How Daily Treasury Bill Rates Differ from Constant-Maturity Yields
Summary
The discussion distinguishes daily rates for recently auctioned Treasury bills from constant-maturity rates. A bill labeled by its original term has less time remaining after issuance, so its quoted market rate reflects the security’s actual remaining maturity rather than a newly issued bill at that exact tenor. The recently auctioned bill is described as on-the-run and typically more actively traded; older bills with comparable remaining terms are off-the-run.
The replies explain that the Treasury reports average bid prices for on-the-run securities, while constant-maturity rates are separate estimates associated with standardized maturities. One answer suggests that rates for a target remaining term could be inferred from securities originally issued at different terms, but its arithmetic and reporting details are presented informally. The discussion does not provide a definitive methodology for the specific Federal Reserve series or fully document its data sources and calculation rules.
Key ideas
- A Treasury bill’s remaining maturity declines continuously after it is issued.
- Daily bill rates can refer to the current on-the-run issue, whose actual remaining term is shorter than its original term.
- Older off-the-run bills may have similar remaining maturities but are less actively traded.
- Constant-maturity rates are reported separately from rates on recently auctioned bills.
- The discussion leaves the exact series methodology and data collection details unresolved.
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Full text
# Why do we have daily series of T-bill yields? # Why do we have daily series of T-bill yields? I understand that each week the US Treasury issues new T-bills at different maturities (1-month, 3-months, 1-year, etc). As far as I understand, this issuance happens every Tuesday. After the auction, agents trade these securities in the secondary market. However, for example, in the day following issuance the 1-month security issued on Tuesday is not a 1-month security anymore. It's a 29-day security. Similarly, the 3-month security issued a month ago is now a 2-month security. The Federal Reserve publishes the H.15 report everyday: see it here. They list, every day, the secondary market rates for different maturities. I am puzzled by how they make this computation since, in any day that is not a Tuesday, there is no US Government security being issued. The 4-week security from two days ago cannot be traded as a 4-week security from the point of view of today and so on. I cannot find the documentation on how the Fed (or by that matter, Yahoo Finance) collects this data. Only once a week they should be able to observe rates on securities that really are 4-week securities, or 3-month ones, etc. I understand how the "Constant Maturity Rates" are computed, but they are a different beast and are reported alongside the t-bill rates on the H.15 report. Those make a lot of sense to me since we see many points of the yield curve every day and we interpolate across them. Importantly, these points move in time. Since we do the interpolation, I can see why we can compute the Constant Maturity Rates for any maturity, and we can do it every day. Since everyone uses this in practice, I am clearly missing something. Is there any reference where I can understand how the measurements are made? Are the t-bill rates also interpolations? What really do I see when I go to Bloomberg and check the rates for different maturities (United States Rates & Bonds - Bloomberg)? Are those rates for the last batch issued? ## Answer by user20429 (score 0, accepted) https://quant.stackexchange.com/a/68858 Not familiar with specific reports like H.15, but as a matter of generality: let's say you are looking at 4 week maturities, and it's Thursday. You could look at the 4 week bill issued two days ago, the 13 week bill issued 65 days (9 weeks and 2 days) ago, and the 52 week bill from 338 days (48 weeks and 2 days) ago. They all mature in 26 days (if I did the math right). The bill from two days ago is still a relatively new issue, it is still actively traded, and therefore its traded price is the best reflection of market conditions for that maturity. That bill is "on the run" - the others are "off the run". The Treasury reports average bid prices for on-the-run bills, notes and bonds for trades of notional value of at least X dollars (it's been a while since I knew such things, but I think X was a million). The remaining term is, in fact, less than 4 weeks; this is stated clearly even in the brief explanation on the Treasury web site. They talk of the most recently auctioned securities - what in jargon is known as on-the-run. And, as you noted, these reports are quite different from the constant maturity rate calculations. ## Answer by JoshK (score 3) https://quant.stackexchange.com/a/68716 The Fed is showing you the current bills on that page. Yes, the 1month will be more like 28 days at that point. That's why they show the cmt's separately.
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