I purchased 2 month t-bills on the 3/16/23 auction through Vanguard. The purchase price ended up being 99.31 according to Vanguard. Unless I am calculating it wrong that gives me an annualized rate of 4.15% give or take a bit. That seems low to me. The 2 month rate at Daily Treasury Yield Par Yield Curve Rates on 3/17 is 4.51%. On 3/16 it was 4.66%. My past purchases have usually been pretty close to what the Treasury was publishing. And on Vanguard they are showing 2 month t-bills on the secondary market around 4.3 or so on Friday. Am I missing something?
Answers
0.69 earned, 99.31 invested, 8 week duration:
(0.69/99.31) x (52/8) = 4.516%
Hope this makes you feel better! (Someone can correct me if this is wrong)
STEVE
https://www.treasurydirect.gov/instit/annceresult/press/preanre/2023/R_20230317_1.pdf
Investment Rate = ((100 – Price)/Price) x (366/days) = ((100 – 99.307778)/ 99.307778) x (366/56) = 0.04556 or 4.556%
This result agrees with the Investment Rate value listed in the Auction Results for the 8-week Treasury Bill which was earlier listed by MAKNYC and is repeated here: https://www.treasurydirect.gov/instit/annceresult/press/preanre/2023/R_20230317_1.pdf This result also agrees favorably with the rate which Steve58 obtained.
Note that the expression listed above normally utilizes the number 365 instead of the number 366. However, the Department of the Treasury specifies that the expression should use 366 if “the year following the issue date includes February 29.” Since the issue date for this Treasury Bill is 3/21/2023 and the year following that issue date includes February 29, 2024 the number 366 should be employed.
Though the correct answer is 0.0454 or 4.54%, and that would be per calculation above - "Coupon Equivalent Yield"
Treasury announced "Investment Rate" is 4.556%
None of this numbers represent actual rates of the return they are purely for the comparison purposes
The Actual or Realized Return depends on the return over remaining? 310 days.
The best way I managed to explain this to myself is that the "Investment Rate" is always higher than "Calculated Yield" because it is implied that the Discount/Coupon is invested at the same Rate before the Annualization of total return. Actual equation is relatively complicated and only relevant to Fund Mangers transacting Billions.
For the most of us, lame, the difference is no more than the rounding error.