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Example 1
Example: 912797JA6 is a tbill with a maturity of 28 days. It was sold for $99.5905 on 2023-12-21. What is the yield?
Ans: For tbills of not more than half-year maturity, the yield is calculated as
i = ((100 - P)/P) * (y/r)
where y is the days in year, r is the days to maturity.
In [1]: def tbill_yield_short_maturity(P, r, y): i = ((100 - P) / P) * (y / r) i = round(i * 100, 3) return i In [2]: tbill_yield_short_maturity(99.5905, 28, 366) Out[2]: 5.375
so the yield is 5.375%
Ref:
- https://www.treasurydirect.gov/instit/annceresult/press/preanre/2004/ofcalc6decbill.pdf shows examples to compute price, yield and rate for tbills.
- rate == discount rate?
- yield == coupon equivalent yield?
- pg-2 shows how to compute the yield for bills of not more than one half-year to maturity.
- https://www.treasurydirect.gov/auctions/announcements-data-results/announcement-results-press-releases/auction-results/ gives “today's auction results”
- https://www.treasurydirect.gov/instit/annceresult/press/preanre/2023/R_20231221_1.pdf shows that it is 28-day tbill, was sold on 2023-12-21 at a price of $99.590500 for an “Investment Rate” of 5.375%. This “Investment Rate” is same as the yield above.
Example 2
On https://www.treasurydirect.gov/auctions/announcements-data-results/ showed
Security Term | CUSIP | Issue Date | Maturity Date | High Rate | Investment Rate |
---|---|---|---|---|---|
4-Week | 912797JB4 | 01/02/2024 | 01/30/2024 | 5.325% | 5.436% |
It was bought on 12/28/2023, settlement date = 1/2/2024 for a price of 99.585833. The yield on it is
In [1]: from tbill_yield import tbill_yield_short_maturity tbill_yield_short_maturity(99.585833, 28, 366) Out[1]: 5.436
The 5.436 matches with the Investment Rate in the table.
So 'Issue Date' in the table is the settlement date.
Example 3
On https://www.treasurydirect.gov/auctions/announcements-data-results/ showed
Security Term | CUSIP | Issue Date | Maturity Date | High Rate | Investment Rate |
---|---|---|---|---|---|
4-Week | 912797JC2 | 01/09/2024 | 02/06/2024 | 5.290% | 5.400% |
It was bought on 01/04/2024, settlement date = 1/9/2024 for a price of 99.588556. The yield on it is
In [2]: from tbill_yield import tbill_yield_short_maturity tbill_yield_short_maturity(99.588556, 28, 366) Out[2]: 5.4
The precision in the price matters. If you only have 4 significant digits after the decimal, the result will not match with the 'Investment Rate'
In [3]: tbill_yield_short_maturity(99.5885, 28, 366) Out[3]: 5.401
Conclusion: Price should have 6 significant digits after the decimal.