Checking Treasury Bond Prices from Yield and Accrued Interest

Summary

The post asks how to convert a US Treasury bond yield into a price by discounting the remaining coupon and principal cash flows. The author reports a calculated value that differs from a quoted market price and tests alternative day-count and compounding conventions, as well as an accrued-interest adjustment. The answer says the quoted yield and price in the example appear inconsistent: the stated yield implies a price close to the calculation, rather than the displayed quote.

As a basic check, the reply notes that a yield modestly above the coupon should put the bond price below par by roughly the present value of that yield difference over the remaining term. It describes Act/365 day count followed by subtraction of accrued interest as the basic method, while acknowledging that other conventions and details also matter. The exchange is an illustrative troubleshooting discussion, not a complete treatment of Treasury settlement, coupon schedules, or pricing conventions.

Key ideas

• Bond price is found by discounting remaining coupons and principal using the yield and applicable conventions.
• A yield above the coupon generally implies a price below par.
• The answer identifies the displayed market quote as likely inconsistent with the yield in the example.
• Act/365 day count and an accrued-interest adjustment are given as a basic approach.
• Additional pricing nuances are acknowledged but not detailed.

Tags

# US Treasury: Calculating Price from Yield


# US Treasury: Calculating Price from Yield












I'm trying to get the basics of bonds by going from yield to price (and vice-versa hopefully). What I want to do is from publicly available source go from the treasury bond yield to the price. So for example using MarketWatch I see:

So I assume the remaining coupons are paid 4 and paid at the end of April and October and calculate the present value of the cashflows using:

From what I obtain a table like this:

Now if I sum all the values I find that the price is 99.89, not really close to the 99 8/32 (99.25) shown by marketwatch. I have tried also changing the conventions to 365 and yearly compounding, but doesn't improve much. I've also tried to account for the accrued interest (0.205) and substract it to see if it matches the clean price, but also doesn't work (result is 99.68).

Could you please help me understand what I'm doing wrong here?

Thanks!

## Answer by dm63 (score 1, accepted)

https://quant.stackexchange.com/a/73825

There is something wrong with that screenshot. The price that corresponds to a 4.475 yield should be 99-26 which is close to the value you calculated. Mentally you can check this because the yield is 10bp higher than the coupon, so the price should be the 100- the PV of 10bp for 2 yrs so about 99.80.

Fwiw The correct method is to use a Act/365 day count and then subtract accrued interest. There are a lot of other nuances but that is basically correct.

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