Hypothetical worked example and primary educational references; not observed market data.
Duration measures sensitivity rather than a deadline
A bond's maturity tells you when a final contractual payment is due. Duration describes how sensitive its value is to yield changes. FINRA treats duration as an interest-rate risk measure. A long maturity can contribute to high sensitivity, but payment timing also matters: receiving substantial cash earlier changes how much value depends on distant payments. Modified duration is the version used in the common small-change price approximation. Identify the duration definition before applying a formula because a figure labeled simply 'duration' can conceal differences in convention or assumptions about changing cash flows.
Supporting references: 1. FINRA: Bonds
Keep yield units consistent
The simplified price-change formula is negative modified duration multiplied by the yield change expressed as a decimal. A rise from 4% to 4.5% is a 0.5 percentage-point change, or 0.005 in decimal form. It is not an input of 0.5 or 50%. With assumed modified duration of six, that shock implies an approximate 3% price decline. A unit mistake would magnify the estimate enormously. Writing the starting yield, ending yield, and decimal difference before calculation is a simple safeguard. The illustration concerns a specified yield change rather than a prediction of policy decisions or market movements.
Hypothetical worked example
Linear sensitivity to a half-point yield rise
Model setup
Read these assumptions before comparing the scenarios.
- All monetary amounts in this example are hypothetical U.S. dollars (USD), not current prices, quoted account terms or observed market data. Percentages, counts, time periods and index levels retain their stated units.
- Each hypothetical position is worth USD 10,000.
- Yield change is +0.005; duration, credit and cash flows stay fixed.
Approximate loss (USD)
- 1. 2
- 100.00
- 2. 6
- 300.00
Shared zero-based value scale. Range: 0.00 to 300.00, in the units above. Case numbers match the labels; no probability or time trend is implied.
Hypothetical model, not observed market data or a forecast. Assumptions above; original values and calculations below.
| Modified duration | Approximate price change (%) | Approximate loss (USD) |
|---|---|---|
| 2 | -1.00 | 100 |
| 6 | -3.00 | 300 |
Calculation details
- Short duration change
- -1.00 %
(((-1 * 2) * 0.0050000000000000001) * 100) - Long duration change
- -3.00 %
(((-1 * 6) * 0.0050000000000000001) * 100) - Short loss
- 100.00 USD
(10000 * 0.01) - Long loss
- 300.00 USD
(10000 * 0.029999999999999999)
Compare two sensitivities with one shock
Consider two hypothetical bond positions, each valued at USD 10,000. One has modified duration of two and the other six. A parallel yield increase of 0.5 percentage points produces linear price-change estimates of minus 1% and minus 3%, equivalent to losses of 100 and 300. The inputs are assumed solely for teaching. Holding credit spreads, payment expectations, and other conditions constant isolates the duration mechanism. The longer-duration position responds more strongly to the same modeled shock. The resulting figures are approximations, not exact trade prices or observed investment losses.
The straight-line model has boundaries
Actual price-yield relationships are curved, so a duration estimate becomes less accurate as the yield change grows. Callable or other option-sensitive bonds can also change their expected payment patterns when yields move, complicating a fixed duration number. A shock may affect short and long yields differently instead of shifting the whole curve in parallel. These boundaries are not reasons to abandon duration. They explain why a single duration statistic should be accompanied by scenario analysis and a clear statement about the kind of yield change assumed. Its strength is a useful first-order comparison, not universal precision.
Total return includes more than repricing
The duration calculation describes an estimated immediate price response. It does not include coupon income over a later holding period, reinvestment, fees, or credit events. A bond position might lose market value when yields rise while subsequently offering different reinvestment opportunities. Whether that helps a particular investor depends on horizon and cash needs. FINRA's yield discussion distinguishes price changes from other components of return. Keeping that separation prevents a one-day sensitivity estimate from being presented as an annual return forecast. Immediate valuation effects and multi-period investment outcomes require different calculations and assumptions.
Supporting references: 2. FINRA: Understanding Bond Yield and Return
Match the measure to the decision
A person expecting a near-term withdrawal should consider the consequences of selling after a yield shock. Someone holding a contractual payment to maturity faces another set of questions about repayment and purchasing power. A fund's duration also changes as holdings, yields, and cash balances evolve, so a dated figure needs a dated interpretation. Use duration to compare interest-rate exposure among otherwise relevant choices and to test portfolio affordability. Do not convert it into a universal instruction that short duration is always better. Reducing sensitivity changes one risk and can change the opportunities and liabilities the portfolio was designed to address.
Test another situationOffsetting asset and liability sensitivities
A separate hypothetical case. Its inputs differ from the main worked example above.
Offsetting asset and liability sensitivities
Assume hypothetical assets of USD 18,000 have modified duration four, while a USD 16,000 modeled liability has duration five. Apply an immediate parallel yield increase of 0.01 in decimal units, holding both durations and cash-flow assumptions fixed. The first-order change in assets minus liability value is positive USD 80. This does not mean usable cash increases by that amount: both sides are present-value estimates. The liability's modeled value falls faster in dollar terms than assets. Reducing asset duration could lower standalone price sensitivity while increasing the mismatch with the obligation, illustrating why the portfolio's purpose matters when interpreting duration.
Ask whether the liability is actually rate-sensitive
FINRA explains the connection between interest rates and bond prices. Extending that framework to a funding comparison requires care about the obligation's definition. A fixed invoice payable soon does not become cheaper to pay just because a discount model reports a lower present value. For an economic funding analysis, use compatible discount assumptions and dates on both sides; for a cash-payment analysis, retain the actual dollars due. Do not net a hypothetical liability valuation gain against an immediate bill as though it were spendable income. The distinction determines whether matching sensitivities is informative or simply distracts from the required cash.
Supporting references: 1. FINRA: Bonds
Check this case’s calculations
- First-order surplus value change
- 80.00 USD
(((16000 * 5) - (18000 * 4)) * 0.01)
Limits of this additional case
- Parallel shocks and fixed durations omit convexity, spread changes and any change in actual liability amounts.
Limits of this analysis
- The linear estimate ignores convexity.
- Real yield curves may shift unevenly.
- Callable cash flows and credit-spread changes can invalidate fixed sensitivity assumptions.
Sources and scope
- FINRA: Bonds
Bondholders face interest-rate, credit, call, inflation and liquidity risks.
Scope: U.S. investor education; supports the stated mechanism, not the hypothetical scenario or a forecast.. Reference accessed 2026-10-06.
- FINRA: Understanding Bond Yield and Return
Coupon, current yield and yield to maturity measure different things.
Scope: U.S. investor education; supports the stated mechanism, not the hypothetical scenario or a forecast.. Reference accessed 2026-10-06.
Illustrative calculations are not forecasts or personal recommendations. Editorial standards
