Duration gap analysis compares how much a bank’s assets and liabilities would change in market value if interest rates moved, using duration as the measure of rate sensitivity on each side of the balance sheet. The output is a single number, expressed in years, that tells managers whether rising or falling rates will help or hurt equity, and by roughly how much. It is a core tool for protecting bank capital, and the 2023 failure of Silicon Valley Bank made clear what happens when the calculation is ignored or the exposure left unhedged.
What Duration Measures
Every loan, bond, or deposit on a bank’s books has a schedule of future cash flows. Duration compresses that schedule into a single figure that captures how much the instrument’s price will move when rates change. Three versions of duration feed into gap analysis, and each answers a slightly different question.
Macaulay and Modified Duration
Macaulay duration is the weighted average time until you receive all of a bond’s cash flows, with each payment weighted by its present value. A 10-year coupon bond has a Macaulay duration shorter than 10 years because coupons arrive along the way. A zero-coupon bond’s Macaulay duration equals its maturity, since the only payment lands at the end.
Modified duration converts that time-weighted figure into a direct price-sensitivity measure. It tells you the approximate percentage change in a bond’s price for a small change in yield. A bond with a modified duration of 6 loses about 6 percent of its value if yields rise by one percentage point, and gains roughly 6 percent if yields fall by the same amount.1Federal Reserve Bank of St. Louis. Investment Improvement: Adding Duration to the Toolbox
Effective Duration
Modified duration assumes cash flows stay fixed no matter where rates go. That assumption fails for callable bonds, mortgage-backed securities, and anything else where the borrower or issuer can change the payment schedule. When mortgage rates fall, homeowners refinance and principal comes back sooner than expected. When rates rise, prepayments dry up and the bank holds long-duration paper it wanted to shed. Modified duration cannot see any of this and consistently overstates the true rate sensitivity of instruments with embedded options.2Society of Actuaries. Back to Basics: Which Duration Is Best?
Effective duration solves this by repricing the instrument under both higher and lower rate scenarios using option-adjusted models, then averaging the price change. A bank with a large mortgage or callable-bond portfolio that relies only on modified duration is almost certainly understating its real exposure.
Portfolio Duration
Portfolio duration is the market-value-weighted average of every instrument’s duration. If 60 percent of a bank’s assets by market value sit in bonds with a duration of 7, and 40 percent sit in short-term loans with a duration of 1, portfolio duration is roughly 4.6 years. Managers calculate this separately for assets and for liabilities, then run the two figures through the gap formula.
Calculating the Duration Gap
The duration gap formula adjusts for the fact that most banks hold more assets than liabilities, with the difference being equity. The calculation takes three steps.
First, compute a leverage ratio by dividing the market value of liabilities by the market value of assets. A bank with $900 million in liabilities and $1 billion in assets has a leverage ratio of 0.9. Second, multiply that ratio by the aggregate duration of liabilities. If liability duration is 3 years, the leverage-adjusted figure is 2.7 years. Third, subtract the adjusted liability duration from asset duration. If assets carry a duration of 5 years, the duration gap is 5.0 minus 2.7, or 2.3 years.
To estimate the actual hit to equity from a rate change, multiply the negative of the duration gap by the rate change divided by one plus the current rate. If rates jump 2 percentage points and the current rate is 5 percent, the impact on equity as a percentage of total assets is roughly negative 2.3 times (0.02 / 1.05), or about negative 4.4 percent of total assets.3Pearson. Duration Gap Analysis: Measuring and Managing Asset-Liability Mismatch On a $1 billion balance sheet, that is a $44 million decline in equity from one rate move.
What Positive, Negative, and Zero Gaps Mean
The sign of the gap determines the direction of the exposure.
- A positive gap means asset duration exceeds the leverage-adjusted liability duration. Rising rates pull asset values down faster than liability values, shrinking equity. Falling rates do the opposite. Most commercial banks carry a positive gap because they fund long-term mortgages and bonds with shorter-term deposits.
- A negative gap means the adjusted liability duration is larger than asset duration. Rising rates actually increase equity because liabilities lose value faster than assets. This shows up at institutions that issue long-term debt to fund shorter-duration lending.
- A zero gap immunizes equity against rate moves in either direction. It also eliminates any upside from favorable moves.
Perfect immunization is hard to hold. Time passes, new loans and deposits arrive, securities mature or get called, and the gap drifts. A manager who lands on zero on Monday will have a nonzero gap within weeks unless the position is actively rebalanced.
Where Duration Gap Analysis Falls Short
Duration draws a straight line through what is actually a curved relationship between bond prices and yields. For small rate moves the straight line is close enough. For larger shocks it misses.
Convexity measures that curvature. For a standard option-free bond, convexity works in the investor’s favor: actual price gains when rates fall exceed what duration predicts, and actual losses when rates rise are smaller than predicted. A convexity adjustment adds a second-order correction equal to one-half times the convexity value times the square of the yield change. A bank running a 200 or 300 basis point stress scenario without this correction will materially misstate the impact on equity.
Mortgage-backed securities and callable bonds show negative convexity. When rates drop below the coupon, issuers call and borrowers refinance, capping the price upside. The investor keeps the full downside when rates rise and gets clipped on the upside when rates fall. Banks holding large concentrations of these instruments and relying on plain duration and standard convexity will understate losses in falling-rate scenarios and overstate gains.
Two more assumptions deserve attention. The formula assumes rates across the entire yield curve move by the same amount at the same time. Short rates and long rates rarely move in lockstep. A flattening curve, where short rates rise while long rates hold, or a steepening curve, where the opposite happens, creates balance sheet effects a single gap number cannot capture.4Federal Reserve Bank of Chicago. Bank Gap Management and the Use of Financial Futures Key rate duration analysis, which measures sensitivity at specific points along the curve, addresses this but adds modeling complexity.
The analysis also assumes a static balance sheet. In real institutions, deposits flow in and out, new loans get booked, and securities mature. A gap calculated today reflects today’s book, not next quarter’s. Behavioral assumptions for non-maturity deposits are particularly sensitive: a savings account has no contractual maturity, so the bank must estimate how long the funds will actually stay, and small changes in that estimate swing the liability duration substantially.
How Banks Close the Gap
Banks adjust their duration gap in one of two ways: by restructuring the balance sheet itself, or by layering derivatives on top of it.
Balance Sheet Moves
To shorten asset duration, a bank shifts out of long-term fixed-rate bonds and into shorter-term securities, floating-rate loans, or cash equivalents. To lengthen it, it buys longer-dated bonds or originates fixed-rate mortgages. On the liability side, pushing customers into longer-term certificates of deposit extends liability duration; leaning more on overnight borrowing or demand deposits shortens it. These moves change the actual composition of the book and take time to execute, especially at a large institution.
Derivatives
Interest rate swaps are the workhorse hedge. A bank with a positive duration gap can enter a pay-fixed, receive-floating swap, which effectively shortens asset duration by converting fixed-rate income into floating. Bid-ask spreads on plain vanilla swaps in liquid maturities are typically measured in fractions of a basis point.
Interest rate futures on Treasury bonds and SOFR contracts offer a hedging channel with exchange-traded liquidity and daily margining. Interest rate caps and floors protect against moves beyond a set threshold while preserving upside from favorable moves, at the cost of an upfront premium that swaps do not require.
Every derivative hedge needs ongoing management. As the underlying book changes and the derivatives age, the hedge ratio drifts, and the position has to be rebalanced.
Regulatory Framework
U.S. regulators treat interest rate risk as a safety and soundness issue, not an optional discipline.
Prompt Corrective Action
Federal law requires banking regulators to intervene when a bank’s capital drops below required levels. The statute sets five capital categories, from well-capitalized down to critically undercapitalized, with mandatory consequences at each stage. An undercapitalized institution must submit a capital restoration plan and faces restrictions on asset growth, dividends, and management fees. A critically undercapitalized institution, defined as tangible equity below 2 percent of total assets, faces potential receivership.5Office of the Law Revision Counsel. 12 USC 1831o – Prompt Corrective Action An unmanaged duration gap is a direct path to these outcomes, because a single rate shock can erase years of accumulated equity.
Basel IRRBB Standards
The Basel Committee sets international standards for interest rate risk in the banking book under Pillar 2.6Bank for International Settlements. Basel Framework – Interest Rate Risk in the Banking Book Banks run six prescribed shock scenarios for Economic Value of Equity: parallel up, parallel down, steepener, flattener, short rates up, and short rates down. Recalibrated shock sizes took effect on January 1, 2026, based on rate data through December 2023. For U.S. dollar exposures, the prescribed shocks are 200 basis points for parallel moves, 300 basis points for short-rate shocks, and 150 basis points for long-rate shocks.7Bank for International Settlements. Recalibration of Shocks for Interest Rate Risk in the Banking Book An EVE decline exceeding 15 percent of Tier 1 capital in any scenario flags the institution as an outlier requiring supervisory attention.
OCC Examination Standards
For nationally chartered banks, the Office of the Comptroller of the Currency evaluates interest rate risk from both an earnings perspective and an economic value perspective. Examiners review gap reports, stress test results, the quality of behavioral assumptions (particularly for non-maturity deposits and mortgage prepayments), and board-level oversight. The OCC notes that simple gap analysis has very limited usefulness and is generally appropriate only for non-complex banks with basic balance sheets. Larger and more complex institutions are expected to run EVE and earnings-at-risk models that capture embedded options and non-parallel curve moves.8Office of the Comptroller of the Currency. Comptroller’s Handbook: Interest Rate Risk For the largest institutions, examiners expect stress tests across scenarios of 300 and 400 basis points in addition to the standard 200 basis point parallel shift.
Silicon Valley Bank as a Case Study
The March 2023 failure of Silicon Valley Bank is the clearest recent example of what an unmanaged duration gap looks like in practice. Between 2018 and 2021, SVB moved deposits into long-duration securities, growing its investment portfolio from $23 billion to $125 billion. Roughly 65 percent of its held-to-maturity securities had maturities beyond five years. The bank was making a concentrated bet that rates would stay low.9Board of Governors of the Federal Reserve System, Office of Inspector General. Material Loss Review of Silicon Valley Bank
When the Federal Reserve raised the federal funds rate from 0.25 percent in March 2022 to 4.5 percent by December 2022, unrealized losses on SVB’s held-to-maturity book went from $1.3 billion at the end of 2021 to $15.2 billion by the end of 2022. The available-for-sale book added another $2.5 billion in losses. SVB’s management had removed interest rate hedges in 2022 based on a projection that rates would reverse. They were wrong, and by the time the losses became public the equity cushion was insufficient to absorb them.
On March 8, 2023, SVB announced the sale of its available-for-sale portfolio at a $1.8 billion loss and a planned $2 billion capital raise. The next day, depositors requested $42 billion in withdrawals, nearly 25 percent of total deposits and almost 300 percent of the bank’s capital. Regulators closed the bank that week. The entire sequence traces back to a duration gap problem: short-duration liabilities that could leave at any time funded long-duration assets with years left until maturity, and the resulting exposure was neither hedged nor reduced before rates moved.