Treasury Bond Yields, Settlement Dates, and Accrued Interest
Summary
The document explains why a bond’s quoted yield may not reproduce its published price when cash flows are discounted from the wrong date or the quoted price is treated as the full settlement value. For US Treasuries, the calculation should use the settlement date, typically the next business day, and account for whether the bond has been issued and when settlement occurs. These details affect the timing of discounted cash flows.
Treasury prices are quoted clean, excluding accrued interest. When settlement falls between coupon dates, add accrued interest to the quoted price to obtain the dirty price that corresponds to the present value of the remaining payments. The worked example calculates accrued interest from the elapsed portion of the coupon period, adds it to the quoted price, and solves for yield using semiannual coupon discounting with fractional periods. The quoted yield is therefore linked to settlement conventions and coupon timing, not simply to cash flows discounted from the observation date. The example is specific to the stated Treasury conventions and dates.
Key ideas
- Yield calculations should discount cash flows from the bond’s settlement date.
- US Treasury quoted prices are clean prices that exclude accrued interest.
- Between coupon dates, add accrued interest to the clean price to obtain the dirty settlement value.
- Coupon cash flows can be discounted using semiannual compounding and fractional coupon periods.
- Issue timing and the next good business day can affect the settlement date used in the calculation.
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Full text
# How are bond prices quoted in the financial press related to bond yields quoted?
# How are bond prices quoted in the financial press related to bond yields quoted?
For example in the FT this month a 10 year US bond with redemption date 05/24, coupon 2.50 has a bid price of 99.52 and a bid yield of 2.56.
Can one calculate the bid yield from the bid price, red date and coupon?
I thought that the bid yield should be the rate y at which if you discount the cash flows of (6 months, 1.25), (1 year, 1.25), ........., (10 years,101.25) at the rate of y and sum these up you should get the bid price. But I dont get this. If i take the quoted bid yield of 2.56 - I get a bond price of 99.33.
For a shorter example - a 2 year US bond with red date of 06/16, coupon 0.50 has bid price 100.02 and bid yield of 0.49.
Can someone help?
## Answer by Helin (score 1)
https://quant.stackexchange.com/a/14341
A few things you'll need to check:
- What's your assumed settlement date? Typically, US Treasuries settle T+1, so you should discount cash flows back to the next good business day, not back to today. Furthermore, has the bond actually been issued? If the bond just got auctioned, it may not have settled. In this case, the settlement date should be the issue date (which could be 1-2 weeks away depending on the term).
- Is the settlement date a coupon date? If not, then the sum of discounted cash flows is equal to "quoted price + accrued interest." The published quotes for USTs are always clean price (i.e., excluding accrued interest).
As an example, today (August 8, 2014), the on-the-run 2-year note is the 0.5s of 31-July-2016. The settlement date is August 11, 2014 (next Monday). The quoted price is 100.1406.
The accrued interest is 0.014946 ( =(8/11/2014 – 7/31/2014) / (1/31/2015 – 7/31/2014) * 0.5 / 2). Therefore, the dirty price is $100.1406 + 0.014946 = 100.1555457$. The yield to maturity is 0.4282479%, and can be solved from
$$ 100.1406 + 0.014946 = \frac{0.25}{(1+y/2)^{0.940217}} + \frac{0.25}{(1+y/2)^{1.940217}} + \frac{0.25}{(1+y/2)^{2.940217}} + \frac{100.25}{(1+y/2)^{3.940217}}.$$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.