How do I calculate the duration gap for a bank balance sheet?

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AcadiFi · Accepted Answer

Duration gap = D_A - (L/A) * D_L, where D_A is the dollar-weighted duration of assets, D_L is the dollar-weighted duration of liabilities, L is total liabilities, and A is total assets. The ratio L/A scales liability duration by leverage because equity is the residual. The change in the market value of equity from a parallel shift dy is approximately -(D_A - (L/A) * D_L) * A * dy. Example: A = $100B with D_A = 5 years, L = $92B with D_L = 2 years. Duration gap = 5 - (92/100) * 2 = 5 - 1.84 = 3.16 years. A 100 bp rate rise drops equity value by approximately 3.16 * $100B * 0.01 = $3.16B. Since equity base is $8B, that is a 40% hit — a material mismatch. Interpretation: a positive duration gap means assets are longer than leverage-adjusted liabilities, so rising rates hurt equity. Banks often run positive duration gaps because mortgages dominate assets while deposits dominate liabilities. Hedging moves include receiving fixed on interest rate swaps (shortens asset duration) or issuing long-term debt (lengthens liability duration). Limitations of duration gap match those of fixed-income duration: linear approximation only, parallel shifts only, and ignores convexity. For options-embedded products (prepayments, deposit withdrawals) effective duration computed from a scenario-based revaluation replaces Macaulay or modified duration. Convexity gap adjustments refine the large-shock estimate.

How do I calculate the duration gap for a bank balance sheet?

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