=Present value of the cash flow due at the end of the period t, which equals CFt × DFt.

Duration of a single instrument

40. To illustrate how duration can be measured for a single debt security, suppose the annual coupon on a eurobond is 8 percent, the face value of the bond is $1,000, and the current yield to maturity (R) is also 8 percent. The calculation of duration (D) is shown in Table A6.5.

Table A6.5.Duration (D) of a Six-Year Eurobond with 8 Percent Coupon and Yield
TimeCFtDFtCFt × DFtCFt × DFt × tCalculation of Duration (D)

41. Many bonds carry floating interest rates linked to market rates. The duration of such floating-rate instruments is the time interval to when the next coupon or interest payment is readjusted to reflect current interest rate conditions, referred to as the time to repricing of the instrument. For instance, if a floating-rate note with a coupon rate set at the beginning of each year is bought in the middle of the first year, it has duration of a half-year.

Duration of a portfolio

42. The duration of a portfolio of financial instruments can be calculated as a simple weighted average of individual durations. This is the measure of duration specified in the memoranda items to the deposit taker’s balance sheet (Table A3.2). For example, if xi represents the share of the portfolio invested in bond i, the portfolio duration is

where Di is the duration of bond i.

43. Thus a portfolio with $100 million, equally invested in five-year bonds and one-year bonds with respective durations of 4.465 years and 1 year, has duration of (0.5 × 4.465) + (0.5 × 1) = 2.733 years.

44. Table A6.6 provides an illustration for a portfolio of two asset and two liability interest-rate-sensitive instruments, where the portfolio duration for assets (DA) is 4.41 years and for liabilities (DL) is 6.25 years.

Table A6.6.Portfolio Duration
Duration DiMarket ValueWeight xiPortfolio Duration xiDi

45. All traded debt instruments that are marked to market or fair valued on the balance sheet can be included in the calculation of portfolio duration.20 Relevant positions in financial derivatives and off-balance-sheet instruments should also be included in the analysis of interest rate risk (see below).

Duration at the sector level

46. Measures of duration at the sector level can be calculated as a simple weighted average of the individual deposit taker’s asset and liability durations, using as weights the market value of the instruments included in the institution’s measure of duration. The market values used as weights may be derived from the instrument analysis shown in Table 4.1 or may be obtained directly from the reporting institutions. To illustrate, Table A6.7 shows the derivation of sector-wide duration data.

Table A6.7.Sector-Level Duration
Duration DiMarket ValueWeight xiPortfolio Duration xiDi
Institution 12.62000.511.33
Institution 23.7720.180.68
Institution 34.61200.311.41
Institution 121800.490.97
Institution 27600.161.14
Institution 331300.351.05

47. While the concept is simple to express, experience has shown that there are practical difficulties in compiling sector-level duration data. For instance, there is a need to ensure consistency among reporting institutions in terms of instrument coverage and discount rate(s) applied to cash flows.

48. Once measures of duration for positions in the assets and liabilities included in the analysis are compiled, assumed changes in interest rates can be measured in terms of their impact on the market values of those assets and liabilities and thus on the capital (E) of an institution (sector), as follows:


[DAkDL]=Adjusted duration gap;
A=Asset size; and
ΔR1+R=Interest rate change.

49. In other words, the total effect of interest rate changes on the value of institutions’ (the sector’s) capital is composed of three effects:

  • The leverage-adjusted duration gap = [DAkDL], where DA = duration of assets; DL = duration of liabilities; and k = the leverage ratio, which is equal to liabilities/assets. This gap is measured in years and reflects the degree of duration mismatch for the assets and liabilities included in the analysis. Specifically, the larger this gap is in absolute terms, the more exposed institutions are to interest rate changes.
  • The size of the institutions = A, where the term A measures the size of institutions’ assets included in the analysis. The larger the assets, the larger the potential capital exposure from any given interest rate changes.
  • The size of the interest rate shock = Δ R/(1 + R). The larger the interest rate change, the greater the impact on capital.

Weaknesses in using duration measures

Large interest rate changes and convexity

50. While duration accurately measures the price sensitivity of fixed-income instruments for small changes in interest rates,21 for large interest rate increases, duration overpredicts the fall in bond prices, and for large interest rate decreases, duration underpredicts the increase in bond prices. This arises because the bond price-yield relationship is convex rather than linear, as assumed by the basic duration model. Further precision can be obtained by recognizing the second derivative of yield changes (convexity) by measuring the change in the slope of the price-yield curve around a given point. Just as duration (D) measures the slope effect (dP/dR), a new parameter can be specified (CX) to measure the curvature effect (d2 P/dR2) of the price-yield curve so that the estimated price change for a fixed-income bond, for example, is given by

51. The first term in the equation is simple duration (D), and the second term is the second-order effect of an interest rate change, that is, the convexity or curvature adjustment.

52. As in the case of duration, the convexity of a portfolio of fixed-income instruments can be derived from a simple weighted average of the components of the portfolio convexity. Thus, if xi is the proportion invested in bond i with convexity CXi portfolio convexity (CXp) can be approximated by

53. A similar approach can be used to derive the convexity of portfolios at the sector level, where CXi represents the convexity of institution i’s portfolio, and xi represents the amount invested by institution i in the portfolio as a proportion of the aggregate investment by all reporting institutions.

The term structure of interest rates

54. A key assumption of the simple duration model outlined above is that the yield curve or the term structure of interest rates is flat (that is, R is the same across all maturities). This assumption is unlikely to hold in practice—the yield curve is often upward or downward sloping across maturities, depending on the expected future path of interest rates. For more precision, alternative measures of duration can account for the possibility of changes in the shape of the yield curve by using specific discount factors for each maturity:

55. To illustrate, the example in Table A6.8 calculates duration for a two-instrument portfolio when the yield curve is not flat. The first row of Table A6.8 uses an upward-sloping yield curve, and the second row repeats the calculation using a yield curve with a steeper slope.

Table A6.8.Duration (D*) When the Yield Curve Is Upward Sloping
Time (t)Instrument 1 CFtInstrument 2 CFtΣ CFUpward Sloping Yield CurveDFtΣ CF × DFtΣ CF × DFt × tCalculation of Duration
180701508.0%1/1.08 = 0.9259138.89138.89D*=8,285.331,790.72=4.62681years
280701508.8%1/(1.088)2 = 0.8448126.72253.43
380701509.4%1/(1.094)3 = 0.7637114.56343.68
480701509.8%1/(1.098)4 = 0.6880103.20412.80
5801,0701,15010.2%1/(1.102)5 = 0.6153707.603,538.02
61,0801,08010.3%1/(1.103)6 = 0.5553599.753,598.50
Steepening of Yield CurveDFtΣ CF × DFtΣ CF × DFt × t
6.8%1/1.068 = 0.9363140.45140.45D*=8,003.981,745.36=4.58586years
8.1%1/(1.081)2 = 0.8558128.36256.73
9.1%1/(1.091)3 = 0.7701115.51346.53
9.6%1/(1.096)4 = 0.6930103.96415.82
10.5%1/(1.105)5 = 0.6070698.053,490.25
11.6%1/(1.116)6 = 0.5176559.033,354.21

Financial derivative positions

56. To assess the extent to which the interest rate duration gap is covered (hedged) by financial derivative positions, the expected gain (loss) on derivative positions for the sector needs to be estimated for the assumed change in interest rates. Such information may be difficult to compile, even if the data are available. While for forwards the change in value arising from changes in interest rates is of a linear nature, this is not true for options, which are complex instruments to price and reprice.

57. The interplay of factors in determining the impact of interest rate changes on deposit takers’ capital is a reason for the growing interest in the use of stress tests. These are described in the next section of this appendix.

Measuring duration for mortgages, mortgage-backed securities, and demand deposits

58. The duration of some instruments can be difficult to calculate, notably mortgages, mortgage-backed securities, and demand deposits.

59. The difficulty with mortgages and mortgage-backed securities arises from the risk of prepayment of principal (prepayment risk). As the level of interest rates falls, mortgage debtors have an incentive to prepay their existing fixed-rate mortgage and refinance with a new mortgage at a lower rate of interest, making the projection of future cash flows uncertain. Most probably, the prepayment behavior of mortgage debtors should be modeled on past behavior.

60. The difficulty with demand deposit accounts arises because, while payable on demand, the actual timing of repayment is uncertain. There are several possible approaches to defining the duration for such deposits.

  • Demand deposits can be considered as bonds that are instantly repayable. Under this assumption, the duration of demand deposits is approximately zero.
  • More directly, the net withdrawal sensitivity of demand deposits (Δ DD/DD) to interest rate changes (Δ R) can be examined. Because demand deposits pay either low explicit or implicit interest—where implicit interest takes forms such as subsidized checking fees—there tend to be increased withdrawals and switching into higher yielding instruments as interest rates rise. Regression analysis can be used to estimate this sensitivity.
  • Simulations, based on forecasts of future interest rates and the net withdrawals of depositors over some future time period, can be used to estimate cash flows. Taking the discounted present values of these cash flows, a duration measure can be calculated.

61. In addition, banks may choose not to move rates paid on deposits in line with market rates, further complicating the measurement of interest rate risk exposure.

Part 3. FSIs and Stress Testing

62. FSIs can be used in conjunction with stress testing to enhance the quality of financial stability analysis. This section of the appendix outlines how this can be done, while highlighting their different roles and the limits this places on their comparability. It briefly describes what a stress test is but does not discuss how to conduct one. Rather, it references relevant analytical work that provides an overview of this complex topic.22

63. Stress testing aims to assess the impact of potential shocks on the soundness of a financial system by applying them to a model of the system. The type of shock is chosen to represent identifiable risks, while the model is customized to reflect the structure of the financial system. For many countries, the model can be quite simple—a spreadsheet of the balance sheets and income statements of banks in the system—while in complex financial systems, institutions’ risk management models can be used.23 Typically, stress tests will evaluate the change in the capital of the financial sector stemming from a particular macroeconomic event, such as an exchange rate depreciation or a recession-induced deterioration in asset quality. The size of stress test shocks should be “large but plausible,” since the results of a shock that is regarded as too extreme may not be credible. Stress tests are used to represent macroeconomic scenarios that can involve several simultaneous (“correlated”) shocks. They are also used for sensitivity analysis where the shock’s impact is evaluated separately to assess the vulnerability of the financial system to specific risk factors.

64. Stress testing and FSIs play different but complementary roles in surveillance. Stress testing is a tool for analyzing the financial system that is forward looking in the sense that it seeks to assess the impact of possible macroeconomic events whose probability is uncertain. In contrast, FSIs are data showing the current condition of the system. Each surveillance tool can contribute to the effectiveness of the other in several ways.

  • An analysis of FSIs can be used prior to a stress-testing exercise to help identify the vulnerabilities that need to be analyzed further through stress testing. For example, if FSIs show that the net open position in foreign currency is significant in either the banking or corporate sectors, this would suggest that stress testing using an exchange rate shock is needed.
  • The output of simple stress tests is often shown as a change in an FSI—the regulatory capital ratio. In some stress tests, changes in other FSIs are also reported, in which case they can provide information on (or “benchmark”) the relationship among the FSIs, allowing them to be used together more effectively.24 For example, shocks to assess credit risk could reveal how much the NPL to gross loans FSI would need to increase to push the capital ratio FSI below 8 percent. This relationship would be based on an assumption built into the stress test about how banks provision against NPLs derived from supervisory guidelines. This information would help users of FSIs judge how concerned they should be when they observe a deterioration in asset-quality FSIs.
  • Stress tests can shed light on the sensitivity of FSIs to institutional or regulatory changes. For example, they could reveal how a change in loan classification or provisioning rules would affect the capital ratio FSI.
  • Stress tests can shed light on vulnerabilities in areas where data for the FSIs are lacking by relying on informed assumptions, which could be based on analogous situations in other countries or qualitative information. For example, if data on the foreign currency liabilities of the corporate sector are lacking, partial data from a few banks could be used as the basis for an assumption about this exposure in a stress test. Of course, the limitations that these assumptions impose on the analysis must be taken into account.

65. The scope for exploiting the complementarity between stress testing and FSIs is probably greatest in the area of market risk, because of the relatively advanced state of market risk modeling and stress testing. This can be an attractive option, because market risk FSIs for interest rate risk (that is, duration) and foreign exchange risk can be technically difficult to compile.25,26 It is most likely to be feasible in more sophisticated financial systems where financial institutions that face significant market risk conduct frequent market risk stress tests as an integral part of their risk management. In principle, the output of these stress tests could be used to generate a measure of potential loss arising from market risk that could serve as a soundness indicator. Since the cost of implementing additional stress tests is low, the authorities may be able to work with these institutions to implement standardized shocks at regular intervals that can then be aggregated (which protects confidentiality) to produce it. The results from these stress tests could be presented in a form comparable to a market risk FSI (for example, as a measure of loss relative to capital for a shock of a given size). However, in implementing such an approach, a number of technical issues would need to be addressed, such as how to accommodate differences in risk management models across institutions.27

66. In using FSIs and stress testing together, however, due attention needs to be paid to their different roles in surveillance and the limits this places on their comparability.

  • Experience has shown that stress testing can play a valuable role in focusing discussions on financial soundness. Specifically, it often helps develop a consensus on the risks a financial system faces and the possible policy responses by highlighting the potential effect and cost of shocks. To serve this purpose, each stress-testing exercise must be tailored to the features of a financial system and needs of the country. Thus, there can be no “standard” method for conducting stress tests comparable to the statistical methodology developed for compiling FSIs and presented in this Guide.
  • Stress tests rely on judgments and assumptions with respect to the size of the shocks and the structure of the models used. They are also subject to the limitation that the probability of a shock is not known with any degree of precision. Thus, stress test output should not be reported or used outside the context of the stress test exercise. This implies that stress test output cannot be regarded as equivalent in any sense to FSIs, which are based on data and measure the actual condition of a financial system. In particular, FSIs can be used on a stand-alone basis and are subject to rigorous standards of data quality.

67. A final consideration when using stress tests and FSIs together is that, to the extent possible, they should rely on the same data sources, as well as methods of aggregation and consolidation. The bank balance sheets and income statements to which shocks are applied in simple stress tests should also be the data on which the FSIs are based. From this perspective, such stress tests can be viewed as a tool for analyzing these data that complements the analysis of FSIs.

68. The output of these stress tests is typically subjected to peer group analysis (for example, domestically owned banks and foreign bank subsidiaries) to analyze the distribution of the impact of shocks across different parts of a financial system. To effectively integrate the analysis of FSIs and stress testing, they would need to use the same peer groups (which would be natural since they are focusing on the same risks). Similarly, for stress tests applied to individual bank balance sheets—which usually are cross-border consolidated and could alternatively be cross-sector consolidated—attention should to be paid to whether FSIs are based on the same data consolidation approach. Finally, in the case of more sophisticated approaches to stress testing that rely on macroeconomic models and banks’ risk management models, it may be difficult to achieve a high degree of comparability, and close attention may need to be paid to the specification of the models when using FSIs and stress tests together.


At the IMF Executive Board meeting on FSIs in July 2001, in developing harmonized standards and practices for compiling FSIs, in consultation with relevant international standard-setting organizations, the Directors stated, “Special attention should be given to improving the international comparability of data for nonperforming assets and provisions, and the valuation of liabilities as well as assets.”


See Laurin and Majnoni (2003). The study drew on data collected by the Basel Core Principles Liaison Group (CPLG) on practices of its 29 members. Countries surveyed included France, Germany, Italy, Japan, the Netherlands, the United Kingdom, and the United States, among the G-10 countries. Non-G-10 countries were Argentina, Australia, Brazil, Chile, China, the Czech Republic, Hong Kong SAR, India, the Republic of Korea, Mexico, Russia, Saudi Arabia, Singapore, South Africa, Spain, and the West African Monetary Union (WAMU).


The IIF is a private sector association of financial institutions that analyzes risks in emerging market economies, serves as forum for members to discuss key policy issues in emerging markets’ finance and regulation, and promotes collaboration between members and multilateral institutions.


Impaired is a supervisory term that implies that there are doubts over whether all the amounts due under a contract will be paid.


Pillar II of the revised Basel Capital Accord (Basel II) recommends a general disclosure by all bank of total gross credit exposures, by major type of credit exposure (such as loans, securities, and OTC derivatives) without taking into account the effects of credit mitigation such as collateral. (See BCBS, 2003a, Table 4, p. 160.)


When general improvements in market borrowing conditions occur, banks may renegotiate loan conditions with their clients that are unrelated to any weaknesses in the loan. Such restructuring does not result in adverse classification of the loan or in provisioning. Thus, regulations must be able to distinguish between restructurings of troubled assets and beneficial restructuring of strong assets.


The BLCP does not deal with possible reasons for this pattern, but if it stems from the greater recoverability of collateral in G-10 countries because of the depth of their markets and efficiency of their legal systems, then the use of collateral for setting provisions may be a special case rather than a general pattern. In any event, no simple one-to-one relationship exists between the market value of the collateral and the offset it can provide for provisioning purposes.


Changes in interest rates change the present value of future cash flows and in some cases the cash flows themselves.


Sources of interest rate risk are discussed in BCBS (2003c).


Amounts payable on demand are included in the first bucket—zero to three months.


Calculated by multiplying 10 by the discount factor of 0.6070.


Measuring the effect of interest rate changes on interest income and expense should include all interest-bearing instruments, whether they are fair valued or not.


Alternatively, cash flows associated with expected future interest income and interest expenses can be specified and discounted to the current period.


If different interest rates are used for assets and liabilities, the assumed change in rates will need to be applied to assets and liabilities separately in each bucket, rather than to the gap between assets and liabilities in each bucket.


(−10 million) × 0.01.


This section is based on Saunders (1999) and Jorion (1997).


Duration is a direct measure of the interest rate sensitivity or elasticity of an asset or liability. The larger the numerical value of duration (D), the more sensitive the price of that asset or liability is to changes in interest rates. For instance, for small changes in interest rates, bond prices move in an inversely proportional fashion according the size of D: dP/P = D[dR/ (1 + R)].


While demand deposits are not usually included in measures of duration used to assess price revaluation effects, at the end of this section there is a discussion of measuring duration for these instruments in the event that they are fair valued.


Saunders (1999) suggests that duration provides an accurate measure of sensitivity to interest rate changes when such changes are of the order of one basis point.


An overview of stress-testing methods is provided in Jones, Hilbers, and Slack (2004) and in Blaschke and others (2001).


For a description of how a stress test was implemented in a complex financial system, see Hoggarth and Whitley (2003).


This point is developed in IMF (2003d).


Market interest rate risk should be distinguished from the liquidity risk arising from the maturity mismatch on banks’ balance sheets, deriving from their maturity transformation role, that is captured by other FSIs such as the ratio of liquid assets to short-term liabilities.


The section on interest rate risk in this appendix highlights how difficult it is to measure this risk.


This complementarity with respect to market risk reflects the close relationship between FSIs and stress testing at the analytic level. For example, the estimated direct loss from a stress test of an exchange rate shock can be approximated by the change in the exchange rate (that is the shock) multiplied by the net open foreign exchange position FSI. This is explained in IMF (2003e).

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