Why Floating-Rate Bond Duration Is Approximately Time to Reset
Summary
The document explains why duration remains meaningful for a floating-rate bond even though later coupon amounts are not yet known. Under the setup described, the bond price is based on the next coupon and face value discounted to the next payment date. Differentiating that price with respect to the relevant risk-free rate shows that the immediate price sensitivity depends on the time until that payment.
The answers interpret this as duration being approximately the time to the next coupon or reset: later payments are reset using then-prevailing rates, so they contribute little current rate sensitivity. One answer also gives a finite-rate-change expression, distinguishing it from the infinitesimal derivative. The explanation is simplified and focuses on a single next payment and the relevant rate; actual bond terms, spreads, reset conventions, and market conditions can affect measured sensitivity.
Key ideas
- Floating-rate bond cash flows after the next reset depend on interest rates prevailing at that time.
- The next coupon payment is the main source of current interest-rate duration in the simplified setup.
- The price derivative implies sensitivity proportional to the time until the next payment.
- The duration approximation describes local rate sensitivity; finite yield changes can produce a different percentage price move.
- Longer-term fixed cash flows generally carry more duration exposure than frequently resetting floating-rate cash flows.
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Full text
# Duration of a floating rate bond
# Duration of a floating rate bond
It is known that the price $p_t$ of a floating rate bond can be calculated discounting $(L+k)$ the sum of the next coupon payment $k$ and the face value $L$ at the relevant risk-free rate.
Hence, with continuous compounding the price of such a bond would be $$p_t=(L+k)e^{-rt}$$ where $r$ is the annual continuous risk-free rate for the period of time that divides us from the first payment and $t$ is its length.
If we want to know how the price changes when $r$ changes we just derive the price to get $$\frac{\partial p_t}{\partial r}=-p_t\cdot t$$
So, does it make sense talking about duration of a floating rate bond? Isn't it enough to refer to the derivative computed above? How could the notion of duration be applied in such a situation where we do not know future cash flows?
Thank you in advance.
## Answer by Alex C (score 3)
https://quant.stackexchange.com/a/23282
Yes. the duration of a floating rate bond is the time t until the next coupon payment, as your equation shows. The payments that come after are not known yet and will be determined based on interest rates then prevailing, so they carry no duration risk.
In general floating rate bonds are what people buy when they want the smallest duration possible. Long term ZCB are what people buy when they want the longest possible duration.
## Answer by Miehleketo Ndlovu (score 0)
https://quant.stackexchange.com/a/71761
Yes it does make sense.
As your equation correctly point out that only the next coupon is exposed to the yield curve changes, the bond price should be sensitive to the yield corresponding only to the next coupon.
The duration of the bond will be approximately $-t = \frac{-p_t \cdot t}{p_t}$.
Approximately because your derived equation gives a change in price for an infinitesimal yield change. A floating rate bond's duration is given by $e^{-\delta r \cdot t}-1$.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.