6 mo T-Bill Auction results 10/3/22: what am I actually earning?

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Fremdon Ferndock
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6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Fremdon Ferndock »

So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
"Risk is what’s left over when you think you’ve thought of everything." ~ Morgan Housel
Zagnificent
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Zagnificent »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3 3.790%
Low Rate 4 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
I literally came here to ask the same question. I wanted to understand what all this meant before going back to park the rest of my home purchase down payment.
mongstradamus
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by mongstradamus »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
For auctions you get investment rate at least that’s what I have been getting for ones bought both at fidelity and treasury direct.

Edit: if you want to check math you can put it in tbill yield calculator
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Tubes
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Tubes »

mongstradamus wrote: Mon Oct 03, 2022 12:26 pm
Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
For auctions you get investment rate at least that’s what I have been getting for ones bought both at fidelity and treasury direct.
Right. The "high rate" is the winning bid in the auction. It has an unfortunate name. When you look at auction results, it also goes deeper than that and shows the low bid and the amount that is filled on the high bid. Those other numbers (Median, Low, Allotted) don't matter to us unless you like to understand the auction in depth. So for practical purposes, us mere mortals can use "Investment Rate" as our comparison to APR.

I think someone like #cruncher can come along and follow up on the idiosyncrasies of this which can differ by a few hundredths of a percent from real APR comparisons.
Last edited by Tubes on Mon Oct 03, 2022 12:43 pm, edited 2 times in total.
student
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by student »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
Let r be the annualized rate. You paid $98.054 and in half a year, you will get $100. So 98.054(1+r/2)=100. So r is about 3.969%.
Nver2Late
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Nver2Late »

(100-98.053611) / 98.053611 = 0.01985 x (365/182 days) = 3.981%
"Better is the enemy of good." Good is good.
FactualFran
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by FactualFran »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
You ‎will get the investment rate. You paid $98.054 per $100 of par value and will get the par value at maturity. The High Rate is an annualized discount rate. The discount of $1.946 per $100 of par value corresponds to that annualized discount rate being applied to the 182-day term of the T-Bill.
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Fremdon Ferndock
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Fremdon Ferndock »

student wrote: Mon Oct 03, 2022 12:41 pm
Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
Let r be the annualized rate. You paid $98.054 and in half a year, you will get $100. So 98.054(1+r/2)=100. So r is about 3.969%.
So, I see the interest rate for the 3/30/23 T-Bill posted on Vanguard currently (bid price) is 3.91%. This is slightly shorter than the 4/6 maturity of today's auction and pretty close to the Investment Rate above. So, what we see dynamically posted in terms of T-Bill price and YTM in the secondary market is the Investment Rate, yes?
"Risk is what’s left over when you think you’ve thought of everything." ~ Morgan Housel
student
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by student »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:56 pm
student wrote: Mon Oct 03, 2022 12:41 pm
Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
Let r be the annualized rate. You paid $98.054 and in half a year, you will get $100. So 98.054(1+r/2)=100. So r is about 3.969%.
So, I see the interest rate for the 3/30/23 T-Bill posted on Vanguard currently (bid price) is 3.91%. This is slightly shorter than the 4/6 maturity of today's auction and pretty close to the Investment Rate above. So, what we see dynamically posted in terms of T-Bill price and YTM in the secondary market is the Investment Rate, yes?
I am afraid I am not positive of what these terms refer to.
fabdog
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by fabdog »

Here's a thread from just a few days ago on the same topic

viewtopic.php?t=387050

Mike
mongstradamus
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by mongstradamus »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:56 pm
student wrote: Mon Oct 03, 2022 12:41 pm
Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
Let r be the annualized rate. You paid $98.054 and in half a year, you will get $100. So 98.054(1+r/2)=100. So r is about 3.969%.
So, I see the interest rate for the 3/30/23 T-Bill posted on Vanguard currently (bid price) is 3.91%. This is slightly shorter than the 4/6 maturity of today's auction and pretty close to the Investment Rate above. So, what we see dynamically posted in terms of T-Bill price and YTM in the secondary market is the Investment Rate, yes?
I am not sure if I am understanding you correctly but if you want to find the Tbills on secondary market for this most recent auction can’t you just enter in your cusip in search. At least you can do that at fidelity.
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by #Cruncher »

Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pmSo, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)?
The short answer it that you're earning the "Investment Rate".
Fremdon Ferndock, in same post, wrote:What the heck is the Investment Rate anyway?
It is the yield comparable to yields reported for Treasury notes or bonds which have coupons. It is, therefore, sometimes called the "Bond Equivalent Yield" or "Coupon Equivalent Yield". If you're interested in a little bit more detail...
  • As Tubes says above, "High Rate" is the winning bid from the competitive bidders at the auction. (It's what all us non-competitive bidders also get.)
  • "Price" is calculated from the High Rate.
  • "Investment Rate" is calculated from the Price.
  • Formulas for Price and Investment Rate (aka "Coupon Equivalent Yield") are shown on the Price, Yield and Rate Calculations for a Treasury Bill PDF.
Here are the calculations for this 26-week bill auction:

Code: Select all

Row               Col A       Col B
  2          Settlement  10/06/2022
  3            Maturity   4/06/2023
  4  High Discount Rate      3.850%
  5        Days in year         365  =DATE(YEAR(B2)+1,MONTH(B2),DAY(B2))-B2
  6        Days in term         182  =B3-B2
  7               Price   98.053611  =100*(1-B4*(B6/360))
  8                   a              =IF(B6>B5/2,B6/(2*B5)-0.25,0)
  9                   b              =IF(B6>B5/2,B6/B5,0)
 10                   c              =IF(B6>B5/2,1-100/B7,0)
 11     Investment Rate      3.981%  =IF(B6>B5/2,(-B9+(B9^2-4*B8*B10)^0.5)/(2*B8),(100/B7-1)*(B5/B6))
 12    Excel YIELD func      3.981%  =YIELD(B2,B3,0,B7,100,IF(B6>B5/2,2,1),1)
 13                 APY      4.021%  =(100/B7)^(B5/B6)-1
Notes:
  • "a", "b", and "c" on rows 8-10 are ignored for this 26-week bill. They are used only for bills that mature in more than half of a year.
  • The formula for Investment Rate on row 11 also handles the much more complicated case of bills that mature in more than one-half of a year. Without handling this case, it could be simply written as
    3.981% = (100/B7-1)*(B5/B6)
  • Row 12 shows that the Investment Rate can also be calculated with the Excel YIELD function.
  • Row 13 shows the bill's "Annual Percentage Yield" for comparison to savings accounts and CDs which report their APY.
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Fremdon Ferndock
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Fremdon Ferndock »

Wow - thanks #Cruncher for this thorough explanation. Never in a thousand years will I understand the math but appreciate the details of how we get the answer to "what am I earning."
"Risk is what’s left over when you think you’ve thought of everything." ~ Morgan Housel
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Tubes »

Fremdon Ferndock wrote: Mon Oct 03, 2022 1:58 pm Wow - thanks #Cruncher for this thorough explanation. Never in a thousand years will I understand the math but appreciate the details of how we get the answer to "what am I earning."
Told you we could count on #Cruncher!
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Kevin M
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Kevin M »

You can also calculate the investment rate (aka, yield to maturity) with the spreadsheet YIELD function, and you will get a result that matches Treasury investment rate to the 3 decimals that are published. For bills with maturity less than 6 months, use frequency parameter 1.

=YIELD("10/06/2022", "04/06/2023", 0%, 98.053611, 100, 1, 1)

= 3.981%.

Kevin
If I make a calculation error, #Cruncher probably will let me know.
student
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by student »

student wrote: Mon Oct 03, 2022 12:41 pm
Fremdon Ferndock wrote: Mon Oct 03, 2022 12:21 pm So, I'm confused. Purchased 6-month T-Bills at auction today via Vanguard Brokerage and here are the results from TreasuryDirect:

Term and Type of Security 182-Day Bill

High Rate 3.850%
Allotted at High 77.40%
Price 98.053611

Investment Rate 3.981%
Median Rate 3.790%
Low Rate 3.700%

On Vanguard, they showed that I paid $98.054 for each T-Bill with a yield of 3.981%, which is the Investment Rate shown at TD above. So, what interest rate am I getting: The High Rate (3.850%) or the Investment Rate (3.981%)? What the heck is the Investment Rate anyway?
Let r be the annualized rate. You paid $98.054 and in half a year, you will get $100. So 98.054(1+r/2)=100. So r is about 3.969%.
My assumption was compound interest. With 3.969% per annum compounded semi-annually (since it was a 6-month investment), an investment of $98.054 will become $100 after 6 months. For T-bill, it is not computed in this way. Others have used the correct way. It is 3.981%. So $98.054(0.03981)/2 is about $1.952 is the interest for 6 months. So 1.952+98.054 is about $100. (Some rounding errors and I used 1/2 rather than 182/365.)
Zagnificent
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Zagnificent »

I have an additional question on this purchase. For my instance, it looks like the purchase had a date of 10/03. The settlement date is 10/06. Is that why the bonds I'm purchasing at auction don't have all the details that you're listing from your purchase? My line item says Treasury Bonds 0.00%. Will that rate show once the auction takes place? I'm a little confused here.
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Kevin M »

Zagnificent wrote: Tue Oct 04, 2022 9:50 am I have an additional question on this purchase. For my instance, it looks like the purchase had a date of 10/03. The settlement date is 10/06. Is that why the bonds I'm purchasing at auction don't have all the details that you're listing from your purchase? My line item says Treasury Bonds 0.00%. Will that rate show once the auction takes place? I'm a little confused here.
What broker? At any rate, you got the 3.981% investment rate (yield) that everyone else got. It will show on your trade confirmation, although they may show the discount rate instead of the investment rate. At least the price should show in your transaction history.
If I make a calculation error, #Cruncher probably will let me know.
Zagnificent
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by Zagnificent »

Kevin M wrote: Tue Oct 04, 2022 2:30 pm
Zagnificent wrote: Tue Oct 04, 2022 9:50 am I have an additional question on this purchase. For my instance, it looks like the purchase had a date of 10/03. The settlement date is 10/06. Is that why the bonds I'm purchasing at auction don't have all the details that you're listing from your purchase? My line item says Treasury Bonds 0.00%. Will that rate show once the auction takes place? I'm a little confused here.
What broker? At any rate, you got the 3.981% investment rate (yield) that everyone else got. It will show on your trade confirmation, although they may show the discount rate instead of the investment rate. At least the price should show in your transaction history.
I used Vanguard. I reread the confirmations and it finally clicked—the rate is not an interest rate, but rather, the discount per $100 reflects the gain, as each note will be redeemed for $100 in 6 months time.
FactualFran
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by FactualFran »

Zagnificent wrote: Tue Oct 04, 2022 9:50 am I have an additional question on this purchase. For my instance, it looks like the purchase had a date of 10/03. The settlement date is 10/06. Is that why the bonds I'm purchasing at auction don't have all the details that you're listing from your purchase? My line item says Treasury Bonds 0.00%. Will that rate show once the auction takes place? I'm a little confused here.
The 0.00% in the line item will likely not change. That part of the line item is the periodic interest rate of the Treasury security. 0.00% indicates that the security does not make periodic interest payments, which is how T-Bills work.
student
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Re: 6 mo T-Bill Auction results 10/3/22: what am I actually earning?

Post by student »

Zagnificent wrote: Tue Oct 04, 2022 9:50 am I have an additional question on this purchase. For my instance, it looks like the purchase had a date of 10/03. The settlement date is 10/06. Is that why the bonds I'm purchasing at auction don't have all the details that you're listing from your purchase? My line item says Treasury Bonds 0.00%. Will that rate show once the auction takes place? I'm a little confused here.
My understanding is that T-bill is a zero-coupon bond. So 0% (no interest but it is sold at a discount). https://www.investopedia.com/terms/z/ze ... onbond.asp
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