Duration Gap

The duration gap is a measure of a financial institution's exposure to changes in interest rates. It compares the average duration of the institution's assets with the average duration of its liabilities, adjusted for how much of the balance sheet is funded by liabilities. Duration expresses how sensitive the present value of a set of cash flows is to a change in rates, so the gap indicates how the economic value of equity, the value of assets minus liabilities, will move when rates rise or fall.

The measure is a tool of asset-liability management and of the supervision of interest rate risk in the banking book. It complements the repricing gap, which looks at the effect of rate changes on net interest income over the near term. Duration gap looks instead at the whole life of the balance sheet and at value, not income.

The standard calculation is:

In this formula $D_A$ is the weighted average duration of assets and $D_L$ the weighted average duration of liabilities, both in years, while $L$ and $A$ are the market values of liabilities and assets.

The approximate change in the value of equity for a change in rates is:

Here $\Delta y$ is the change in the interest rate and $y$ is its starting level. Suppose a bank has assets of 1,000 with a duration of 4 years and liabilities of 900 with a duration of 2 years, so equity is 100. The duration gap is $4 - 0.9 \times 2 = 2.2$ years. If rates rise from 5% to 6%, equity changes by about $-2.2 \times 1{,}000 \times 0.01 \div 1.05 \approx -21$. A one-point rise in rates therefore removes roughly a fifth of the bank's economic net worth.

• Positive gap. Assets are longer than liabilities. Rising rates reduce the value of assets by more than they reduce the value of liabilities, so equity falls; falling rates raise it. This is the usual position of a bank that funds long-term loans and bonds with deposits, a result of maturity transformation.
• Negative gap. Liabilities are longer than assets. Equity gains when rates rise and loses when they fall. Life insurers and pension funds with long-dated obligations are often in this position, as discussed under insurance asset-liability management.
• Zero gap. The value of equity is, to a first approximation, immunised against a small parallel shift in rates.

An institution can change its gap on the balance sheet, by shortening assets or lengthening liabilities, for example making more floating-rate loans or issuing longer-term debt. More often it uses derivatives. Entering an interest rate swap in which the bank pays a fixed rate and receives a floating rate shortens the effective duration of its assets without selling them. Futures, options, caps and floors are used in the same way. This hedging is run by the treasury function under limits set by the asset and liability committee, as part of wider balance sheet management.

Closing the gap completely is rarely the goal. A positive gap normally earns the extra yield available on longer assets, so the gap chosen reflects a trade-off between income and risk to capital.

Duration gap is a simplification.

• Small, parallel shifts only. The formula assumes all rates move by the same amount. Changes in the slope of the yield curve affect long and short items differently, and for large moves the curvature of prices, known as convexity, matters.
• Uncertain cash flows. Mortgages can be prepaid and deposits withdrawn at will. Their duration depends on models of customer behaviour, especially for current and savings accounts with no stated maturity.
• Constant recalculation. Durations drift as time passes and as rates change, so a matched position does not stay matched.
• Other risks ignored. The measure captures neither credit losses nor the gap between different reference rates.

For these reasons, banks supplement it with full revaluation of the balance sheet under a range of rate scenarios.

The Basel Committee's 2016 standard on interest rate risk in the banking book requires banks to measure the change in economic value of equity under prescribed rate shocks and to disclose the results. Supervisors treat a loss above 15% of Tier 1 capital under any of the scenarios as an outlier calling for review. The measure is the regulatory descendant of duration gap analysis and forms part of the assessment of structural interest rate risk.

The danger of a large positive gap was shown in March 2023 by the failure of Silicon Valley Bank, which had invested a surge of deposits in long-dated bonds, many classed as held-to-maturity securities. When rates rose sharply, the bonds lost value, and depositors withdrew funds once the losses became apparent. The savings and loan crisis in the United States in the 1980s had the same root cause.

• Basel Committee on Banking Supervision: Interest rate risk in the banking book