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Alan
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Basic fixed income question: the meaning of "one month ahead"

March 20th, 2023, 12:02 pm

As a fixed income novice, I am trying to wrap my head around the conversion of US Treasury par yield rates to spot rates (zero-coupon rates) using exact US market conventions. Take the par yield curve here: Resource Center | U.S. Department of the Treasury

If you want to associate a maturity date to "1 mo", say on Jan 29, 30, or 31 -- what is the market convention?
Is this convention universal?
Thanks!
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 21st, 2023, 1:11 pm

The US Treasury Direct website does not provide an answer. Grrr. I've always defaulted to Modified Following per the ISDSA definitions - if the trial date falls on a non-business day, go forward in time to the next good business day unless that results in moving into the next month, in which case go backwards in time to the closest previous business day. Another candidate is  the ISDA FRN Convention. I bet the answer is in Kenneth Garbade's textbook collection of Bankers Trust papers on the UST markets. Alas, my copy is mislaid.     

P.S. The US Treasury has its own weird "Treasury Convention" for quoting price/yield in which the next (i.e. current) coupon payment is discounted using money market math, whereas the remainder of the coupons and return of principal are discounted using compound interest. Rarely used in the market place apart from when UST bonds age to the point where they become bills and are quoted as bills.
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 22nd, 2023, 2:21 am

Bill tenors are usually quoted in weeks, that is used to establish a trial date. A "date roll" is then applied to adjust the trial date if it falls on a non-business date (weekend or holiday). So the question is what is the UST date roll convention. The date roll is not the same thing as the day count. The date roll establishes the dates, the day count is used to count (i.e. accrue) the time between them.     
 
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Alan
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Re: Basic fixed income question: the meaning of "one month ahead"

March 22nd, 2023, 6:00 pm

Thanks, David -- that's very helpful.  

BTW, as a follow-up for you or anybody with access to a Bloomberg terminal (or similar). If the vendor provides a set of spot rates (semi-annual compounding) computed from the Daily Treasury Par Yield Curve Rates at any Date, I would much appreciate a screen shot of it. (Even better might be those tricky end of January dates in my original post!)
 
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katastrofa
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Re: Basic fixed income question: the meaning of "one month ahead"

March 22nd, 2023, 9:12 pm

Is "modified following" that DavidJN writes about the same? I think for bonds they use 30/360 convention or similar. Don't ask me to explain more, though. There was one moment in my life when I had to figure this out. Now i just want to un-know it (-:
 
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bearish
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Re: Basic fixed income question: the meaning of "one month ahead"

March 23rd, 2023, 1:15 am

There are technically three separate but closely related concepts at work here: business day conventions (like modified following), holiday calendar (like NY banks), and daycount convention (like 30/360). Each has real life subtleties, so the combinatorics can easily get out of hand.
 
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Paul
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Re: Basic fixed income question: the meaning of "one month ahead"

March 23rd, 2023, 9:21 am

Is "modified following" that DavidJN writes about the same? I think for bonds they use 30/360 convention or similar. Don't ask me to explain more, though. There was one moment in my life when I had to figure this out. Now i just want to un-know it (-:
I feel your pain!
 
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Alan
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Re: Basic fixed income question: the meaning of "one month ahead"

March 27th, 2023, 4:09 pm

Thanks for all the answers so far. So, thinking about it some more, the Treasury has an email link for questions on the CMT par rates and I sent them these two questions:

I have two questions regarding the interpretation of the {“1 Mo”, “2 Mo”, “3 Mo” and “4 Mo”} maturity headings.
 
Q1. Since these maturities were all introduced associated to the offering
of benchmark “4-week”, “8-week”, “13-week”, and “17-week” Treasury Bills, should I interpret those month headings
as actually referring to week-ahead maturities: {4 week, 8 week, 13 week, 17 week}?
 
So, for example, the CMT par yield on  Date:  01/31/2023 for a maturity of “3 Mo” should be interpreted
as the (bond-equivalent) yield for a hypothetical bond maturing in exactly 13 weeks on 05/02/2023 ?
 
Q2.  If my maturity assumption in Q1 is correct, and moving say exactly 13-weeks into the future from a Date should
land one on a (banking) holiday, is there any further adjustment of the maturity date by a business day convention,
or is the exact 13-week ahead calendar date accepted as the (standardized) bond’s maturity date?

Any further thoughts on what their answers, should they choose to respond, might be?
 
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Cuchulainn
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Re: Basic fixed income question: the meaning of "one month ahead"

March 28th, 2023, 6:24 pm

Stumbled on this from Quantlib, might throw up something

https://github.com/lballabio/QuantLib/issues/1574
 
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Alan
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Re: Basic fixed income question: the meaning of "one month ahead"

March 29th, 2023, 2:20 pm

Thanks.

After some correspondence with a very helpful guy at the NY Fed, I've gotten some clarity on the issue. He didn't know for sure, but his guess was that "months mean months" and without regard to holidays, as these are hypothetical securities.

Also, I am now sure that 1 Mo, 2 Mo, etc definitely do *not" mean 4 weeks, 8 weeks, etc.
That's because I now see the Treasury reports (bond-equivalent) T-bill rates at

Daily Treasury Bill Rates

and you can see that they are different.

This does not fully nail it down, but it's less ambiguous to me, anyway.
If anybody learns something definitive, I'm still interested ...
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 29th, 2023, 3:12 pm

The Treasury Direct website does identify the reset rate of UST FRNs (floating rate notes) as the 13-week T-bill rate rather than the 3-month. 

I started in bonds, and when I asked these questions more than 30 years ago an old bond honk told me that Following was the payment convention because the government will never pay you early. I didn't believe him. 

The swap market is a good place to look for details about holiday calendars, day counts and date rolls. Being OTC products all terms are negotiable, so swappers have to be very clear about this stuff to avoid lawsuits. The US Treasury market conventions are almost certainly to be found within the suite of the ISDA definitions, although they won't be identified or named as such. 

Swaps have their own date peculiarities. There may be two or three sets of such parameters for even a vanilla single currency swap - conventions for fixed and floating swap legs can and often do differ, and the underlying reference floating rate can prove to have yet different conventions.

Even when the conventions for the reference floating rate and a swap floating leg are identical, date mismatches (gaps or overlaps) can still obtain because the reference floating rate maturity dates reset to the then-spot date in question, whereas swap dates are generally set relative to a single date - either the start or maturity date of the particular swap in question. This can and does create small date matches and a potential need for subtle and very small convexity corrections. And it turns out that how one deals with gaps and overlap in swap floating legs is the theoretical difference between the FRN and Forecast methods for valuing floating swap legs. Getting bogged down in swaps may end up confusing more than enlightening.

The UST holiday calendar is likely New York for domestic currency products and a merged one for a cross currency products. I'd say the Treasury date roll is either Following, or Modified Following (there are lots of others). 

It seems the ISDA swap people are just a little clearer than the people trading the underlyings. 

I have a put call in to friendly people at the Bank of Canada...
 
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Alan
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Re: Basic fixed income question: the meaning of "one month ahead"

March 30th, 2023, 1:26 am

I have a put call in to friendly people at the Bank of Canada...
 That's very helpful -- thank you!
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 30th, 2023, 5:56 pm

The Canadian central bank has responded. Turns out the old bond honk had it right more than 30 years ago, in Canada the Following date roll is used on treasury bonds with the "Ontario" (read Toronto) holiday calendar:  

"If any payment of the principal or interest falls due on a day which is not a Business Day, payment thereof shall be made on the next succeeding Business Day and no further interest or other payment shall be paid in respect of the delay in such payment. "Business Day" means a day other than a Saturday or a Sunday or a day recognized as a holiday by the laws of Canada or of the Province of Ontario. Therefore the holiday schedule that is followed is the federal government holiday calendar as well as the Province of Ontario. These holidays are reflected in the Bank of Canada holiday schedule. You can disregard any provincial holidays in other Canadian provinces other than Ontario for these purposes."

Cute how the coupons are not adjusted, you always get half the annual coupon ("equal coupon", sometimes dangerously confused with 30/360) regardless of the actual days in the coupon period. Weekends and holidays are YOUR problem, not the governments. 
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 30th, 2023, 6:00 pm

Here is the source, there has to be a US equivalent: Legal Terms and Conditions for Government of Canada Domestic Debt Securities - Canada.ca

Unfortunately the auction processes are not described, hence no further insight on T-bill maturity date selection.
 
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DavidJN
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Re: Basic fixed income question: the meaning of "one month ahead"

March 30th, 2023, 6:00 pm

Here is the source, there has to be a US equivalent: Legal Terms and Conditions for Government of Canada Domestic Debt Securities - Canada.ca

Unfortunately the auction processes are not described, hence no further insight on T-bill maturity date selection.