### Post by Admin/YBB on Aug 8, 2023 18:27:04 GMT -6

**T-Bill Coupon-Equivalent Yield**

According to several web sources, Treasury simply uses this formula for Coupon-Equivalent Yield of T-Bills,

Coupon-Equivalent Yield = 100*[(Par Value - Purchase Price)/Purchase Price]* 360/d, where d = days to maturity.

So, Coupon-Equivalent Yield = Total Return * 360/d.

d must be counted properly taking into account specific T-Bill issue and maturity dates. Just because their name says 13-wk, 26-wk, 52-wk, that doesn't mean 13*7, 26*7, 52*7 days.

Don't ask my why the Treasury wants to put all T-Bills on 360 day standard.

The 52-wk T-Bill today (8/8/23) will be issued on 8/10/23 but will mature on 8/8/24, so that is 2-3 days less than a full year (or, 362-363 days). It seems that Treasury used d = 362.76.

Price was 94.883778, so TR = 100*(100 - 94.883778)/94.883778 = 5.392%.

So, Coupon-Equivalent Yield = 5.392*360/362.76 = 5.351%. That is what Treasury provides, but I don't like this at all. It doesn't related to any realistic TR or YTM that one may calculate.

To me, if the TR is 5.392% for 362.76 days (implied by Treasury), I would annualize it as 5.392*365/362.76 = 5.425% annualized.

52-Wk T-Bill Auction on 8/8/23 www.treasurydirect.gov/instit/annceresult/press/preanre/2023/R_20230808_2.pdf

www.investopedia.com/terms/c/couponequivalentrate.asp

www.bogleheads.org/forum/viewtopic.php?t=248337

www.wallstreetmojo.com/bond-equivalent-yield-formula-bey/

corporatefinanceinstitute.com/resources/fixed-income/discount-yield/

Edit/Add, 8/9/23. There are various month-day/year-day conventions: 30/360, actual/actual, actual/360, actual/364, actual/365; there can also be leap year adjustments.

en.wikipedia.org/wiki/Day_count_convention

www.investopedia.com/ask/answers/06/daycountconvention.asp

content.next.westlaw.com/Glossary/PracticalLaw/I7080fe88accb11eabea3f0dc9fb69570?transitionType=Default&contextData=(sc.Default)

Edit/Add, 8/13/23. More from Treasury.

These note that the different methods are used for T-Bills up to 6 months and for 6-12 months. An approximation is used for T-Bills up to 6 months. But a precise quadratic formula is used for T-Bills between 6-12 months; 365-day year is used in these calculations; the difference in days in two nominally 6-month periods is accounted for (the first 6-month period is 365/2, the second 6-month period is the remaining year). MFO LINK1 MFO LINK2

Treasury Formulas www.treasurydirect.gov/instit/annceresult/press/preanre/2004/ofcalc6decbill.pdf

Methodology from CFR www.ecfr.gov/current/title-31/subtitle-B/chapter-II/subchapter-A/part-306/subpart-E/appendix-Appendix%20to%20Subpart%20E%20of%20Part%20306