Δ Net Worth ≈ - Duration Gap × Assets × [ Δi / (1 + i) ]
The Duration Gap measures the mismatch in timing of cash flows. A gap of zero means Equity value is preserved even if interest rates change (Immunization).
The Definitive Guide to Duration Gap: Immunizing Financial Risk
In banking and institutional finance, the greatest threat isn't always default risk—it's the silent erosion of equity caused by mismatched interest rate exposures.
Duration Gap is a financial metric used by banks, pension funds, and insurance companies to measure the sensitivity of their Net Worth (Equity) to changes in interest rates. It compares the weighted average duration of assets to the weighted average duration of liabilities.
It answers the critical question: "If interest rates rise by 1%, will my firm lose equity value?"
The Mechanics: Calculating the Gap
The calculation considers that Assets are funded by both Liabilities and Equity. Therefore, the duration of liabilities must be adjusted by the Leverage Ratio (Liabilities/Assets) to be comparable.
DG = D(Assets) - [(L/A) × D(Liabilities)]
Where:
D(Assets): Macaulay or Modified duration of all assets.
D(Liabilities): Duration of all debts and deposits.
L/A: Leverage Ratio (Total Liabilities / Total Assets).
Positive vs. Negative Gap Analysis
Positive Gap (+ Years)
Asset Duration > Liability Duration
The institution is "Asset Sensitive."
Risk: Rising interest rates reduce the value of assets more than liabilities, causing Equity to fall.
Benefit: Falling rates boost Equity.
Negative Gap (- Years)
Liability Duration > Asset Duration
The institution is "Liability Sensitive."
Risk: Falling interest rates increase the value of liabilities more than assets, hurting Equity.
Benefit: Rising rates boost Equity.
The Strategy of Immunization
Immunization is the process of structuring a balance sheet so that the Duration Gap is zero. When the gap is zero, changes in interest rates affect the value of assets and liabilities equally, leaving the Net Worth unchanged.
This is often achieved using interest rate swaps (e.g., swapping fixed-rate asset income for floating-rate income to lower asset duration).
Limitations of Duration Analysis
While powerful, Duration Gap has flaws:
Convexity: It assumes a linear relationship between price and rates. For large rate moves, this is inaccurate.
Parallel Shifts: It assumes the entire yield curve moves up or down uniformly. It fails to capture risk from "twists" (e.g., short-term rates rising while long-term rates fall).
Dynamic Behavior: Prepayments on mortgages (Assets) or early withdrawals of deposits (Liabilities) change duration dynamically as rates move.
Frequently Asked Questions
Expert answers on ALM and Risk Management
What is the "Ideal" Duration Gap?
For a risk-averse institution, the ideal gap is zero (Immunized). However, many banks intentionally maintain a small gap based on their interest rate forecast to generate speculative profit.
Why are banks typically Asset Sensitive (Positive Gap)?
Banks often lend long-term (Mortgages, 30 years) but borrow short-term (Deposits, 0 years). This structural mismatch naturally creates a positive duration gap, making them vulnerable to rising rates.
How does Net Worth change with rates?
The formula is intuitive: Change in Equity = - (Duration Gap) × Assets × Change in Rates. The negative sign means that if you have a positive gap, a positive rate change hurts you.
Can I use Modified Duration here?
Yes, Modified Duration is preferred as it already accounts for yield levels. Macaulay Duration must be divided by (1+yield) to be accurate for price sensitivity.
What is "Convexity"?
Convexity measures the curvature of the price-yield relationship. It is the "second derivative." If duration is speed, convexity is acceleration. A highly convex portfolio is more protected against large rate shocks.
How do swaps affect the gap?
A "Pay Fixed / Receive Float" swap reduces asset duration (or increases liability duration), effectively lowering a positive gap. It converts a fixed asset into a floating asset with near-zero duration.
Does this apply to personal finance?
Rarely. Individuals don't usually mark their liabilities (mortgage) to market. However, for a bond portfolio, duration gap is crucial to match the time horizon of the investment with the time horizon of the goal.
What is a "Parallel Shift"?
It assumes that 1-year, 5-year, and 30-year interest rates all increase by the exact same amount (e.g., +1%). In reality, yield curves often steepen or flatten.
How often should I calculate this?
Banks calculate this daily or even intra-day. For general portfolio management, quarterly reviews are typically sufficient.
Summary
The Duration Gap Calculator helps you visualize the interest rate risk embedded in your balance sheet.
It is the cornerstone of modern Asset-Liability Management (ALM).
Use it to ensure your net worth is protected against unexpected rate shocks.
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Estimate duration gap to assess asset-liability interest rate risk exposure.
How to use Duration Gap (Interest Rate Risk) Calculator
Step-by-step guide to using the Duration Gap (Interest Rate Risk) Calculator:
Enter your values. Input the required values in the calculator form
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Frequently asked questions
How do I use the Duration Gap (Interest Rate Risk) Calculator?
Simply enter your values in the input fields and the calculator will automatically compute the results. The Duration Gap (Interest Rate Risk) Calculator is designed to be user-friendly and provide instant calculations.
Is the Duration Gap (Interest Rate Risk) Calculator free to use?
Yes, the Duration Gap (Interest Rate Risk) Calculator is completely free to use. No registration or payment is required.
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Yes, the Duration Gap (Interest Rate Risk) Calculator is fully responsive and works perfectly on mobile phones, tablets, and desktop computers.
Are the results from Duration Gap (Interest Rate Risk) Calculator accurate?
Yes, our calculators use standard formulas and are regularly tested for accuracy. However, results should be used for informational purposes and not as a substitute for professional advice.