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.
Which just goes to show that you can't believe everything you read on the web. (In all fairness, the
second post in the Bogleheads thread correctly says that 365 days are used and references the same Treasury sources I'm relying on below. Except it misses an added complication for T-bills maturing in more than six months.)
According to the Treasury (the authoritative source), the above formula is not what is used for Coupon Equivalent Yield of T-bills. It is almost correct for T-bills maturing in six months or less, except that the correct formula uses 365 or 366 day years. For T-bills with longer maturities (still under a year), a quadratic equation must be solved.
Some people may not be clear about what Coupon Equivalent Yield represents.
The Coupon Equivalent, also called the Bond Equivalent, or the Investment Yield, is the bill's yield based on the purchase price, discount, and a 365- or 366-day year. The Coupon Equivalent can be used to compare the yield on a discount bill to the yield on a nominal coupon security that pays semiannual interest with the same maturity date.
https://home.treasury.gov/resource-center/data-chart-center/interest-rates/TextView?type=daily_treasury_bill_rates&field_tdr_date_value_month=202209In plain English, if you have a bond with a 4%
coupon purchased at par ($
100), then every six months it pays $2. To compute the annualized rate of return one assumes that the coupons are reinvested at the original rate. So after one year, one would have:
$
100 x (
1 + 2%) x (
1 + 2%) = $
100 x
1.0404 = $
104.04. That's an annual
yield of 4.04%.
T-bills don't have coupons, but if they did, this particular T-bill would pay coupons at an annual
rate of 5.35
1%. That is, a six month coupon would pay half of that, or 2.6755%.
When one applies the same compounding as above (though reducing the second coupon by 2 days simple interest), one finds that the government figures are correct:
Rate (i) 5.351%
Price per $100 $94.883778
Days in 2024 (y) 366
1/2 year coupon 2.6755% (1/2 X 5.351%)
Total days to maturity 364
2nd half frac of year 0.494535519 (364 - 366/2) / 366
2nd half coupon 2.6463% (0.494... x 5.351%)
Compounding the coupons as before (except the second coupon isn't for a complete half year):
(
1 + 2.6755%) x (
1 + 2.6463%) =
105.3926%.
As in the OP, 5.392% is the actual total return. It is higher than the six month (coupon equivalent) yield, because coupons compound.
This is important. New issue T-bills have APYs greater than their coupon equivalent yields.
If a new six month T-bill has a 5.0% "coupon equivalent yield" it will pay 2.5% (half of 5%) after six months by definition. That would compound to 5.06&frac
14;% APY if reinvested at the same rate for another six months. That beats a six month CD with a 5.0% APY, paying just 2.47% at its six month maturity.
Treasury page with coupon equivalent yield formulae, examples
Treasury Regulation (Code of Federal Regulations) rules on calculating T-bill discount rates.
Note that the 360 day calendar is used when calculating the
bank discount rate, but a 365 or 366 day calendar is used when calculating the "
true discount" rate.