Mapping Treasury Yield Curve Tenors to Calendar Dates
Summary
The document explains how to interpret Treasury yield curve tenors when assigning calendar dates before fitting a curve with cubic splines. Its answer recommends advancing by calendar months for month-based terms and by calendar years for year-based terms, rather than converting every tenor into a fixed number of days. The examples map a three-month term from June 1, 2015 to September 1, 2015, and a thirty-year term to June 1, 2045.
The explanation relates annual increments to Treasury note and bond issuance conventions. It also notes that a three-month Treasury bill is more closely represented by a thirteen-week bill, so counting weeks may be appropriate when estimating an actual bill maturity date. The guidance addresses tenor-to-date mapping, not the full construction or interpolation of a yield curve; instrument-specific maturity conventions may matter for other applications.
Key ideas
- Represent month-based curve terms by advancing the calendar month count.
- Represent year-based terms by advancing the calendar year count.
- For a three-month Treasury bill maturity, a thirteen-week convention may be more appropriate than a calendar-month approximation.
- The mapping guidance supports date assignment before curve fitting but does not explain spline construction.
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Full text
# How do I interpret yield curve data points given by the US Treasury? # How do I interpret yield curve data points given by the US Treasury? Given the Daily US Treasury Yield Curve Rates for a specific date I will fit the curve with the cubic spline method, but first I need to know how to use the data points given by the Treasury. For example, if today is June 1st, 2015, and the 3 months rate is 0.8%, does this mean that I need to simply add 3 to today's month (resulting in September 1st, 2015) or I need to add 90 days to today's date (resulting in August 30th, 2015) ? Similarly with the 30 years rate, should I add 365 x 30 days, should I consider leap years, or simply add 30 to the year (following the example above, it will result in June 1st, 2045) ? ## Answer by aparkerlue (score 1) https://quant.stackexchange.com/a/18167 Your question is really about how to map between term-to-maturity and calendar dates, which can be a tricky problem since the number of days in a month varies by month. In short, you should increment using months if your incremental term is in months, and increment using years if your incremental term is in years. In your examples, three months (or 0.25 years) forward from 2015-06-01 is 2015-09-01, and 30 years forward from 2015-06-01 is 2045-06-01. In the case of annual increments, this is consistent with Treasury note and bond issuance conventions. In the case of monthly increments, this is consistent with common sense. As far as Treasury securities are concerned, the closest "3-month" securities are 13-week T-bills, so you might consider counting by weeks if you're looking for a T-bill maturity date. These pages from the TreasuryDirect website might help: - Treasury Bill Rates & Terms - Treasury Note Rates & Terms
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