Duration Gap at Cedar Bank
Cedar Bank has $10 billion in assets and a duration gap: asset duration is 6.5 years, liability duration is 4.0 years, and equity is 8% of assets. It holds a $2 billion bond portfolio with modified duration 5.2 and $500 million of floating-rate loans. Regulators require CET1 of 7%, Tier 1 of 8.5%, total capital of 10.5%, a leverage ratio of 4%, an LCR of 100%, and an NSFR of 100%. Actual ratios are CET1 9.6%, Tier 1 11.0%, total capital 13.2%, leverage 5.1%, LCR 118%, and NSFR 106%. Rates are expected to rise 150 bp over the next year. Loan growth is 14% and deposit growth is 5%; NIM has fallen from 3.1% to 2.6%. The board wants to know whether to hedge, raise capital, or slow growth.
1. Calculate the change in equity value from a 150 bp parallel upward shift using duration gap, and compare it with the bond portfolio's loss.
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Duration gap = DA − (L/A)DL = 6.5 − 0.92 × 4.0 = 6.5 − 3.68 = 2.82 years. Here L/A = 0.92 because equity is 8% of assets.
ΔE ≈ −DGAP × A × Δi = −2.82 × 10,000 × 0.015 = −423 million. Equity is 8% × 10,000 = 800 million, so the loss is 52.9% of equity.
The bond portfolio's own loss is −5.2 × 2,000 × 0.015 = −156 million. The bond loss is part of the total equity loss, not additional. The remaining loss comes from the mismatch between asset and liability repricing: assets are longer than liabilities, so the value of assets falls more than the value of liabilities when rates rise. This is a classic positive duration gap.
2. Evaluate hedging with a pay-fixed interest rate swap. What notional and direction would be needed, and what basis risk remains?
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A pay-fixed swap gains when rates rise: the bank pays a fixed rate below the new market rate and receives a higher floating rate. That gain offsets the fall in equity from the positive duration gap.
A rough notional is desired gain divided by swap duration times the rate change. If the swap duration is 5 years, notional ≈ 423 / (5 × 0.015) = 5.64 billion. That is large relative to assets, so Cedar might hedge only the bond portfolio and part of the gap rather than the whole bank.
Basis risk remains: the swap's floating leg may reset to SOFR while loans and deposits reprice off prime, fed funds, or contractual caps. Deposit betas are uncertain, and prepayment risk changes the asset duration. There is also counterparty credit risk and collateral calls. A swap can reduce the duration gap but cannot eliminate the economic mismatch unless the bank models its actual repricing.
3. Assess capital and liquidity buffers. Should Cedar raise capital, securitize loans, or slow growth?
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CET1 is 9.6% of RWA. If RWA are about 8.5 billion, CET1 capital is 816 million. A 423 million loss leaves 393 million, or 4.6% of RWA-below the 7% CET1 buffer and barely above the 4.5% minimum. That is a solvency warning.
Liquidity looks adequate: LCR 118% and NSFR 106%. But loan growth of 14% versus deposit growth of 5% is draining liquidity and increasing reliance on wholesale funding. The bank should:
- Raise CET1 or issue convertible capital before the rate move.
- Securitize or sell part of the bond portfolio and floating-rate loans to reduce asset duration and fund growth.
- Slow loan growth to a sustainable pace.
- Use the swap to hedge residual duration.
Regulation is procyclical: raising capital in a downturn is hard, so the bank should build buffers while profitable. The leverage ratio of 5.1% is above 4% but would fall after the loss. Capital, not just liquidity, is the binding constraint.