How to buy 3 month treasuries

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josephny
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How to buy 3 month treasuries

Post by josephny »

I just bough 3 month treasuries through Morgan Stanley and am confused.

I spent $1,250,414.17, at a price of $98.6909, with a maturity value of $1,267,000.

Reverse engineering the math (because I don't how this is supposed to work), I get:

$100 - $98.6909 = 1.3091

3/12 months means 4 of these in a year for an annual return of $5.2364 (5.2364%)

Alternatively, ($1,267,000 - $1,250,414.17)/$1,250,414.17 = .013264269

4 of these per year yields 5.3057%

So, the calculations don't match each other, and neither matches what I see online as today's rate of 5.378%

https://www.marketwatch.com/investing/B ... tryCode=BX

What am I missing?
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Rocinante Rider
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Re: How to buy 3 month treasuries

Post by Rocinante Rider »

josephny wrote: Thu Jun 06, 2024 3:20 pm $100 - $98.6909 = 1.3091
What am I missing?
Maybe missing the need to divide 1.3091 by 98.6909, then you get the same result and yield as your other calc.
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Thu Jun 06, 2024 3:20 pm I just bough 3 month treasuries through Morgan Stanley and am confused.

I spent $1,250,414.17, at a price of $98.6909, with a maturity value of $1,267,000.

Reverse engineering the math (because I don't how this is supposed to work), I get:

$100 - $98.6909 = 1.3091

3/12 months means 4 of these in a year for an annual return of $5.2364 (5.2364%)

Alternatively, ($1,267,000 - $1,250,414.17)/$1,250,414.17 = .013264269

4 of these per year yields 5.3057%

So, the calculations don't match each other, and neither matches what I see online as today's rate of 5.378%

https://www.marketwatch.com/investing/B ... tryCode=BX

What am I missing?
The calculations are done using the number of days until maturity. Assuming your 3-mo T-Bill matures in 90 days:

((100 / 98.6909) - 1) * (365 / 90) = 0.0537955... which is very close to the 5.378% you listed as today's rate.
p1db
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Re: How to buy 3 month treasuries

Post by p1db »

OP, did you buy the 3 month t-bill at auction or in secondary market? What is the CUSIP?
IDpilot
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Re: How to buy 3 month treasuries

Post by IDpilot »

josephny wrote: Thu Jun 06, 2024 3:20 pm I just bough 3 month treasuries through Morgan Stanley and am confused.

I spent $1,250,414.17, at a price of $98.6909, with a maturity value of $1,267,000.

Reverse engineering the math (because I don't how this is supposed to work), I get:

$100 - $98.6909 = 1.3091

3/12 months means 4 of these in a year for an annual return of $5.2364 (5.2364%)

Alternatively, ($1,267,000 - $1,250,414.17)/$1,250,414.17 = .013264269

4 of these per year yields 5.3057%

So, the calculations don't match each other, and neither matches what I see online as today's rate of 5.378%

https://www.marketwatch.com/investing/B ... tryCode=BX

What am I missing?
Not sure just exactly what you bought today so can't really help you figure it out. There was a three-month T-bill, which is actually a 13 week, issued today but its price was 98.672917 which doesn't match your numbers. Did you, perhaps, buy some treasury note/bond that is three months from maturity?
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

Rocinante Rider wrote: Thu Jun 06, 2024 4:15 pm
josephny wrote: Thu Jun 06, 2024 3:20 pm $100 - $98.6909 = 1.3091
What am I missing?
Maybe missing the need to divide 1.3091 by 98.6909, then you get the same result and yield as your other calc.
This is the answer. They current yield will not match the yield when the bill was bought, but it is close.
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Kevin M
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Re: How to buy 3 month treasuries

Post by Kevin M »

So, you're not asking how to buy them, but how to calculate the yield.

I use the spreadsheet YIELD function. For terms of less than six months, I use freq = 1, but for longer maturities freq = 2. Standard daycountconvention for Treasuries is Actual/365, which is day count convention = 1 with the Google sheets version of YIELD.

The Treasury uses this for short-term Treasury bill calculations:

Image

Source: https://www.treasurydirect.gov/instit/a ... ecbill.pdf
If I make a calculation error, #Cruncher probably will let me know.
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

Wow, what a tremendous wealth of info here (that's a money pun).

The process I used: I emailed my guy at MS and told him to buy $1.25MM in 3 month treasuries. I suspect I should have provided more specificity, but I don't know exactly what specifics.

The CUSIP they bought for me is 912797GL5 at a price of $98.6909 for a total cost of $1,250,414.17

It shows up online as a quantity of 1,267,000

I looked up 912797GL5 and it looks like this CUSIP is reused every 6 months. Most recently (from what I can tell) on 6/6/2024 where is sold for $98.672917

But, I do not know if I bought the 6/6/2024 issue or the 3/4/2024.

https://www.treasurydirect.gov/auctions ... =912797GL5

Correcting for my math error (thank you!), my cost of $98.6909 results in a 13 week yield of 1.32646% (5.306%).

Math: (100 - 98.6909) / 98.6909 = .0132646

And, doing the math on the entire purchase provides the same (close enough) results:

(1267000 - 1250414.17) / 1250414.17 = .0132643

I am making certain assumptions about rounding to 4 places and what exactly 13 weeks means (13 * 7) and whether multiplying by 4 is the right way to get to an annual yield (13 * 7 * 4 = 354 days).

But, given these assumptions, the numbers work -- anything in the 5.30 and higher is good enough (a phrase I've learned a deeper meaning to, perhaps ironically, on this board).

Am I close?

Nonetheless, thank you all for the deeper understanding: Yield formula and excel function, yields on secondary purchases not matching original issuance yield, 13 weeks is what is meant by 3 months, triple check my math before making a public spectacle of myself, etc.

Thank you!
MrJedi
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Re: How to buy 3 month treasuries

Post by MrJedi »

Annual yield would be a little higher than your estimate of 4x 3 month because annual yield normally includes compound effects. If you buy 3 month bills you can reinvest both the principal and interest, and then compound a few times in a single year. Your calculation ignores reinvesting the new interest with each matured bill.
MGBMartin
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Re: How to buy 3 month treasuries

Post by MGBMartin »

What day did your T-Bill purchase execute on?
I’m having trouble understanding the price you paid versus the auction price.
That T-Bill auction price was 98.672917 and you would of ended up with a yield of 5.365%

I’m thinking MS purchased on open market of a previous issue of that CUSID rather than the reissue at auction on Jun 6.
All moot though if you’re happy with the results.

I use this site to see the auction results…
https://www.treasurydirect.gov/auctions ... a-results/
And this site to keep an eye on the daily yields which gives me an idea of what my next T-Bill will be…
https://home.treasury.gov/resource-cent ... value=2024
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RyeBourbon
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

You didn't buy at auction on 6/3 so that price is irrelevant. You didn't say what day your order was placed, but you got the price at the time. It could have been more or less than Monday's auction price. You got 5.3% which I would be pleased with.
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

MrJedi wrote: Fri Jun 07, 2024 6:22 am Annual yield would be a little higher than your estimate of 4x 3 month because annual yield normally includes compound effects. If you buy 3 month bills you can reinvest both the principal and interest, and then compound a few times in a single year. Your calculation ignores reinvesting the new interest with each matured bill.
Of course -- duh! Totally forgot about compounding every 3 months.

Thank you for pointing that out.
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

MGBMartin wrote: Fri Jun 07, 2024 6:32 am What day did your T-Bill purchase execute on?
I’m having trouble understanding the price you paid versus the auction price.
That T-Bill auction price was 98.672917 and you would of ended up with a yield of 5.365%

I’m thinking MS purchased on open market of a previous issue of that CUSID rather than the reissue at auction on Jun 6.
All moot though if you’re happy with the results.

I use this site to see the auction results…
https://www.treasurydirect.gov/auctions ... a-results/
And this site to keep an eye on the daily yields which gives me an idea of what my next T-Bill will be…
https://home.treasury.gov/resource-cent ... value=2024
This is the online record:

"Transaction Date 06/06/24
Activity Date 06/06/24
Settlement Date 06/07/24
Description UNITED STATES TREASURY BILL
RATE: N/A/N/A DUE: 2024-09-05
CUSIP 912797GL5"

I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP.

EDITED:
5.365% vs. 5.3% is something to think about -- $500 for the 3 month period is more than enough to keep my wife in coffee every day.
Last edited by josephny on Fri Jun 07, 2024 7:08 am, edited 1 time in total.
RyeBourbon
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

josephny wrote: Fri Jun 07, 2024 6:55 am
MGBMartin wrote: Fri Jun 07, 2024 6:32 am What day did your T-Bill purchase execute on?
I’m having trouble understanding the price you paid versus the auction price.
That T-Bill auction price was 98.672917 and you would of ended up with a yield of 5.365%

I’m thinking MS purchased on open market of a previous issue of that CUSID rather than the reissue at auction on Jun 6.
All moot though if you’re happy with the results.

I use this site to see the auction results…
https://www.treasurydirect.gov/auctions ... a-results/
And this site to keep an eye on the daily yields which gives me an idea of what my next T-Bill will be…
https://home.treasury.gov/resource-cent ... value=2024
This is the online record:

"Transaction Date 06/06/24
Activity Date 06/06/24
Settlement Date 06/07/24
Description UNITED STATES TREASURY BILL
RATE: N/A/N/A DUE: 2024-09-05
CUSIP 912797GL5"

I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP.

3.65% vs. 3.5% is something to think about -- $500 for the 3 month period is more than enough to keep my wife in coffee every day.
You got the price on 6/6. The auction was held 6/3, so you couldn't get that price.
https://www.treasurydirect.gov/instit/a ... 0603_2.pdf

If you had placed your order on Monday for the auction, you would have paid $1,250,186, about $228 less than you paid on Thursday (actually paid today as it will settle today). Of course, the price might have fallen between Monday and Thursday and you would have paid less. Treasury prices change constantly and are not predictable. (In fact, I'm surprised it moved so little in three days.) You have to take what you get at the time - no room for buyer's remorse.

I'm not really sure what you are talking about with 3.65% and 3.5% - you got just over 5.3% which I would be happy with.
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Fri Jun 07, 2024 6:05 am The CUSIP they bought for me is 912797GL5 at a price of $98.6909 for a total cost of $1,250,414.17

It shows up online as a quantity of 1,267,000

I looked up 912797GL5 and it looks like this CUSIP is reused every 6 months. Most recently (from what I can tell) on 6/6/2024 where is sold for $98.672917

But, I do not know if I bought the 6/6/2024 issue or the 3/4/2024.
Given the price you paid, I think you bought it on the secondary market, not at the 6/6/2024 auction.
Correcting for my math error (thank you!), my cost of $98.6909 results in a 13 week yield of 1.32646% (5.306%).

Math: (100 - 98.6909) / 98.6909 = .0132646

And, doing the math on the entire purchase provides the same (close enough) results:

(1267000 - 1250414.17) / 1250414.17 = .0132643

I am making certain assumptions about rounding to 4 places and what exactly 13 weeks means (13 * 7) and whether multiplying by 4 is the right way to get to an annual yield (13 * 7 * 4 = 354 days).
As I stated above, the yield calculation is based on the number of days from when your trade settles to the maturity date.

The maturity date for that CUSIP is 09/05/2024. Assume your trade settles today (June 7, 2024). There are 90 days until maturity and the calculations is:

90 Days from settlement to maturity:
(100 - 98.6909) / 98.6909 = .0132646
.0132646 / 90 * 365 = 0.053795

What if it doesn't settle until tomorrow? That's 89 days: 89 days: .0132646 / 89 * 365 = 0.054399

Or maybe it settled yesterday, then you have 91 days until maturity: 91 days: .0132646 / 91 * 365 = 0.053204

ETA: We were posting at the same time. I see you posted that your settlement date is today, June 7, 2024. That's 90 days until maturity so your yield is the first calculation above: 5.3795%.

ETA: If the leap year calculations are still in effect, replace 365 with 366 in the calculations above.
Last edited by Chip Munk on Fri Jun 07, 2024 8:00 am, edited 2 times in total.
Topic Author
josephny
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Re: How to buy 3 month treasuries

Post by josephny »

RyeBourbon wrote: Fri Jun 07, 2024 7:04 am
josephny wrote: Fri Jun 07, 2024 6:55 am
MGBMartin wrote: Fri Jun 07, 2024 6:32 am What day did your T-Bill purchase execute on?
I’m having trouble understanding the price you paid versus the auction price.
That T-Bill auction price was 98.672917 and you would of ended up with a yield of 5.365%

I’m thinking MS purchased on open market of a previous issue of that CUSID rather than the reissue at auction on Jun 6.
All moot though if you’re happy with the results.

I use this site to see the auction results…
https://www.treasurydirect.gov/auctions ... a-results/
And this site to keep an eye on the daily yields which gives me an idea of what my next T-Bill will be…
https://home.treasury.gov/resource-cent ... value=2024
This is the online record:

"Transaction Date 06/06/24
Activity Date 06/06/24
Settlement Date 06/07/24
Description UNITED STATES TREASURY BILL
RATE: N/A/N/A DUE: 2024-09-05
CUSIP 912797GL5"

I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP.

3.65% vs. 3.5% is something to think about -- $500 for the 3 month period is more than enough to keep my wife in coffee every day.
You got the price on 6/6. The auction was held 6/3, so you couldn't get that price.
https://www.treasurydirect.gov/instit/a ... 0603_2.pdf

If you had placed your order on Monday for the auction, you would have paid $1,250,186, about $228 less than you paid on Thursday (actually paid today as it will settle today). Of course, the price might have fallen between Monday and Thursday and you would have paid less. Treasury prices change constantly and are not predictable. (In fact, I'm surprised it moved so little in three days.) You have to take what you get at the time - no room for buyer's remorse.

I'm not really sure what you are talking about with 3.65% and 3.5% - you got just over 5.3% which I would be happy with.
Ugh -- messing up the numbers in my head. I edited for correction.

6/3 auction explains it all. Thank you.

Yes, great lesson 5.3% is good and I should be (and am) happy with that.
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PizzaEater
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Re: How to buy 3 month treasuries

Post by PizzaEater »

josephny wrote: Fri Jun 07, 2024 6:55 am
This is the online record:

"Transaction Date 06/06/24
Activity Date 06/06/24
Settlement Date 06/07/24
Description UNITED STATES TREASURY BILL
RATE: N/A/N/A DUE: 2024-09-05
CUSIP 912797GL5"

I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP.
A bill with the same CUSIP is the same bill. The price (on the market) changes every day, just like a stock price would. A 4-week Bill at auction reuses the same CUSIP from an 8-week bill issued 4 weeks earlier at auction, because they have the same maturity date. They're the same bill, just auctioned at different times. Because they are auctioned at different times they will have a different price. So the statement "I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP" is meaningless.

For example, look at the auction results for this 8-week bill:
https://treasurydirect.gov/instit/annce ... 0509_2.pdf

and this 4-week bill:
https://treasurydirect.gov/instit/annce ... 0606_2.pdf

Same maturity date, same CUSIP, but different issue date and different price. They are the same bill. A bill's price will change every day, converging to 100.0 at maturity. Auctions are special in that everybody gets the same price, whereas on the market you need a buyer and seller to agree on a price for each transaction. However, auction prices are extremely close to market prices around the same date (as others have already mentioned).

Implementation detail: For my T-Bills I only enter prices when I buy (and of course when they mature), so prices rarely get updated in my financial tracking software. This means my present-day net worth is a little off, since I don't update T-Bill prices every day. I haven't found an easy way to import historical prices, so I don't bother. Historical prices are available (https://www.treasurydirect.gov/GA-FI/Fe ... riceDetail), but that's too clumsy to grab prices for every day.
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

PizzaEater wrote: Fri Jun 07, 2024 7:23 am
josephny wrote: Fri Jun 07, 2024 6:55 am
This is the online record:

"Transaction Date 06/06/24
Activity Date 06/06/24
Settlement Date 06/07/24
Description UNITED STATES TREASURY BILL
RATE: N/A/N/A DUE: 2024-09-05
CUSIP 912797GL5"

I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP.
A bill with the same CUSIP is the same bill. The price (on the market) changes every day, just like a stock price would. A 4-week Bill at auction reuses the same CUSIP from an 8-week bill issued 4 weeks earlier at auction, because they have the same maturity date. They're the same bill, just auctioned at different times. Because they are auctioned at different times they will have a different price. So the statement "I don't know if this helps identify if it was a previous CUSIP or the 6/6/24 CUSIP" is meaningless.

For example, look at the auction results for this 8-week bill:
https://treasurydirect.gov/instit/annce ... 0509_2.pdf

and this 4-week bill:
https://treasurydirect.gov/instit/annce ... 0606_2.pdf

Same maturity date, same CUSIP, but different issue date and different price. They are the same bill. A bill's price will change every day, converging to 100.0 at maturity. Auctions are special in that everybody gets the same price, whereas on the market you need a buyer and seller to agree on a price for each transaction. However, auction prices are extremely close to market prices around the same date (as others have already mentioned).

Implementation detail: For my T-Bills I only enter prices when I buy (and of course when they mature), so prices rarely get updated in my financial tracking software. This means my present-day net worth is a little off, since I don't update T-Bill prices every day. I haven't found an easy way to import historical prices, so I don't bother. Historical prices are available (https://www.treasurydirect.gov/GA-FI/Fe ... riceDetail), but that's too clumsy to grab prices for every day.
Great explanation.

OP, I wouldn't worry over a few hundred dollars on a 7 figure buy. As I said, you just as easily could have gotten an extra $500 a couple days after the auction.

It's really impossible to know where rates are going on a day-to-day basis, but I felt good when I bought some long-term bonds last week when yields spiked. I was going to buy them anyway, so I would have been happy with the price I was originally looking at, but I ended up spending $8000 less than I thought I was going to.
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IDpilot
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Re: How to buy 3 month treasuries

Post by IDpilot »

Chip Munk wrote: Fri Jun 07, 2024 7:05 am
josephny wrote: Fri Jun 07, 2024 6:05 am The CUSIP they bought for me is 912797GL5 at a price of $98.6909 for a total cost of $1,250,414.17

It shows up online as a quantity of 1,267,000

I looked up 912797GL5 and it looks like this CUSIP is reused every 6 months. Most recently (from what I can tell) on 6/6/2024 where is sold for $98.672917

But, I do not know if I bought the 6/6/2024 issue or the 3/4/2024.
Given the price you paid, I think you bought it on the secondary market, not at the 6/6/2024 auction.
Correcting for my math error (thank you!), my cost of $98.6909 results in a 13 week yield of 1.32646% (5.306%).

Math: (100 - 98.6909) / 98.6909 = .0132646

And, doing the math on the entire purchase provides the same (close enough) results:

(1267000 - 1250414.17) / 1250414.17 = .0132643

I am making certain assumptions about rounding to 4 places and what exactly 13 weeks means (13 * 7) and whether multiplying by 4 is the right way to get to an annual yield (13 * 7 * 4 = 354 days).
As I stated above, the yield calculation is based on the number of days from when your trade settles to the maturity date.

The maturity date for that CUSIP is 09/05/2024. Assume your trade settles today (June 7, 2024). There are 90 days until maturity and the calculations is:

90 Days from settlement to maturity:
(100 - 98.6909) / 98.6909 = .0132646
.0132646 / 90 * 365 = 0.053795

What if it doesn't settle until tomorrow? That's 89 days: 89 days: .0132646 / 89 * 365 = 0.054399

Or maybe it settled yesterday, then you have 91 days until maturity: 91 days: .0132646 / 91 * 365 = 0.053204

ETA: We were posting at the same time. I see you posted that your settlement date is today, June 7, 2024. That's 90 days until maturity so your yield is the first calculation above: 5.3795%.

ETA: If the leap year calculations are still in effect, replace 365 with 366 in the calculations above.
The decision on when to use 365 or 366 is based on the number of days in the year following the issue date of the original bill. Since CUSIP 912797GL5 was originally issued on 5/9/2024, 365 is the correct number.
FactualFran
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Re: How to buy 3 month treasuries

Post by FactualFran »

josephny wrote: Fri Jun 07, 2024 6:05 am The process I used: I emailed my guy at MS and told him to buy $1.25MM in 3 month treasuries. I suspect I should have provided more specificity, but I don't know exactly what specifics.
Based on other posts, some of the specifics are:
  • The transaction was a trade on the secondary market, not a purchase at auction.
  • The trade date was the same day as the settlement date of an auction of 91-day Bills.
  • The maturity date of the Bills is 90 days after the settlement date of the trade.
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

Thank you all so much for the crash course in bills!

I don't understand how one can buy a bill on the secondary market (for example, one that was auctioned by the govt at an earlier date) and still be able to hold it for 90 (or 91) days? In my example, I bought the bill on 6/6/24 that was sold at govt auction on 3/6/2024, and yet the bill I have has a maturity date of 9/5/2024. Maybe "maturity" doesn't mean what I think it means.
Geologist
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Re: How to buy 3 month treasuries

Post by Geologist »

josephny wrote: Sat Jun 08, 2024 6:14 pm Thank you all so much for the crash course in bills!

I don't understand how one can buy a bill on the secondary market (for example, one that was auctioned by the govt at an earlier date) and still be able to hold it for 90 (or 91) days? In my example, I bought the bill on 6/6/24 that was sold at govt auction on 3/6/2024, and yet the bill I have has a maturity date of 9/5/2024. Maybe "maturity" doesn't mean what I think it means.
The Treasury issues bills at a range of maturities from 4 weeks up to 52 weeks. Consequently, it is not difficult to buy a bill on the secondary market that has roughly a 3-month maturity but was issued at an earlier time (perhaps with 26 or 52 week original maturity).

Edit: your auction date isn't quite right. It was a 26-week bill auctioned on 3/4/24 (see https://www.treasurydirect.gov/instit/a ... 0304_1.pdf) and issued on 3/7/24.
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Sat Jun 08, 2024 6:14 pm Thank you all so much for the crash course in bills!

I don't understand how one can buy a bill on the secondary market (for example, one that was auctioned by the govt at an earlier date) and still be able to hold it for 90 (or 91) days? In my example, I bought the bill on 6/6/24 that was sold at govt auction on 3/6/2024, and yet the bill I have has a maturity date of 9/5/2024. Maybe "maturity" doesn't mean what I think it means.
That particular T-Bill (CUSIP 912797GL5 with a maturity date of 09/05/2024) has been offered at auction three times: 1) in Sep 2023 as a 52-week T-Bill, 2) in Mar 2024 as a 26-wk T-Bill, and 3) in June 2024 as a 13-wk T-Bill. https://www.treasurydirect.gov/auctions ... =912797GL5 The ones you bought were originally purchased at auction in either Sep 2023 or Mar 2024.

To keep things simple, assume you bought this T-Bill from the original owner (i.e., they bought at auction and not on the secondary market). It could have been purchased in either Sep 2023 for $94.823111 or Mar 2024 for $97.419139. You bought it from that owner at a price of $98.6909. So the owner made some money by selling it to you for more than they paid, and you will make money when it matures and are paid $100 by the US Treasury on Sep 5, 2024, 90 days after you bought it.
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

You might find this article by Harry Sit ("The Finance Buff") helpful. "How to Buy Treasury Bills & Notes On the Secondary Market" https://thefinancebuff.com/buy-treasury ... arket.html

It is a follow on to an article he published earlier: "How To Buy Treasury Bills & Notes Without Fee at Online Brokers" https://thefinancebuff.com/treasury-bil ... arket.html
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

Geologist wrote: Sat Jun 08, 2024 6:55 pm
josephny wrote: Sat Jun 08, 2024 6:14 pm Thank you all so much for the crash course in bills!

I don't understand how one can buy a bill on the secondary market (for example, one that was auctioned by the govt at an earlier date) and still be able to hold it for 90 (or 91) days? In my example, I bought the bill on 6/6/24 that was sold at govt auction on 3/6/2024, and yet the bill I have has a maturity date of 9/5/2024. Maybe "maturity" doesn't mean what I think it means.
The Treasury issues bills at a range of maturities from 4 weeks up to 52 weeks. Consequently, it is not difficult to buy a bill on the secondary market that has roughly a 3-month maturity but was issued at an earlier time (perhaps with 26 or 52 week original maturity).

Edit: your auction date isn't quite right. It was a 26-week bill auctioned on 3/4/24 (see https://www.treasurydirect.gov/instit/a ... 0304_1.pdf) and issued on 3/7/24.
I see -- so I might have bought a bill that was 13 weeks old (since the original auction date) that was originally auctioned as a 26 week bill?

And are they are auctioned frequently enough so I can pick any trading day to buy any length note on the secondary market at any of the origal lengths?
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Re: How to buy 3 month treasuries

Post by josephny »

Chip Munk wrote: Sat Jun 08, 2024 7:04 pm
josephny wrote: Sat Jun 08, 2024 6:14 pm Thank you all so much for the crash course in bills!

I don't understand how one can buy a bill on the secondary market (for example, one that was auctioned by the govt at an earlier date) and still be able to hold it for 90 (or 91) days? In my example, I bought the bill on 6/6/24 that was sold at govt auction on 3/6/2024, and yet the bill I have has a maturity date of 9/5/2024. Maybe "maturity" doesn't mean what I think it means.
That particular T-Bill (CUSIP 912797GL5 with a maturity date of 09/05/2024) has been offered at auction three times: 1) in Sep 2023 as a 52-week T-Bill, 2) in Mar 2024 as a 26-wk T-Bill, and 3) in June 2024 as a 13-wk T-Bill. https://www.treasurydirect.gov/auctions ... =912797GL5 The ones you bought were originally purchased at auction in either Sep 2023 or Mar 2024.

To keep things simple, assume you bought this T-Bill from the original owner (i.e., they bought at auction and not on the secondary market). It could have been purchased in either Sep 2023 for $94.823111 or Mar 2024 for $97.419139. You bought it from that owner at a price of $98.6909. So the owner made some money by selling it to you for more than they paid, and you will make money when it matures and are paid $100 by the US Treasury on Sep 5, 2024, 90 days after you bought it.
So the CUSIP alone does not tell us the original auction date or the original maturity date (and therefore the time length of the bill)?

Fascinating stuff!
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Re: How to buy 3 month treasuries

Post by Frugalmen »


So the CUSIP alone does not tell us the original auction date or the original maturity date (and therefore the time length of the bill)?

Fascinating stuff!
Not true, An internet search on the term "912797GL5 T-bill" will yield a few results:

https://www.treasurydirect.gov/instit/a ... 0603_2.pdf
and
https://www.treasurydirect.gov/auctions ... =912797GL5

Here is some info:
Original Auction = 1-year T-bill
Original Auction date = 9/5/23
Original Issue = 9/7/23

The Maturity date is always static. In this case it was always going to mature on 9/5/24.
Treasurydirect.gov is your best friend / main resource when you researching treasuries.

Something to think about after this T-bill matures. If you do not need the money in all one lump sum, think about a treasury ladder. Break-up the cash into 3 rungs say (416K on a 4week t-bill, 415K on a 8week t-bill, and 415K on a 13week) This way you'll have something maturing every month and also take advantage of rates should it increase. BTW, you can sell these t-bills anytime you want and still realize the interest gain as interest is calculated daily. There is so much more...but I will not bore you with it for now.

OH what Fun!
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Mon Jun 10, 2024 3:43 am
Chip Munk wrote: Sat Jun 08, 2024 7:04 pm That particular T-Bill (CUSIP 912797GL5 with a maturity date of 09/05/2024) has been offered at auction three times: 1) in Sep 2023 as a 52-week T-Bill, 2) in Mar 2024 as a 26-wk T-Bill, and 3) in June 2024 as a 13-wk T-Bill. https://www.treasurydirect.gov/auctions ... =912797GL5 The ones you bought were originally purchased at auction in either Sep 2023 or Mar 2024.

To keep things simple, assume you bought this T-Bill from the original owner (i.e., they bought at auction and not on the secondary market). It could have been purchased in either Sep 2023 for $94.823111 or Mar 2024 for $97.419139. You bought it from that owner at a price of $98.6909. So the owner made some money by selling it to you for more than they paid, and you will make money when it matures and are paid $100 by the US Treasury on Sep 5, 2024, 90 days after you bought it.
So the CUSIP alone does not tell us the original auction date or the original maturity date (and therefore the time length of the bill)?

Fascinating stuff!
Bills with the same CUSIP have the same maturity date. As stated above, this particular T-Bill -- CUSIP 912797GL5 has a maturity date of 09/05/2024. The Treasury has auctioned this particular T-Bill three times, but at auctions #2 and #3, there was less time remaining until the maturity date so while it was a 52-week bill the first time it was auctioned (Sep 2023), it was a 26-week bill the second time it was auctioned (six months later in Mar 2023) and a 13-week bill the third time it was auctioned (in Jun 2024) because that was the amount of time left until that fixed maturity date. Same CUSIP, same maturity date.
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Re: How to buy 3 month treasuries (BOND CONFUSION follow up)

Post by josephny »

I'm confused still (or again).

I just bought 912797LP0 on 6/17/2024 for $97.4685.

Settlement date is 6/18/2024.

Maturity date is 12/12/2024.

This is a 6 month T-bill.

I was told the annual yield is 5.35%, but I can't get the calculations to work out.

From 6/17/2024 to 12/12/2024 is 178 days (No idea if I should use 6/17 or 6/18, include or exclude the end date, so I might be off by a day)

100 - 97.4685 = 2.5315

2.5315 / 178 = 0.014222 (interest per day).

0.014222 * 365 = 5.191

0.014222 * 360 = 5.12

What am I doing wrong?
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Re: How to buy 3 month treasuries

Post by IDpilot »

The equation is ((100-price)/price)*(days in year/term)

So ((100-97.4685)/97.4685)*(365/177) = 5.356%

You use days from settlement date to maturity date
Last edited by IDpilot on Mon Jun 17, 2024 11:19 am, edited 1 time in total.
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Re: How to buy 3 month treasuries

Post by josephny »

IDpilot wrote: Mon Jun 17, 2024 11:15 am The equation is ((100-price)/price)*(days in year/term)

So ((100-97.4685)/97.4685)*(365/177)
I would not have gotten that last piece -- *(365/177)

No it makes perfect sense: There are (365/177) 2.0621469 periods in a year.

Thank you!
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Mon Jun 17, 2024 11:18 am
IDpilot wrote: Mon Jun 17, 2024 11:15 am The equation is ((100-price)/price)*(days in year/term)

So ((100-97.4685)/97.4685)*(365/177)
I would not have gotten that last piece -- *(365/177)

No it makes perfect sense: There are (365/177) 2.0621469 periods in a year.

Thank you!
I don't like to have to enter the price two times into the calculator, so I use this slight simplification.

Instead of: (100-price) / price
I use: (100/price) - 1

So in your example: ( (100 / 97.4685) - 1) * (365/177)
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Re: How to buy 3 month treasuries

Post by josephny »

Chip Munk wrote: Mon Jun 17, 2024 6:55 pm
josephny wrote: Mon Jun 17, 2024 11:18 am
IDpilot wrote: Mon Jun 17, 2024 11:15 am The equation is ((100-price)/price)*(days in year/term)

So ((100-97.4685)/97.4685)*(365/177)
I would not have gotten that last piece -- *(365/177)

No it makes perfect sense: There are (365/177) 2.0621469 periods in a year.

Thank you!
I don't like to have to enter the price two times into the calculator, so I use this slight simplification.

Instead of: (100-price) / price
I use: (100/price) - 1

So in your example: ( (100 / 97.4685) - 1) * (365/177)
That's all fine and good but what about those treasury instruments with a face value of $116.78?

(This is someone who knows so very close to nothing about bonds trying to make a bond-math joke.)

Nice math work!

Now how can we simply the: 365 / days-to-maturity? That is, I need to use an online calculator to figure out the days to maturity, and then plug it into that formula. That's a lot of steps.
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

josephny wrote: Mon Jun 17, 2024 10:09 pm Now how can we simply the: 365 / days-to-maturity? That is, I need to use an online calculator to figure out the days to maturity, and then plug it into that formula. That's a lot of steps.
I bring up two instances of the Windows calculator. I set one of them to "Date Calculation" mode to calculate the days to maturity, then use the result in the other instance (in Standard mode) to do the rest of the calculation.
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

Chip Munk wrote: Mon Jun 17, 2024 10:25 pm
josephny wrote: Mon Jun 17, 2024 10:09 pm Now how can we simply the: 365 / days-to-maturity? That is, I need to use an online calculator to figure out the days to maturity, and then plug it into that formula. That's a lot of steps.
I bring up two instances of the Windows calculator. I set one of them to "Date Calculation" mode to calculate the days to maturity, then use the result in the other instance (in Standard mode) to do the rest of the calculation.
I just trust that the YTM shown by the brokerage is correct and don't need to do my own calculations.
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Re: How to buy 3 month treasuries

Post by Geologist »

I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
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Re: How to buy 3 month treasuries

Post by josephny »

Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
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Re: How to buy 3 month treasuries

Post by IDpilot »

josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
My point was that when I buy a bond, whether at auction or secondary, I trust the YTM or Investment Rate that is provided by the brokerage or Treasury Dept. I don't feel the need to cross-check it. The numbers are provided to be able to compare bonds and if I had to compute yield for all the bonds I am considering, it would be way too tedious.
Retired June 2023. LMP (TIPS Ladder/SS Bridge) 25%/Risk Portfolio 75%, AA = 60/30/10
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Chip Munk
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Re: How to buy 3 month treasuries

Post by Chip Munk »

RyeBourbon wrote: Tue Jun 18, 2024 9:54 am
IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
My point was that when I buy a bond, whether at auction or secondary, I trust the YTM or Investment Rate that is provided by the brokerage or Treasury Dept. I don't feel the need to cross-check it. The numbers are provided to be able to compare bonds and if I had to compute yield for all the bonds I am considering, it would be way too tedious.
Yes but when you're new to buying T-Bills as the OP seems to be, there's nothing wrong with being curious about how the brokerage or the Treasury Dept arrived at the number they provided.
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Re: How to buy 3 month treasuries

Post by RyeBourbon »

Chip Munk wrote: Tue Jun 18, 2024 10:25 am
RyeBourbon wrote: Tue Jun 18, 2024 9:54 am
IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
My point was that when I buy a bond, whether at auction or secondary, I trust the YTM or Investment Rate that is provided by the brokerage or Treasury Dept. I don't feel the need to cross-check it. The numbers are provided to be able to compare bonds and if I had to compute yield for all the bonds I am considering, it would be way too tedious.
Yes but when you're new to buying T-Bills as the OP seems to be, there's nothing wrong with being curious about how the brokerage or the Treasury Dept arrived at the number they provided.
Oh yes, I did the same when starting out. It's good to understand where the number comes from.
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Re: How to buy 3 month treasuries

Post by IDpilot »

RyeBourbon wrote: Tue Jun 18, 2024 10:27 am
Chip Munk wrote: Tue Jun 18, 2024 10:25 am
RyeBourbon wrote: Tue Jun 18, 2024 9:54 am
IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am

Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
My point was that when I buy a bond, whether at auction or secondary, I trust the YTM or Investment Rate that is provided by the brokerage or Treasury Dept. I don't feel the need to cross-check it. The numbers are provided to be able to compare bonds and if I had to compute yield for all the bonds I am considering, it would be way too tedious.
Yes but when you're new to buying T-Bills as the OP seems to be, there's nothing wrong with being curious about how the brokerage or the Treasury Dept arrived at the number they provided.
Oh yes, I did the same when starting out. It's good to understand where the number comes from.
And it is good to understand what the number means ... and that was my point. They are not interchangeable.
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
This is great -- thank you.

I was just going by intuition on YTM, but the fact that there are terms specific to the type of investment instrument makes perfect sense (although I did not realize how much is clarified things before you identified these terms).

Investopia is useful:

"The coupon equivalent rate (CER) is an alternative calculation of coupon rate used to compare zero-coupon and coupon fixed-income securities. It is the annualized yield on a zero-coupon bond when calculated as if it paid a coupon. It is also known as the bond equivalent yield (BEY) or the coupon equivalent yield (CEY)"

"Yield to maturity (YTM) is considered a long-term bond yield but is expressed as an annual rate. It is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity, with all payments made as scheduled and reinvested at the same rate."

But BH is better (;-):

viewtopic.php?t=391594

What I was thinking of all along was the "investment rate."

Thank you!
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josephny
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Re: How to buy 3 month treasuries

Post by josephny »

Chip Munk wrote: Tue Jun 18, 2024 10:25 am
RyeBourbon wrote: Tue Jun 18, 2024 9:54 am
IDpilot wrote: Tue Jun 18, 2024 8:32 am
josephny wrote: Tue Jun 18, 2024 7:29 am
Geologist wrote: Tue Jun 18, 2024 7:15 am I agree with RyeBourbon. You are not the first person to post to ask whether the brokerage interest rate (or even the Treasury's interest rate for auction results) is correct and invariably the brokerage/Treasury was correct. So just take the published rate and go on with your life.
Morgan's dashboard does not indicate the YTM.

It only indicated the settlement date, price, and maturity date.

It was my guy at Morgan that verbally told me the YTM.

I'm far (far far) from experienced at this, but sure seems to me that Morgan's dashboard is subpar in many ways.
I added the bold.

Earlier in this thread, josephny, you also posted "I was told the annual yield is 5.35%, but I can't get the calculations to work out." Again, I added the bold.

The value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) nor is it the annual yield. It is the coupon equivalent yield which is also referred to as the Investment Rate on the auction results sheet. 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.
My point was that when I buy a bond, whether at auction or secondary, I trust the YTM or Investment Rate that is provided by the brokerage or Treasury Dept. I don't feel the need to cross-check it. The numbers are provided to be able to compare bonds and if I had to compute yield for all the bonds I am considering, it would be way too tedious.
Yes but when you're new to buying T-Bills as the OP seems to be, there's nothing wrong with being curious about how the brokerage or the Treasury Dept arrived at the number they provided.
I am indeed new to buying t-bills. Combined with an overall excess of curiousity and desire to understand, mixed with a dollop of skepticism, suspicion, and mistrust in people and institutions, often leads me to double check things.
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Re: How to buy 3 month treasuries

Post by #Cruncher »

IDpilot wrote: Tue Jun 18, 2024 8:32 amThe value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) ... It is ... also referred to as the Investment Rate on the auction results sheet.
The Coupon Equivalent Yield (aka Investment Rate) may not be the same as the YTM, but it is close. Both are based on the increase of price to 100. Both multiply this increase by a fraction where the denominator is the number of days from settlement to maturity. They differ only in the numerator. For the Investment Rate it is the number of days in a year. For the YTM it is twice the number of days in the current six-month period.

In most cases, this will not equal the number of days in the year. Then the YTM will differ slightly from the Investment Rate. This is shown in cells B10 and B11 below. But in some cases, twice the number of days in the current six-month period will equal the number of days in the year. Then the YTM and the Investment Rate will be the same. This is shown below in cells C10 and C11.

Code: Select all

Row                           Col A       Col B       Col C
  2                      Settlement   3/21/2024  12/21/2023
  3                         Matures   9/19/2024   6/20/2024
  4                           Price   97.406500   97.406500
  5    Percent increase at maturity    +2.6626%    +2.6626%  =100/B4-1
  6         Start of 6 month period   3/19/2024  12/20/2023  =EDATE(B3,-6)
  7     Days settlement to maturity         182         182  =B3-B2
  8  Days in current 6 month period         184         183  =B3-B6
  9                    Days in year         365         366  =EDATE(B2,12)-B2
 10          T Bill Investment Rate      5.340%      5.354%  =B5*(B9/B7)
 11         Yield to maturity (YTM)      5.384%      5.354%  =B5*(2*B8/B7)
 12  YTM calculated with YIELD func      5.384%      5.354%  =YIELD(B2,B3,0,B4,100,2,1)
Notes:
  • Column B shows the 6-month bill auctioned 3/18/2024.
  • Column C shows the 6-month bill auctioned 12/18/2023.
  • I've added row 12 just to show that the YTM calculated on row 11 is the same as that from the Excel YIELD function.
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Re: How to buy 3 month treasuries

Post by IDpilot »

#Cruncher wrote: Wed Jun 19, 2024 7:46 am
IDpilot wrote: Tue Jun 18, 2024 8:32 amThe value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) ... It is ... also referred to as the Investment Rate on the auction results sheet.
The Coupon Equivalent Yield (aka Investment Rate) may not be the same as the YTM, but it is close. Both are based on the increase of price to 100. Both multiply this increase by a fraction where the denominator is the number of days from settlement to maturity. They differ only in the numerator. For the Investment Rate it is the number of days in a year. For the YTM it is twice the number of days in the current six-month period.

In most cases, this will not equal the number of days in the year. Then the YTM will differ slightly from the Investment Rate. This is shown in cells B10 and B11 below. But in some cases, twice the number of days in the current six-month period will equal the number of days in the year. Then the YTM and the Investment Rate will be the same. This is shown below in cells C10 and C11.

Code: Select all

Row                           Col A       Col B       Col C
  2                      Settlement   3/21/2024  12/21/2023
  3                         Matures   9/19/2024   6/20/2024
  4                           Price   97.406500   97.406500
  5    Percent increase at maturity    +2.6626%    +2.6626%  =100/B4-1
  6         Start of 6 month period   3/19/2024  12/20/2023  =EDATE(B3,-6)
  7     Days settlement to maturity         182         182  =B3-B2
  8  Days in current 6 month period         184         183  =B3-B6
  9                    Days in year         365         366  =EDATE(B2,12)-B2
 10          T Bill Investment Rate      5.340%      5.354%  =B5*(B9/B7)
 11         Yield to maturity (YTM)      5.384%      5.354%  =B5*(2*B8/B7)
 12  YTM calculated with YIELD func      5.384%      5.354%  =YIELD(B2,B3,0,B4,100,2,1)
Notes:
  • Column B shows the 6-month bill auctioned 3/18/2024.
  • Column C shows the 6-month bill auctioned 12/18/2023.
  • I've added row 12 just to show that the YTM calculated on row 11 is the same as that from the Excel YIELD function.
Agree they are close but not the same.

YTM is the internal rate of return (IRR) of an investment in a bond if the investor holds the bond until maturity. If you compute the IRR you get a different answer than yours above. For your example in Column B the XIRR value is 5.411% and so is (100/Price)^(days in year/days to maturity) -1 which is the closed form solution for the discounted cash flow model with only a beginning and ending cash flow. Clearly this is different from the YIELD function results and your (100/Price -1)*(2*days in current 6 month period/days to maturity). What am I missing? Is this some sort of "by bond convention" thing?
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Re: How to buy 3 month treasuries

Post by Kevin M »

#Cruncher wrote: Wed Jun 19, 2024 7:46 am
IDpilot wrote: Tue Jun 18, 2024 8:32 amThe value we have been discussing is the Coupon Equivalent Yield and that is NOT the Yield To Maturity (YTM) ... It is ... also referred to as the Investment Rate on the auction results sheet.
The Coupon Equivalent Yield (aka Investment Rate) may not be the same as the YTM, but it is close. Both are based on the increase of price to 100. Both multiply this increase by a fraction where the denominator is the number of days from settlement to maturity. They differ only in the numerator. For the Investment Rate it is the number of days in a year. For the YTM it is twice the number of days in the current six-month period.

In most cases, this will not equal the number of days in the year. Then the YTM will differ slightly from the Investment Rate. This is shown in cells B10 and B11 below. But in some cases, twice the number of days in the current six-month period will equal the number of days in the year. Then the YTM and the Investment Rate will be the same. This is shown below in cells C10 and C11.

Code: Select all

Row                           Col A       Col B       Col C
  2                      Settlement   3/21/2024  12/21/2023
  3                         Matures   9/19/2024   6/20/2024
  4                           Price   97.406500   97.406500
  5    Percent increase at maturity    +2.6626%    +2.6626%  =100/B4-1
  6         Start of 6 month period   3/19/2024  12/20/2023  =EDATE(B3,-6)
  7     Days settlement to maturity         182         182  =B3-B2
  8  Days in current 6 month period         184         183  =B3-B6
  9                    Days in year         365         366  =EDATE(B2,12)-B2
 10          T Bill Investment Rate      5.340%      5.354%  =B5*(B9/B7)
 11         Yield to maturity (YTM)      5.384%      5.354%  =B5*(2*B8/B7)
 12  YTM calculated with YIELD func      5.384%      5.354%  =YIELD(B2,B3,0,B4,100,2,1)
Notes:
  • Column B shows the 6-month bill auctioned 3/18/2024.
  • Column C shows the 6-month bill auctioned 12/18/2023.
  • I've added row 12 just to show that the YTM calculated on row 11 is the same as that from the Excel YIELD function.
I guess it depends how you define YTM. The spreadsheet YIELD function has two frequency parameters and five day count conventions (I'm using the Google Sheets version parameter names). I've found that as long as there are 365 days in a year (the way Treasury counts them), then for bills of not more than one half-year to maturity, using freq param = 1 and DCC = 3 generates a number that agrees with Treasuries Tbill investment rate formula.
For bills with investment rates using 366 days in a year and not more than one-half year to maturity, the formula sometimes works with those parameters and sometimes is 15 basis points low.

For bills with more than one-half year to maturity, YIELD works most of the time with freq=2 and dcc=1 to 3 decimal places, which is all Treasury reports. With one exception, when the when YIELD doesn't match the reported value, it's 0.001 percentage point or 0.1 basis point different.

So I would say that investment rate and bond equivalent yield are versions of yield to maturity.
If I make a calculation error, #Cruncher probably will let me know.
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Re: How to buy 3 month treasuries

Post by #Cruncher »

IDpilot wrote: Wed Jun 19, 2024 8:50 am... If you compute the IRR you get a different answer than yours above. For your example in Column B the XIRR value is 5.411% and so is (100/Price)^(days in year/days to maturity) -1 ... Clearly this is different from the YIELD function results and your (100/Price -1)*(2*days in current 6 month period/days to maturity). What am I missing? Is this some sort of "by bond convention" thing?
There are two issues here:
1. "(100/Price)^(days in year/days to maturity) -1" and the XIRR function return an Annual Percentage Yield or APY. Treasury yields (for bills, notes, and bonds) on the other hand are semi-annual rates doubled. For example, a 5% note selling at par will be reported as having a 5% YTM. But this is equivalent to a 5.0625% APY.
5.0625% = (1 + 0.05 / 2) ^ 2 - 1

2. The other issue is whether to use linear or exponential extrapolation for a partial six-month period. The Treasury convention is to use linear. Besides T-Bills it implicitly uses this when computing the price of a note or bond from the yield determined at auction. The table below illustrates this for the 19-year 10-month T-Bond auctioned 4/17/2024. It shows, step by step, how the Treasury computed the 95.958772 price from the auction's 4.818% YTM.

Code: Select all

Row                     Col A        Col B   Formula in Column B
  2                 Principal      100.000
  3                Issue Date    4/30/2024
  4             Maturity Date    2/15/2044
  5    Interest Rate (coupon)       4.500%
  6  High Yield (to maturity)       4.818% <===

Code: Select all

  7  Start of interest period    2/15/2024  =COUPPCD(B3,B4,2,1)
  8  Next interest date (NID)    8/15/2024  =COUPNCD(B3,B4,2,1)
  9      Days in first period          182  =B8-B7
 10         Days before issue           75  =B3-B7
 11          Days after issue          107  =B8-B3
 12  Number full 6 mo periods           39  =COUPNUM(B3,B4,2,1)-1
 13   Present value $1 on NID   0.39519652  =1/(1+B6/2)^B12
 14      PV $1 annuity on NID    25.105998  =IF(B6=0,B12,(1-B13)/(B6/2))
 15           Total PV on NID    98.258146  =B2*(B13+(B14+1)*(B5/2))
 16  Present value issue date    96.885970  =B15/(1+(B6/2)*(B11/B9))
 17          Accrued interest     0.927198  =B2*ROUND((B5/2)*(B10/B9),8)
 18   Net of accrued interest    95.958772  =B16-B17 <===
Steps
  • Rows 9-11 show the initial 182-day interest period is broken down between 75 days before the bond is issued and 107 days after.
  • Row 12 shows that there are 39 full six-month periods following the first interest period.
  • Rows 13-15 compute the present value as of 8/15/2024 of the principal and coupon interest exponentially over the 39 full periods.
  • Row 16 computes the present value 107 days earlier on the 4/30/2024 issue date. Note that the 4.818% / 2 semi-annual rate is treated linearly, not exponentially. I.e., it is multiplied by 107 / 182.
  • Row 18 shows the clean price excluding the accrued interest that is implicitly included in the dirty price on row 16.
The YIELD function also uses linear extrapolation for a partial interest period -- but only when there are no full interest periods following the initial period. This is why it returns the same value as the Investment Rate in the table in my previous post. However, if there is at least one full period following the partial period, it extrapolates the partial period exponentially.

We can see this by modifying cell B16 above to handle the partial period exponentially. We get a slightly different price (after deducting the accrued interest):
95.965412 = 98.258146 / (1 + 0.04818 / 2) ^ (107 / 182) - 0.927198

If we then feed this altered price back into the YIELD function, we get exactly 4.818%, confirming that the function does handle the partial period exponentially.
4.818000% = YIELD(DATE(2024, 4, 30), DATE(2044, 2, 15), 4.5%, 95.965412, 100, 2, 1)
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Re: How to buy 3 month treasuries

Post by IDpilot »

#Cruncher wrote: Wed Jun 19, 2024 3:46 pm
IDpilot wrote: Wed Jun 19, 2024 8:50 am... If you compute the IRR you get a different answer than yours above. For your example in Column B the XIRR value is 5.411% and so is (100/Price)^(days in year/days to maturity) -1 ... Clearly this is different from the YIELD function results and your (100/Price -1)*(2*days in current 6 month period/days to maturity). What am I missing? Is this some sort of "by bond convention" thing?
There are two issues here:
1. "(100/Price)^(days in year/days to maturity) -1" and the XIRR function return an Annual Percentage Yield or APY. Treasury yields (for bills, notes, and bonds) on the other hand are semi-annual rates doubled. For example, a 5% note selling at par will be reported as having a 5% YTM. But this is equivalent to a 5.0625% APY.
5.0625% = (1 + 0.05 / 2) ^ 2 - 1

2. The other issue is whether to use linear or exponential extrapolation for a partial six-month period. The Treasury convention is to use linear. Besides T-Bills it implicitly uses this when computing the price of a note or bond from the yield determined at auction. The table below illustrates this for the 19-year 10-month T-Bond auctioned 4/17/2024. It shows, step by step, how the Treasury computed the 95.958772 price from the auction's 4.818% YTM.

Code: Select all

Row                     Col A        Col B   Formula in Column B
  2                 Principal      100.000
  3                Issue Date    4/30/2024
  4             Maturity Date    2/15/2044
  5    Interest Rate (coupon)       4.500%
  6  High Yield (to maturity)       4.818% <===

Code: Select all

  7  Start of interest period    2/15/2024  =COUPPCD(B3,B4,2,1)
  8  Next interest date (NID)    8/15/2024  =COUPNCD(B3,B4,2,1)
  9      Days in first period          182  =B8-B7
 10         Days before issue           75  =B3-B7
 11          Days after issue          107  =B8-B3
 12  Number full 6 mo periods           39  =COUPNUM(B3,B4,2,1)-1
 13   Present value $1 on NID   0.39519652  =1/(1+B6/2)^B12
 14      PV $1 annuity on NID    25.105998  =IF(B6=0,B12,(1-B13)/(B6/2))
 15           Total PV on NID    98.258146  =B2*(B13+(B14+1)*(B5/2))
 16  Present value issue date    96.885970  =B15/(1+(B6/2)*(B11/B9))
 17          Accrued interest     0.927198  =B2*ROUND((B5/2)*(B10/B9),8)
 18   Net of accrued interest    95.958772  =B16-B17 <===
Steps
  • Rows 9-11 show the initial 182-day interest period is broken down between 75 days before the bond is issued and 107 days after.
  • Row 12 shows that there are 39 full six-month periods following the first interest period.
  • Rows 13-15 compute the present value as of 8/15/2024 of the principal and coupon interest exponentially over the 39 full periods.
  • Row 16 computes the present value 107 days earlier on the 4/30/2024 issue date. Note that the 4.818% / 2 semi-annual rate is treated linearly, not exponentially. I.e., it is multiplied by 107 / 182.
  • Row 18 shows the clean price excluding the accrued interest that is implicitly included in the dirty price on row 16.
The YIELD function also uses linear extrapolation for a partial interest period -- but only when there are no full interest periods following the initial period. This is why it returns the same value as the Investment Rate in the table in my previous post. However, if there is at least one full period following the partial period, it extrapolates the partial period exponentially.

We can see this by modifying cell B16 above to handle the partial period exponentially. We get a slightly different price (after deducting the accrued interest):
95.965412 = 98.258146 / (1 + 0.04818 / 2) ^ (107 / 182) - 0.927198

If we then feed this altered price back into the YIELD function, we get exactly 4.818%, confirming that the function does handle the partial period exponentially.
4.818000% = YIELD(DATE(2024, 4, 30), DATE(2044, 2, 15), 4.5%, 95.965412, 100, 2, 1)
As usual a most excellent explanation. Thanks for the time and effort you put into your answer.
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