Accrued Interest on Treasury Bonds and Settlement Dates
Summary
The document describes how accrued interest is determined for a Treasury bond sale or purchase. Accrued interest compensates the seller for coupon interest earned since the previous coupon date, even though the buyer will receive the upcoming coupon. It gives the calculation as the accrued-interest fraction multiplied by the annual coupon rate and divided by coupon frequency. Under Actual/Actual, the fraction is the elapsed days from the previous coupon date to settlement divided by the days in the coupon period.
For ordinary Treasury trades, the answer identifies settlement as the next business day after the trade; when-issued trades settle on the issue date. Accrued interest is zero on coupon dates and generally positive on other dates after interest begins accruing, including before the first coupon if settlement occurs after accrual starts. The explanation is specific to US Treasury conventions and does not cover other bond types, day-count rules, or market-specific exceptions beyond the stated when-issued case.
Key ideas
- Accrued interest reflects coupon interest earned between the previous coupon date and settlement.
- Under Actual/Actual, the accrued fraction is the elapsed portion of the coupon period.
- Treasury trades generally settle on the next business day, while when-issued trades settle on the issue date.
- Accrued interest is zero on coupon dates and can be positive before the first coupon if accrual has begun.
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Full text
# Understanding how to calculate Accrued Interest of Bonds
# Understanding how to calculate Accrued Interest of Bonds
When calculating the accrued Interest of Treasury Bonds, how does one set the settlement date? And, is it possible for certain bonds that there are no coupon payments before the settlement date and hence there will be no accrued interest (i.e. the case when the bond is bought before the first coupon payment and after the issue date)?
Although I asked a very similar question here, I am still unclear about these particular details.
Thank You
## Answer by Helin (score 1, accepted)
https://quant.stackexchange.com/a/19197
Conceptually, let's say you sell a bond three months after the previous coupon date. Because you've sold the bond, you won't receive the next coupon payment, which happens in three months' time. But you deserve half of the next coupon payment, because you've held onto it for half the coupon period. That's what accrued interest is.
Accrued interest, in general, is calculated as $$\text{AI} = \text{AIF} \times \frac{c}{f}, $$ where AIF is the accrued interest fraction, and $c$ is the annual coupon rate, and $f$ is the coupon frequency.
AIF is simply the day count fraction between the previous coupon date and the settlement date. For US Treasuries, which follows the Actual/Actual convention, it is calculated as $$\text{AIF} = \frac{\text{settlement date} - \text{previous coupon date}}{\text{next coupon date} - \text{previous coupon date}}.$$
As mentioned, US Treasuries follows $T+1$ settlement convention, which means the settlement date is always the next business day following the trade date. More specifically, if you bought the Treasury today, then it settles tomorrow. (An exception is made for Treasuries trading in the when-issued market, in which case the settlement date is the issue date.)
Accrued interest is zero on all coupon dates. On any other date, it would be non-zero. So if a bond settlement before the first coupon date and after the first interest accrual date, it would have a non-zero AI.
P.S. I think the preference is for you to edit your old question, and we can update the answers accordingly (the questions are so similar...).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.