Duration is quoted in years. Maturity is quoted in years. A five-year zero-coupon bond has a Macaulay duration of exactly five years. It is easy to conclude that the two are versions of one idea.
They are not. Maturity tells you when the bond ends. Duration tells you how much the bond's price moves when yields change. They share a unit and are related in size, but they answer different questions.
Fixed Income questions are built around that overlap. Several of the most dependable distractors in the topic exist only because candidates treat duration and maturity as interchangeable.
Two Definitions That Answer Different Questions
Maturity is the time remaining until the final principal payment. It is a contractual fact. It does not depend on the market, the yield or the coupon.
Duration measures a bond's price sensitivity to changes in yield. It depends on the whole pattern of cash flows and on the yield used to discount them. Two bonds with identical maturity can have very different durations.
In practice, maturity answers "when is the principal repaid?" Duration answers "how much will this position gain or lose if rates move?" A portfolio manager hedging interest-rate risk works with duration, because maturity alone does not describe the exposure.
Maturity is a date. Duration is a sensitivity. Only one of them measures interest-rate risk.
Macaulay vs Modified Duration: What Level I Expects
Macaulay duration is the weighted average time until the bond's cash flows are received. Each weight is the present value of that cash flow as a share of the bond's price. This is where the "years" come from, and it is the bridge between the two concepts.
Modified duration converts that timing measure into a price sensitivity:
Modified duration = Macaulay duration / (1 + r)
Here r is the yield per period. For an annual-pay bond it is the annual yield. If Macaulay duration is measured in semiannual periods, divide by (1 + yield/2), then divide by 2 to express the result in years. Modified duration then gives the approximate percentage price change for a change in yield:
%ΔP ≈ -Modified duration × Δyield
You are expected to know both, and to know which one a question needs. Macaulay duration describes timing. Modified duration estimates price change.
Level I also introduces effective duration for bonds with embedded options, whose cash flows change as yields move, and money duration, which states the same sensitivity in currency rather than percent. The formulas sit together on the Level I formula sheets.
What Moves Duration: Coupon, Maturity and Yield
Three drivers matter at Level I, each holding the others constant:
- Coupon: a higher coupon means lower duration. More of the bond's value arrives early, so the weighted average time falls.
- Maturity: a longer maturity usually means higher duration, because the principal payment moves further out. The relationship is not proportional, and for some long-dated bonds trading at a deep discount it can even reverse.
- Yield: a higher yield means lower duration. Distant cash flows are discounted more heavily, so they carry less weight in the average.
Illustrative figures make the point. Take a five-year bond with a 5% annual coupon, priced at a 5% yield: its Macaulay duration is about 4.55 years.
Raise the coupon to 10% and it falls to about 4.25. Extend the maturity to ten years and it rises to about 8.11, not ten. Raise the yield on the original bond to 8% and it slips to about 4.51.
Doubling the maturity did not double the duration. This is where candidates make mistakes: maturity is an input to duration, not a proxy for it.
Worked Example: Estimating a Price Change
Use the same illustrative bond: five-year maturity, 5% annual coupon, priced at par (100) with a 5% yield to maturity.
Macaulay duration is about 4.546 years. Modified duration is 4.546 / 1.05, about 4.329.
If the yield rises by 100 basis points to 6%, the estimate is %ΔP ≈ -4.329 × 0.01 = -4.33%. That puts the estimated price at about 95.67.
Repricing the bond at 6% gives an actual price of about 95.79, a fall of about 4.21%. The estimate overstates the loss. For a 100 basis point fall in yield, the estimate is +4.33%, while the actual gain is about 4.45%.
The gap is convexity. Duration is a linear approximation of a curved price-yield relationship, so for an option-free bond it overstates losses and understates gains. For small yield changes the estimate is close; for large ones, you add the convexity adjustment.
Now the trap. A candidate who uses the maturity, 5, as the sensitivity estimates a 5% loss. That is exactly the kind of number a distractor is built from.
The Classic Exam Traps
The zero-coupon equality
For a zero-coupon bond, Macaulay duration equals maturity, because there is only one cash flow. Modified duration does not. A five-year zero priced at a 5% yield has a modified duration of 5 / 1.05, about 4.76. If the question asks for price sensitivity, "five" is wrong.
The high-coupon intuition
A higher coupon can feel riskier because the bond "pays more". For interest-rate risk, the opposite holds. Higher coupons pull the weighted average time forward and reduce duration. Do not confuse income with sensitivity.
The "years" confusion
Macaulay duration is a time measure in years. Modified duration is read as the approximate percentage price change for a 1 percentage point change in yield. A modified duration of 7 does not mean anything happens in seven years: it means a 100 basis point rise in yield cuts the price by roughly 7%.
A floating-rate note shows how far the concepts can separate. Its maturity can be long, but because the coupon resets toward market rates, its duration is short. Long maturity, low sensitivity.
What to Take Into the Exam
This is not about memorization. It is about asking, every time, whether the question wants timing or sensitivity. If it asks when cash flows arrive, it wants maturity or Macaulay duration. If it asks how the price moves, it wants modified duration, plus convexity for large yield changes.
The habit is worth building under exam conditions: the Wall Street Uni question bank includes Fixed Income practice questions with worked explanations, organized by topic.