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--- tbill_yield_methodology [2023/12/29 19:12] – raju
+++ tbill_yield_methodology [2024/02/27 23:03] (current) – [Example 4] raju
@@ Line 1: / Line 1: @@
-==== dummy ====
+===== dummy =====
+==== 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?
@@ Line 10: / Line 11: @@
 </code>
-where y is 366, r is the days to maturity.
+where y is the days in year, r is the days to maturity.
 <code>
-In [25]:
+In [1]:
-def tbill_yield(P, r):
+def tbill_yield_short_maturity(P, r, y):
-    y = 366
+    i = ((100 - P) / P) * (y / r)
-    i = ((100 - P) / P) * (y/r)
+    i = round(i * 100, 3)
-    i = round(i*100, 3)
+    return i
-    return(i)
-In [26]:
+In [2]:
-tbill_yield(99.5905, 28)
+tbill_yield_short_maturity(99.5905, 28, 366)
-Out[26]:
+Out[2]:
 .375
 </code>
@@ Line 37: / Line 38: @@
-Example 2:
+==== 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
+<code>
+In [1]:
+from tbill_yield import tbill_yield_short_maturity
+tbill_yield_short_maturity(99.585833, 28, 366)
+Out[1]:
+.436
+</code>
+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
+<code>
+In [2]:
+from tbill_yield import tbill_yield_short_maturity
+tbill_yield_short_maturity(99.588556, 28, 366)
+Out[2]:
+.4
+</code>
+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'
+<code>
+In [3]:
+tbill_yield_short_maturity(99.5885, 28, 366)
+Out[3]:
+.401
+</code>
+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 |
+https://www.treasurydirect.gov/auctions/announcements-data-results/ -> CMBs tab shows
+^ 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% | $99.384000 |
+Notice how yield (Investment Rate) went down (from 5.401% to 5.397%) even though price went down (from \$99.384000 to \$99.382833) for the first entry? This is because the 'days in year' changes from 366 to 365.
+<code>
+$ ipython
+In [1]:
+from tbill_yield import tbill_yield_short_maturity
+tbill_yield_short_maturity(99.384000, 42, 366)
+Out[1]:
+.401
+In [2]:
+tbill_yield_short_maturity(99.382833, 42, 365)
+Out[2]:
+.397
+</code>
+Ref: https://github.com/KamarajuKusumanchi/market_data_processor/blob/master/src/tbills/tbill_yield.py -> tbill_yield_short_maturity()