What is duration gap analysis and how do banks use it to manage interest rate risk?

Duration gap analysis is a tool banks use to measure the sensitivity of their equity (net worth) to changes in interest rates. The idea is straightforward: if a bank's assets have different duration than its liabilities, interest rate changes will affect them unequally, creating gains or losses in equity.

The Duration Gap Formula

Duration Gap (DGAP) = D_A − (L/A) x D_L

Where:

• D_A = Weighted average duration of assets
• D_L = Weighted average duration of liabilities
• L/A = Leverage ratio (liabilities / assets)

Impact on Equity

Delta_Equity ≈ −DGAP x A x (Delta_r / (1 + r))

Worked Example

Palmerston Savings Bank has:

• Total assets = $800 million, D_A = 5.2 years
• Total liabilities = $720 million, D_L = 2.8 years
• Equity = $80 million
• Current market rate = 4%

Step 1: Duration Gap

DGAP = 5.2 − (720/800) x 2.8 = 5.2 − 0.9 x 2.8 = 5.2 − 2.52 = 2.68 years

Step 2: Impact of a 100 bp rate increase

Delta_Equity = −2.68 x $800M x (0.01 / 1.04) = −2.68 x $800M x 0.009615 = −$20.6 million

The bank's equity drops from $80M to ~$59.4M — a 25.8% decline from a 1% rate move.

Interpreting the Gap

Most banks have a positive duration gap because they borrow short (deposits, D~0.5 years) and lend long (mortgages, D~5+ years). This is the classic 'borrow short, lend long' maturity transformation.

Strategies to Close the Gap:

• Enter pay-fixed interest rate swaps (reduces effective asset duration)
• Shorten loan portfolio duration (adjustable-rate mortgages)
• Extend liability duration (issue longer-term CDs or bonds)

Exam Tip: Watch the leverage ratio L/A. Even if D_L > D_A, the gap can be positive because liabilities are scaled down by the leverage ratio.

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