Two bonds can mature on the same date and still move very differently when yields change. The reason is duration.
Maturity tells you when the contractual principal is due. Duration tells you something different: how the timing of all the bond’s cash flows translates into sensitivity to changes in yield.
A low-coupon bond leaves more value sitting far in the future. A high-coupon bond returns more value earlier. A callable bond can shorten its expected life when rates fall. A portfolio can be highly exposed to one maturity point and much less exposed to another. One date on the bond certificate cannot capture all of that.
This article is part of Batch 034 of the eduKateSG Finance Authority 400. Why Bond Prices and Yields Move in Opposite Directions owns the general price–yield engine. This page owns the measurement of price sensitivity. The preceding Yield Curve article owns the cross-maturity term structure.
Duration is not how long the bond exists. It is how strongly the bond’s value reacts when the market reprices time.
Educational boundary: duration is a model-based sensitivity measure. The exact method depends on cash-flow structure, yield convention and embedded options. Duration does not capture credit, liquidity or all nonlinear price effects.
The short answer: what is bond duration?
Duration is a measure of a bond’s or bond portfolio’s sensitivity to changes in yield, built from the timing and present value of its cash flows.
FINRA describes duration as the degree to which a bond investment is likely to change in value when interest rates rise or fall, and distinguishes it explicitly from maturity. FINRA also notes the practical rule of thumb that a bond with duration of 10 would be expected to move by roughly 10% in the opposite direction for a one-percentage-point move in rates, as a first-order approximation. See FINRA on bond duration.
The negative direction comes from the bond price–yield relationship:
YIELD UP → PRICE DOWN.
YIELD DOWN → PRICE UP.
Maturity and duration are different clocks
Maturity asks when the final principal is contractually due. Duration asks how far into the future the bond’s present-value-weighted cash flows effectively sit and how that affects price sensitivity.
A zero-coupon bond with ten years to maturity has all of its contractual value arriving at the end. A high-coupon ten-year bond returns a significant part of its value before Year 10. The two bonds share a legal maturity. The zero-coupon bond generally has the longer duration.
Investor.gov similarly notes that longer maturity and lower coupon generally increase interest-rate sensitivity. See Investor.gov on fixed-rate bond price sensitivity.
Macaulay duration: a weighted time to cash flow
Macaulay duration is the present-value-weighted average time at which the bond’s cash flows are received.
Conceptually:
MACAULAY DURATION = Σ(time × present value of cash flow) ÷ bond price.
Every coupon and principal payment gets a weight based on how much it contributes to the bond’s current value. Large early coupons pull duration shorter. A distant principal payment pulls it longer.
Macaulay duration is stated in years, but it should not be mistaken for the contractual life of the bond. It is a weighted timing statistic.
A simple Macaulay example
Take a fictional two-year bond with S$1,000 face value, 5% annual coupons and a 5% yield. It pays S$50 after Year 1 and S$1,050 after Year 2.
| Cash flow | Time | Present value at 5% | Time-weighted PV |
|---|---|---|---|
| S$50 | 1 year | About S$47.62 | About 47.62 |
| S$1,050 | 2 years | About S$952.38 | About 1,904.76 |
| Total | S$1,000 | 1,952.38 |
Macaulay duration is approximately 1.952 years. The bond matures in two years, but some value arrives after one year, pulling the weighted timing slightly earlier.
Modified duration: converting timing into price sensitivity
Modified duration adjusts Macaulay duration for the bond’s yield convention to approximate price sensitivity.
For a simple annual-pay bond:
Modified duration ≈ Macaulay duration ÷ (1 + yield).
In the two-year example, 1.952 ÷ 1.05 is approximately 1.859.
If yield rises by 0.50 percentage points, or 0.005, the first-order estimate is:
Approximate price change = −1.859 × 0.005 ≈ −0.93%.
The bond’s exact repricing will differ slightly because the price–yield relationship is curved. Duration gives the local slope.
Why longer maturity usually means higher duration
Future cash flows are more sensitive to the discount rate the further away they are. A payment due next month is barely affected by a modest change in a ten-year rate environment. A payment due twenty years from now can move materially in present value.
This creates the familiar rule:
ALL ELSE EQUAL, LONGER MATURITY → LONGER DURATION → GREATER PRICE SENSITIVITY.
The phrase all else equal protects the claim. Coupon, yield and options can change the ordering.
Why lower coupons usually mean higher duration
Coupons return value before maturity. A high-coupon bond receives more cash early. A low-coupon bond leaves more value waiting for the final principal payment.
Consider two ten-year, S$1,000 bonds with the same yield. One pays 8% coupons; the other pays 2%. The 8% bond brings more present value forward through larger interim coupons. The 2% bond leaves a larger portion of value in Year 10 and generally has longer duration.
FINRA’s duration guidance makes the same general observation: higher coupon tends to reduce duration, while longer maturity tends to increase it.
Zero-coupon bonds make the rule visible
A conventional zero-coupon bond pays nothing until maturity. Under a simple framework, its Macaulay duration equals its maturity because all contractual cash flow arrives at one point.
A ten-year zero therefore has Macaulay duration of ten years. A ten-year coupon bond generally has Macaulay duration below ten because some value arrives earlier.
This is the cleanest demonstration that duration is about the timing of value, not merely the legal maturity label.
Yield level also changes duration
When yields are high, distant cash flows are discounted more heavily relative to near-term cash flows. That tends to reduce their weight in the current price and can shorten duration.
When yields are low, distant cash flows retain more present value and can contribute more heavily to the bond’s price, increasing duration.
Duration can therefore change even if maturity and coupon remain unchanged.
Duration is local, not a guaranteed move
Suppose modified duration is 8. A one-percentage-point rise in yield gives an approximate −8% price change.
That does not mean every one-percentage-point move produces exactly 8%. Duration is a first-order approximation around the current price and yield. As rates move further, the slope itself changes.
The missing second-order term is convexity.
Convexity improves the approximation
Conventional option-free bonds usually have positive convexity: the price–yield curve bends outward.
A common approximation is:
ΔP/P ≈ −Duration × Δy + ½ × Convexity × (Δy)².
The convexity term becomes more important for larger yield moves and longer-duration bonds.
The practical lesson is not to memorise the formula alone. It is to know when a straight-line duration estimate stops being precise enough.
Callable bonds can have negative convexity
A callable bond gives the issuer a right to redeem under specified conditions. When yields fall, the bond’s high coupon becomes more expensive for the issuer and the probability of a call can rise.
That caps the price appreciation. The investor does not receive unlimited benefit from lower yields because the issuer owns the option to end the old high-coupon contract.
The result can be negative convexity over relevant yield ranges: the bond’s upside from falling yields becomes compressed compared with an option-free bond.
Effective duration for bonds whose cash flows can change
Modified duration assumes the cash-flow schedule remains fixed when yield changes. That assumption becomes weak for callable, puttable or mortgage-like securities where the expected cash-flow path itself can change.
Effective duration estimates sensitivity by repricing the instrument under small upward and downward shifts in the relevant yield environment while allowing modelled cash flows to respond.
The concept is especially useful when options are embedded inside the security rather than traded separately.
Portfolio duration: one number for many bonds
A bond portfolio can be assigned an approximate duration from the market-value-weighted durations of its holdings.
If half the portfolio has duration 2 and half has duration 10, the simple weighted duration is approximately 6, assuming the same sensitivity convention and no other adjustments.
That does not mean every bond in the portfolio moves 6%. It means the portfolio’s first-order aggregate sensitivity to a broadly parallel yield move is around that level.
Portfolio duration compresses a distribution of maturity exposures into one number. Compression is useful only when the missing shape information is not forgotten.
Why one duration number fails when the curve twists
The Yield Curve article showed that short and long yields can move differently.
Imagine Portfolio A is concentrated around two-year bonds and Portfolio B around twenty-year bonds. Both happen to have the same overall duration through different constructions. If the two-year yield rises sharply while the twenty-year yield is unchanged, the portfolios will not behave the same.
This is why more advanced interest-rate risk management uses key-rate duration or related measures that estimate sensitivity to particular maturity points.
Key-rate duration: which part of the curve owns the risk?
Key-rate duration asks how a security or portfolio responds when one selected point on the yield curve moves while other maturity points are held approximately constant under the model.
A portfolio can therefore have:
- little two-year duration;
- large five-year duration;
- moderate ten-year duration;
- little thirty-year duration.
Adding these exposures can help reconstruct total duration, but the profile shows where curve twists create risk.
A duration hedge matches sensitivity, not face value
Suppose an investor wants to hedge the interest-rate exposure of S$10 million in bonds with modified duration 8. The approximate dollar duration is proportional to S$80 million-duration units.
A hedging instrument with duration 4 would need roughly twice the market value, all else equal, to offset the same first-order sensitivity. Equal face amounts do not necessarily hedge equal interest-rate risk.
Real hedging also needs basis, curve, credit, liquidity and convexity considerations. The teaching point is narrower: match the sensitivity, not the label.
Duration and liability matching
Pension funds, insurers and other long-horizon institutions can use duration to compare the sensitivity of assets with the sensitivity of promised liabilities.
If liabilities become more valuable when long yields fall but the asset portfolio has much shorter duration, the funding position can deteriorate even if bond asset prices rise.
Matching duration can reduce first-order sensitivity of the surplus—the difference between assets and liabilities—to yield changes.
Duration therefore matters beyond trading. It is a balance-sheet design tool.
Duration does not measure credit risk
A short-duration distressed bond can still lose most of its value through default. A long-duration government bond can carry substantial interest-rate risk while having relatively low expected credit loss.
FINRA explicitly cautions that low duration does not mean low total risk: bonds also carry credit, inflation, call and other risks.
This ownership boundary is essential. Duration answers one family of questions. It does not become a universal risk score.
Duration can change when credit spreads move
For a corporate bond, price sensitivity can be discussed relative to changes in government yields, credit spreads or total yield. A “spread duration” can measure sensitivity to changes in credit spread while holding the benchmark curve separately.
This separation matters because a corporate bond can lose value when Treasury yields fall if its credit spread widens enough.
The next article, Credit Spread vs Term Premium, will separate those yield components before they are turned into duration exposures.
Duration and reinvestment risk move against each other
A low-coupon long-duration bond has high price sensitivity because cash arrives late. But it also has less coupon cash that must be reinvested before maturity.
A high-coupon bond has shorter duration and more interim cash. That reduces price sensitivity but increases the amount of return exposed to future reinvestment rates.
One risk does not disappear. The timing of the risk changes.
Worked comparison: same maturity, different duration
Consider two fictional ten-year bonds with the same issuer and the same 5% market yield.
| Bond A | Bond B | |
|---|---|---|
| Coupon | 1% | 8% |
| Maturity | 10 years | 10 years |
| Value returned early | Low | High |
| Expected duration | Longer | Shorter |
| Price sensitivity to small yield rise | Greater | Lower |
The table shows why maturity alone is an incomplete risk measure. The coupon schedule changes when the investor receives value.
Worked comparison: same duration, different curve risk
Now imagine two portfolios both report duration 6.
Portfolio X holds mostly six-year securities. Portfolio Y combines short two-year bonds and long twenty-year bonds in proportions that produce the same weighted duration.
A parallel one-percentage-point shift can produce similar first-order responses.
A twist where two-year yields rise and twenty-year yields fall can produce very different outcomes. One total duration number hid the maturity distribution.
This is why yield-curve risk needs more than one scalar.
Failure-first reading: when would the duration estimate fail?
- The yield move is too large for a linear approximation.
- The curve moves non-parallel while only one duration number is used.
- Credit spreads move independently of government yields.
- Embedded options change expected cash flows.
- Liquidity disappears and market prices gap.
- The issuer defaults and contractual cash flows no longer remain fixed.
Duration is most powerful when its assumptions are visible. It becomes dangerous when the number is treated as a universal law of price movement.
The duration diagnostic
- Which duration measure is being quoted?
- What maturity does the bond have?
- What coupon pattern brings cash forward?
- What yield level is used?
- Are the cash flows fixed?
- Does the security contain call, put or conversion options?
- Is the move assumed to be parallel across the curve?
- How large is the contemplated yield change?
- Does convexity materially affect the result?
- Where are the key-rate exposures?
- Is credit-spread duration separate from government-rate duration?
- What other risks sit outside duration?
Observable mastery test
Bond A matures in fifteen years and has modified duration 9. Bond B matures in twenty years and has modified duration 7. A reader says Bond B must be more interest-rate-sensitive because it matures later.
The correction is simple: maturity alone does not determine sensitivity. Under the stated duration measures and a small parallel yield move, Bond A is expected to move more. Bond B may have a higher coupon, different yield or embedded feature that pulls its effective duration shorter.
You understand duration when the legal end date stops being a substitute for the present-value timing of the cash flows.
The World Return: why duration matters outside the bond desk
Yield-curve move → bond and liability repricing → balance-sheet gains or losses → funding and capital decisions → borrowing, hedging and investment choices → real economic consequences.
A bank, insurer, pension fund or company can be economically exposed to long-term rates even when no one is actively trading bonds. Duration turns that hidden sensitivity into something that can be measured, compared and managed.
The measure earns its place when it changes a real decision: maturity choice, asset allocation, hedge size, liquidity buffer or liability structure.
Research anchors
FINRA’s duration guide distinguishes duration from maturity and explains duration as bond-price sensitivity to rate changes. Investor.gov’s fixed-income interest-rate bulletin explains why longer maturity and lower coupon generally increase price sensitivity. The worked calculations and key-rate examples are original teaching illustrations.
Continue through Batch 034
Read The Yield Curve for the maturity map. Continue to Credit Spread vs Term Premium and Yield-Curve Inversion. Return to How Finance Works for the complete system.