 # bond question

The duration of a floating rate bond that has 6 years remaining to maturity and has semiannual cupons is closest to: (assume a flat term structure of 6%) A.0.285 B.0.500 C.6.000 D12.000

B

b)

I’ll go for B, since duration is the weighted time when cash flows are received… It can not exceed the maturity term, so D => No It can’t be equal to 6, since it is not a zero coupoin bond, so C=> No. Then , left A and B. B seems to me the best, since it is a floating rate bond, then reset each 6 months (since semiannual coupons…), I’ll take the one whci is equal to the payment frenquency which is here equal to 0.5. Correct me if I am wrong. Thanks. Malek.

either a or b. Not quite sure about the workings though.

I think it’s closest to 0.285 but only because 0 isn’t on the list. A typical floating rate note resets at the beginning of every payment period. There might be a couple of days there in which they owe you money at a fixed rate but it’s only the coupon payment.

ANS is B The duration of a floating rate bond is equal to the time until the next cupon payment takes place, as the cupon rate changes semiannually. The floating rate bond has the same duration as a pure discount bond with time to maturity equal to the time of the next cupon payment. Good job guys

Nope. Almost all FRN’s are not paid in arrears and even if they were it’s just the coupon payment. Whoever wrote this question got confused with swaps and the 0.5 isn’t even right for swaps. If you see a question like this on the exam, the duration of a floating rate note is essentially 0.

It’s a question from Schweser

So think about it a bit. Suppose the bond resets at the beginning of each 6 month period and pays you that interest at the end of the period (the longest duration possible in this question). So one day before reset, there is no interest rate risk because I will be lending money at the going rate. One day after reset, the only interest rate risk I have is that I have lent them the coupon payment for 6 months at a fixed rate, but the principal is still at a floating rate. If the coupon is 6% then only 6% of the bond value is interest rate sensitive and it’s only got duration of 6 months for one day going down to 0. That means average duration is something like 6%*1/2*1/2=0.015 which is pretty close to 0.

So Joey, you’re pretty confident on the exam CFAI will have it correct and we should answer closest to zero?

Yep.

Thanks.

With an FRN paying Libor flat, the duration of the FRN is the time until the next interest payment. If it pays a spread over Libor, that spread will tend to increase the duration quote from http://www.riskglossary.com/link/floater.htm

I will pick A, usually the duration is anywhere between 0 to 0.5 for this floating rate bond, I will find the average to be 0.25 (answer A seems to be closest)