could someone please simplify, “The coupon rate for the next period is set using the current reference rate for the reset period, and the payment at the end of the period is based on this rate. For this reason, we say interest is paid in arrears”
You just issued a USD 1,000 par, semiannual pay, 10-year floating rate note that pays USD LIBOR. Today’s 6-month USD LIBOR rate is, say, 0.6%.
The payment six months from today will be 0.6% times USD 1,000, or USD 6.00.
Six months from today, the 6-month USD LIBOR rate is, say, 0.75%.
The payment 12 months from today will be USD 7.50.
OH! That was very helpful! Thank you so much!
My pleasure.
Btw, tell me if I interpreted this right. The interest is said to be paid in arrears because, in the 0-6 month period the LIBOR was 0.6 percent, so the coupon for the period got set at $6. But it is during that 0-6 month period itself, the LIBOR increased to 0.75 and hence $1.5 that was remaining was paid in the 6-12 month period as $6+$1.5. But shouldn’t it have been $7.5 anyway? How was the arrear or the past phase paid then?
The rate is set at the beginning of each period. What happens to the rate between payment dates doesn’t matter.
For example, suppose that a USD 1,000 par, floating rate bond pays 6-month USD LIBOR on 15 January and 15 July. Suppose that these are the 6-month USD LIBOR rates on various dates:
- 15 Jan 2021: 0.50%
- 5 Mar 2021: 0.75%
- 17 June 2021: 0.40%
- 15 Jul 2021: 0.65%
- 22 Sep 2021: 0.80%
- 11 Nov 2021: 0.75%
- 14 Dec 2021: 0.35%
- 15 Jan 2022: 0.45%
The coupon rate for the payment on 15 July 2021 will be set on 21 January 2021: 0.50%. The coupon payment on 15 July 2021 will be 0.50% × USD 1,000 = USD 5.00.
The coupon rate for the payment on 15 January 2022 will be set on 21 July 2021: 0.65%. The coupon payment on 15 January 2022 will be 0.65% × USD 1,000 = USD 6.50.
The coupon rate for the payment on 15 July 2022 will be set on 21 January 2022: 0.45%. The coupon payment on 15 July 2022 will be 0.45% × USD 1,000 = USD 4.50.
The rates on any dates other than 15 January and 15 July have no effect on the coupon payments. The coupon rates are set only on 15 January (for the payment the following July) and on 15 July (for the payment the following January).
I seriously appreciate the efforts you put in to answer that. Once again, thanks a lot! This helped.
My pleasure.
Glad to hear that it did some good.