Why Bond Duration Is Shorter Than Maturity
Summary
The document distinguishes a bond or fund’s maturity from its duration. Maturity is the time until the final contractual payment, while duration reflects the timing of cash flows and, in the effective-duration setting, the sensitivity of price to a change in yield. Because coupons or returned principal arrive before the final payment, duration is generally shorter than maturity; a zero-coupon bond is the limiting case in which the measures can coincide under the simplified explanation given. Thus, larger coupon payments can contribute to a wider gap, but they are not the only reason.
The answers also point to embedded repayment options and early principal return as important causes. Callable corporate bonds can be repaid before their stated term, and mortgage-backed securities can return principal early through prepayments or refinancing. Those features shorten the cash flows’ effective timing relative to legal maturity. The discussion is qualitative and cautions that definitions of “effective” maturity and duration carry caveats, so the precise comparison depends on the instrument and measurement method.
Key ideas
- Maturity measures when the final payment is due, while duration reflects the timing of payments and price sensitivity to yields.
- Interim coupon payments generally make duration shorter than maturity.
- A zero-coupon bond can have duration equal to maturity in the simplified account.
- Callable bonds and mortgage prepayments can return principal before the stated maturity.
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Full text
# Answer by demully (score 1) # Why do some mutual funds or indexes have an average effective maturity that is way larger (2-4 times larger) than the average effective duration? I would like to know if this difference occurs when the coupon payments are very large and/or if there are other reasons. ## Answer by demully (score 1) https://quant.stackexchange.com/a/51278 Hard to be too specific when there’s a lot of caveats in both “effective” measures, and their definitions, above :-) This said, there are two complimentary reasons for maturity>>duration. The first of which is that duration, as a measure of the derivative of price with respect to yield given time, will (almost) always be lower than time. That is just is just a mathematical and a logical given. However I choose to measure “duration”, any cashflows received before maturity, duration > maturity. Simples... Less trivial become callable corporate bonds, and/or MBS pre-payments. The former allow the borrower to prepay their debt earlier than term. The latter simply allow borrowers to not only repay, but refinance at fixed future long-term rates. Either shortens financial “duration”, compared to legal “maturity”. ## Answer by Preston Lui (score 1) https://quant.stackexchange.com/a/55810 Assume there is no interest rate, you loan me 1 dollar and then I give you 0.5 dollar half year and then 1 year later. The duration of my payment is 0.75 years and maturity is 1 year. Duration is the average of the time I made the payment and maturity is when I made my last payment. We can easily proof that maturity is larger or equal to duration, and equality only hold when we have a zero coupon bond ## Answer by Charles Fox (score 0) https://quant.stackexchange.com/a/48893 In some cases, a portion of the principal can be returned before maturity. Mortgage bonds are one example.
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