Duration Gap

Duration gap measures the difference between the interest-rate sensitivity of assets and the liability-funded portion of those assets.

Duration gap measures the difference between the interest-rate sensitivity of assets and the liability-funded portion of those assets. Banks and other asset-liability managers use it as a simplified estimate of how a rate change could affect the economic value of equity.

A positive duration gap generally means asset value is more sensitive than liability value to a parallel rate increase, so economic value of equity would tend to fall. A negative duration gap generally indicates the opposite direction under the same assumptions.

Key Takeaways

  • Duration gap compares asset duration with leverage-adjusted liability duration.
  • The measure estimates economic-value sensitivity, not near-term net interest income.
  • Modified duration allows a direct first-order rate-shock approximation.
  • A positive, zero, or negative gap is not automatically good or bad; interpretation depends on the rate scenario and risk objective.
  • Parallel-shift assumptions can miss yield-curve, basis, option, and behavioral risk.
  • Cash-flow timing for deposits, prepayments, and other products may depend heavily on models.

Duration-Gap Formula

Using modified duration:

$$ DG = D_A - \left(\frac{L}{A}\right)D_L $$

where:

  • (DG) is duration gap
  • (D_A) is the modified duration of assets
  • (D_L) is the modified duration of liabilities
  • (A) is the market or economic value of assets
  • (L) is the market or economic value of liabilities

The leverage adjustment (L/A) reflects that liabilities fund only part of the asset base. Equity funds the remainder.

For a small parallel change in rates:

$$ \Delta EVE \approx -DG \times A \times \Delta y $$

where (\Delta EVE) is the approximate change in economic value of equity and (\Delta y) is the rate change in decimal form.

If Macaulay rather than modified duration is used, the conversion to price sensitivity requires an additional yield adjustment. Analysts should state the duration convention.

Worked Example

Assume a bank has:

  • assets of $100 million
  • liabilities of $90 million
  • asset modified duration of 4.5
  • liability modified duration of 2.0

First calculate the duration gap:

$$ DG = 4.5 - \left(\frac{90}{100}\right)(2.0) $$
$$ DG = 4.5 - 1.8 = 2.7 $$

For a parallel rate increase of one percentage point:

$$ \Delta EVE \approx -2.7 \times \$100\text{ million} \times 0.01 $$
$$ \Delta EVE \approx -\$2.7\text{ million} $$

The simplified estimate indicates a $2.7 million decline in economic value of equity.

This is not a forecast or exact valuation. It assumes small and parallel rate changes, stable cash flows, accurate duration estimates, and no important nonlinear options.

How to Interpret Duration Gap

Duration gapSimplified effect of rising ratesSimplified effect of falling rates
PositiveAsset value falls more than liability valueAsset value rises more than liability value
Near zeroFirst-order value changes are approximately matchedFirst-order value changes are approximately matched
NegativeLiability value falls more than asset valueLiability value rises more than asset value

A near-zero aggregate gap can still hide risk. Exposures at different yield-curve maturities can offset under one parallel scenario but produce losses when the curve twists. Different benchmark rates can also diverge.

Duration Gap vs. Repricing Gap

MeasurePrimary focusTypical horizonMain limitation
Duration gapPresent-value sensitivity of assets and liabilitiesEconomic life of cash flowsDepends on valuation and duration assumptions
Repricing gapAmounts resetting or maturing within time bucketsOften near-term earnings horizonDoes not measure full economic-value sensitivity

A repricing gap may indicate how rate changes affect net interest income over a stated period. Duration gap indicates how present values respond. A bank can appear balanced under one measure and exposed under the other.

See Interest-Rate Risk for repricing, yield-curve, basis, and option risk.

Building the Measure

A defensible duration-gap calculation requires:

  1. a complete asset, liability, and off-balance-sheet inventory
  2. consistent valuation dates and curves
  3. cash-flow schedules and contractual reset dates
  4. prepayment, deposit, withdrawal, and renewal assumptions
  5. embedded-option treatment
  6. duration measures by currency and relevant benchmark
  7. aggregation rules for hedges and derivatives
  8. scenario and model-validation evidence

Nonmaturity deposits are especially assumption-sensitive because they have no contractual maturity that directly describes customer behavior. Loans can prepay, commitments can be drawn, and deposit balances can migrate when rates change.

Key Limitations

Parallel-Shift Assumption

A single duration gap is most useful for a small parallel yield-curve move. It can miss steepening, flattening, and localized maturity shocks. Key-rate duration or full revaluation can provide more detail.

Linear Approximation

Duration is a first-order measure. Convexity and embedded options matter for large moves and nonlinear instruments.

Basis Risk

Assets, liabilities, and hedges may reference different rates. Similar durations do not ensure that those benchmarks move together.

Behavioral Assumptions

Deposit stability, loan prepayment, early withdrawal, and product renewal can change with rates. Modeled durations can therefore differ materially from contractual cash-flow timing.

Earnings Effects

Duration gap measures economic-value sensitivity. It does not replace net-interest-income simulations, margin analysis, or liquidity stress testing.

Aggregation

Offsetting positions across currencies, entities, or legal restrictions may not be economically interchangeable.

How Duration Gap Is Used

Duration gap can support:

  • asset-liability management
  • economic-value limits
  • rate-shock and yield-curve scenarios
  • hedge sizing
  • capital and risk-appetite discussions
  • comparison with net-interest-income sensitivity
  • model review and assumption governance

Possible responses include changing asset or liability duration, adjusting the fixed-floating mix, using derivatives, altering funding terms, or accepting the exposure within an approved limit. Each response introduces cost and potentially other risks.

Common Mistakes

  • Omitting the liability-to-asset adjustment: asset and liability duration cannot be compared directly when their values differ.
  • Mixing Macaulay and modified duration: the formulas are not interchangeable without adjustment.
  • Treating a zero gap as zero risk: curve shape, basis, options, and model error remain.
  • Using book values with market-value durations without explanation: measurement bases should be consistent.
  • Ignoring off-balance-sheet positions: swaps, commitments, and options can materially change sensitivity.
  • Assuming contractual maturity equals behavioral duration: deposits and prepayable assets require supported assumptions.
  • Using duration gap as an earnings forecast: it is principally an economic-value measure.

Authoritative Sources

Regulatory scenarios, disclosure requirements, and acceptable model assumptions vary by institution and jurisdiction. Verify the current applicable framework.

FAQs

What does a positive duration gap mean?

Under a small parallel rate increase, it generally means asset value is expected to fall more than liability value, reducing economic value of equity. Other curve and option effects can alter the result.

Is a zero duration gap risk-free?

No. A zero aggregate gap offsets only the modeled first-order sensitivity. Yield-curve, basis, option, liquidity, and model risks can remain.

Is duration gap the same as repricing gap?

No. Duration gap focuses on present-value sensitivity. Repricing gap groups balances by when their rates reset or mature and is often used for near-term earnings analysis.

Why are deposit assumptions important?

Many deposits do not have a contractual maturity that predicts actual customer behavior. Their modeled cash flows and rate sensitivity can materially change the calculated liability duration.

Educational Use

This article is for financial education only. It does not evaluate a specific institution, balance sheet, capital level, or hedge and is not personalized investment, accounting, legal, regulatory, or risk-management advice.

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