T-Bill Coupon-Equivalent Yield

[yogibearbull]

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 - 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

[anitya]

yogibearbull ,

Very interesting. Their coupon equivalent yield calc makes no sense to me.

However, 30 / 360 days is a term fixed income instrument convention everybody in the industry follows for calculating interest payments for redemptions and other dispositions between coupon payments. When we buy or sell notes / bonds between coupons, this is the convention used to pay or receive accrued interest (coupon) in addition to the price. I never bothered to check the interest Fidelity / Vanguard / Schwab deduct from my account and pay the seller for the many secondary market Treasury purchases I made but I presume that is how they calculate. (If the purchase happens in a 31 day month and in large size, distortions vs a 365 day year can be perceived but 360 day year is the industry reality.)

I did overlook the fewer than 2 days to 1 year part in the instrument we bought today. So, a 5.425% (vs 5.392%) YTM is more accurate.

[yogibearbull]

anitya, I see what you mean. 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

[anitya]

Aug 9, 2023 13:59:38 GMT yogibearbull said:

anitya , I see what you mean. 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

The 30/360 convention is used in the finance industry in the US, UK, India, and many other countries.   The use of this convention is usually disclosed in the terms of the transaction, unless one is dealing with standardized contracts in which case one has to dig deeper.

[yogibearbull]

For those interested, there are further details on this. Treasury used different methods for the coupon-equivalent yield for T-Bills up to 6m, and for T-Bills for 6m-12m. In particular, the puzzle about the recent 52-wk Auction has been resolved. LINK