#Cruncher wrote: Sat Oct 18, 2025 8:54 am
p1db wrote: Fri Oct 17, 2025 10:58 pmThe 5 year real yield in the market as of today was 1.30%. The Treasury will set the coupon rate based on the prevailing market rate on Oct 22 and it will likely be in the range of 1.125% to 1.250%. The TIPS would be likely priced a shade below par to account for real yield around 1.3%.That’s not how Treasury auctions work. The coupon isn’t set the day before the auction. At an initial auction like this one, both the yield and the coupon are determined by the auction itself. Here’s a summary of the process:
- The Treasury announces an auction including the amount being offered. E.g., this one October 23rd.
- Non-competitive bidders — like you or me — submit bids for the amount we want. We are guaranteed to get this amount, but we won’t know the yield, coupon, or price until after the auction.
- Competitive bidders (usually big institutions) submit bids for an amount they want and the corresponding yield they demand for that amount. The Treasury arranges these bids in order according to yield.
- Treasury subtracts the total amount of the non-competitive bids (usually a relatively small amount) from the total offering amount.
- Adding up the amount of each competitive bid, the Treasury works up the list of yields from lowest to highest until the total amount reaches the amount being offered (net of the non-competitive amount). The yield where this occurs is called the “High Yield” and is the yield all successful competitive bidders (those who bid the High Yield or lower) and all non-competitive bidders receive. See this old post for a hypothetical example of how this works.
- The coupon or “Interest Rate” is then set at the 1/8% increment equal to or lower than the High Yield. (Unless the High Yield is lower than 0.125%, in which case the coupon is set at the minimum of 1/8%.)
- The Price everyone pays is calculated by formula based on the High Yield and the Interest Rate. Unless the High Yield is less than 0.125%, the Price will always be at par (100) or slightly lower.
Here are the actual 2014 auction results for the example from the old post referenced in step 5 above. The High Yield was 1.670%, the resulting Interest Rate 1.625%, and the resulting Price 99.784997 [*].
The process at a reopening auction is the same except the Interest Rate will be that set at the initial auction. Therefore, the Price will be above par if the High Yield comes in lower than the Interest Rate.
TIPS auctions work the same as auctions for Treasury Notes and Bonds that are not inflation-indexed, except the Price determined by the auction process above will be the “Unadjusted Price”. The auction will also report an “Adjusted Price” which is the Unadjusted Price indexed to inflation. For example, here are the results from last April’s 5-year initial auction where the “Unadjusted Price” was 99.634784 and the “Adjusted Price” was 99.855973 after multiplying by an inflation “Index Ratio” of 1.00222.
* Since there is no accrued interest at the 2014 auction of this 5-year note, the price formula is fairly simple if we use the Excel PV function, remembering that Treasury notes pay interest semi-annually:
99.784997 = -PV(1.67% / 2, 5 * 2, 1.625 / 2, 100, 0)
This is a shortcut for computing the sum of the discounted cash flow, which is the price, as shown in cell C17 below:
Code: Select all
Row Col A Col B Col C Formula in Column C
2 Face value 100
3 Years 5
4 Coupon 1.625%
5 Yield 1.670%
6 Period Cash Flow DiscountedCode: Select all
7 1 0.8125 0.805772 =B7/(1+B$5/2)^A7
8 2 0.8125 0.799099 | | |
9 3 0.8125 0.792482 | | |
10 4 0.8125 0.785920 | | |
11 5 0.8125 0.779412 | | |
12 6 0.8125 0.772957 | | |
13 7 0.8125 0.766557 | | |
14 8 0.8125 0.760209 | | |
15 9 0.8125 0.753914 v v v
16 10 100.8125 92.768676 =B16/(1+B$5/2)^A16
---------
17 Sum 99.784997 =SUM(C7:C16)
Good explanation, thanks #Cruncher
