### Site Tools

tbill_yield_methodology

## dummy

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: ### Example 2 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 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. ### Example 4 https://www.treasurydirect.gov/auctions/upcoming/ → Auction Results shows Bills CMB CUSIP Issue Date High Rate Investment Rate Price per$100
42-Day Yes 912797HF7 02/29/2024 5.290% 5.397% $99.382833 42-Day Yes 912797GZ4 02/22/2024 5.280% 5.401%$99.384000
Security Term CUSIP Issue Date Maturity Date High Rate Investment Rate
42-Day 912797HF7 02/29/2024 04/11/2024 5.290% 5.397%
42-Day 912797GZ4 02/22/2024 04/04/2024 5.280% 5.401%

Combining both, we get

Security Term CMB CUSIP Issue Date Maturity Date High Rate Investment Rate Price per $100 42-Day Yes 912797HF7 02/29/2024 04/11/2024 5.290% 5.397%$99.382833
42-Day Yes 912797GZ4 02/22/2024 04/04/2024 5.280% 5.401% $99.384000 Notice how yield (Investment Rate) went down (from 5.401% to 5.397%) even though price went down (from \$99.384000 to \$99.382833) for the first entry? This is because the 'days in year' changes from 366 to 365. $ ipython

In [1]:
from tbill_yield import tbill_yield_short_maturity
tbill_yield_short_maturity(99.384000, 42, 366)
Out[1]:
5.401

In [2]:
tbill_yield_short_maturity(99.382833, 42, 365)
Out[2]:
5.397

Ref: https://github.com/KamarajuKusumanchi/market_data_processor/blob/master/src/tbills/tbill_yield.py → tbill_yield_short_maturity()