treasury yield to maturity

[marginal]

Hi, I'm calculating investment rate or yield to maturity for 4-week treasury I bought:
https://www.treasurydirect.gov/auctions ... a-results/

Security Term CUSIP Issue Date Maturity Date High Rate Investment Rate
4-Week XXX 03/21/2023 04/18/2023 4.220% 4.304%

This is email I got:

Code: Select all

Security Description:	US Treasury BILL 04/18/2023
Action:	BOUGHT
Security No./CUSIP:	XXX
Type:	Cash
Trade Date:	03/17/23
Settle Date:	03/21/23
Quantity	Price	Principal	Charge and/or Interest	Total Amount
12,000	$99.671778	$11,960.61	
N/A	 
$11,960.61
Additional information for this security:

- Yield to Maturity 4.293%
- Moody's Rating NR , S&P Rating NR
- Schwab acted as your agent.

Here is my investment rate calculation:
interest = 100 - 99.671778 = 0.328222
[Marginal: Original message changed 365 to 366 days, because Treasury Direct looks at 1 year period ahead and includes February 29/2024.]
annualized return = interest/28 * 365 366 = 4.27860821 4.29033043
investment rate = annualized return / price paid = 4.27860821 4.29033043 /99.671778 = 4.293% 4.304% (matches email but not TD investment rate matches TD investment rate but not email)
High rate calculation:
annualized return = interest/28 * 360 = (0.328222/28) * 360 = 4.2199
high rate (discount rate) = 4.2199 / 100 = 4.22 % (matches both email and TD investment rate)

[Marginal: email from brokerage account assumes 365 days!]
So high rate is right but not investment rate

Question:
Do you know what is discrepancy for investment rate?

Thanks.

[MrJedi]

We're within a year of a leap day so you need to use 366 days instead of 365 days

[HueyLD]

Mr. Jedi is right. Short term T bill’s investment rate (aka coupon equivalent yield) uses the number of days one year forward.

https://www.treasurydirect.gov/instit/a ... ecbill.pdf

[marginal]

MrJedi has a good hint and discrepancy is from that assumption. But 2023 is not leap year, February was 28-days.
It means TD is thinking 2023 is leap year by mistake ! am I right?

[HueyLD]

The one year forward, 3/21/23 to 3/21/24 = 366 days.

[MrJedi]

MrJedi has a good hint and discrepancy is from that assumption. But 2023 is not leap year, February was 28-days.
It means TD is thinking 2023 is leap year by mistake ! am I right?

You are not quite thinking correctly, at least with Treasury logic.

The number of days from March 21, 2023 to March 21, 2024 is 366 days. So 366 days is used for annualized rate. You will see 366 used for all bills issued from March 1, 2023 through February 28, 2024.

[marginal]

Great it's clear, thanks for clarification !
I also correct original message in a case somebody reads it in future.

[marginal]

When Schwab email calculated "yield to maturity" terminology actually assumed 365 days.
Is that incorrect or justified because maturity date (28 days) falls within non-leap year?
Thanks.

[HueyLD]

Schwab apparently did not know the official Treasury Department calculation method (see the link above).

However, the difference is so immaterial that it is not worth your time. And the difference has no bearing on the amount of interest you will receive.