Pricing a Newly Issued Treasury Note from Its Yield
Summary
The document shows how to estimate a three year Treasury note’s price per 100 of face value from its yield and assumed coupon. It treats the note as six semiannual coupon payments plus repayment of principal at maturity. Each cash flow is discounted at the yield per half year, and the present values are added to obtain a price near 98.89 for the stated example. The worked calculation separates principal value from coupon value and lists discount factors for the coupon payments.
This provides a basic fixed coupon bond pricing illustration for the example’s stated dates, yield, and coupon. It does not explain how a when issued quote convention maps to an actual Treasury market quote, or discuss accrued interest, settlement conventions, day count, or timing adjustments. Those details can matter when matching a platform’s trade ticket, so the example should not be treated as a complete explanation of every platform’s pricing method.
Key ideas
- A fixed coupon note can be valued as the present value of its coupons and principal repayment.
- For semiannual coupons, the yield is applied per half year and the coupon amount is divided by two.
- The example discounts each of six coupon payments separately and adds the discounted principal.
- Settlement and market quoting conventions may affect platform prices beyond the simplified calculation.
Tags
Full text
# How to convert a When Issue US Treasury Note price expressed in yield terms to par value 100 terms # How to convert a When Issue US Treasury Note price expressed in yield terms to par value 100 terms Between October 3, 2024 (announcement date) and auction date October 8, 2024 the US Treasury 3 Year Note is tradeable and trade prices are expressed in yield terms. I need the formula to convert the trade price expressed in yield terms to par value 100 terms. Here is an example from on a very common trading platform for cusip: 91282CLQ2 ``` dated and issue date = 10/15/2024 trade date = 10/07/2024 settlement date = 10/15/2024 maturity date = 10/15/2027 assumed coupon rate = 3.5 trade price in yield terms = 3.895 ``` How does the VERY COMMON trading platform I entered a trade ticket for the above example arrive at a price in par value 100 terms = 98.891755 I have tried MANY fixed income formulas, none provide this price in par value 100 terms. ## Answer by Felix (score 2) https://quant.stackexchange.com/a/80924 First of all, the discount rate/yield is 3.895, which is for bond principal and interests discounted. And the coupon is 3.5 which is for interest calculation. Bond tenor is 3y, so there are 6 interests payment usually treasury bond is semi-annually interest payment. So, assume principal is 100, discount rate is 3.895, the Principal-PV is 100÷((1+(3.895%÷2))^6)= 89.07; Interest for semi-annually payment is 100×3.5%÷2 = 1.75, there are total 6 interest payments, we need discount the all 6 interest cash flows based on the 1, 2, 3,... 6 interest periods. Eg, the 3rd one interest payment, discount the 1.75, the discount factor is 1÷((1+(3.895%÷2))^3) = 0.9438, and the 3rd interest PV is 1.75 x 0.9438 = 1.65. For all the interest cash flow PV is like below, ``` (Period // Interest // Discount factor // Interest PV) 1st one (1 // 1.75 // 0.9809 // 1.72), 2nd one (2 // 1.75 // 0.9622 // 1.68), 3rd one (3 // 1.75 // 0.9438 // 1.65), 4th one (4 // 1.75 // 0.9257 // 1.62), 5th one (5 // 1.75 // 0.9081 // 1.59), 6th one (6 // 1.75 // 0.8907 // 1.56). ``` And the total interests PV is 9.82 Then, we have all the principal PV and interests PV, 89.07 + 9.82 = 98.89. Finally, we have the bond face value=100, the all the repayment cash flows PV=98.89, so the issuance price is 98.89÷100×100 = 98.891755. You could calculate it in Excel like below,
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.