1. This annex provides a brief overview of the various techniques used by banks to measure the exposure of earnings and of economic value to changes in interest rates. The variety of the techniques ranges from calculations that rely on simple maturity and repricing tables, to static simulations based on current on- and off-balance sheet positions, to highly sophisticated dynamic modelling techniques that incorporate assumptions about the behaviour of the bank and its customers in response to changes in the interest rate environment. Some of these general approaches can be used to measure interest rate risk exposure from both an earnings and an economic value perspective, while others are more typically associated with only one of these two perspectives. In addition, the methods vary in their ability to capture the different forms of interest rate exposure: the simplest methods are intended primarily to capture the risks arising from maturity and repricing mismatches, while the more sophisticated methods can more easily capture the full range of risk exposures.

2. As this discussion suggests, the various measurement approaches described below have their strengths and weaknesses in terms of providing accurate and reasonable measures of interest rate risk exposure. Ideally, a bank's interest rate risk measurement system would take into account the specific characteristics of each individual interest-sensitive position, and would capture in detail the full range of potential movements in interest rates. In practice, however, measurement systems embody simplifications that move away from this ideal. For instance, in some approaches, positions may be aggregated into broad categories, rather than modelled separately, introducing a degree of measurement error into the estimation of their interest rate sensitivity. Similarly, the nature of interest rate movements that each approach can incorporate may be limited: in some cases, only a parallel shift of the yield curve may be assumed or less than perfect correlations between interest rates may not be taken into account. Finally, the various approaches differ in their ability to capture the optionality inherent in many positions and instruments. The discussion in the following sections will highlight the areas of simplification that typically characterise each of the major interest rate risk measurement techniques.

A. Repricing Schedules

1. The simplest techniques for measuring a bank's interest rate risk exposure begin with a maturity/repricing schedule that distributes interest-sensitive assets, liabilities and off-balance sheet positions into a certain number of predefined time bands according to their maturity (if fixed rate) or time remaining to their next repricing (if floating rate). Those assets and liabilities lacking definitive repricing intervals (e.g. sight deposits or savings accounts) or actual maturities that could vary from contractual maturities (e.g. mortgages with an option for early repayment) are assigned to repricing time bands according to the judgement and past experience of the bank.

2. Gap analysis: Simple maturity/repricing schedules can be used to generate simple indicators of the interest rate risk sensitivity of both earnings and economic value to changing interest rates. When this approach is used to assess the interest rate risk of current earnings, it is typically referred to as gap analysis. Gap analysis was one of the first methods developed to measure a bank's interest rate risk exposure, and continues to be widely used by banks. To evaluate earnings exposure, interest rate sensitive liabilities in each time band are subtracted from the corresponding interest rate sensitive assets to produce a repricing "gap" for that time band. This gap can be multiplied by an assumed change in interest rates to yield an approximation of the change in net interest income that would result from such an interest rate movement. The size of the interest rate movement used in the analysis can be based on a variety of factors, including historical experience, simulation of potential future interest rate movements, and the judgement of bank management.

3. A negative, or liability-sensitive, gap occurs when liabilities exceed assets (including off-balance sheet positions) in a given time band. This means that an increase in market interest rates could cause a decline in net interest income. Conversely, a positive, or asset-sensitive, gap implies that the bank's net interest income could decline as a result of a decrease in the level of interest rates.

4. These simple gap calculations can be augmented by information on the average coupon on assets and liabilities in each time band. This information can be used to place the results of the gap calculations in context. For instance, information on the average coupon rate could be used to calculate estimates of the level of net interest income arising from positions maturing or repricing within a given time band, which would then provide a "scale" to assess the changes in income implied by the gap analysis.

5. Although gap analysis is a very commonly used approach to assessing interest rate risk exposure, it has a number of shortcomings. First, gap analysis does not take account of variation in the characteristics of different positions within a time band. In particular, all positions within a given time band are assumed to mature or reprice simultaneously, a simplification that is likely to have greater impact on the precision of the estimates as the degree of aggregation within a time band increases. Moreover, gap analysis ignores differences in spreads between interest rates that could arise as the level of market interest rates changes (basis risk). In addition, it does not take into account any changes in the timing of payments that might occur as a result of changes in the interest rate environment. Thus, it fails to account for differences in the sensitivity of income that may arise from option-related positions. For these reasons, gap analysis provides only a rough approximation to the actual change in net interest income which would result from the chosen change in the pattern of interest rates. Finally, most gap analyses fail to capture variability in non-interest revenue and expenses, a potentially important source of risk to current income.

6. Duration: A maturity/repricing schedule can also be used to evaluate the effects of changing interest rates on a bank's economic value by applying sensitivity weights to each time band. Typically, such weights are based on estimates of the duration of the assets and liabilities that fall into each time band. Duration is a measure of the percent change in the economic value of a position that will occur given a small change in the level of interest rates. It reflects the timing and size of cash flows that occur before the instrument's contractual maturity. Generally, the longer the maturity or next repricing date of the instrument and the smaller the payments that occur before maturity (e.g. coupon payments), the higher the duration (in absolute value). Higher duration implies that a given change in the level of interest rates will have a larger impact on economic value.

7. Duration-based weights can be used in combination with a maturity/repricing schedule to provide a rough approximation of the change in a bank's economic value that would occur given a particular change in the level of market interest rates. Specifically, an "average" duration is assumed for the positions that fall into each time band. The average durations are then multiplied by an assumed change in interest rates to construct a weight for each time band. In some cases, different weights are used for different positions that fall within a time band, reflecting broad differences in the coupon rates and maturities (for instance, one weight for assets, and another for liabilities). In addition, different interest rate changes are sometimes used for different time bands, generally to reflect differences in the volatility of interest rates along the yield curve. The weighted gaps are aggregated across time bands to produce an estimate of the change in economic value of the bank that would result from the assumed changes in interest rates.

8. Alternatively, an institution could estimate the effect of changing market rates by calculating the precise duration of each asset, liability and off-balance sheet position and then deriving the net position for the bank based on these more accurate measures, rather than by applying an estimated average duration weight to all positions in a given time band. This would eliminate potential errors occurring when aggregating positions/cash flows. As another variation, risk weights could also be designed for each time band on the basis of actual percent changes in market values of hypothetical instruments that would result from a specific scenario of changing market rates. That approach - which is sometimes referred to as effective duration - would better capture the non-linearity of price movements arising from significant changes in market interest rates and, thereby, would avoid an important limitation of duration.

9. Estimates derived from a standard duration approach may provide an acceptable approximation of a bank's exposure to changes in economic value for relatively non-complex banks. Such estimates, however, generally focus on just one form of interest rate risk exposure - repricing risk. As a result, they may not reflect interest rate risk arising - for instance - from changes in the relationship among interest rates within a time band (basis risk). In addition, because such approaches typically use an average duration for each time band, the estimates will not reflect differences in the actual sensitivity of positions that can arise from differences in coupon rates and the timing of payments. Finally, the simplifying assumptions that underlie the calculation of standard duration means that the risk of options may not be well-captured.

B. Simulation Approaches

1. Many banks (especially those using complex financial instruments or otherwise having complex risk profiles) employ more sophisticated interest rate risk measurement systems than those based on simple maturity/repricing schedules. These simulation techniques typically involve detailed assessments of the potential effects of changes in interest rates on earnings and economic value by simulating the future path of interest rates and their impact on cash flows.

2. In some sense, simulation techniques can be seen as an extension and refinement of the simple analysis based on maturity/repricing schedules. However, simulation approaches typically involve a more detailed breakdown of various categories of on- and off-balance sheet positions, so that specific assumptions about the interest and principal payments and non-interest income and expense arising from each type of position can be incorporated. In addition, simulation techniques can incorporate more varied and refined changes in the interest rate environment, ranging from changes in the slope and shape of the yield curve to interest rate scenarios derived from Monte Carlo simulations.

3. In static simulations, the cash flows arising solely from the bank's current on- and off-balance sheet positions are assessed. For assessing the exposure of earnings, simulations estimating the cash flows and resulting earnings streams over a specific period are conducted based on one or more assumed interest rate scenarios. Typically, although not always, these simulations entail relatively straightforward shifts or tilts of the yield curve, or changes of spreads between different interest rates. When the resulting cash flows are simulated over the entire expected lives of the bank's holdings and discounted back to their present values, an estimate of the change in the bank's economic value can be calculated.

4. In a dynamic simulation approach, the simulation builds in more detailed assumptions about the future course of interest rates and the expected changes in a bank's business activity over that time. For instance, the simulation could involve assumptions about a bank's strategy for changing administered interest rates (on savings deposits, for example), about the behaviour of the bank's customers (e.g. withdrawals from sight and savings deposits) and/or about the future stream of business (new loans or other transactions) that the bank will encounter. Such simulations use these assumptions about future activities and reinvestment strategies to project expected cash flows and estimate dynamic earnings and economic value outcomes. These more sophisticated techniques allow for dynamic interaction of payments stream and interest rates, and better capture the effect of embedded or explicit options.

5. As with other approaches, the usefulness of simulation-based interest rate risk measurement techniques depends on the validity of the underlying assumptions and the accuracy of the basic methodology. The output of sophisticated simulations must be assessed largely in the light of the validity of the simulation's assumptions about future interest rates and the behaviour of the bank and its customers. One of the primary concerns that arises is that such simulations do not become "black boxes" that lead to false confidence in the precision of the estimates.

C. Additional Issues

1. One of the most difficult tasks when measuring interest rate risk is how to deal with those positions where behavioural maturity differs from contractual maturity (or where there is no stated contractual maturity). On the asset side of the balance sheet, such positions may include mortgages and mortgage-related securities, which can be subject to prepayment. In some countries, borrowers have the discretion to prepay their mortgages with little or no penalty, a situation that creates uncertainty about the timing of the cash flows associated with these instruments. Although there is always some volatility in prepayments resulting from demographic factors (such as death, divorce, or job transfers) and macroeconomic conditions, most of the uncertainty surrounding prepayments arises from the response of borrowers to movements in interest rates. In general, declines in interest rates result in increasing levels of prepayments, as borrowers refinance their loans at lower yields. In contrast, when interest rates rise unexpectedly, prepayment rates tend to slow, leaving the bank with a larger than anticipated volume of mortgages paying below current market rates.

2. On the liability side, such positions include so-called non-maturity deposits such as sight deposits and savings deposits, which can be withdrawn, often without penalty, at the discretion of the depositor. The treatment of such deposits is further complicated by the fact that the rates received by depositors tend not to move in close correlation with changes in the general level of market interest rates. In fact, banks can and do administer the rates on the accounts with the specific intention of managing the volume of deposits retained.

3. The treatment of positions with embedded options is an issue of special concern in measuring the exposure of both current earnings and economic value to interest rate changes. In addition, the issue arises across the full spectrum of approaches to interest rate measurement, from simple gap analysis to the most sophisticated simulation techniques. In the maturity/repricing schedule framework, banks typically make assumptions about the likely timing of payments and withdrawals on these positions and "spread" the balances across time bands accordingly. For instance, it might be assumed that certain percentages of a pool of 30 year mortgages prepay in given years during the life of the mortgages. As a result, a large share of the mortgage balances that would have been assigned to the time band containing 30 year instruments would be spread among nearer term time bands. In the simulation framework, more sophisticated behavioural assumptions could be employed, such as the use of option-adjusted pricing models to better estimate the timing and magnitude of cash flows under different interest rate environments. In addition, the simulations can incorporate the bank's assumptions about its likely future treatment of administered interest rates on non-maturity deposits.

4. As with other elements of interest rate risk measurement, the quality of the estimates of interest rate risk exposure depends on the quality of the assumptions about the future cash flows on the positions with uncertain maturities. Banks typically look to the past behaviour of such positions for guidance about these assumptions. For instance, econometric or statistical analysis can be used to analyse the behaviour of a bank's holdings in response to past interest rate movements. Such analysis is particularly useful to assess the likely behaviour of non-maturity deposits, which can be influenced by bank-specific factors such as the nature of the bank's customers and local or regional market conditions. In the same vein, banks may use statistical prepayment models - either models developed internally by the bank or models purchased from outside developers - to generate expectations about mortgage-related cash flows. Finally, input from managerial and business units within the bank could have an important influence, since these areas may be aware of planned changes to business or repricing strategies that could affect the behaviour of the future cash flows of positions with uncertain maturities.

ANNEX B

1. This annex provides a brief overview of some of the factors that supervisory authorities might consider in obtaining and analysing information on individual banks' exposures to interest rate risk. As discussed in Section VII of the text, supervisory authorities should obtain information sufficient to assess banks' exposures to interest rate risk in a timely fashion. Such information may be obtained through on-site examinations, through reports that are submitted by banks on a regular basis, or through other means.

2. While the precise information that is obtained will differ across supervisory authorities, one approach that some may adopt is a reporting framework that collects information on a bank's positions by remaining maturity or time to next repricing. Under such an approach, a bank would categorise its interest-sensitive assets, liabilities and off-balance sheet positions into a series of repricing time bands or maturity categories. The two sections that follow discuss the considerations that a supervisor should take into account in specifying the number of time bands and the grouping of positions in the reporting framework. The final section of this annex describes some general approaches that supervisory authorities may wish to consider in analysing the information that is obtained through such a reporting framework.

A. Time Bands

1. If a reporting framework is used in which information is collected by time to next repricing, the number and specific categories of time bands chosen should be sufficient to provide supervisors with a reasonable basis for identifying potentially significant repricing mismatches. The bands, however, could vary materially across countries, both in number and in range, depending on the lending and investing practices and experiences of banks in individual markets.

2. The usefulness of supervisory analysis crucially depends on the precision with which maturities of the positions and cash flows are recorded in the system. In analysing interest rate sensitivities, it is not enough to know when an instrument matures. Rather, the critical factor is when the instrument reprices. Therefore, the emphasis of this section is on repricing rather than maturity. For cash flows whose repricing is unambiguous, the most precise approach is to use the exact repricing date. Any aggregation of positions/cash flows in time bands or zones necessarily implies a loss of information and a lower degree of precision. For this reason, the number of time bands in a repricing ladder framework always reflects a decision regarding the necessary level of precision and the cost of pursuing greater accuracy. Supervisory authorities could use the repricing ladder in the standardised approach of the Amendment to the Capital Accord as a starting point when developing a reporting framework that meets their particular needs. The breakdown can, of course, be modified by supervisors either in a general way or in a specific way for banks where the nature of business activities warrants or justifies a different reporting form.

B. Items

1. As with the time bands, the breakdown of assets and liabilities could differ among supervisors. A reporting system should include information for all rate sensitive assets, liabilities and OBS positions, and should also identify balances, by specific types of instruments, when those instruments have or may have materially different cash flow characteristics. Specific attention should be given to items whose behavioural repricings differ from contractual maturities such as savings deposits and in some countries mortgage related instruments. Further information on these issues is provided in Annex A. If the volume of these positions is significant, they should be reported separately so as to facilitate an assessment of the underlying options risk in the bank balance sheet structure.

2. The analysis of interest rate risk may be more difficult if a bank is engaged in trading activities. As a general rule, it is desirable for any measurement system to incorporate interest rate risk exposures arising from the full scope of a bank's activities, including both trading and non-trading sources. This does not preclude different measurement systems and risk management approaches being used for different activities; however, management should have an integrated view of interest rate risk across products and business lines. Supervisors may wish to permit banks that manage their interest rate risk exposures on an integrated basis to aggregate trading and non-trading positions in the overall reporting framework. However, it is important to recognise that in many countries different accounting rules may apply to the trading book and the traditional banking book. Under these accounting rules, losses in the trading book may not always be offset by profits in the banking book if the latter are unrealised. Furthermore, unlike the banking book, the composition of the trading portfolio changes significantly from week to week or even day to day because it is managed separately and according to a different (shorter) risk horizon than the banking book. This means that a hedge that is present on a given day may disappear a few days later. Supervisors should, therefore, review the risk management practices and information systems of banks that conduct material trading activities and should obtain the information necessary to ensure that interest rate risk in both trading and non-trading activities is properly managed and controlled.

C. Supervisory Analysis

1. A reporting framework designed along these lines may provide supervisors with a flexible tool for analysing interest rate risk. Supervisors can use this basic information to perform their own assessments of a bank's exposure and risk profile.

2. Such assessments may provide insights regarding an institution's exposure to parallel shifts, a flattening or steepening of the yield curve or its inversion with rate changes of different magnitude either based on statistical probabilities or a worst case analysis. For banks with important exposures in foreign currencies, analysis investigating different assumptions on correlations between interest rates in different currencies can be useful. With respect to instruments with behavioural maturities, supervisors may wish to assess alternative assumptions than those used by the institution.

3. The focus of supervisors' quantitative analysis can either be the impact of interest rate changes on current earnings or on the economic value of the banks' portfolio. In conducting their analysis information about average yields on assets and liabilities in each time band may be useful and supervisors may wish to collect such information in addition to pure position data.

4. Depending on their overall approach, supervisors may conduct their analysis of interest rate risk either on a case by case basis or as part of a broader system designed to identify outliers with apparently excessive risk-taking.

5. By conducting an assessment of interest rate risk using the proposed framework, supervisors may gain more insight into an institution's risk profile than with a reporting system that reduces the complexity of interest rate risk to a single number. In doing so, supervisors can become more familiar with the sensitivity of risk measures to changes in the underlying assumptions, and the evaluation process may produce as many insights as the quantitative result itself.

6. Regardless of the extent of a supervisor's own independent quantitative analysis, a bank's own interest rate risk measure, whether reported as part of a basic supervisory reporting system or reviewed as part of an individual assessment of a bank's risk management, is an important consideration in the supervisory process. Reviewing the results of a bank's internal model can be highly informative, but can also be a difficult process because of the multitude of assumptions and modelling techniques that are important, but which need to be made transparent to supervisors. To be most useful, the information received should indicate the contribution of principal elements of a bank's portfolio to the risk profile under different assumptions with respect to interest rate changes and the market response. Finally, any quantitative analysis should be supplemented by a review of internal management reports in order to gain greater insights into management's evaluation and management of risks, its methods for measuring exposures, and factors not reflected in the information available in the limited reporting to supervisors.