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A method for evaluating interest rate risk in U.S. commercial banks.

When interest rates change, the economic values of the loans, securities, and deposits at banks also change, but not necessarily in offsetting ways. The net effect of these changes is reflected in a bank's earnings and net worth. The risk that changes in rates might adversely affect a bank's financial condition is referred to as interest rate risk.

As financial intermediaries, banks and other depository institutions accept interest rate risk as a normal part of their business. They assume the risk whenever the interest rates paid on their liabilities do not adjust in unison with the rates earned on their assets. Such mismatches often present institutions with opportunities to profit from favorable changes in interest rates, but they also expose a bank's capital and earnings to adverse changes. Effective management of interest rate risk is a fundamental element of the banking business.

Banks have many ways of managing their risk. Most banks change their exposures by altering the rates (or prices) and maturities at which they are willing to originate loans, buy or sell securities, and accept deposits. With the emergence of many new financial products and markets during the 1980s, banks have acquired even more alternatives for managing interest rate risk while meeting customer preferences on the terms of loans and deposits. Interest rate swaps and financial futures, forwards, and options are some of the growing number of tools banks now use to adjust their exposures.

In the United States, the combination of a volatile interest rate environment, deregulation, and the growing array of new on- and off-balance-sheet products has made the management of interest rate risk a growing challenge. Accordingly, bank supervisors are placing increased emphasis on evaluating the interest rate risk of banks. This focus has become particularly sharp in light of the current implementation of risk-based capital charges. The 1988 international agreement on capital standards known as the Basle Accord represents an important milestone in supervisory policy by making a bank's minimum capital requirements sensitive to the credit risk of its assets and off-balance-sheet positions.(1) The agreement, however, focuses primarily on credit risk; it does not impose an explicit capital charge tied to interest rate risk.

One possible effect of this focus is that banks may have an incentive to substitute interest rate risk for credit risk in structuring their balance sheets. Indeed, this may already be happening. The emergence of large positions in mortgage-backed securities is particularly noticeable. At the end of 1988, these securities accounted for 17 percent of the aggregate securities portfolio of the commercial banking industry and less than 3 percent of its total assets; by early 1991 these shares had doubled, to 35 percent of all bank securities and 6.5 percent of total banking assets. Although the share of mortgage-backed securities in total assets is still small, the rapid growth within such a short period may be an indication of increasing interest rate risk exposure among banks. Regardless of whether banks are increasing their exposure, interest rate risk is a fundamental element of the business and should be considered in assessing the adequacy of bank capital.


The Basle Accord tailors a bank's minimum capital requirement to the credit risk embodied in the institution's assets and off-balance-sheet instruments. Under the agreement, those balances perceived to carry greater credit risk must be backed by levels of capital higher than those required for lower-risk positions. Overall, the standard requires internationally active banks to have total capital (including equity, reserves, and subordinated debt) equal to at least 8 percent of their fisk-weighted assets by the end of 1992.2 The capital treatment of interest rate risk was deferred in the construction of the existing agreement and is now being addressed by another international committee working, once again, under the aegis of the Bank for International Settlements (BIS).

The Federal Reserve System is actively participating in the work of the BIS committee. However, several reasons suggest the need for simultaneous steps to supplement the current "domestic" approach to the supervision of interest rate risk. One reason is that the time required to develop and implement an international standard is uncertain. Moreover, the international approach under development is aimed primarily at the largest and most internationally active banks, which conduct activities in a variety of currencies (each with its own interest rate exposure) often involving complex transactions. An approach for incorporating interest rate risk into the risk-based capital standard developed for them may have to be modified for application to many of the 12,000 small and medium-size U.S. banks. Indeed, once an international framework emerges for the assessment of interest rate risk, every country may need to tailor that framework to the specific characteristics and structure of its own banking system.

In view of these considerations, staff members at the Federal Reserve are investigating a possible supervisory approach to assessing interest rate risk that would supplement existing examination procedures and provide an additional off-site monitoring tool for understanding potential exposures to interest rate changes. The approach, which would be further developed and field tested before its formal incorporation in the examination process, is consistent with that being pursued internationally and would therefore be adaptable to any international agreement that is likely to emerge.


Depending on their objectives and the complexity of their operations, banks use a variety of techniques to manage interest rate risk, ranging from relatively simple maturity "gap" calculations to more sophisticated duration or simulation analyses. Maturity gap analysis begins with a report that categorizes assets and liabilities by their repricing dates to identify mismatches within specific time periods. Those reports are typically used by banks to estimate the effect of interest rate changes on their near-term reported earnings. By focusing on reported earnings to judge rate sensitivity, this accounting approach to evaluating interest rate risk tends to ignore or downplay the effect of mismatches among medium-or long-term positions.

Contrasting with techniques that take an accounting perspective are those that focus on estimating the interest rate sensitivity of the economic value of a bank's on- and off-balance-sheet positions. Duration analysis is one such technique. The duration of a financial instrument is the weighted average maturity of the instrument's total cash flows in present value terms. When modified to reflect an instrument's discrete compounding of interest, duration provides a concise measure of the sensitivity of the present value of the instrument to changing interest rates. Specifically, modified duration can be viewed as an elasticity that estimates the percentage change in the value of an instrument for each percentage point change in market interest rates. The greater the modified duration of the instrument, the more sensitive is its value to changing rates. (Hereafter, modified duration will be referred to simply as duration. See the appendix for details.)

By estimating the durations of assets, liabilities, and off-balance-sheet positions, a bank can estimate the net duration of its portfolio and the interest sensitivity of the present value of its net worth. In this sense, duration analysis offers a more comprehensive approach to measuring interest rate risk by incorporating the entire spectrum of a bank's repricing mismatches. It expands the basic maturity gap approach to assess the effects of changes in rates on the present value of all future earnings, not just on next year's book earnings.

Duration analysis has several disadvantages, however. Its accuracy as a measure of interest rate sensitivity declines as the size of the rate change increases. In addition, its use typically assumes instantaneous parallel shifts in the yield curve. Duration analysis also requires a number of assumptions and complexities in order to incorporate the effects of options embedded in many bank assets, liabilities, and off-balance-sheet positions. Finally, many managers have difficulty translating duration measures into reported net interest income and other accounting measures on which they have traditionally focused.

To overcome the limitations of both maturity gap and duration analyses, some banks turn to computer simulation. Sophisticated computer models are used to simulate the effects of a wide array of interest rate scenarios on a bank's financial condition. Simulation models can generate measures that address both the accounting and economic perspectives of an institution's interest rate risk exposure. However, as with many computer modeling techniques, simulations are highly data intensive, and the results rely heavily on assumptions. Moreover, the effects of these assumptions on the target variable a model assesses (for example, net interest income) make it difficult to isolate objectively the influence of changing interest rates. The chief benefit of simulation models resides, to a large degree, in revealing the sensitivity of results to the assumptions used.

For their part, bank examiners assess an institution's approach to managing both the accounting and economic aspects of interest rate risk during their overall review of a bank's funds management process. Traditionally, examiners have evaluated the stability of net interest margins and net interest income as well as the underlying nature and apparent riskiness of the positions a bank holds. Their review places much importance on the adequacy of internal reporting, auditing, and information systems and on the bank's policies and procedures for measuring and controlling its risk. If the exposure is considered excessive given the bank's capital and expertise, the supervisor reviews the matter with the bank's senior management and directors and requests corrective action. If necessary, the bank will be required to develop and implement a formal plan for reducing the risk and for restructuring the bank's risk management and control systems.

To date, this supervisory process has been generally satisfactory. However, with the rising importance of interest rate risk management, the process is increasingly hampered by the absence of a systematic method to monitor interest rate risk and by the lack of quantitative standards for adjusting capital to cover that risk. More specific procedures for quantifying and assessing a bank's risk, if proven valid and effective, would supplement and strengthen the supervision of interest rate risk. To be effective, any quantification of risk must consider the entire spectrum of mismatches. An approach that incorporates a monitoring system and related guidelines based on the economic perspective is consistent with this principle.


Several considerations are relevant in the development of a supervisory framework for measuring and evaluating interest rate risk. First, the more than 1,200 bank failures in the past decade demonstrate that the principal risk to commercial banks is credit risk. Although other risks-such as operating risk, foreign exchange risk, and interest rate risk-can prove costly and must be controlled, they are dominated in most cases by the threat of credit losses on loans. This situation could change, of course, as the nature of banking evolves. Indeed, even in the past, interest rate movements have produced significant losses at some banks and have caused others to increase risk in other areas to offset problems caused by rate movements. Nevertheless, interest rate risk by itself has rarely caused a commercial bank to fail when it was in otherwise sound condition. Credit risk, therefore, should account for most of the industry's capital requirement.

Second, the complexity of a model's algorithms and the precision of the data collected are often dominated by the underlying assumptions used to derive a measure of interest rate risk. Even the most sophisticated measures of interest rate risk require certain assumptions that can materially affect the results. Many of these assumptions relate to assets and liabilities with embedded options that make their cash flows especially difficult to predict. The interest rate sensitivity of core deposits is just one example. The overriding influence of such assumptions suggests the need for caution in trying to estimate levels of interest rate risk across the entire industry.

Third, information requirements of any supervisory or regulatory system should be held to a necessary minimum. The dominance of credit risk, combined with the considerable difficulties in measuring interest rate risk, creates a tradeoff: gains in the accuracy of interest rate risk measures must be balanced against the associated increase in costs and reporting burdens and the degree to which the overall precision of a capital standard that included interest rate risk would be improved. Moreover, supervisory agencies do not need the same level of precision that bank management may need. Regulators are concerned principally with identifying significant threats to a bank's solvency; they are less concerned with small changes to the bank's reported earnings.

These factors argue for a comparatively simple supervisory approach to evaluating interest rate risk. One way to achieve that simplification would be to interpret the current risk-based capital standard as covering "normal" levels of a bank's interest rate risk. The assumption avoids the need for an absolute measure of interest rate risk and requires only a relative measure. Banks that have more risk than the majority of banks could be identified through an off-site screening process, and a subsequent on-site review would consider the specific circumstances of the identified "outlier" banks.

The measure to be used in this screening process would need to identify only relative orders of magnitude of interest rate risk among commercial banks. Some underlying assumptions may be imprecise, but if used consistently, they are not likely to mask the exposures of banks facing the highest risk or cause truly low-risk institutions to appear as outliers.


A measure of interest rate risk under consideration for use in the screening process applies the principles of duration analysis to the familiar maturity gap report. An advantage of duration analysis over the use of simulation is its relative simplicity in reflecting the economic effects of changes in rates. It has the attractive attribute of summarizing the interest rate risk exposure of an institution in a single number.

In brief, the risk measure under consideration is calculated by first classifying a bank's assets, liabilities, and off-balance-sheet positions on the basis of their contractual maturity or repricing dates and their cash flow characteristics. These positions would then be weighted by risk factors that approximate their modified durations. The sum of these weighted positions would be the measure of interest rate risk to be used in comparing exposures among banks.

Spread among eight maturity/repricing periods ("time bands"), the information used to derive this measure fits on a single page (table I is a sample report for a hypothetical bank). In the interest of simplicity, only maturity/repricing data are recorded; assumptions regarding coupon rates on assets and liabilities and other features of financial contracts are made in developing the risk weights.

The characteristics of duration heavily influenced the structure of the repricing schedule portrayed in table 1. One feature of duration is that, other things equal, it is positively related to the maturity of the underlying instrument. As maturity extends, however, the duration of most instruments increases at a decreasing rate so that the durations of the longest-term instruments are generally less than ten years (chart 1). This pattern suggests that perhaps eight to ten time bands with equally spaced durations could capture the interest rate sensitivity of most loan or investment portfolios. At the same time, however, one must consider the actual repricing periods of bank assets and liabilities; most are heavily concentrated in the short-term. Taking both points into account, the illustrated repricing schedule employs eight time bands that incorporate more precision in the shorter time periods.

The nature of duration also influenced the choice of the specific line items in table 1. The duration of a financial instrument depends upon the timing of its cash flows, which are a function of maturity, coupon rate, amortization, and other factors. The cash flows of most bonds and commercial loans consist of periodic payments of interest only, and repayment of all principal at maturity. Mortgages and consumer loans, in contrast, generally amortize; that is, their periodic payments include both principal and interest. Still other instruments, such as deep-discount and zero coupon bonds, have most or all of their payments of both principal and interest occur at maturity. These distinctions alone can cause the durations of instruments with similar maturities to be significantly different.

For example (chart 2), a 30-year, 10 percent coupon Treasury bond yielding 10 percent has a duration of about 9.5 years. However, the duration of a 30-year, 10 percent amortizing mortgage yielding 10 percent with no prepayment is about 8 years but could be as short as 4-6 years if common levels of prepayment are assumed. The duration of a 30-year zero coupon bond yielding 10 percent is 28.6 years.(3) To capture the effect of these distinctly different payment strearns, the repricing schedule categorizes all securities, loans, and off-balance-sheet items into one of three groups according to their inherent cash flow structures: amortizing, nonamortizing, and deep-discount. In the interest of simplicity and of minimizing the burdens of collecting data, the balances of loans and securities are generally distributed across the time bands of table I using the contractual maturity or repricing date of the instrument. Anticipated prepayments on amortizing instruments are incorporated in the calculation of the interest rate risk weights using standardized assumptions. The only exception to this distribution procedure is the treatment of tranches of collaterized mortgage obligations (CMOs) and real estate mortgage investment conduits (REMICs). Because of their wide diversity, such tranches are slotted according to their current average life as calculated by bank management.(4)

Core Deposits

Time deposits and other liabilities with well-defined maturities are easily distributed across the time bands of table 1. However, the indefinite maturities of core deposits (demand deposits, NOW accounts, money market deposit accounts, and savings deposits) pose significant problems. These deposits are usually stable but can be withdrawn at any time. In addition, their repricing tends to lag changes in market rates and can vary from bank to bank according to each institution's geographic location, pricing strategies, and depositor base.

Because of their uncertain maturities, core deposits could be placed into a single time band or spread among several bands. If a single band is chosen, the shortest one would be a logical choice because the deposits are all subject to immediate withdrawal. However, the experience of most banks indicates that these deposits could have longer effective maturities or repricing periods. A standard industry practice is to distribute deposits among several periods to reflect the fact that they tend to run off over time.(5) Table I illustrates a possible distribution of core deposits among the time bands, which produces an average maturity of 2.5 years. Some such standardized distribution for all banks would be used in practice.

High-Risk Assets

The repricing schedule gives special treatment to certain positions in highly volatile and complex derivative instruments, such as interest-only and principal-only stripped mortgage-backed securities and CMO residuals (shown in table I as high-risk instruments).(6) Examiners would also give them special attention during on-site examinations and would closely assess the risk they present to an individual institution.

Derivation of Risk Weights

In the measurement system under consideration, each recorded position is multiplied by a risk weight that approximates its duration to produce a risk-weighted value. Table 2 illustrates the calculation. The top panel summarizes the positions reported in table 1. The middle panel displays the risk weights. The system employs four sets of risk weights: one set for each of the three types of assets (amortizing, nonamortizing, and deep-discount) and one set for all liabilities. The weights are calculated as the duration of an instrument with a remaining maturity equal to the midpoint of each time band and an assumed coupon and market yield. For simplicity, a single coupon is assumed for each of the three sets of assets and another coupon is assumed for all liabilities; these coupons are assumed to equal market yields. For illustrative purposes, the weights presented here are based on a 10 percent coupon for assets and an 8 percent semiannual coupon for liabilities.

To handle the problem posed by the prepayment options embedded in amortizing assets, prepayment adjustments are made to the weights for the amortizing assets. Intermediate- and long-term amortizing assets are assumed to be primarily mortgages and mortgage securities. For those instruments, a market consensus of the rate at which mortgages with the assumed coupon are expected to prepay is used to construct their weights. For example, a weight of 4.6 is used for amortizing assets with maturities of more than twenty years. This weight is the duration of a 10 percent, thirty-year mortgage with a remaining term to maturity of twenty-five years and an assumed 9 percent constant annual prepayment rate. That rate was the average prepayment estimate of eight U.S. securities firms as of June 1, 1991, for a Government National Mortgage Association pass-through security with a gross coupon of 10 percent. For amortizing assets with remaining maturities of less than five years, a prepayment rate of I percent is assumed. In implementing the proposed measurement system, the weights for these assets can be updated periodically to reflect changes both in coupon assumptions and in the market consensus of prepayment rates.


In the construction of the risk weights, the estimated durations are multiplied by 0.01 to convert them into percentages. As a result, the weights estimate the percentage decrease in the present value of a position that results from a 1 percentage point increase in market rates (or the increase in value that results from a decrease in rates).

Multiplying a position by a risk weight estimates the dollar change in the present value of the position for a I percentage point change in market rates. For example, in line 1 of table 2, the $1,294 million position in interest-bearing assets maturing or repricing in less than three months is weighted by multiplying each of its three components (lines 2-4) by their respective weights (lines 9-1 1) and summing. The result is a weighted value of $1.91 million (line 13). Assuming that current balances yield market rates, this weighted value can be interpreted as the decline in the present value of the recorded positions for a I percentage point increase in rates (or the increase in value that results from a decline in rates).

The summation of afl weighted values for assets, liabilities, and off-balance-sheet items (lines 13-16, first column) shows that the bank's net worth is vulnerable to rising interest rates. Overall, a 1 percentage point increase in market rates would reduce the present value of the bank's assets an estimated $39.66 million (line 13) and lower the present value of its liabilities $35.14 million (line 14). The illustrated off-balance-sheet positions offset the decline in the value of assets by $0.2 million (line 15), producing an initial estimate of exposure of $4.32 million (line 16) for a 1 percentage point increase in rates.

At this point, an adjustment to the exposure is made for the presence of high-risk instruments (line 8) in the portfolio. The complexity of these instruments makes them difficult to incorporate into the proposed screening measure. To maintain a practical level of simplicity in the assessment process, high-risk instruments are given the same weight as that of deep-discount assets (line 11) in the corresponding time band and the same sign as that of the initial estimate of exposure (line 16). In this way, the process draws the attention of the examiner to the high-risk position because that position is always portrayed as increasing the absolute value of the initial estimate of exposure. The actual interest rate risk profile of these instruments, as well as their appropriateness for a particular institution, would be assessed on-site by the examiner.

In the example, the $2 million high-risk position (line 8, last column) is multiplied by the risk weight of 23.8 percent (line 11); because the initial estimate of exposure (line 16) is positive, the product-$0.48 million-is added to the $4.32 million subtotal to derive the overall weighted net position of the institution of $4.80 million (line 18). Had the initial estimate of exposure been negative, a negative sign would have been assigned to the high-risk position to increase the negative exposure of the institution. Recognition of the potential macro- or micro-hedging capabilities of these instruments is left to the discretion of the examiner.

The weighted net position (line 18) is a key statistic. When divided by net worth and multiplied by 100, it represents the implied risk weight for the bank's net worth and gives a summary measure of interest rate risk exposure. In the example, the estimated exposure of net worth to a 1 percent increase in rates is 2.28 percent of the bank's total net worth. When multiplied by 100, this implied risk weight can be used as an estimate of the bank's duration of net worth and as a measure of the vulnerability of the institution to insolvency as a result of interest rate changes. This measure of the duration of net worth is of central importance in the screening process and can play an important role in an examiner's assessment of interest rate risk.(7)

Considered alone, however, this estimate of the duration of net worth might not detect those banks that have significant mismatches but high capital ratios. Apart from the risk to the solvency of the bank that any asset-liability mismatch may present, the degree of interest rate sensitivity is also important to know. That knowledge provides insights into the nature of the bank's business and its managerial approach. Moreover, some banks need relatively strong capital ratios to support greater-than-average exposure to asset quality problems or other banking risks. Viewing those institutions as having low interest rate risk simply because they have high capital ratios could be inappropriate. Expressing the weighted net position as a percent of total assets (line 20) provides a second measure, called the "sensitivity index," which focuses directly on the degree of sensitivity of the bank's positions to changing interest rates (0. 15 percent in the example).

Both risk measures have a parallel in the analysis of bank profitability. That is, using both the duration of net worth and the sensitivity index to evaluate a bank's interest rate risk could be compared to using return on equity (ROE) and return on assets (ROA) to evaluate its profitability. The ROE and ROA compare reported earnings with their respective denominators. The two interest rate risk measures compare estimates of the expected change in the present value of future earnings (which is the change in net worth) with those same denominators: The duration of net worth indicates the interest rate sensitivity relative to equity; the sensitivity index indicates the interest rate sensitivity relative to the asset base. Combined, the two interest rate risk measures enable examiners to quantify the rate sensitivity of a bank's on- and off-balance-sheet positions and assess its ability to absorb losses that the mismatches might produce.


As described above, this approach recognizes that a certain amount of interest rate risk is inherent in banking. Consequently supervisory attention would be directed at those banks identified as having relatively high risk-outliers. Using an outlier approach, however, requires information about the distributions of both the sensitivity index and duration of net worth for the industry.

The data to develop these distributions as accurately as would be required are not available from financial reports currently filed with regulatory agencies. Maturity and repricing data, for example, are reported for only four time bands, and the longest period contains aU positions repricing in more than five years. These constraints, and similar ones regarding information about the cash-flow structure of assets, require a number of assumptions in order to use existing data. To construct an estimate, we have used existing call report data to illustrate how the distributions might look, subject to the above caveats, and how outliers could be identified.

Outliers would be defined on the basis of both their sensitivity index and their durations of net worth. For both measures, outliers would be taken from both tails of an industry distribution curve to recognize exposures to rising and declining rates. The riskiest 25 percent, for example, could be considered outliers.

In constructing a distribution of the industry's exposure to changing interest rates, the placement of core deposits is of primary importance. When core deposits are spread to produce a weighted average maturity of 2.5 years, the median institution appears to be virtually balanced in terms of its sensitivity index (chart 3, middle curve).

Placing core deposits at an average maturity of either 1.5 months or 5 years yields significantly different results and illustrates the sensitivity of the measure to changes in the selected maturity of deposits. A short-term placement sharply increases the apparent exposure of the industry to rising interest rates; placing the deposits at 5 years would indicate that the industry is highly exposed to declining rates. These distributions, while only illustrative, suggest that viewing core deposits as having a maturity of two to three years is not only operationally useful in constructing a measurement system but is also consistent with a perception that the large majority of commercial banks do not have high exposures to interest rate risk.

In the middle distribution of chart 3, the median bank has an estimated sensitivity index of 0.02 percent. A cut-off point around 0.6-0.7 percent on each tail of the distribution would capture approximately 25 percent of the banks: about 16 percent that are exposed to rising interest rates (those on the right side in chart 3) plus another 9 percent that are exposed to declining rates (those on the left).

A similar approach could be used to identify outliers on the basis of their durations of net worth. Once again, the median bank appears to be almost balanced, with 0.23 percent of its equity at risk from a I percentage point increase in rates (chart 4). Outliers could be defined, for example, as those institutions with roughly 7-8 percent or more of their net worth at risk. That cut-off would capture approximately 25 percent of the industry: about 15 percent from the banks with relatively high exposure to rising rates and another 10 percent from those with a large exposure to declining rates. These 25 percent would then be compared with the outliers identified with the sensitivity index to determine which institutions appear to warrant the most concern.

As with many elements of the measure, the identification of outliers must be carefully monitored and updated as conditions change. If the industry became much more cautious, for example, fewer institutions would be identified as outliers. Conversely, more banks would become outliers if the overall exposure of the industry grew.

The distributions illustrated in charts 3 and 4 are estimates based on the limited data currently reported by the banking industry and are shown here not as empirical evidence but only for heuristic purposes. No information is available about the repricing periods of the industry's off-balance-sheet positions; much of the placement of balances among time bands was estimated; and core deposits were distributed uniformly, and thus somewhat arbitrarily, for all banks.


Bank supervision entails both off-site surveillance and on-site examinations. If implemented, the procedure described here for measuring interest rate risk would be another tool to help bank supervisors screen banks off-site to identify those with relatively high levels of measured interest rate risk. Supervisors could then take appropriate follow-up actions, such as requesting additional information from the bank or considering the apparent risk when planning future examinations. Once on-site, examiners could use the interest rate risk measures as an indicator of how they might allocate their time and resources. Institutions with apparently high interest rate risk would be more likely to receive more detailed reviews of their asset and liability management procedures than would those exhibiting lower risk.

No firm conclusions would be based on these measures alone. Examiners would need to confirm or reject the measure based on their assessment of many of the elements they currently review: the bank's own policies, controls, information systems, and risk-measurement techniques. Examiners would continue to apply significant flexibility in their consideration of the conditions at each bank. In particular, nothing in the approach described here would preclude examiners from employing other relevant techniques based on the bank's own internal reports, systems, and controls regarding interest rate risk.

Nevertheless, the approach can provide examiners with a reference point for evaluating the riskiness of a bank's positions and guidelines for evaluating the adequacy of its capital. Also, bankers may find the comparison of their banks with the industry useful. The measurements require no more than simple spreadsheet calculations and thus can be performed on-site to test the effect of different assumptions, such as those regarding the maturity of core deposits.

The more sophisticated simulation analyses conducted by some banks could offer further insights into the likely losses (or gains) under a variety of scenarios. Combined, these measures and techniques could lead to reasonably firm conclusions about the bank's overall exposure to interest rate risk and what corrective steps may be needed.


The measurement approach described above represents the first phase of a supervisory program for evaluating interest rate risk in commercial banks. These guidelines and principles will be further developed and field-tested before their formal incorporation in examination procedures. Limited field testing to date indicates that this approach can be used to identify institutions that may be exposed to high levels of interest rate risk and to establish an initial reference point for examiners in evaluating a bank's management of its investment and funding activities. At the same time, it allows examiners significant flexibility to consider many other factors that are important to assessing this aspect of the bank's business, such as its policies, procedures, controls, and operating systems.

The measurement and management of interest rate risk is a complex topic but one that may be of growing importance to banks and bank supervisors. Fundamentally, the management of interest rate risk and the allocation of capital to support that risk is a bank function that, like others, must be conducted in a reasoned and prudent manner. In its consideration of this risk, the approach described here recognizes the limits to precision and the reporting cost to banks. A measurement system based on relative levels of exposure that gives examiners sufficient flexibility appears to avoid many of the disadvantages of other techniques.


Duration is a widely accepted measure of a financial instrument's interest rate risk. In its most basic form, "Macaulay duration," it is a measure of the effective maturity of an instrument. Specifically, duration is the weighted average maturity of an instrument's cash flows, where the present values of the cash flows serve as the weights. The Macaulay duration of an instrument can be calculated by first multiplying the time until the receipt of each cash flow by the ratio of the present value of that cash flow to the instrument's total present value. The sum of these weighted time periods is the Macaulay duration of the instrument. [Mathematical expression omitted]

Because a zero coupon instrument has only one cash flow, its Macaulay duration is equal to its maturity. In contrast, instruments with periodic cash flows, such as coupon bonds and amortizing mortgages, have durations smaller than their maturity.

Duration is measured in units of time. Relative to the more traditional measure of term to maturity, duration represents a significantly more sophisticated measure of the effective life of a financial instrument. Moreover, when modified to reflect an instrument's discrete compounding of interest, duration measures the instrument's price volatility relative to changes in market yields. Modified duration is calculated as follows:
 Macaulay duration
 Modified duration= ___________________________
 1 + R/c
 R = Per-period internal rate of return of the
 c = Number of times per period that interest is
 compounded (for example, 2 for a semi-annual
 coupon bond when R is an annual rate).

Modified duration is the price elasticity of an instrument with respect to changes in rates. It represents the percentage change in the present value of a financial instrument for a given percentage point change in market yields; this relationship is defined as follows:
 basis point
 change = - Modified in yield
 in price _________ x _________
 duration 100

For example, with a modified duration of 10, a bond changes 10 percent in price for every 100 basis point change in the market yield of that bond.

In the above equation, the inverse relationship between the price of a bond and its market yield is established by the minus sign preceding the term for modified duration. Modified duration acts as a multiplier in translating the effect of changing interest rates on the present value of an instrument: The larger the duration, the greater the effect for a given change in interest rates; and for a given duration, large changes in market rates lead to large percentage changes in price. Therefore, to the extent that the riskiness of an Regulation, prepared this article. Regulation, prepared this article. Regulation, prepared this article. instrument is equated with its price sensitivity, modified duration acts as a measure of interest rate risk.

Modified duration provides a standard measure of price sensitivity for different types of instruments. The standardization allows the duration of a portfolio to be calculated as the weighted average of the durations of its individual components. Because a financial institution can be thought of as a portfolio of assets and liabilities, the duration of an institution's net worth is simply a weighted average of the durations of assets and liabilities. Therefore, by weighting assets, liabilities, and off-balance-sheet positions by their estimated durations, a single measure of interest rate risk exposure can be derived.

Modified duration is a powerful concept for measuring interest rate risk, but it does have several limitations. The most noteworthy is that the accuracy of duration depends on the assumption of small, instantaneous, parallel shifts in the yield curve. Errors in its use as a measure of interest rate risk increase as actual changes in market yields diverge from these assumptions.(8)

(1). The Basle Accord, reached on July 11, 1988, covers the twelve industrial countries participating in the Basle Committee on Banking Regulations and Supervisory Practices under the auspices of the Bank for International Settlements, in Basle, Switzerland Belgium, Canada, France, Germany, Italy, Japan, Luxembourg, the Netherlands, Sweden, Switzerland, the United Kingdom, and the United States). In the United States, the Federal Reserve Board on January 19, 1989, adopted requirements implementing the Basle Accord for state banks that are members of the Federal Reserve System and for bank holding companies. Interim requirements became effective at the end of 1990, and final requirements will take effect at the end of 1992.

(2). As defined, risk-weighted assets include credit exposures contained in off-balance-sheet instruments.

(3). The Macaulay duration of a thirty-year zero coupon bond is indeed thirty years. Because zero coupon yields are quoted as semiannual equivalents, their modified duration is slightly less than maturity (see the appendix for the calculation of modified duration).

(4). Most off-balance-sheet items are recorded on the repricing schedule with a double-entry system of offsetting long and short positions. The two offsetting entries result in an aggregate net position that changes the repricing structure of the portfolio without changing its face value.

(5). Note that with careful selection of the time bands, spreading the liabilities among many repricing periods will produce the same result as putting them in one period.

(6). In January 1991 the Federal Financial Institutions Examination Council (FFIEC) issued for public comment a proposed supervisory policy statement that would, in part, designate certain types of securities with volatile price or other high-risk characteristics as generally unsuitable investments for depository institutions. Such securities include stripped mortgage-backed securities, high-risk CMO tranches, and CMO residuals. The FFIEC is expected to announce a policy statement on this issue in the near future..

(7). The use of this measure in screening banks may identify some institutions as having high interest rate risk simply because their capital ratios were low; although that assessment would not be incorrect, interest rate risk is most likely to be overwhelmed by other problems that already are the focus of supervisory attention.

(8). Further information on duration is available in Livingston G. Douglas, Bond Risk Analysis: A Guide to Duration and Convexity (New York: New York Institute of Finance, 1990); and Gerald 0. Bierwag, Duration Analysis: Managing Interest Rate Risk (Cambridge, Mass.: Ballinger, 1987).
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Author:Embersit, James A.
Publication:Federal Reserve Bulletin
Date:Aug 1, 1991
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