## Trading Treasuries (nominal and TIPS)

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exodusing
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### Re: Trading Treasuries (nominal and TIPS)

Now I'm wondering about Excel's tbillyield function for the T-bills I just bought. If I plug in the numbers from the screenshot above (settle 3/9/23, mature 4/25/23, price 99.395) I get a yield of 4.662% rather than the 4.721% in the screenshot.

If I use the formula ((100-price)/price) * (365/days) using 47 days, I get 4.727%, which is much closer.

I'm guessing the problem is either Excel or my understanding, but why is Excel doing this? Did I get the formula wrong or is this just rounding error?
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Use YIELD with freq parameter = 1 for maturities of 26 weeks or less, and 2 for longer (i.e., 52 weeks); use freq = 2 for the latter. Use day count convention = 1 (actual/actual). This will give results that match to at least 3 decimal places, which is all Treasury publishes.
If I make a calculation error, #Cruncher probably will let me know.
exodusing
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Wed Mar 08, 2023 2:49 pm Use YIELD with freq parameter = 1 for maturities of 26 weeks or less, and 2 for longer (i.e., 52 weeks); use freq = 2 for the latter. Use day count convention = 1 (actual/actual). This will give results that match to at least 3 decimal places, which is all Treasury publishes.
=YIELD(DATE(2023,3,9),DATE(2023,4,25),0,99.395,100,1,1)*100 results in 4.727, the same as the formula in my post above, but a touch off from the 4.721 quoted by Vanguard. Much better than the tbillyield function.
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

exodusing wrote: Wed Mar 08, 2023 3:21 pm
Kevin M wrote: Wed Mar 08, 2023 2:49 pm Use YIELD with freq parameter = 1 for maturities of 26 weeks or less, and 2 for longer (i.e., 52 weeks); use freq = 2 for the latter. Use day count convention = 1 (actual/actual). This will give results that match to at least 3 decimal places, which is all Treasury publishes.
=YIELD(DATE(2023,3,9),DATE(2023,4,25),0,99.395,100,1,1)*100 results in 4.727, the same as the formula in my post above, but a touch off from the 4.721 quoted by Vanguard. Much better than the tbillyield function.
Vanguard uses more than 3 digits for price. To get the actual price, divide the amount paid by the face value, then use that in the yield calc. To see the actual price, pretend to buy a bill, and see the price at the preview screen (then cancel).
If I make a calculation error, #Cruncher probably will let me know.
exodusing
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Wed Mar 08, 2023 3:46 pmVanguard uses more than 3 digits for price. To get the actual price, divide the amount paid by the face value, then use that in the yield calc. To see the actual price, pretend to buy a bill, and see the price at the preview screen (then cancel).
I ran Excel's Yield (and the above formula, which produces the same results) against my actual purchase prices (e.g., 49698.55/500 for the 4/25) and compared the yield quoted by Vanguard to the value I calculated. Results were 4/25 maturity, 4.711 v 4.710; 6/27, 5.016 v 5.006; and 8/31, 5.226 v 5.212. I'm only pushing this out of academic interest, the practical difference is minimal at most.
#Cruncher
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### Re: Trading Treasuries (nominal and TIPS)

exodusing wrote: Wed Mar 08, 2023 1:25 pmNow I'm wondering about Excel's tbillyield function for the T-bills I just bought. ... I'm guessing the problem is either Excel or my understanding, ...
Avoid the TBILLYIELD function. As shown in the bottom row of the table below, it computes neither the Discount Rate (aka High Rate) nor the Investment Rate (aka Coupon Equivalent Yield). [1] Instead use the TBILLEQ, YIELD, or YIELDDISC function for an approximation of the Investment Rate.
Kevin M wrote: Wed Mar 08, 2023 2:49 pmUse YIELD with freq parameter = 1 for maturities of 26 weeks or less, and 2 for longer (i.e., 52 weeks); ... This will give results that match to at least 3 decimal places, which is all Treasury publishes. (underline added)
Unfortunately this is no longer true for T-Bills issued March 1st or later. The investment rate calculation for these bills uses 366 as the number of days in the year. [2] For example, the YIELD function with freq = 1 returns the correct 4.977% as the Investment Rate for the 17-week bill issued 2/28 shown in column B below. But it returns 5.202% instead of the correct 5.216% Investment Rate for the 17-week bill issued 3/14 shown in column C.

Code: Select all

``````Row             Col A      Col B      Col C   Formula in Column B Copied Right to Column C
2            Issued  2/28/2023  3/14/2023
3           Matures  6/27/2023  7/11/2023
4             Price  98.403417  98.332347
5      Days in term        119        119  =B3-B2
6      Days in year        365        366  =DATE(YEAR(B2)+1,MONTH(B2),DAY(B2))-B2
7  Fraction of year    119/365    119/366  =B5/B6
8     Discount Rate     4.830%     5.045%  =(1-B4/100)*(360/B5)
9   Investment Rate     4.977%     5.216%  =IF(B7<=0.5,(100/B4-1)/B7,(-B7+SQRT(B7^2-(2*B7-1)*(1-100/B4)))/(B7-0.5))
10           TBILLEQ     4.977%     5.202%  =TBILLEQ(   B2,B3,  B8)
11             YIELD     4.977%     5.202%  =YIELD(     B2,B3,0,B4,100,IF(B7<=0.5,1,2),1)
12         YIELDDISC     4.977%     5.202%  =YIELDDISC( B2,B3,  B4,100,1)
13        TBILLYIELD     4.908%     5.131%  =TBILLYIELD(B2,B3,  B4)``````
1. See this post for a thorough discussion of the problems of the TBILLYIELD function.
2. The Treasury formulas for Investment Rate are on pages 2 and 3 of Price, Yield and Rate Calculations for a Treasury Bill. Note the formula is much more complicated for bills maturing in more than 1/2 year.
Last edited by #Cruncher on Wed Mar 08, 2023 10:12 pm, edited 1 time in total.
exodusing
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### Re: Trading Treasuries (nominal and TIPS)

#Cruncher wrote: Wed Mar 08, 2023 4:42 pm [*]The Treasury formulas for Investment Rate are on pages 2 and 3 of Price, Yield and Rate Calculations for a Treasury Bill. Note the formula is much more complicated for bills maturing in more than 1/2 year.[/list]
If I'm reading this correctly, the formula for bills maturing in less than 1/2 year is the formula I posted above, ((100-price)/price) * (365/days) , although for T-bills issued after 2023-03-01 you should use 366 rather than 365.

Applying this formula to the T-bill in viewtopic.php?p=7155981#p7155981 (which was issued before March 1), gives 4.727 rather than the 4.721 listed. Is this likely due to rounding?

Applying the formula to the T-bills listed in viewtopic.php?p=7156609#p7156609 produces results that are off by about 1bp or less, although I didn't round the purchase price. Any idea why?
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Treasury uses 366 days whenever the next year includes a Feb with 29 days. So, 366 days was used for bills issued between 3/1/2019 and 2/27/2020, for example. I had forgotten that YIELD does not give the same yields for 366 day years.
If I make a calculation error, #Cruncher probably will let me know.
texasfight
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Mon Feb 20, 2023 1:25 pm Here is the short-term TIPS yield curve from Friday:

(SA = seasonally adjusted)

As mentioned, TIPS that are very close to maturity trade more like a nominal Treasury of same maturity. We know the inflation adjustments through 4/1/2023, so there are only 15 days for which the adjustments are unknown for the 4/15/2023 TIPS. I have a spreadsheet in which I was comparing the 1/15/2023 TIPS to the 1/15/2023 nominal once we knew all the inflation adjustments; maybe I'll fire that up again for the 4/15/2023 TIPS soon.

Kevin
Kevin

any way we can get an update of this with all the recent crazy moves? curious about real yields sub 1 yr
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

texasfight wrote: Mon Mar 13, 2023 6:40 pm
Kevin M wrote: Mon Feb 20, 2023 1:25 pm Here is the short-term TIPS yield curve from Friday:

(SA = seasonally adjusted)

As mentioned, TIPS that are very close to maturity trade more like a nominal Treasury of same maturity. We know the inflation adjustments through 4/1/2023, so there are only 15 days for which the adjustments are unknown for the 4/15/2023 TIPS. I have a spreadsheet in which I was comparing the 1/15/2023 TIPS to the 1/15/2023 nominal once we knew all the inflation adjustments; maybe I'll fire that up again for the 4/15/2023 TIPS soon.

Kevin
Kevin

any way we can get an update of this with all the recent crazy moves? curious about real yields sub 1 yr
Sure.

I saw this morning that the short-term Treasury and TIPS ETF prices were up fairly big, so I knew that the yields would be down. Here is the TIPS curve from this morning when I pulled the data:

Here are nominal Treasuries out to 1-year maturity:

I was buying nominal Treasuries last week at a little over 5% out to at least 6 month maturities.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
texasfight
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Mon Mar 13, 2023 9:15 pm
texasfight wrote: Mon Mar 13, 2023 6:40 pm
Kevin M wrote: Mon Feb 20, 2023 1:25 pm Here is the short-term TIPS yield curve from Friday:

(SA = seasonally adjusted)

As mentioned, TIPS that are very close to maturity trade more like a nominal Treasury of same maturity. We know the inflation adjustments through 4/1/2023, so there are only 15 days for which the adjustments are unknown for the 4/15/2023 TIPS. I have a spreadsheet in which I was comparing the 1/15/2023 TIPS to the 1/15/2023 nominal once we knew all the inflation adjustments; maybe I'll fire that up again for the 4/15/2023 TIPS soon.

Kevin
Kevin

any way we can get an update of this with all the recent crazy moves? curious about real yields sub 1 yr
Sure.

I saw this morning that the short-term Treasury and TIPS ETF prices were up fairly big, so I knew that the yields would be down. Here is the TIPS curve from this morning when I pulled the data:

Here are nominal Treasuries out to 1-year maturity:

I was buying nominal Treasuries last week at a little over 5% out to at least 6 month maturities.

Kevin
Thanks! I've been using TUA but I sold some and moved down on the curve today after the insane 3 day move in preparation for a retrace.
Doc
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Mon Mar 13, 2023 9:15 pm

I was buying nominal Treasuries last week at a little over 5% out to at least 6 month maturities.

Kevin
Kevin, do you have an explanation for the sever drop at 5 months?
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Doc wrote: Tue Mar 14, 2023 10:28 am
Kevin M wrote: Mon Mar 13, 2023 9:15 pm

I was buying nominal Treasuries last week at a little over 5% out to at least 6 month maturities.

Kevin
Kevin, do you have an explanation for the sever drop at 5 months?
I can tell you the characteristics of the Treasuries with the low yields. Maturity date for all is 8/15/2023.

912833LM0, stripped interest STRIPS, 4.15%
912803BC6, stripped principal STRIPS, 3.96%
912810EQ7, bond, 6.25% cpn, 3.91%

BTW, I see that short term Treasury ETFs are up big today, so yields should be higher. Let me check ...

Yep:

High yields not back up to 5%, but much of the yield ground lost yesterday was recovered today.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
Doc
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Tue Mar 14, 2023 1:23 pm
Doc wrote: Tue Mar 14, 2023 10:28 am
Kevin M wrote: Mon Mar 13, 2023 9:15 pm
(Image deleted. See prior post.)

I was buying nominal Treasuries last week at a little over 5% out to at least 6 month maturities.

Kevin
Kevin, do you have an explanation for the sever drop at 5 months?
I can tell you the characteristics of the Treasuries with the low yields. Maturity date for all is 8/15/2023.

912833LM0, stripped interest STRIPS, 4.15%
912803BC6, stripped principal STRIPS, 3.96%
912810EQ7, bond, 6.25% cpn, 3.91%

Kevin
The bond with a 6.25% coupon may be the problem. Are there adverse tax consequences for this issue that adjoining issues don't have?
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
Hector
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### Re: Trading Treasuries (nominal and TIPS)

Fidelity treasurys money market fund shows 7 day yield as of 2/28. Does anyone have a formula to calculate its current yield? I am curious to see if money makers pays more than new 4 week bill considering recent drop in the yield.
rockstar
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### Re: Trading Treasuries (nominal and TIPS)

I was able to get 6 month t bills at 4.97%. I feel good about that since the bond market this morning is pretty awful again. Lots of volatility in treasuries.
Hector
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### Re: Trading Treasuries (nominal and TIPS)

Hector wrote: Wed Mar 15, 2023 9:46 am Fidelity treasurys money market fund shows 7 day yield as of 2/28. Does anyone have a formula to calculate its current yield? I am curious to see if money makers pays more than new 4 week bill considering recent drop in the yield.
nvm!
I can see 7 day yield as of today on Desktop.
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Hector wrote: Wed Mar 15, 2023 9:46 am Fidelity treasurys money market fund shows 7 day yield as of 2/28. Does anyone have a formula to calculate its current yield? I am curious to see if money makers pays more than new 4 week bill considering recent drop in the yield.
You can see 1 day yield here: U.S. Treasury MM (FDLXX) | Fidelity Institutional

Interestingly, as of yesterday, 1 day yield was higher at 4.29% with 7 day at 4.28%.

Currently I see a bill maturing 4/13/2023 at 4.009% and one maturing 4/18/2023 at 4.070%.

Here are yields out to 6 month maturity:

Note the spike at about 1.5 months, which is for this note:

Code: Select all

``91282CBX8	N/A	UNITED STATES TREAS SER AZ-2023         0.12500% 04/30/2023 NTS NOTE	0.125	4/30/23	AAA	--	99.396	99.398	5.01	5.00``
You need to scroll to the right to see the yield; the high ask yield is 5.00%. It matures on a Sunday, but the yield is much higher than a couple of other notes that mature the same day.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Ignore the Treasury yield curve shown in previous post. I went to buy some of the 5% note, and the yield had dropped to 4.4%. Here is the updated chart:

Kevin
If I make a calculation error, #Cruncher probably will let me know.
Electron
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Wed Mar 15, 2023 1:37 pm Ignore the Treasury yield curve shown in previous post. I went to buy some of the 5% note, and the yield had dropped to 4.4%.
I noticed the same thing yesterday in my chart showing the one, two, three, and six month T-Bill rates in comparison with VUSXX.

The change in yields has been quite dramatic.

Does anyone have any thoughts on the best T-Bill maturities to replace and outperform VUSXX?

I have been using a T-Bill ladder now that VUSXX is investing more in repurchase agreements.

Electron
Hector
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Wed Mar 15, 2023 1:32 pm
Hector wrote: Wed Mar 15, 2023 9:46 am Fidelity treasurys money market fund shows 7 day yield as of 2/28. Does anyone have a formula to calculate its current yield? I am curious to see if money makers pays more than new 4 week bill considering recent drop in the yield.
You can see 1 day yield here: U.S. Treasury MM (FDLXX) | Fidelity Institutional

Interestingly, as of yesterday, 1 day yield was higher at 4.29% with 7 day at 4.28%.

Currently I see a bill maturing 4/13/2023 at 4.009% and one maturing 4/18/2023 at 4.070%.

Here are yields out to 6 month maturity:

Note the spike at about 1.5 months, which is for this note:

Code: Select all

``91282CBX8	N/A	UNITED STATES TREAS SER AZ-2023         0.12500% 04/30/2023 NTS NOTE	0.125	4/30/23	AAA	--	99.396	99.398	5.01	5.00``
You need to scroll to the right to see the yield; the high ask yield is 5.00%. It matures on a Sunday, but the yield is much higher than a couple of other notes that mature the same day.

Kevin
Thanks Kevin!'

Does anyone know how to see 1 day yield for Vanguard and Schwab MM?
exodusing
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### Re: Trading Treasuries (nominal and TIPS)

Hector wrote: Wed Mar 15, 2023 2:34 pmDoes anyone know how to see 1 day yield for Vanguard and Schwab MM?
Vanguard doesn't publish 1 day yields, but you could compare 1 and 7 day yields for a similar fund that does publish the information and estimate that there will be a similar spread between 1 and 7 day yields for Vanguard. For example, see https://am.jpmorgan.com/us/en/asset-man ... #/overview Its 1 day yield is 0.08 lower than its 7 day yield (at the moment), so I'd guess Vanguard's 1 day is 0.08 lower than its 7 day.
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Wed Mar 15, 2023 1:37 pm Ignore the Treasury yield curve shown in previous post. I went to buy some of the 5% note, and the yield had dropped to 4.4%. Here is the updated chart:

Kevin
Vanguard short-term government ETF (VGSH) is down 0.36% today, which is a pretty big daily change, and recovers much of the yield ground lost yesterday. So we should expect short term Treasury yields to be higher today than yesterday. Here is the same chart for today (0 to 6m):

The peak yield 4.90% is at 3.8 months (7/11/2023).

I had \$100K of Treasuries mature two days ago at Fidelity, but was not happy with the Treasury yields, so I put half into VUSXX (Vanguard Treasury MM fund) and put half in FZDXX with the intention of buying more Treasuries if and when I'm happier with the yields. I'm tempted by the 4.9% issue, but think I'll wait a bit more.

Yes, this is market timing, pure and simple.

VUSXX SEC yield was 4.57% yesterday, unchanged since 3/13/2023; this is a TEY of 5.19% for me (assuming that 2023 income will be 100% USGO, which may be a bit optimistic given the recent repo holdings percentages). FZDXX 7-day and 1-day yields were both 4.46% as of yesterday. I prefer trading Treasuries at Fidelity over Vanguard, which is why I'm keeping half in FZDXX for now.

I think the Treasury volatility is mainly due to the recent large bank failures, with traders trying to figure out if it's going to develop into a broader financial crisis or not.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
rockstar
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### Re: Trading Treasuries (nominal and TIPS)

Lots of volatility. Hard to know when to buy when yields are moving 20bps a day on the short end.
Elmo
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### Re: Trading Treasuries (nominal and TIPS)

rockstar wrote: Thu Mar 16, 2023 2:12 pm Lots of volatility. Hard to know when to buy when yields are moving 20bps a day on the short end.
Along those lines - anyone know why my auction purchase of 8 week T-bills that were supposed to execute 3/16/23 didn't until this morning sometime on the 17th? Never seen that before - is this a result of the "volatility"? Is this happening only at Fidelity? What's going on?
rockstar
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### Re: Trading Treasuries (nominal and TIPS)

Elmo wrote: Fri Mar 17, 2023 11:44 am
rockstar wrote: Thu Mar 16, 2023 2:12 pm Lots of volatility. Hard to know when to buy when yields are moving 20bps a day on the short end.
Along those lines - anyone know why my auction purchase of 8 week T-bills that were supposed to execute 3/16/23 didn't until this morning sometime on the 17th? Never seen that before - is this a result of the "volatility"? Is this happening only at Fidelity? What's going on?
No idea.

I ended up buying 1 year TIPS this morning on the secondary without any problems.
jeffyscott
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### Re: Trading Treasuries (nominal and TIPS)

^Does the transaction history show the transaction being "as of" the 16th or something like that?

I've seen that sort of thing, but only with mutual funds, at Schwab a few times.
And so it goes, And so it goes, And so it goes, And so it goes, But where it's goin' no one knows
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

Elmo wrote: Fri Mar 17, 2023 11:44 am
rockstar wrote: Thu Mar 16, 2023 2:12 pm Lots of volatility. Hard to know when to buy when yields are moving 20bps a day on the short end.
Along those lines - anyone know why my auction purchase of 8 week T-bills that were supposed to execute 3/16/23 didn't until this morning sometime on the 17th? Never seen that before - is this a result of the "volatility"? Is this happening only at Fidelity? What's going on?
This was discussed in another thread. Apparently there was a system problem that resulted in Treasury delaying the close of auctions from the 16th to the 17th.
If I make a calculation error, #Cruncher probably will let me know.
kalarama
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Fri Mar 03, 2023 11:51 am By contrast, the 2052 TIPS has a decent book at Fidelity, with yield for min qty 1 of 1.500 compared to high yield of 1.503 for min qty 50. So, it seems that it is just a matter of time for a decent book to develop.

Schwab historically has had best pricing for min qty 1 (typically as good or better than a larger quantity) for nominals, and it seems that they are carrying on that tradition for TIPS.
Update two weeks later: bid and ask depth of book for 2053 TIPS on fidelity is still only for qty 50 or 75.... I spoke to the fixed income rep at Fidelity and he was also not able to put in an order for less than 50.
Electron
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### Re: Trading Treasuries (nominal and TIPS)

Does anyone have any thoughts on the best T-Bill maturities to replace and outperform VUSXX?
A 2 Month T-Bill ladder appears to have provided the highest return in recent months. See the attached chart showing the comparison with VUSXX.

I created a model in Excel that calculates the average T-Bill yield over the term of each ladder using the daily Treasury Par Yield Curve Data.

The return of a typical T-Bill ladder investing at less frequent intervals might differ from the model by a small amount.

The results are quite interesting. I calculated the return of each T-Bill ladder relative to VUSXX and averaged the data.

1 Month T-Bill Ladder - Return averaged 9 basis points higher than VUSXX
2 Month T-Bill Ladder - Return averaged 14 basis points higher than VUSXX
3 Month T-Bill Ladder - Return averaged 12 basis points higher than VUSXX
6 Month T-Bill Ladder - Return averaged 7 basis points lower than VUSXX

The data goes back to 4-01-22 for the 1, 2, and 3 month ladders and 7-01-22 for the 6 month ladder.

We have been in a period of rising short term interest rates. The longer maturity ladders may provide the higher returns as rates level off. It will also be interesting to see the comparison when short term rates eventually decline.

Electron
retiringwhen
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### Re: Trading Treasuries (nominal and TIPS)

Electron wrote: Sat Mar 18, 2023 1:05 pm 1 Month T-Bill Ladder - Return averaged 9 basis points higher than VUSXX
2 Month T-Bill Ladder - Return averaged 14 basis points higher than VUSXX
3 Month T-Bill Ladder - Return averaged 12 basis points higher than VUSXX
6 Month T-Bill Ladder - Return averaged 7 basis points lower than VUSXX
I would be interested in your source data, but I am also confused, what is a 1 month ladder? How many tranches do you have in the ladder? 4 tranches with one every week? Similar patterns for the other ones?

My laddering scheme showed 4 week ladders (4 steps equally entered into a ladder one every 1/4 every week on a delayed basis into 4 week T-Bills) beating all other durations for investors at a 6.37% state income tax rate. The benefit was pretty minor though 4week ladders beat VUSXX by 4bp, an 8 week by 2bp and 13 weeks losing by 5 to 8 bp depending on how many steps I used.
Electron
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### Re: Trading Treasuries (nominal and TIPS)

retiringwhen wrote: Sat Mar 18, 2023 1:16 pm I would be interested in your source data, but I am also confused, what is a 1 month ladder? How many tranches do you have in the ladder? 4 tranches with one every week? Similar patterns for the other ones?

My laddering scheme showed 4 week ladders (4 steps equally entered into a ladder one every 1/4 every week on a delayed basis into 4 week T-Bills) beating all other durations for investors at a 6.37% state income tax rate. The benefit was pretty minor though 4week ladders beat VUSXX by 4bp, an 8 week by 2bp and 13 weeks losing by 5 to 8 bp depending on how many steps I used.
I used data from this site.

https://home.treasury.gov/resource-cent ... nth=202303

The model would have had a T-Bill of the stated maturity roll over every day. That would imply many holdings in each ladder. This would not be practical in the real world but it would also provide smoother results. It would also assume purchase in the secondary market.
Electron
Doc
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### Re: Trading Treasuries (nominal and TIPS)

Electron wrote: Sat Mar 18, 2023 1:05 pm I created a model in Excel that calculates the average T-Bill yield over the term of each ladder using the daily Treasury Par Yield Curve Data.

The return of a typical T-Bill ladder investing at less frequent intervals might differ from the model by a small amount.
retiringwhen wrote: Sat Mar 18, 2023 1:16 pm I would be interested in your source data, but I am also confused, what is a 1 month ladder? How many tranches do you have in the ladder? 4 tranches with one every week? Similar patterns for the other ones?

I'm confused also. My T-bill ladder consists only of 26 week bills and has 10 or 12 rungs. But the rung timing was chosen based on the FOMC meeting schedule. I don't really know how to compared it to a 13 week ladder.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
retiringwhen
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### Re: Trading Treasuries (nominal and TIPS)

Electron wrote: Sat Mar 18, 2023 1:40 pm
retiringwhen wrote: Sat Mar 18, 2023 1:16 pm I would be interested in your source data, but I am also confused, what is a 1 month ladder? How many tranches do you have in the ladder? 4 tranches with one every week? Similar patterns for the other ones?

My laddering scheme showed 4 week ladders (4 steps equally entered into a ladder one every 1/4 every week on a delayed basis into 4 week T-Bills) beating all other durations for investors at a 6.37% state income tax rate. The benefit was pretty minor though 4week ladders beat VUSXX by 4bp, an 8 week by 2bp and 13 weeks losing by 5 to 8 bp depending on how many steps I used.
I used data from this site.

https://home.treasury.gov/resource-cent ... nth=202303

The model would have had a T-Bill of the stated maturity roll over every day. That would imply many holdings in each ladder. This would not be practical in the real world but it would also provide smoother results. It would also assume purchase in the secondary market.
No offense, but that does not provide any actionable results since it cannot be implemented. Ironically, it does show that Repos can provide that kind of smoothing

I will share my simulated auto-roll and ladders for the last year soon. I am cleaning up the worksheets now. It was surprising to me on first blush that in reality, 4 week ladders (4 tranches staggered weekly) beat VUSXX pretty handily. But upon reflection that result is almost tautological in an almost completely uniform rising interest rate period, varied periods will be have differently.
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### Re: Trading Treasuries (nominal and TIPS)

retiringwhen wrote: Sat Mar 18, 2023 1:47 pm I will share my simulated auto-roll and ladders for the last year soon.
Last year?

I would also like to see the past 6 months. That's the period when the FOMC started their rapid rate increases.

The problem I see with the prior 1 year study is that the flat first half distorts the more recent data.
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
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### Re: Trading Treasuries (nominal and TIPS)

Doc wrote: Sat Mar 18, 2023 5:10 pm
retiringwhen wrote: Sat Mar 18, 2023 1:47 pm I will share my simulated auto-roll and ladders for the last year soon.
Last year?

I would also like to see the past 6 months. That's the period when the FOMC started their rapid rate increases.

The problem I see with the prior 1 year study is that the flat first half distorts the more recent data.
I would have loved to know this in hindsight. I would have bought fewer 6 month t bills.
retiringwhen
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### Re: Trading Treasuries (nominal and TIPS)

My tool is configurable for time frame
Electron
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### Re: Trading Treasuries (nominal and TIPS)

Doc wrote: Sat Mar 18, 2023 5:10 pm I would also like to see the past 6 months. That's the period when the FOMC started their rapid rate increases.
The FRED database has T-Bill data from the secondary markets. It is available for download.

https://fred.stlouisfed.org/categories/116

https://fred.stlouisfed.org/series/WTB6MS

Here is six months of weekly data for the 6 month Treasury Bill. The average yield over this period is 4.47%. The average is 9 basis points less than the 4.56% yield on VUSXX on 3-10-23. That differential appears to be in line with the chart that I posted.

Historical auction results might be preferable if anyone knows of a source for that data.

Code: Select all

``````6-Month Treasury Bill Secondary Market Rate

2022-09-16	3.64
2022-09-23	3.77
2022-09-30	3.82
2022-10-07	3.90
2022-10-14	4.10
2022-10-21	4.29
2022-10-28	4.35
2022-11-04	4.45
2022-11-11	4.46
2022-11-18	4.44
2022-11-25	4.54
2022-12-02	4.53
2022-12-09	4.57
2022-12-16	4.55
2022-12-23	4.53
2022-12-30	4.59
2023-01-06	4.65
2023-01-13	4.67
2023-01-20	4.66
2023-01-27	4.67
2023-02-03	4.66
2023-02-10	4.75
2023-02-17	4.83
2023-02-24	4.92
2023-03-03	4.94
2023-03-10	5.03``````
Electron
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### Re: Trading Treasuries (nominal and TIPS)

Electron wrote: Sat Mar 18, 2023 6:24 pm Historical auction results might be preferable if anyone knows of a source for that data.
Sure.

https://www.treasurydirect.gov/auctions/auction-query/

Under Security-Term, put in the term, like "4-Week", and you can get the price per \$100 for Bills auctioned from November 1998.

Currently, 4, 8, 13, 17, and 26 week are auctioned every week.
52 week is auctioned every 4 weeks.

Until they became "official" weekly auctions in October 2022, 17-week bills were auctioned every week as "119-Day" Cash Management bills from December 2020, and most weeks since April 2020.

Recent auctions are posted here: https://www.treasurydirect.gov/auctions ... a-results/, where they list the high rate and investment rate calculated from the auction price.

Formulas for calculating those rates from auction prices are in CFR, §356.20, Appendix B, linked from TreasuryDirect's Understanding Pricing page.
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### Re: Trading Treasuries (nominal and TIPS)

Lyrrad wrote: Sat Mar 18, 2023 10:00 pm https://www.treasurydirect.gov/auctions/auction-query/

Under Security-Term, put in the term, like "4-Week", and you can get the price per \$100 for Bills auctioned from November 1998.
Thanks for the links and information. I had used the Treasury Direct Query Tool in the past but had forgotten about the capabilities.

I downloaded the data for the 26 Week T-Bills and calculated the discount rate and investment rate for the most recent 26 auctions. The 26 week average for the discount rate came out at 4.517% which is quite close to the average from the FRED database. The 26 week average for the investment rate came out at 4.688% which assumes a 365 day year. The latest yield on VUSXX is 4.58% which is 6 basis points higher than the average 26 week discount rate, and 11 basis points lower than the average 26 week investment rate.

The chart that I posted will not reflect actual results investing in T-Bills over the last year but I think the message it presents is correct.

In a period of rising short term interest rates, shorter maturity T-Bills may outperform the longer maturities. Actual investment results in any given period are also affected by the day to day variations in T-Bill yields.

With rates starting to level off, the longer maturities may now provide the higher returns. That should also be the case when rates eventually decline.

T-Bill ladders will provide a 100% exemption for any state income tax. We won't know the status of VUSXX until early next year.
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VictoriaF
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### Re: Trading Treasuries (nominal and TIPS)

By following recent news about SVB and other institutions, I came across a concept of banks being required to carry a collateral in the form of the U.S. Treasuries. It seems that the need to satisfy this requirement is greater than the banks' sensitivity to the Treasury rates, and therefore they place relatively low bids in Treasury auctions. If this is true, then would buying Treasuries in the secondary market be more advantageous than buying at auctions?

As I understand it, individuals place noncompetitive bids at Treasury auctions and get the greatest available yield. Nevertheless, the auctions could be dominated by the price-insensitive banks whereas the secondary market may offer some "bargains."

Victoria
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exodusing
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### Re: Trading Treasuries (nominal and TIPS)

VictoriaF wrote: Mon Mar 20, 2023 11:48 am By following recent news about SVB and other institutions, I came across a concept of banks being required to carry a collateral in the form of the U.S. Treasuries. It seems that the need to satisfy this requirement is greater than the banks' sensitivity to the Treasury rates, and therefore they place relatively low bids in Treasury auctions. If this is true, then would buying Treasuries in the secondary market be more advantageous than buying at auctions?

As I understand it, individuals place noncompetitive bids at Treasury auctions and get the greatest available yield. Nevertheless, the auctions could be dominated by the price-insensitive banks whereas the secondary market may offer some "bargains."

Victoria
Please be more specific about what you've heard. There's a new program under which the Fed will loan money to banks, on a full recourse basis with interest, with collateral being US treasuries valued at par. However, it only applies to treasuries owned on March 12. Is that what you're thinking of?

Press release with term sheet at https://www.federalreserve.gov/newseven ... 30312a.htm
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

VictoriaF wrote: Mon Mar 20, 2023 11:48 am By following recent news about SVB and other institutions, I came across a concept of banks being required to carry a collateral in the form of the U.S. Treasuries. It seems that the need to satisfy this requirement is greater than the banks' sensitivity to the Treasury rates, and therefore they place relatively low bids in Treasury auctions. If this is true, then would buying Treasuries in the secondary market be more advantageous than buying at auctions?

As I understand it, individuals place noncompetitive bids at Treasury auctions and get the greatest available yield. Nevertheless, the auctions could be dominated by the price-insensitive banks whereas the secondary market may offer some "bargains."

Victoria
I haven't observed any auction results that indicate that pricing is worse than the secondary market--if anything, it's the opposite.

Everyone gets the same price and yield at auctions. Some large banks are designated as primary dealers, and they are expected to comply with certain standards:
Primary dealers are trading counterparties of the New York Fed in its implementation of monetary policy. They are also expected to make markets for the New York Fed on behalf of its official accountholders as needed, and to bid on a pro-rata basis in all Treasury auctions at reasonably competitive prices.
Source: Primary Dealers - Federal Reserve Bank of New York - FEDERAL RESERVE BANK of NEW YORK

Kevin
If I make a calculation error, #Cruncher probably will let me know.
MarginalUtility
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### Re: Trading Treasuries (nominal and TIPS)

Holding Treasury debt can help banks meet both liquidity and capital requirements.

Banks are subject to risk-based capital requirements. They need less capital to support a portfolio of Treasuries than to support a portfolio of, say, commercial loans, because Treasuries pose less credit risk than commercial loans. Other capital requirements apply regardless of the riskiness of a bank's assets.

Short-term Treasury bills can help a bank meet liquidity requirements - the need to have sufficient liquid assets on hand to meet expected withdrawals. Assets with substantial credit risk or long-term assets with substantial interest rate risk are ill-suited to meet liquidity requirements. As happened to SVB, a bank might incur losses when selling these assets to meet withdrawals.

Banks' preferences for holding Treasury debt presumably do not affect the relative attractiveness of buying Treasuries at auction versus buying them on the secondary market. A bank can use Treasuries to meet its liquidity and risk-based capital requirements regardless of whether it acquires them at auction or on the secondary market.
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### Re: Trading Treasuries (nominal and TIPS)

MarginalUtility wrote: Mon Mar 20, 2023 12:51 pm A bank can use Treasuries to meet its liquidity and risk-based capital requirements regardless of whether it acquires them at auction or on the secondary market.
This.
Electron
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### Re: Trading Treasuries (nominal and TIPS)

The latest T-Bill Investment Rates listed on Treasury Direct now appear to be using 366 day years for all Investment Rate calculations.

https://www.treasurydirect.gov/auctions ... a-results/

The information below provides an explanation. 2024 is a leap year. This change occurred fairly recently with 1-year periods now including February 29, 2024.

https://www.ecfr.gov/current/title-31/s ... Part%20356

VI. Computation of Purchase Price, Discount Rate, and Investment Rate (Coupon-Equivalent Yield) for Treasury Bills
D. Calculation of investment rate (coupon-equivalent yield) for Treasury bills:
1. For bills of not more than one half-year to maturity:

y = number of days in year following the issue date; normally 365, but if the period from the issue date to the same date 1 year ahead contains February 29, then y is 366. (e.g., 2020 is a leap year. Suppose the issue date for a 26-week bill is February 28, 2019. The date 1 year ahead is February 28, 2020. That 1-year period from the issue date of the bill does not contain “February 29,” therefore y = 365. Now suppose the issue date of a 26-week bill is March 1, 2019. The date 1 year ahead is March 1, 2020. That 1-year period from the issue date of the bill contains “February 29,” therefore y = 366.)
Electron
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Kevin M
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### Re: Trading Treasuries (nominal and TIPS)

^Correct. And the YIELD function does not provide results that agree with Treasury published bill yields when 366 days are used in the calcs.
If I make a calculation error, #Cruncher probably will let me know.
exodusing
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### Re: Trading Treasuries (nominal and TIPS)

Instead of YIELD you can use the formula

Code: Select all

``((100-price)/price) * (365/days)``
with 365 or 366 as appropriate. See the discussion above.
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### Re: Trading Treasuries (nominal and TIPS)

Is there anything in the wiki that needs a correction? See: Bond pricing (Day count conventions)

The table shows US Treasuries using actual days, whereas corporate bonds use the 30/360 day count convention.
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### Re: Trading Treasuries (nominal and TIPS)

Kevin M wrote: Thu Feb 09, 2023 12:03 pm
exodusing wrote: Thu Feb 09, 2023 8:18 am There was an earlier discussion of the mechanics of rolling tbills at Vanguard, including whether the proceeds from maturing bills could be used to settle the next auction, but I'm not seeing the conclusion. viewtopic.php?p=6721037#p6721037 Apologies since I'm probably missing something.

There's a 13 week tbill auction every Monday (other than holidays) which settles on Thursday.

Does that mean if I participate in the Monday Feb 13 auction by ordering through a Vanguard brokerage account I'd need available funds on Thursday the 16th and would receive funds at maturity on Thursday May 18 that could be used to settle the 13 week tbill auction on Monday May 15 that settles on Thursday May 18?

If so, does this mean I'd be fully invested at all times, other than that tbills normally trade at a discount, so there would be some rounding error?

I realize that there are alternatives, such as Fidelity autoroll, the secondary market, treasury money market funds, etc.
I'm pretty sure we've seen posts that indicate that you can use the proceeds of a Treasury that matures on the settlement date of a Treasury purchase to settle the purchase at Vanguard. I personally have not tried it yet (per the post you linked, I meant to, but forgot and sold before maturity).
Test of the above bolded text in process

My settlement account did not have enough funds to cover the purchase.

CUSIP 912796U31 matures tomorrow...the 23D
CUSIP I912797FX0 (Settles tomorrow on the 23D) just purchased at Vanguard ("order executed on 03/22/2023 at 8:53 AM, Eastern time") (4.806%)

The email and text I got after the order executed did not warn me about a shortage of funds.

I think that this was a secondary market purchase; the bond market must open before 9:30.