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Assume I have a bond that pays 5% coupon anually on the last day of the year. The day count method used to calculate accrued interest over time is "days actual / 360". The day before the coupon payment, accrued interest would be something like (364/360) * 5% which is (obviously) more than 5%.

When I receive my coupon payment on the 31st of December, will the payment be 5% or (365/360) * 5%? In other words, does my payment equal the coupon rate * nominal or does it equal the accrued interest at that point of time?

This is, of course, only relevant for day count methods that allow accrued interest to become higher than the coupon rate.

Thanks in advance for your answers.

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Do you have an actual example of this ?

In practice I don't think you'll find bonds that have day count conventions that give an accrual factor > 1. Most Treasury bonds across the world are quoted using 30/360 or Actual/Actual so the accrual factor is always less than or equal to 1.

Conventions that give accrual factors > 1 are mostly confined to derivatives markets where the coupon is also day count adjusted so there is no anomaly.

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For most fixed-coupon bonds in most markets, the convention is that the daycount is only used to calculate the accrued coupon in the middle of the coupon period. If the complete coupon is paid at the end of the coupon period, then this is the quoted coupon.

There are exceptions to this, for example, Mexico MBONOs are fixed coupon, but if the coupon date (always a Thursday) is bumped (always backwards) because it falls on some holiday, then the prior coupon pays 1 day less, and the next coupon pays 1 day more. In addition, almost all floaters, such as Norwegian FRNs (https://227825-www.web.tornado-node.net/wp-content/uploads/2019/10/NFF_Conventions_Certificate_Bond_Markets_May_2015.pdf pg10 under point 5) and some Singaporean bonds (https://links.sgx.com/FileOpen/lta%20series%204.ashx?App=Announcement&FileID=575651) compute the coupon payment for the period based on the actual day count in the period compared to the year.

In contrast, coupons are daycounted for fixed-coupon swap legs (e.g. in interest rate swap); for most loans and loan participation notes (they are similar to bonds in most respects, but not in this).

Custom structured notes are usually bond-like rather than swap-like, but don't assume - read the documentation if in any doubt.

In your example, if your instrument is a vanilla fixed-coupon bond, then the coupon will probably be 5%. But if your instrument is a loan or LPN or a floater, then the coupon is probably daycounted, like a swap. You need a separate flag in the instrument's indicative data to indicate whether the coupon is daycounted when it is actually paid out. You can't tell from the daycount convention: 30/360 and Actual/365 instruments are usually not daycounted; Actual/360 usually are (being loans or LPNs), but a few examples are not.

If you trade the bond in the middle of the coupon period, then the accrued coupon is daycounted until the settlement date and added to the clean price to get the dirty price.

But in practice, when you trade a bond, you usually negotiate the yield, rather than the price. The price is calculated from the yield. It is not important that in your example, the proceeds include the accrued coupon that may on rare occasions shortly before the ex-date be more than coupon that will be paid. For example in Excel =YEARFRAC(DATE(2020,10,1),DATE(2020,12,31),2) is 0.25277... ("2" denotes Actual/360), which is a little more than 0.25. On the ex-date, the proceeds drop to clean price, the accrued becoming zero. The yield is smooth - only reacts to interest rates changes and news. The clean price is slightly less smooth - includes pull to par, the noise that you describe, etc. The dirty price (proceeds) is zizaggy: grows every day with the accrued, then drops the coupon.

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