How are bond prices quoted in the financial press related to bond yields quoted?

Question

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 1

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

$$ 100.1406 + 0.014946 = \frac{0.25}{(1+y/2)^{0.940217}} + \frac{0.25}{(1+y/2)^{1.940217}} + \frac{0.25}{(1+y/2)^{2.940217}} + \frac{100.25}{(1+y/2)^{3.940217}}.$$