# Duration of floating/fixed interest rate

Why do floating rate bonds have little duration?

coupon resets every 6 months for a 6 month bond - so the bond now sells at its par value.

so the max duration of the bond will be the time between interest rate resets

To be accurate: floating-rate bonds have very low effective duration.

Their price doesn’t change much because the coupon resets periodically to a rate based on market interest rates.

Assuming that the coupon is the same as the bond’s YTM.

Ok then but floating-rate bonds can also have long maturity right?

They can have any maturity the issuer wants.

It can be shown that a floating rate note is effectively a short term bullet bond that is rolled at every reset date. The duration of a bullet bond is its maturity. The only maturity that matters is the one for the first bullet since for all the subsequent ones, the coupon will reset at the prevailing rate. There is thus no rate sensitivity for these. So at the onset, the floating rate bond has a duration equivalent to the time until the next payment.

Won’t they both be equal on the reset date? Since coupons are set to market interest rates.

It depends on the bond. Assuming that LIBOR is the reference rate, some floating-rate bonds reset to LIBOR, some to LIBOR + 50bp, some to LIBOR + 100bp, and so on.

Furthermore, the bond’s YTM isn’t necessarily LIBOR, or LIBOR + 50bp, or LIBOR + 100bp. The market will decide how risky the bond is and set the YTM accordingly.

Hi,

Why floating rate bonds have little duration?

You know that duration measures the change in price for a 1% change in the yield of the bond. Forget for a second about mathematics, derivations etc and think only practicallly. If you lend for 10 years at 7% and the next day the 10 year rate moved to 9% you are very unhappy. Because giving the loan today would secure a 9% instead of the 7%. so you have LOCKED yourself for 10 years with that 7% rate so your opportunity cost is 2% for 10 LONG YEARS.

now imagine the same loan will reset every year. This means that at the end of the year, whatever the new 1 year rate is, you will get it. So imagine rates went up the next day like earlier, you are also unhappy. But you have only locked yourself with that rate for ONE year instead of 10 because at the end of the year your loan will pay you the now higher rate. So that loan will loose value less than the one above, which had an opportunity cost for ten long years.

practically you can think like the above.

mathematically of course, the higher rate of 9 instead of 7% will discount EVERY CASH FLOW of the 10 year loan so the value drops significantly. While for the floating rate loan, the Cash Flows are NOW HIGHER since they are based on the now higher rate. SO even if the disocunt rate increased, the INCREASE in the cash flows mean the loan would loose much less value.

If you like a pure technical explanation with duration let me know.

hope that helps.

cheers

4 Likes

Sorry for rehashing an old thread.

I appreciate your eplanation - makes sense to me. I would however like to ask someone to please briefly tell me how exactly are floating rate bonds priced and how their duration is calculated.

Am I correct in saying that to price a flaoter, one can treat it as if it were a fixed-rate bond which will “mature” on the next coupon date at with a known coupon (that being floating rate already locked in + spread). I read about this method somewhere online before - bot sure if it’s correct.

Example: next coupon in 0,5 years, maturity in 4 years, semiannual coupon, LIBOR at last coupon was 1,5%, spread is 1%. At next coupon it “matures”, we receive 100 + (2,5 / 2), and we can discount this value by (1 + Rfr)^0,5. Is this a correct valuation of the floater? If not, please correct me!

Now, how about duration? If the bond “matures” in 0,5 years than the effective duration will be approx. 0,5. What about Macauley and Modified duration? Only one cashflow’s value is certain (while all the remaining ones are not - we don’t know future LIBOR rates). Not sure how to find Macauley and Modified.

Any help would be appreciated, thanks!

amazing explaination

thanks - very good explanation