# Fixed Income: Duration interpretation

What is the duration of a floating rate bond that has six years remaining to maturity and has semi-annual coupon payments. Assume a flat-term structure of 6%. Which of the following is closest to the correct duration? A) 0.500. B) 4.850. C) 6.000. D) 12.000. Your answer: D was incorrect. The correct answer was A) 0.500. The duration of a floating rate bond is equal to the time until the next coupon payment takes place. As the coupon rate changes semi-annually with the level of the interest rate, a floating rate bond has the same duration as a pure discount bond with time to maturity equal to the time to the next coupon payment of the floating rate bond. K i IGNORED THE “floating rate” hint… too bad yeah. But, has duration been calculated like this ? duration = [period for which bond is susceptible to interest rate risk] / ONE YEAR = 06/12 = 0.5 Why is one year in the denominator (as 12 months) ? Is it because earliest forms of duration measurement (like the Macaulay duration) measured it in years ? If the coupon was reset every TWO years… would the duration be 2 ? or (1/12)th if it was reset every month ?

I dont know why you marked it as 12 anyway. I thought it should have been six irrespective of anything. Duration is % change in the bond rate which is normally close to the number of years to maturity?

Darius-I Wrote: ------------------------------------------------------- > What is the duration of a floating rate bond that > has six years remaining to maturity and has > semi-annual coupon payments. Assume a flat-term > structure of 6%. Which of the following is closest > to the correct duration? > > A) 0.500. > B) 4.850. > C) 6.000. > D) 12.000. > > > > Your answer: D was incorrect. The correct answer > was A) 0.500. > > The duration of a floating rate bond is equal to > the time until the next coupon payment takes > place. As the coupon rate changes semi-annually > with the level of the interest rate, a floating > rate bond has the same duration as a pure discount > bond with time to maturity equal to the time to > the next coupon payment of the floating rate > bond. > > > K i IGNORED THE “floating rate” hint… too bad > yeah. But, > has duration been calculated like this ? > > duration = / ONE YEAR > = 06/12 = 0.5 > > Why is one year in the denominator (as 12 months) > ? > > Is it because earliest forms of duration > measurement (like the Macaulay duration) measured > it in years ? > > If the coupon was reset every TWO years… would > the duration be 2 ? > Yes > > or (1/12)th if it was reset every month ? > Yes The way to think about it is that at issuance, a FRN sells at par regardless of the maturity of the note. That means that at each reset date the FRN is “new” in that it sells at par. For the bond abve that means that 6 yrs before maturity, you can pretend you are going to sell it at 5 1/2 years for which you will get 1000 + known coupon payment. That means you own a 6-month zero which has duration 6 months = 1/2 year. As for measuring duration in years, we do that because we quote interest rates in annual terms (i.e., 6%/year) and interest rate chanages in %/yr. If we quoted them in months, we would do duration in months.

Thanks Joey thats like super clear , esp the with the “6 mth zero” analogy… hope i remember it. And Amit… i don’t know why 12… perhaps i thought like “12 compounding periods”… 6 would have been true if it were a Zero coupon bond, but not for a floater (or any coupon paying bond for that matter) and i didn’t see the ‘floater’ hint so got it horribly wrong

Thanks Joey !! Just another question. What if in the question its given, that coupon reset is done every 2 years ?