2 year Treasury Note net return question.

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Galen
Posts: 1
Joined: Sat Mar 25, 2023 10:25 am

2 year Treasury Note net return question.

Post by Galen »

Here are the facts listed on my information sheet.

Settlement Date 3/02/2023
Yield 5.188%
CUSIP 91282CEG2
US Treasury Note CPN 2.250%
Due Date 3/31/2024
Quantity 28,000 / 96.951438
Principle 27,146.00
Interest 264.81
Net Amount 27,411.21

Is my money earning me 5.188% from March 2, 2023 till March 31, 2024 ? Or is that 5.188% a red herring ?

If so can someone give me a simple approx. explanation as to how they got 5.188% ?

Things I think I know. Maybe.

It was purchased on March 2, 2023 and matures March 31, 2024. I will own the 2 Year Note for 394 days.

I paid $588.79 less than issued value of $28,000. 28,000 - 27,411.21 = 588.79

It has a coupon rate of 2.250%. Meaning it will pay 28,000 x 2.250% = $630 annually or $310 semi annual Yes or No ??

I think this 2 Year Note will make interest payments every 6 months, 4 payments over its life. Am I wrong about these dates or the # of payments ?

Issued Date March 31, 2022.
1st ------ Sept. 31, 2022 This payment went to the previous owner.
2nd ----- March 31.2023 I will receive this payment. I do not know the amount. Is it 28,000 x 2.250% = $315.00 Yes or No
3rd-------Sept. 31, 2024 I will receive this payment. I do not know the amount. Will this payment also be $315.00 Yes or No
4th-------March 31, 2024 Is there a 4th payment ? $315.00 Yes or No

I know I am responsible for taking any interest payments and reinvesting them before maturity.

Does the amount I get on the reinvested interest payments play any part in the 5.188% yield. I would think not.

I know there is a long mathematical formula for figuring US Notes and Bonds.

Can anyone show me an appox. income for this investment and appox. return on this investment ? Math does not have to be to exact penny.
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DaveTH
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Joined: Thu Apr 05, 2007 7:23 pm

Re: 2 year Treasury Note net return question.

Post by DaveTH »

Your discount of $588.79 is included in the stated yield since you will get the full par value at maturity. That is how lower yielding bonds are adjusted to current market rates. Your actual interest payments are based on the coupon rate of 2.250%.
cas
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Re: 2 year Treasury Note net return question.

Post by cas »

Galen wrote: Sat Mar 25, 2023 12:29 pm
Interest 264.81

[. . .]

2nd ----- March 31.2023 I will receive this payment. I do not know the amount. Is it 28,000 x 2.250% = $315.00 Yes or No
Yes, but you had to pay $264.81 of that $315 to the previous owner (because they owned it for most of that 6 months.)

You are allowed to subtract this accrued-interest-paid-to-seller on your 2023 tax return (due April 2024). See megathread "Taxation of Treasury bills, notes and bonds" for more information.
goaties
Posts: 542
Joined: Fri Jan 29, 2010 3:15 pm

Re: 2 year Treasury Note net return question.

Post by goaties »

To answer your questions: yes, you'll get three payments of 315.00. You'll also get 28000 back at maturity. Total winnings: 588.79 + (315 * 3) = 1533.79. What you do with the interest it throws off is up to you, so of course any compounding cannot be included in the stated yield.

It will be invested for 394/365 days, or 1.079 year. (I'm assuming your 394 days figure is correct.)

(1533.79 / 27411.21) / 1.079 = roughly .0519
miket29
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Re: 2 year Treasury Note net return question.

Post by miket29 »

Galen wrote: Sat Mar 25, 2023 12:29 pm Is my money earning me 5.188% from March 2, 2023 till March 31, 2024 ? Or is that 5.188% a red herring
Yes and no. It depends on what you mean by "my money earning me".

The replies pointed out the returns you will get and, as you suspected, the coupon payments do not take part in this calculation.

In colloquial usage earning a rate means your money compounds at that rate. So if I have a 1-year bond selling for $1000 that has a $50 payment one year from now then I will indeed have 5% more in one year. And to generalize, many people mean by "earning a rate" that their purchase today will grow by that amount at maturity (or, for bonds with more than a 1-year maturity, their purchase today compounded at that rate).

But you are unlikely to have exactly 5.1888% compounded for 394 days more than your purchase price when the bond matures. You'll be close, it depends on what you can ears as you reinvest the coupon payments. 5.1888% comes from a solution to a present-value equation.
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jeffyscott
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Re: 2 year Treasury Note net return question.

Post by jeffyscott »

miket29 wrote: Sat Mar 25, 2023 2:50 pm
Galen wrote: Sat Mar 25, 2023 12:29 pm Is my money earning me 5.188% from March 2, 2023 till March 31, 2024 ? Or is that 5.188% a red herring
Yes and no. It depends on what you mean by "my money earning me".

The replies pointed out the returns you will get and, as you suspected, the coupon payments do not take part in this calculation.

In colloquial usage earning a rate means your money compounds at that rate.
Only the money that remains invested is expected to earn the rate and compound.

If it were a savings account, any money withdrawn is no longer earning or compounding. The Treasury coupon payments are like a (forced) withdrawal.
dbr
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Re: 2 year Treasury Note net return question.

Post by dbr »

This business of what becomes of the money paid out in interest along the way causes yield and return to be two slightly different things. You can compute yield exactly from the start but return on this investment is a little ambiguous as it is on any investment with cash flows along the way.
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#Cruncher
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Re: 2 year Treasury Note net return question.

Post by #Cruncher »

Galen wrote: Sat Mar 25, 2023 12:29 pmIs my money earning me 5.188% from March 2, 2023 till March 31, 2024? ... If so can someone give me a simple approx. explanation as to how they got 5.188%?
Yes. The 5.188% is the "yield-to-maturity" which is the rate that makes the discounted cash flows net to $0. You can see this in cell D19 of the following table where the rate is calculated in cell B7 with the Excel YIELD function:

Code: Select all

  1               Col A        Col B      Col C       Col D  Selected Formulas
  2          Face value       28,000
  3          Settlement    3/02/2023
  4              Mature    3/31/2024
  5              Coupon       2.250%
  6               Price    96.951438
  7   Yield to maturity       5.188%                         Col B: =YIELD(B3,B4,B5,B6,100,2,1)
  8    Prev coupon date    9/30/2022
  9    Next coupon date    3/31/2023
 10      Days in period          182                         Col B: =B9-B8
 11  Days before settle          153                         Col B: =B3-B8
 12   Days after settle           29                         Col B: =B9-B3

Code: Select all

 13                Date    Cash Flow    Periods  Disc CFlow
 14           3/02/2023   -27,146.40    0        -27,146.40  Col B: =-B2*(B6/100)
 15           3/02/2023      -264.81    0           -264.81  Col B: =-B2*(B5/2)*(B11/B10)
 16           3/31/2023       315.00     29/182      313.72  Col D: =B16/(1+B$7/2)^C16
 17           9/30/2023       315.00   1+29/182      305.79  Col D: =B17/(1+B$7/2)^C17
 18           3/31/2024    28,315.00   2+29/182   26,791.71  Col D: =B18/(1+B$7/2)^C18
 19                 Sum     1,533.79                   0.00  Col D: =SUM(D14:D18)
jeffyscott wrote: Sat Mar 25, 2023 3:31 pmIf it were a savings account, any money withdrawn is no longer earning or compounding. The Treasury coupon payments are like a (forced) withdrawal.
Correct. The following table shows the cash flows of the bond as if its purchase (including accrued interest) were a deposit into a savings account and the coupon and principal payments were withdrawals. When viewed this way, the yield-to-maturity is the interest rate on the savings such that the account balance is zero after the principal and coupon payment at maturity.

Code: Select all

  1               Col A       Col B     Col C      Col D  Selected Formulas
  2          Face value      28,000
  3          Settlement   3/02/2023
  4              Mature   3/31/2024
  5              Coupon      2.250%
  6               Price   96.951438
  7   Yield to maturity      5.188%                       Col B: =YIELD(B3,B4,B5,B6,100,2,1)
  8    Prev coupon date   9/30/2022
  9    Next coupon date   3/31/2023
 10      Days in period         182                       Col B: =B9-B8
 11  Days before settle         153                       Col B: =B3-B8
 12   Days after settle          29                       Col B: =B9-B3

Code: Select all

 13                Date   Cash Flow   Periods    Balance
 14           3/02/2023   27,146.40   0        27,146.40  Col B: =B2*(B6/100)
 15           3/02/2023      264.81   0        27,411.21  Col B: =B2*(B5/2)*(B11/B10)
 16           3/31/2023     -315.00    29/182  27,208.29  Col D: =D15*(1+B$7/2)^C16+B16
 17           9/30/2023     -315.00   1        27,599.08  Col D: =D16*(1+B$7/2)^C17+B17
 18           3/31/2024  -28,315.00   1             0.00  Col D: =D17*(1+B$7/2)^C18+B18
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