tbill_yield_methodology
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tbill_yield_methodology [2024/01/05 16:26] – raju | tbill_yield_methodology [2024/02/27 23:03] (current) – [Example 4] raju | ||
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- | ==== 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? | 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: | ||
</ | </ | ||
- | where y is 366, r is the days to maturity. | + | where y is the days in year, r is the days to maturity. |
< | < | ||
- | 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, | + | 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]: |
5.375 | 5.375 | ||
</ | </ | ||
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- | Example 2: | + | ==== Example 2 ==== |
On https:// | On https:// | ||
Line 47: | Line 48: | ||
< | < | ||
In [1]: | In [1]: | ||
- | from tbill_yield import | + | from tbill_yield import |
- | tbill_yield(99.585833, 28) | + | tbill_yield_short_maturity(99.585833, 28, 366) |
Out[1]: | Out[1]: | ||
5.436 | 5.436 | ||
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So 'Issue Date' in the table is the settlement date. | So 'Issue Date' in the table is the settlement date. | ||
- | Example 3: | + | ==== Example 3 ==== |
On https:// | On https:// | ||
^ Security Term ^ CUSIP ^ Issue Date ^ Maturity Date ^ High Rate ^ Investment Rate ^ | ^ Security Term ^ CUSIP ^ Issue Date ^ Maturity Date ^ High Rate ^ Investment Rate ^ | ||
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< | < | ||
- | In [1]: | + | In [2]: |
- | from tbill_yield import | + | from tbill_yield import |
- | tbill_yield(99.588556, 28) | + | tbill_yield_short_maturity(99.588556, 28, 366) |
- | Out[1]: | + | Out[2]: |
5.4 | 5.4 | ||
</ | </ | ||
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The precision in the price matters. If you only have 4 significant digits after the decimal, the result will not match with the ' | The precision in the price matters. If you only have 4 significant digits after the decimal, the result will not match with the ' | ||
< | < | ||
- | In [4]: | + | In [3]: |
- | tbill_yield(99.5885, 28) | + | tbill_yield_short_maturity(99.5885, 28, 366) |
- | Out[4]: | + | Out[3]: |
5.401 | 5.401 | ||
</ | </ | ||
Conclusion: Price should have 6 significant digits after the decimal. | Conclusion: Price should have 6 significant digits after the decimal. | ||
+ | |||
+ | ==== Example 4 ==== | ||
+ | https:// | ||
+ | |||
+ | ^ 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:// | ||
+ | |||
+ | ^ 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, | ||
+ | Out[1]: | ||
+ | 5.401 | ||
+ | |||
+ | In [2]: | ||
+ | tbill_yield_short_maturity(99.382833, | ||
+ | Out[2]: | ||
+ | 5.397 | ||
+ | </ | ||
+ | |||
+ | Ref: https:// | ||
tbill_yield_methodology.1704471961.txt.gz · Last modified: 2024/01/05 16:26 by raju