## Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Tue Sep 05, 2023 5:02 pm
Thanks physicist
But unless I missed it, none of your proposed math takes into account the mix of CTD contenders that is explained in one of my links https://quant.stackexchange.com/questio ... acking-ctd

The CME website clearly says futuresDV01 = cashDV01 / conversionfactor
which means they don't consider the other CTD contenders. But they should be considered, as stated on the stackexchange page. That means CME just does a per-CTD-contender calc, but not the final step of calculating the probabilistic mix. But we need to do the latter to arrive at the "real life" futures DV01 (our real life interest rate exposure) and for a meaningful comparison to SOFR strips, or not?

Other than that, I'm still not understanding why the basic equation "DV01 = Duration x Market Value/100" doesn't hold for the futures DV01, futures duration, and futures market values on treasuryanalytics. Hard to argue that formula, if we take the "futures" version of all variables, right?

An explanation would perhaps be that everything except the "futures price" is CTD-specific. Only the "futures price" is the real observed price, which naturally must consider all CTD contenders?
So "market value" would not be the futures price, but a theoretical market value if only one CTD were considered? Or just the CTD market value (which is greyed out on the analytics page)?

B.t.w. the second link below suggests to use the forward DV01 (not the present DV01) of the cash treasury. I presume that means taking only the time between delivery and maturity as duration. Makes sense to me, because the futures contract settles into the treasury at time of delivery, not now; so the effect of interest rate changes on the treasury between now and delivery won't benefit or hurt you if you hold the futures contract. Sorry I was thinking wrong, it makes no sense - we are indirectly already invested in the treasury before delivery.
But changes in forward interest rates for forward times between now and delivery (futures expiration) will affect the implied financing cost of the futures contract between now and delivery, and therefore affect the futures contract price and therefore affect the futures DV01, right? Where in the calcs and formulas is that reflected? I don't see it reflected in the CME formula "futuresDV01 = cashDV01 / conversionfactor".
The effect should be opposite:
Forward interest rate (for forward times between now and delivery) rises -> CTD value decrease (but it won't hurt us because it's before delivery)
Forward interest rate (for forward times between now and delivery) rises -> Implied financing cost rises -> Futures value increases, right?
EDIT: The effects will perhaps offset
https://www.cmegroup.com/trading/intere ... _Point.pdf says "Futures DV01 = Cash DV01 / Conversion Factor". But https://quant.stackexchange.com/questio ... v01-of-ctd instructs to use forward DV01. https://quant.stackexchange.com/questio ... acking-ctd points out that the futures DV01 should be a probabilistic mix of the CTD contenders, if I understand it right. That would make the SOFR futures / treasury futures comparison again tricky, because I don't have the historical evolution of the CTD contenders and the resulting futures DV01.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Tue Sep 05, 2023 5:02 pm I have not tried the probabilistic mix yet. It is not clear to me that the treasury analytics page is doing this. I do agree that you would want to do the probabilistic mix, but I wonder if the ctd is "good enough" for the purposes of comparing SOFR performance to treasury futures performance. I will look into it (unless you solve this issue before then.)
The second link in my previous post suggests that the error can be significant when just using the currently "best" CTD candidate.

Then also the timing option, Last Day vs. First Day - I don't know what the impact is nor which of the two is more relevant and why.

But before we figure out the difference of your cash DV01 vs. that of the analytics site, all efforts to understand the futures DV01 seem in vain.
Like I mentioned before, if you go to the analytics site and change the 2y contracts (Sep23 -> Dec23 -> Mar24), the CTDs and CTD durations change as expected, but the futures DV01 doesn't change much. The conversion factors also don't change much, so the can't explain it. But futures DV01 on the analytics page is definitely CTD-specific so the other contenders don't come into play here yet.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Tue Sep 05, 2023 5:02 pm Price and DV01 checks for 91282CFK2, 3.5%, Maturing on 09/15/2025: (Two year note futures december contract ctd, last delivery date)

Scrape time: 2023-09-05 17:01:18.480308 EST
Scraped Yield: 4.965%
Clean Price calculated from Yield: 97.20294
Dirty Price: 98.866955
(Accrued Interest = Dirty-Clean = 1.664015) <- The small discrepancy between me and my broker comes from T+1 settlement; I think I'm using 175 days instead of 176
Calculated Modified Duration: 1.892707 (slight difference between me and the broker probably comes from my smaller value of the accrued interest and the slightly different clean price, I will look into it)

Calculated cash DV01 (If I follow Burghardt's suggestion)
0.01*1.892707*(\$98.866955)*2000*0.01=\$37.425

From my broker:
Ask Yield: 4.927%
Bid Yield: 4.985%
Ask Price: 97.28125
Bid Price: 97.171875
Mid Price: 97.2265625
176 days Accrued Interest: 1.6739, hence dirty price = 97.2265625+1.6739=98.9004625
Modified Duration: 1.891

Calculated cash DV01 (If I follow Burghardt's suggestion)
0.01*1.891*(\$98.9004625)*2000*0.01=\$37.404

CME screenshot at bond market close:

I haven't even included the conversion factor yet and the DV01s are way off. Using the clean price does not help much:
0.01*1.891*(\$97.2265625)*2000*0.01=\$36.77

And a quick guesstimate for the forward price of the note also does not help:
0.01*1.891*(\$97.2265625*exp(-0.055*116/365))*2000*0.01=\$36.13
This is the lowest bound I can think of.

I don't see how the treasury analytics numbers can be correct for this contract.
Look at the "delivery years" on the analytics page. I think they use indeed only the time between delivery and maturity for duration.

They show 1.75 delivery years for your 09/15/2025 3.5 coupon bond.

Plugging into your proposed formula "Modified duration = (Macaulay duration, or just duration)/(1+yield/200)":
modified duration = 1.75 / (1 + 4.952/200) -> 1.7077
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)

Plugging into your DV01 formula "Calculated cash DV01 (If I follow Burghardt's suggestion) 0.01*1.892707*(\$98.866955)*2000*0.01=\$37.425" instead of your "calculated modified duration" (emphasis mine):
0.01*1.7077*(\$98.866955)*2000*0.01=\$33.767

Not yet there, but closer to their cash DV01 of \$31.60. But the next coupon is paid very soon; so if you find me a "better" (lol) formula for modified duration from Macaulay duration, or an independent formula, then who knows, perhaps we'll match the CME DV01.

Also for whatever reason, their delivery years don't seem to be accurate: The 09/15/2025 and the 09/30/2025 maturity bonds have the same 1.75 delivery years, although they should be ca. 1/24 years or 0.04166 years apart. The other bonds have a granularity of 0.01 delivery years.

But like I said in my recent post, if we use "delivery years" for the CTD, then I think we have to reflect the effect of forward interest rates on the implied financing cost and futures price, for forward times between now and delivery, in the futures DV01 - which they clearly don't do. The Fed makes a surprise hike at the next meeting, the deliverable goes down, but your futures prices will go up (or at least down not so much), because the embedded financing cost (debt) is marked to market - the movement of the embedded debt will go the opposite direction of a long T-bill position.
Crossed out my first sentence - I was thinking backwards. I think CME is correct. We only want to consider the "delivery years" for the Macaulay duration and then the modified duration of the CTD. The effect of any changes to forward rates for forward times before delivery on the value of the CTD, will offset against the effect on the embedded debt in the futures contracts. You can probably prove that mathematically if you sit down with pencil and paper. Or perhaps it's explained in your Burghardt book.

My biggest open questions are which delivery date to assume (one of the futures timing options), and what is the effect of the CTD contenders on the futures DV01. Once I know which ZT treasury futures DV01 to use, I can adjust my SOFR strip and I'll re-do the calc in my empirical comparative backtest.

Another open question is what is the definition of "duration" and "modified duration" under the CTD section on the analytics page. I just checked, the duration is also not the delivery years divided by the conversion factor.

Great teamwork and brainstorming so far. I wouldn't be where I am without the tireless contributors to this thread.
Last edited by comeinvest on Wed Sep 06, 2023 1:26 pm, edited 1 time in total.
unemployed_pysicist
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
couldn't afford the h | | BUY BONDS | WEAR DIAMONDS
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Wed Sep 06, 2023 1:21 pm
comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

...

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
I'm at work I'll check later; but for every mathematical formula it's good to check the semantics of the variables and the conditions under which it was derived. Should be easy to check. E = m*c2 says nothing without a description of the observable experimental setup that it applies to

We could also verify using an edge case: how about if the last coupon is paid tomorrow and the bond matures in 1 year.
comeinvest
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Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Wed Sep 06, 2023 1:21 pm
comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

...

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
I can't find duration information for bonds at Interactive Brokers.
But I think here https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 on page 163 they derive the formula while considering fractions of years to the next coupon.
So we have to find another way to get to the CME durations.

Last Delivery Day is the third business days of the next following calendar month https://www.cmegroup.com/trading/intere ... eFINAL.pdf , which is Thu 01/04/2024. Then the correct "delivery years" to 09/15/2025 calculating in days would be ca. 619/365 -> 1.69589, not 1.75.
Then
modified duration = 1.69589 / (1 + 4.952/200) -> 1.65491
DV01 = 0.01*1.65491*(\$98.866955)*2000*0.01 -> \$32.723
We are inching closer to the CME value of \$31.60.

It can only be the bond price or a timing difference, right?

Using clean price instead of dirty price:
DV01 = 0.01*1.65491*(\$97.20294)*2000*0.01 -> \$32.172

The calc of modified duration on page 163 of https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 clearly refers to the dirty price, which means the dirty price must be used here.

My result for the cash DV01 of \$32.723 is very close to the futures DV01 of the CTD of \$32.95 per the CME page!!!

Your "Clean Price calculated from Yield" was based on a "scraped yield" of 4.965%. But the CME page shows a yield of 4.952%. Can you please re-generate the "clean price from yield" based on the CME yield, and verify the math? I'm running out of ideas.

The difference in futures DV01 is about 4%. I will re-do the treasury futures / SOFR futures backtest based on the CME DV01. Of course we still don't know if the other CTD contenders play a role.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

And here I discovered another mistake in my treasury futures / SOFR futures comparison: The SOFR strip should start with the delivery date, and not at the beginning of the backtest period. Because changes to forward rates between now and delivery have no bearing on the value of the CTD at time of delivery. Makes sense. But which delivery date should I assume? Last Day, First Day, or something in between?
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Interesting (perceived?) anomalies also in the EUR forward rate curve. Rational explanation, liquidity induced market forces, numerical error in curve construction, and/or artifacts of interpolation and smoothing?
Article is here: https://seekingalpha.com/article/463336 ... converging

comeinvest wrote: Wed Aug 30, 2023 4:16 am Donald van Deventer periodically publishes thoughts and charts on term premia based on a statistical model. I find the forward yield curve quite interesting. My first reaction was that the fluctuations in forward yields are results of numerical errors when deriving the forward yields from the coupon bonds; but then again I would think that the coupon bonds are traded on (zero coupon equivalent) yields in the first place.

If I read the first chart right, it would seem to me that based on this model, the 20y treasuries would currently promise the largest term premium per duration.

The articles:
https://seekingalpha.com/article/463172 ... ry-spreads
https://seekingalpha.com/article/461932 ... ne-30-2023

comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Those are the swaps spreads per NAIC from 01/31, 02/28, 03/31, and 08/31. They publish monthly data, for those who like to track the swap spreads over time.
The -4.25 bps at 3M is similar to the 3-month Term SOFR to treasuries spreads that I am observing.
Assuming a static swap spread curve, the -7 bps at 2y, corresponding to a 2y SOFR futures strip, would settle into rates with a spread around -4.25% bps (taking the shortest observable term of 3M as an approximation of overnight rates), if my interpretation is right, for an average performance drag of the swap, strip, or futures contract of about 2.75 bps p.a.?
All the while the "long-term" numbers (15 year rolling averages of estimated historical SOFR swap spreads) would be almost the same at the 2y and the 3M terms, but with an "anomaly" at 6M.
SOFR futures strips should have had a tailwind vs treasuries during the last 7 months, as spreads were decreasing. Assuming that SOFR futures and SOFR swaps follow the same pattern.

Last edited by comeinvest on Mon Sep 11, 2023 11:40 pm, edited 1 time in total.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

What kind of SOFR does ICE refer to? The numbers are not those of CME or other data sources. I cannot believe and would not assume that such a prominent institution just puts out garbage.
I think the relevant reference rate for quarterly futures would be the 3-months Term SOFR, which is about 20 bps higher than what ICE indicates.

unemployed_pysicist
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Thu Sep 07, 2023 6:16 am
unemployed_pysicist wrote: Wed Sep 06, 2023 1:21 pm
comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

...

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
I can't find duration information for bonds at Interactive Brokers.
But I think here https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 on page 163 they derive the formula while considering fractions of years to the next coupon.
So we have to find another way to get to the CME durations.

Last Delivery Day is the third business days of the next following calendar month https://www.cmegroup.com/trading/intere ... eFINAL.pdf , which is Thu 01/04/2024. Then the correct "delivery years" to 09/15/2025 calculating in days would be ca. 619/365 -> 1.69589, not 1.75.
Then
modified duration = 1.69589 / (1 + 4.952/200) -> 1.65491
DV01 = 0.01*1.65491*(\$98.866955)*2000*0.01 -> \$32.723
We are inching closer to the CME value of \$31.60.

It can only be the bond price or a timing difference, right?

Using clean price instead of dirty price:
DV01 = 0.01*1.65491*(\$97.20294)*2000*0.01 -> \$32.172

The calc of modified duration on page 163 of https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 clearly refers to the dirty price, which means the dirty price must be used here.

My result for the cash DV01 of \$32.723 is very close to the futures DV01 of the CTD of \$32.95 per the CME page!!!

Your "Clean Price calculated from Yield" was based on a "scraped yield" of 4.965%. But the CME page shows a yield of 4.952%. Can you please re-generate the "clean price from yield" based on the CME yield, and verify the math? I'm running out of ideas.

The difference in futures DV01 is about 4%. I will re-do the treasury futures / SOFR futures backtest based on the CME DV01. Of course we still don't know if the other CTD contenders play a role.
The formula and its derivation in your linked document is the same as what I use to generate Macaulay durations and modified durations. So this aligns with my understanding.

The yield of 4.952% is lower than my scraped yield of 4.965%. This means that the price will go up and the Macaulay duration will go up, and the result will be worse. I get a clean price of 97.2288 (+1.6739 accrued interest if you use the dirty price), and a Macaulay duration of 1.939 years.

However, I just noticed that 1.9414/(1+5.0474/200)=1.8936; CME uses the forward yield to calculate the duration and modified duration for the future. When I use the 5.0474 yield to calculate a bond price and the Macaulay duration, I get 1.9426 years instead of 1.9414; this amounts to a negligible 10.5 hours difference.

I don't think delivery years is relevant for this calculation. Delivery years is specifically the term to maturity of the note or bond in question from the first day of the contract month - given by the formula n+z, where:

- n is the number of whole years from the first day of the delivery month to the maturity (or call) date of the bond or note
- z The number of whole months between n and the maturity (or call) date rounded down to the nearest quarter for the 10-Year U.S. Treasury Note and 30-Year U.S. Treasury Bond futures contracts, and to the nearest month for the 2-Year, 3-Year and 5-Year U.S. Treasury Note futures contracts.

This is used as part of the calculation for the conversion factor. It is a term to maturity that is constant for the life of the contract; it is not a duration. Reference info about the calculation of the conversion factor:
https://www.cmegroup.com/trading/intere ... actors.pdf
couldn't afford the h | | BUY BONDS | WEAR DIAMONDS
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Wed Sep 13, 2023 10:15 am
comeinvest wrote: Thu Sep 07, 2023 6:16 am
unemployed_pysicist wrote: Wed Sep 06, 2023 1:21 pm
comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

...

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
I can't find duration information for bonds at Interactive Brokers.
But I think here https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 on page 163 they derive the formula while considering fractions of years to the next coupon.
So we have to find another way to get to the CME durations.

Last Delivery Day is the third business days of the next following calendar month https://www.cmegroup.com/trading/intere ... eFINAL.pdf , which is Thu 01/04/2024. Then the correct "delivery years" to 09/15/2025 calculating in days would be ca. 619/365 -> 1.69589, not 1.75.
Then
modified duration = 1.69589 / (1 + 4.952/200) -> 1.65491
DV01 = 0.01*1.65491*(\$98.866955)*2000*0.01 -> \$32.723
We are inching closer to the CME value of \$31.60.

It can only be the bond price or a timing difference, right?

Using clean price instead of dirty price:
DV01 = 0.01*1.65491*(\$97.20294)*2000*0.01 -> \$32.172

The calc of modified duration on page 163 of https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 clearly refers to the dirty price, which means the dirty price must be used here.

My result for the cash DV01 of \$32.723 is very close to the futures DV01 of the CTD of \$32.95 per the CME page!!!

Your "Clean Price calculated from Yield" was based on a "scraped yield" of 4.965%. But the CME page shows a yield of 4.952%. Can you please re-generate the "clean price from yield" based on the CME yield, and verify the math? I'm running out of ideas.

The difference in futures DV01 is about 4%. I will re-do the treasury futures / SOFR futures backtest based on the CME DV01. Of course we still don't know if the other CTD contenders play a role.
The formula and its derivation in your linked document is the same as what I use to generate Macaulay durations and modified durations. So this aligns with my understanding.

The yield of 4.952% is lower than my scraped yield of 4.965%. This means that the price will go up and the Macaulay duration will go up, and the result will be worse. I get a clean price of 97.2288 (+1.6739 accrued interest if you use the dirty price), and a Macaulay duration of 1.939 years.

However, I just noticed that 1.9414/(1+5.0474/200)=1.8936; CME uses the forward yield to calculate the duration and modified duration for the future. When I use the 5.0474 yield to calculate a bond price and the Macaulay duration, I get 1.9426 years instead of 1.9414; this amounts to a negligible 10.5 hours difference.

I don't think delivery years is relevant for this calculation. Delivery years is specifically the term to maturity of the note or bond in question from the first day of the contract month - given by the formula n+z, where:

- n is the number of whole years from the first day of the delivery month to the maturity (or call) date of the bond or note
- z The number of whole months between n and the maturity (or call) date rounded down to the nearest quarter for the 10-Year U.S. Treasury Note and 30-Year U.S. Treasury Bond futures contracts, and to the nearest month for the 2-Year, 3-Year and 5-Year U.S. Treasury Note futures contracts.

This is used as part of the calculation for the conversion factor. It is a term to maturity that is constant for the life of the contract; it is not a duration. Reference info about the calculation of the conversion factor:
https://www.cmegroup.com/trading/intere ... actors.pdf
Just commenting on your paragraphs in red for now.
I'm not quite understanding the rationale behind your "n+z" definition of delivery years. What's the point of the rounding instructions? Where did you copy this definition, and what was the context from where you copied it?
Did you mean "first day of delivery month" when you said "first day of contract month"? If yes, and given the uncertainties around the actual "best" delivery day for purpose of duration and other calcs, perhaps this definition is identical to my definition / interpretation of "delivery years"?

Like I said before,
comeinvest wrote: Thu Sep 07, 2023 6:44 am And here I discovered another mistake in my treasury futures / SOFR futures comparison: The SOFR strip should start with the delivery date, and not at the beginning of the backtest period. Because changes to forward rates between now and delivery have no bearing on the value of the CTD at time of delivery. Makes sense. But which delivery date should I assume? Last Day, First Day, or something in between?
it makes rationally sense to calculate the duration using the Macaulay duration starting with the delivery date, doesn't it? (Exact delivery date yet to be determined.) Because forward interest rate changes for any time periods before delivery won't affect the value of the deliverable at time of delivery, and therefore not the value of the futures contract. Isn't my logic correct? (Inspired by a stackexchange.com comment that I referenced earlier.)
Perhaps a better name for "delivery years" would be "forward Macaulay duration", where "forward" means duration at time of delivery?

An example for illustration. Say the Fed announces to raise or lower short-term rates dramatically during Nov 2023 only, but revert back to normal rates in Dec and onward; as a result, instantaneous forward rates for the month of Nov 2023 rise to 50% p.a. or sink to 0% or even -30% p.a., while Dec, Jan, etc. forward rates don't budge. Any current bonds that mature after Nov, including the deliverable treasuries (not the futures themselves) will fluctuate a lot and literally go crazy because of this news, because their yields to maturity will be affected by any movement in short-term rates between now and maturity (expectations hypothesis). But not so the current treasury futures contracts with Dec 2023 expirations. At time of delivery of the current futures contracts (Dec 2023 or Jan 2024), the value of the deliverable won't be affected a single bit by whatever happened to Nov 2023 short-term rates. Nov 2023 will be history at that time.
Therefore almost all bond math for futures based on their underlying deliverable bonds should be based on the time starting with the (yet to be determined) delivery day, right?
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

I almost feel like a smartass today as I sold the MES calendar spread at the ASK of 49.00 (traded in another account not seen in the picture), and then the ES spread at the BID of 49.00 later in the session, when the MES and ES quotes almost crossed, and later actually crossed but in the opposite direction. I'm usually not that lucky; but the lesson learned is that the MES/ES differential does not seem to be completely and instantaneously arbitraged away.
There is a possibility though that the Interactive Brokers data had issues.
The astute reader of this thread knows that I'm a bit stubborn as I'm short ES and MES and long EMD and large cap ETFs.

comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Possibly relevant to our ongoing discussion of treasury futures and SOFR futures financing spreads - risk based explanations?
I'm not sure what exactly the implications are - I gather that both cash treasuries and treasury futures could move in opposite directions in different scenarios; though I feel I should be on the hedge fund side, or if I'm on the "large asset managers" side I will pay more for the leverage.

"Fed economists sound alarm on hedge funds gaming US Treasuries" https://finance.yahoo.com/news/fed-econ ... 15173.html
NEW YORK (Reuters) - Researchers at the Federal Reserve have issued warnings in recent weeks about possible disruptions in U.S. Treasuries due to the return of a popular hedge fund trading strategy that exacerbated a crash in the world's biggest bond market in 2020.

Hedge funds' short positions in some Treasuries futures - contracts for the purchase and sale of bonds for future delivery - have recently hit record highs as part of so-called basis trades, which take advantage of the premium of futures contracts over the price of the underlying bonds, analysts have said.

The trades - typically the domain of macro hedge funds with relative value strategies - consist of selling a futures contract, buying Treasuries deliverable into that contract with repurchase agreement (repo) funding, and delivering them at contract expiry.

In two separate notes in recent weeks, economists at the Fed have highlighted potential financial vulnerability risks related to these trades, which are taking place at a time of volatility in the U.S. government bond market due to higher interest rates and uncertainty over future monetary policy actions.

"Cash-futures basis positions could again be exposed to stress during broader market corrections," Fed economists said in an Aug. 30 note. "With these risks in mind, the trade warrants continued and diligent monitoring."

Separately, in a Sept. 8 note that looked among other things at hedge funds' Treasury exposures, Fed economists said there was a risk of a rapid unwind of basis trade positions in case of higher repo funding costs.

This would exacerbate episodes of market stress, they warned, "potentially contributing to increased Treasury market volatility and amplifying dislocations in the Treasury, futures, and repo markets."

Commodity Futures Trading Commission (CFTC) data showed leveraged funds' net shorts on some Treasuries futures were at near record highs in recent weeks, matched by large asset managers' long positions - an indication of basis trades.

"The Fed is unlikely to view this accumulation of basis positions under too favorable a light and may eventually want to clamp down on them," said Steven Zeng, U.S. rates strategist at Deutsche Bank. "However, the approach they take may not be straightforward as the Fed does not have direct regulatory oversight over hedge funds," he said.

The Fed declined to comment on possible policy actions.

LIQUIDITY CONCERNS

The unwinding of basis trades contributed to illiquidity in Treasuries in March 2020, when the market seized up amid rising fears about the coronavirus pandemic, prompting the U.S. central bank to buy \$1.6 trillion of government bonds.

Some market players fear a repeat of a similar situation may still be in the cards.

"Cash futures basis trades are vulnerable to two risks: higher margin costs on the futures short and higher financing costs on the cash long position," Barclays said in a note on Tuesday.

Should financing costs increase in the repo market - where hedge funds obtain short-term loans against Treasury and other securities - the spread, or premium, of futures contracts over underlying cash Treasuries would also need to increase to maintain basis trade positions profitable.

Conversely, a sudden deterioration in the economy and a rapid drop in interest rates could push futures higher, triggering limits on maximum losses and forcing basis trade exits.

"This could potentially bring about a repeat of the March 2020 market turmoil and it is something that the Fed is keen to prevent," Deutsche's Zeng said.
unemployed_pysicist
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Wed Sep 13, 2023 4:34 pm
unemployed_pysicist wrote: Wed Sep 13, 2023 10:15 am
comeinvest wrote: Thu Sep 07, 2023 6:16 am
unemployed_pysicist wrote: Wed Sep 06, 2023 1:21 pm
comeinvest wrote: Tue Sep 05, 2023 7:20 pm
(Are you sure your formula is correct? Shouldn't it depend on the time length between present and the next coupon payment? Is it valid even if the next coupon is paid sooner than coupon period i.e. we already consumed part of a coupon period?)
I'm not completely sure. However,

- It is the formula listed on wikipedia
- The formula is also shown in Burghardt's book
- The formula gives a very close answer to what I see with my broker:

...

1.935/(1+5.035/200)=1.8874 (bid)
1.935/(1+5.013/200)=1.8877 (ask)

I presume my broker will try to get this detail right. Can you check in interactive brokers for an additional confirmation?
I can't find duration information for bonds at Interactive Brokers.
But I think here https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 on page 163 they derive the formula while considering fractions of years to the next coupon.
So we have to find another way to get to the CME durations.

Last Delivery Day is the third business days of the next following calendar month https://www.cmegroup.com/trading/intere ... eFINAL.pdf , which is Thu 01/04/2024. Then the correct "delivery years" to 09/15/2025 calculating in days would be ca. 619/365 -> 1.69589, not 1.75.
Then
modified duration = 1.69589 / (1 + 4.952/200) -> 1.65491
DV01 = 0.01*1.65491*(\$98.866955)*2000*0.01 -> \$32.723
We are inching closer to the CME value of \$31.60.

It can only be the bond price or a timing difference, right?

Using clean price instead of dirty price:
DV01 = 0.01*1.65491*(\$97.20294)*2000*0.01 -> \$32.172

The calc of modified duration on page 163 of https://onlinelibrary.wiley.com/doi/pdf ... 06002.app2 clearly refers to the dirty price, which means the dirty price must be used here.

My result for the cash DV01 of \$32.723 is very close to the futures DV01 of the CTD of \$32.95 per the CME page!!!

Your "Clean Price calculated from Yield" was based on a "scraped yield" of 4.965%. But the CME page shows a yield of 4.952%. Can you please re-generate the "clean price from yield" based on the CME yield, and verify the math? I'm running out of ideas.

The difference in futures DV01 is about 4%. I will re-do the treasury futures / SOFR futures backtest based on the CME DV01. Of course we still don't know if the other CTD contenders play a role.
The formula and its derivation in your linked document is the same as what I use to generate Macaulay durations and modified durations. So this aligns with my understanding.

The yield of 4.952% is lower than my scraped yield of 4.965%. This means that the price will go up and the Macaulay duration will go up, and the result will be worse. I get a clean price of 97.2288 (+1.6739 accrued interest if you use the dirty price), and a Macaulay duration of 1.939 years.

However, I just noticed that 1.9414/(1+5.0474/200)=1.8936; CME uses the forward yield to calculate the duration and modified duration for the future. When I use the 5.0474 yield to calculate a bond price and the Macaulay duration, I get 1.9426 years instead of 1.9414; this amounts to a negligible 10.5 hours difference.

I don't think delivery years is relevant for this calculation. Delivery years is specifically the term to maturity of the note or bond in question from the first day of the contract month - given by the formula n+z, where:

- n is the number of whole years from the first day of the delivery month to the maturity (or call) date of the bond or note
- z The number of whole months between n and the maturity (or call) date rounded down to the nearest quarter for the 10-Year U.S. Treasury Note and 30-Year U.S. Treasury Bond futures contracts, and to the nearest month for the 2-Year, 3-Year and 5-Year U.S. Treasury Note futures contracts.

This is used as part of the calculation for the conversion factor. It is a term to maturity that is constant for the life of the contract; it is not a duration. Reference info about the calculation of the conversion factor:
https://www.cmegroup.com/trading/intere ... actors.pdf
Just commenting on your paragraphs in red for now.
I'm not quite understanding the rationale behind your "n+z" definition of delivery years. What's the point of the rounding instructions? Where did you copy this definition, and what was the context from where you copied it?
Did you mean "first day of delivery month" when you said "first day of contract month"? If yes, and given the uncertainties around the actual "best" delivery day for purpose of duration and other calcs, perhaps this definition is identical to my definition / interpretation of "delivery years"?

Like I said before,
comeinvest wrote: Thu Sep 07, 2023 6:44 am And here I discovered another mistake in my treasury futures / SOFR futures comparison: The SOFR strip should start with the delivery date, and not at the beginning of the backtest period. Because changes to forward rates between now and delivery have no bearing on the value of the CTD at time of delivery. Makes sense. But which delivery date should I assume? Last Day, First Day, or something in between?
it makes rationally sense to calculate the duration using the Macaulay duration starting with the delivery date, doesn't it? (Exact delivery date yet to be determined.) Because forward interest rate changes for any time periods before delivery won't affect the value of the deliverable at time of delivery, and therefore not the value of the futures contract. Isn't my logic correct? (Inspired by a stackexchange.com comment that I referenced earlier.)
Perhaps a better name for "delivery years" would be "forward Macaulay duration", where "forward" means duration at time of delivery?

An example for illustration. Say the Fed announces to raise or lower short-term rates dramatically during Nov 2023 only, but revert back to normal rates in Dec and onward; as a result, instantaneous forward rates for the month of Nov 2023 rise to 50% p.a. or sink to 0% or even -30% p.a., while Dec, Jan, etc. forward rates don't budge. Any current bonds that mature after Nov, including the deliverable treasuries (not the futures themselves) will fluctuate a lot and literally go crazy because of this news, because their yields to maturity will be affected by any movement in short-term rates between now and maturity (expectations hypothesis). But not so the current treasury futures contracts with Dec 2023 expirations. At time of delivery of the current futures contracts (Dec 2023 or Jan 2024), the value of the deliverable won't be affected a single bit by whatever happened to Nov 2023 short-term rates. Nov 2023 will be history at that time.
Therefore almost all bond math for futures based on their underlying deliverable bonds should be based on the time starting with the (yet to be determined) delivery day, right?
As I mentioned, the main purpose of the rounding instructions is to use these as inputs for calculating the conversion factor for every note/bond in the delivery basket. And this is always to the first day of the contract month, not necessarily the first delivery day. E.g., 1 December for december note/bond futures contracts. Delivery years is the time from e.g. 1 December until the maturity of the note/bond. I think this is the same as your interpretation of delivery years.

I think I originally copied the explanatory text from CME's document on conversion factors, which I linked to in my post. For the text I pasted above, I just copied from the comments in my code - I use the algorithm from their document to calculate the conversion factors to use as inputs for the other calculations that I do (IRR, etc.)

I'm still considering the scenario you outlined with the boxcar interest rate function from the Fed. But I made a small breakthrough with respect to reconciling the CME DV01 numbers. Consider the on the run two year treasury note: (all numbers are after bond market close)

DV01 as calculated from the details given by my broker, \$0.261 accrued interest for the on the run two year treasury note:
0.01*1.83*(\$99.932 (midpoint) + \$0.261)*2000*0.01=\$36.670638

Now look at what CME has posted for the DV01 of the on the run (at around the same time)

Note the close agreement between these DV01s. So the DV01 of the on-the-run treasury at least makes sense.
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comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Fri Sep 15, 2023 4:55 pm As I mentioned, the main purpose of the rounding instructions is to use these as inputs for calculating the conversion factor for every note/bond in the delivery basket. And this is always to the first day of the contract month, not necessarily the first delivery day. E.g., 1 December for december note/bond futures contracts. Delivery years is the time from e.g. 1 December until the maturity of the note/bond. I think this is the same as your interpretation of delivery years.

I think I originally copied the explanatory text from CME's document on conversion factors, which I linked to in my post. For the text I pasted above, I just copied from the comments in my code - I use the algorithm from their document to calculate the conversion factors to use as inputs for the other calculations that I do (IRR, etc.)
Just commenting on this part for now.
I am re-posting the screenshot from this viewtopic.php?p=7448371#p7448371 and previous posts that was the basis of our discussion.
The time between Dec 1st 2023 until the maturity of the bond (09/15/2025 - your screenshot uses British notation, perhaps because you are located in Europe) would be ca. 43 half-months, or 43/24 years -> 1.792 years, not 1.75 years. Seems to refute your theory.
But like I said before, if your go 2 lines further down, the 09/30/2025 bond shows the same 1.75 delivery years, which makes me question the quality of the data altogether, unless you can offer an explanation for that.
The other delivery years shown on the screenshot have a granularity of 0.01 years; so they don't generally round the years to quarters.

Frankly I never had time to really read up on the conversion factor logic, so I cannot currently comment on it. I'm still not understanding the economic rationale for the "first day of contract month" - I gather it's a convention, not a rationale? You are not telling me that the conversion factor "beginning of contract month" convention has a bearing on or accounts for a similar convention for the duration input to futures interest rate sensitivity, so basically two conventions that offset in DV01 results, are you?

comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Fri Sep 15, 2023 4:55 pm Note the close agreement between these DV01s. So the DV01 of the on-the-run treasury at least makes sense.
... A further indication that the math is different for the treasuries that are underlying futures contracts; at least for the purpose of eventually calculating the futures DV01. Perhaps in some way connected to the mysterious "delivery years". Also notice the different terminology "cash DV01" vs "OTR DV01".
We could re-do the math for futures DV01 for a different day based on different quotes perhaps at different times of the day; but I think we established that the sensitivity of DV01 with respect to quotes is not that big, is it?
unemployed_pysicist
Posts: 186
Joined: Sat Oct 09, 2021 2:32 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Fri Sep 15, 2023 5:39 pm
unemployed_pysicist wrote: Fri Sep 15, 2023 4:55 pm As I mentioned, the main purpose of the rounding instructions is to use these as inputs for calculating the conversion factor for every note/bond in the delivery basket. And this is always to the first day of the contract month, not necessarily the first delivery day. E.g., 1 December for december note/bond futures contracts. Delivery years is the time from e.g. 1 December until the maturity of the note/bond. I think this is the same as your interpretation of delivery years.

I think I originally copied the explanatory text from CME's document on conversion factors, which I linked to in my post. For the text I pasted above, I just copied from the comments in my code - I use the algorithm from their document to calculate the conversion factors to use as inputs for the other calculations that I do (IRR, etc.)
Just commenting on this part for now.
I am re-posting the screenshot from this viewtopic.php?p=7448371#p7448371 and previous posts that was the basis of our discussion.
The time between Dec 1st 2023 until the maturity of the bond (09/15/2025 - your screenshot uses British notation, perhaps because you are located in Europe) would be ca. 43 half-months, or 43/24 years -> 1.792 years, not 1.75 years. Seems to refute your theory.
But like I said before, if your go 2 lines further down, the 09/30/2025 bond shows the same 1.75 delivery years, which makes me question the quality of the data altogether, unless you can offer an explanation for that.
The other delivery years shown on the screenshot have a granularity of 0.01 years; so they don't generally round the years to quarters.

Frankly I never had time to really read up on the conversion factor logic, so I cannot currently comment on it. I'm still not understanding the economic rationale for the "first day of contract month" - I gather it's a convention, not a rationale? You are not telling me that the conversion factor "beginning of contract month" convention has a bearing on or accounts for a similar convention for the duration input to futures interest rate sensitivity, so basically two conventions that offset in DV01 results, are you?

You did not get the correct answer of 1.75 years here because you did not follow the calculation steps.

Step 1: calculate the number of whole years from the first day of the delivery month to the maturity of the bond (round down, in python "notation" here)

n=np.floor((pd.to_datetime('2025-09-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years

Step 2: Number of whole months between n and the maturity date rounded down to the nearest month for the 2-year treasury note futures contracts.

z=np.floor(12*((pd.to_datetime('2025-09-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 9 months

n + z = 1 year + 9 months/(12 months) = 1.75 years. If you plug in '2025-09-30' to the above formulas you also get 1 year, 9 months.

Let's do a different deliverable for the two year note futures, 91282CAZ4, which matures on '2025-11-30':

n=np.floor((pd.to_datetime('2025-11-30)-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years
z=np.floor(12*((pd.to_datetime('2025-11-30')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 11 months

n + z = 1 year + 11 months/(12 months) = 1.916, which is rounded to 1.92 on the Treasury analytics page. I get the same answer for 91282CFW6, with maturity 2025-11-15.

'2025-10-15':
n=np.floor((pd.to_datetime('2025-10-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years
z=np.floor(12*((pd.to_datetime('2025-10-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 10 months

n + z = 1 year + 10 months/(12 months) = 1.83

I see no mystery about what "delivery years" means on the CME analytics page. I do note that CME appears to use this same calculation of delivery years for all contracts, not just the shorter maturity; they are not rounding to the nearest quarter for the 10 year, T bond, Ultra bond, etc. for this column.

Using the first day of the month is just a convention to calculate conversion factors, and I do not suggest that it should be used as an input for interest rate sensitivity. I'm trying to suggest the opposite - it does not make sense to be using delivery years because this is an artificial construct that has nothing to do with the actual Macaulay/Modified duration of the note or bond. It could be possible that these delivery years are used in CME's calculation of the DV01s, in which case, I would come up with a different calculation because it makes no sense.
couldn't afford the h | | BUY BONDS | WEAR DIAMONDS
comeinvest
Posts: 2370
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Sat Sep 16, 2023 1:55 am
comeinvest wrote: Fri Sep 15, 2023 5:39 pm
unemployed_pysicist wrote: Fri Sep 15, 2023 4:55 pm As I mentioned, the main purpose of the rounding instructions is to use these as inputs for calculating the conversion factor for every note/bond in the delivery basket. And this is always to the first day of the contract month, not necessarily the first delivery day. E.g., 1 December for december note/bond futures contracts. Delivery years is the time from e.g. 1 December until the maturity of the note/bond. I think this is the same as your interpretation of delivery years.

I think I originally copied the explanatory text from CME's document on conversion factors, which I linked to in my post. For the text I pasted above, I just copied from the comments in my code - I use the algorithm from their document to calculate the conversion factors to use as inputs for the other calculations that I do (IRR, etc.)
Just commenting on this part for now.
I am re-posting the screenshot from this viewtopic.php?p=7448371#p7448371 and previous posts that was the basis of our discussion.
The time between Dec 1st 2023 until the maturity of the bond (09/15/2025 - your screenshot uses British notation, perhaps because you are located in Europe) would be ca. 43 half-months, or 43/24 years -> 1.792 years, not 1.75 years. Seems to refute your theory.
But like I said before, if your go 2 lines further down, the 09/30/2025 bond shows the same 1.75 delivery years, which makes me question the quality of the data altogether, unless you can offer an explanation for that.
The other delivery years shown on the screenshot have a granularity of 0.01 years; so they don't generally round the years to quarters.

Frankly I never had time to really read up on the conversion factor logic, so I cannot currently comment on it. I'm still not understanding the economic rationale for the "first day of contract month" - I gather it's a convention, not a rationale? You are not telling me that the conversion factor "beginning of contract month" convention has a bearing on or accounts for a similar convention for the duration input to futures interest rate sensitivity, so basically two conventions that offset in DV01 results, are you?

You did not get the correct answer of 1.75 years here because you did not follow the calculation steps.

Step 1: calculate the number of whole years from the first day of the delivery month to the maturity of the bond (round down, in python "notation" here)

n=np.floor((pd.to_datetime('2025-09-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years

Step 2: Number of whole months between n and the maturity date rounded down to the nearest month for the 2-year treasury note futures contracts.

z=np.floor(12*((pd.to_datetime('2025-09-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 9 months

n + z = 1 year + 9 months/(12 months) = 1.75 years. If you plug in '2025-09-30' to the above formulas you also get 1 year, 9 months.

Let's do a different deliverable for the two year note futures, 91282CAZ4, which matures on '2025-11-30':

n=np.floor((pd.to_datetime('2025-11-30)-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years
z=np.floor(12*((pd.to_datetime('2025-11-30')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 11 months

n + z = 1 year + 11 months/(12 months) = 1.916, which is rounded to 1.92 on the Treasury analytics page. I get the same answer for 91282CFW6, with maturity 2025-11-15.

'2025-10-15':
n=np.floor((pd.to_datetime('2025-10-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24) = 1.0 years
z=np.floor(12*((pd.to_datetime('2025-10-15')-pd.to_datetime('2023-12-01'))/np.timedelta64(1,'D')/365.24-n)) = 10 months

n + z = 1 year + 10 months/(12 months) = 1.83

I see no mystery about what "delivery years" means on the CME analytics page. I do note that CME appears to use this same calculation of delivery years for all contracts, not just the shorter maturity; they are not rounding to the nearest quarter for the 10 year, T bond, Ultra bond, etc. for this column.

Using the first day of the month is just a convention to calculate conversion factors, and I do not suggest that it should be used as an input for interest rate sensitivity. I'm trying to suggest the opposite - it does not make sense to be using delivery years because this is an artificial construct that has nothing to do with the actual Macaulay/Modified duration of the note or bond. It could be possible that these delivery years are used in CME's calculation of the DV01s, in which case, I would come up with a different calculation because it makes no sense.
Thanks, I agree. I got on the wrong track because the CME "delivery months" are almost the same as what I call "forward time to maturity" and "forward Macaulay duration"; minus the rounding to the beginning of the month, and assuming a zero coupon bond which is of course not accurate.
So yes, let's forget the "delivery months" - especially as we don't even get the cash duration that CME shows, even with the delivery months as input which makes no sense in the first place.

But based on my illustration in my recent post, I think that my "forward time to maturity" and "forward Macaulay duration", the remaining time to maturity at the time of delivery, should be used as an input to the futures duration, i.e. to the futures sensitivity to interest rate changes.
Perhaps also forward yield which you mentioned before, if it is different from the current yield.
Then plug all of that into the formula for modified duration, then DV01. That should give us the futures contract sensitivity to interest rate changes, right? I'm thinking purely from my economic rationale point of view.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

I'd appreciate if someone can summarize the wisdom from 55 pages of this thread

Specifically, I am currently at 100% stocks and considering diversification with adding treasury futures.
To keep things simple, i am considering buying some /ZN (and BOXX with new savings) in my taxable account. How does that sound?
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Sat Sep 16, 2023 4:45 pm I'd appreciate if someone can summarize the wisdom from 55 pages of this thread

Specifically, I am currently at 100% stocks and considering diversification with adding treasury futures.
To keep things simple, i am considering buying some /ZN (and BOXX with new savings) in my taxable account. How does that sound?
There are some partial summaries in the original post and some later posts; there are many aspects to it. But I would strongly, extremely strongly advise not just "following instructions", without reading and understanding the 55 pages. It would be a disservice. Nobody knows the outcome of this strategy, and you won't be able to understand the risks and the return potential without reading the entire thread. Also, everybody implements it in a different way and with different allocations.
unemployed_pysicist
Posts: 186
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Sat Sep 16, 2023 3:39 am
But based on my illustration in my recent post, I think that my "forward time to maturity" and "forward Macaulay duration", the remaining time to maturity at the time of delivery, should be used as an input to the futures duration, i.e. to the futures sensitivity to interest rate changes.
Perhaps also forward yield which you mentioned before, if it is different from the current yield.
Then plug all of that into the formula for modified duration, then DV01. That should give us the futures contract sensitivity to interest rate changes, right? I'm thinking purely from my economic rationale point of view.
I am considering this possibility.

I tried the following for the TUZ23 contract, using the slightly different numbers from this screenshot:

I thought, let's take the modified duration and subtract the unrounded amount of time between 15-September 2023 (the date of the screenshot) and 1-December 2023 (I think this would be the first possible delivery day, just using this as a placeholder for now). This is 77 days, or 0.2108 years. I also plugged the futures yield into the function to get bond price, which gave me a clean price of \$96.86. With settlement on monday, there would be \$0.0385 in accrued interest. So the calculation would be:

0.01*(1.8991-0.2108)*(\$96.85886527272123+\$0.0385)*2000*0.01=\$32.72, very close to \$32.87.

Unfortunately, this approach did not work for the five year contract:

0.01*(4.0248-0.2108)*(\$98.14546796366446+\$0.2088)*1000*0.01=\$37.51. So this is not quite right.

Interesting to note that for the three year contract, the on the run was the cheapest to deliver:

I can't find 91282CHY0 at my broker (probably not available yet.) But it is strange that the durations are the same for the future and for the on-the-run, since it generally seems like CME uses the futures yield in the calculation of the duration. Why are the durations exactly the same when the OTR yield is different than the futures yield?

But indeed, the DV01s are quite different, as is the cash ctd dv01 listed in the table, so there is clearly something else going on. The next thing we can try is changing the duration calculation so that the term to maturity of all cashflows starts from the first or last delivery date, which I think aligns with your suggestion that I quoted in this post. If we do it this way, it will not necessarily be exactly the same as simply subtracting the 0.2108 or whatever years off from the modified duration. Perhaps this level of precision is needed to get the same numbers as CME.

I am very interested to see how Z3N will evolve over the next few months - I think it's not too often that we see an on-the-run as the cheapest to deliver for the major contracts in recent history (ignoring the ultra 10 and 20 year contracts).
couldn't afford the h | | BUY BONDS | WEAR DIAMONDS
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Sun Sep 17, 2023 3:12 pm I thought, let's take the modified duration and subtract the unrounded amount of time between 15-September 2023 (the date of the screenshot) and 1-December 2023 (I think this would be the first possible delivery day, just using this as a placeholder for now). This is 77 days, or 0.2108 years. I also plugged the futures yield into the function to get bond price, which gave me a clean price of \$96.86. With settlement on monday, there would be \$0.0385 in accrued interest. So the calculation would be:
Not sure if your math is correct. Perhaps we should calculate the "forward modified duration" ourselves based on "forward Macaulay duration"? Basically forget CME; just do the math as it makes sense based on economic rationale and definition of "DV01".
EDIT: That's what you suggested further down in your post.

Strictly speaking I think we also want to discount the forward changes in value of the deliverable, for the time between now and delivery, right? I think the difference would be ca. 1.25% (ca. 5% risk-free rate for 3 months).
Last edited by comeinvest on Sun Sep 17, 2023 4:13 pm, edited 1 time in total.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Sun Sep 17, 2023 3:12 pm I can't find 91282CHY0 at my broker (probably not available yet.) But it is strange that the durations are the same for the future and for the on-the-run, since it generally seems like CME uses the futures yield in the calculation of the duration. Why are the durations exactly the same when the OTR yield is different than the futures yield?
Probably the CTD duration on the CME page is then just the CTD duration and nothing else? Nothing to do with the futures contract.

I know it's confusing because they list the "futures yield" and "futures DV01" in the same line as the "duration" and "modified duration"; but based on the evidence, I must assume that "duration" and "modified duration" refer just to the CTD and have nothing to do with the futures contract.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Sun Sep 17, 2023 3:12 pm But indeed, the DV01s are quite different, as is the cash ctd dv01 listed in the table, so there is clearly something else going on.
I think we established before that the CME "futures DV01" is exactly the CME "cash DV01" divided by the conversion factor. By implication, the "cash DV01" must be something different from the CTD DV01. I gather that the "cash DV01" is a number specifically crafted for the purpose of calculating futures DV01 based on "cash DV01", and therefore must be different from the CTD DV01 - perhaps based on the forward durations etc. - basically everything needed for the economic impact on the present futures contract fair value, except the division by the conversion factor.
unemployed_pysicist wrote: Sun Sep 17, 2023 3:12 pm The next thing we can try is changing the duration calculation so that the term to maturity of all cashflows starts from the first or last delivery date, which I think aligns with your suggestion that I quoted in this post. If we do it this way, it will not necessarily be exactly the same as simply subtracting the 0.2108 or whatever years off from the modified duration. Perhaps this level of precision is needed to get the same numbers as CME.
I agree that's the way to go. Also, discount everything to present value (present = now, not delivery date). I think futures convexity should also be considered, but is probably negligible for a 3 months period.
Also, can we verify the "futures yield" of CME? I don't trust anything.
Then the everlasting question should we take First Delivery Day or Last Delivery Day or a combination. But if we hit the target of the DV01 that CME shows with any delivery date, we are getting closer to the resolution.
Last edited by comeinvest on Sun Sep 17, 2023 4:45 pm, edited 1 time in total.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

unemployed_pysicist wrote: Sun Sep 17, 2023 3:12 pm
The futures DV01 and the OTR DV01 (which in this case is identical to CTD DV01) differ by a whopping 6%. The "cash DV01" and the OTR DV01 (which in this case is identical to CTD DV01) differ by a whopping 10% (both before dividing by the conversion factor). Therefore it is important to understand and accurately calculate the futures DV01 - for 2 major immediate reasons relating to mHFEA:
1. Comparing treasury futures performance to SOFR futures performance - impossible without adjusting for DV01 differences
2. Rebalancing and asset allocation - ok 10% off probably won't move the needle (or we could just trust CME published futures DV01 as a black box); but I prefer to know exactly what my interest rate exposure is and why.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Sat Sep 16, 2023 4:59 pm
klaus14 wrote: Sat Sep 16, 2023 4:45 pm I'd appreciate if someone can summarize the wisdom from 55 pages of this thread

Specifically, I am currently at 100% stocks and considering diversification with adding treasury futures.
To keep things simple, i am considering buying some /ZN (and BOXX with new savings) in my taxable account. How does that sound?
There are some partial summaries in the original post and some later posts; there are many aspects to it. But I would strongly, extremely strongly advise not just "following instructions", without reading and understanding the 55 pages. It would be a disservice. Nobody knows the outcome of this strategy, and you won't be able to understand the risks and the return potential without reading the entire thread. Also, everybody implements it in a different way and with different allocations.
Thanks for your response.
I understand there are a lot of nuances of this (SOFR ?). I am no stranger to the thread, i made some contributions at the beginning and bailed at the right time

At this point, i am not looking for the optimal implementation. I just want to slightly diversify my portfolio using some insights from this thread.

As a first step, i bought 11% (of my portfolio worth) /ZN. I had 4.5% gold. 11% /ZN is the volatility equivalent.
I'll direct my future savings to build 11% position in BOXX. By buying /ZN now, i think i eliminated some interest rate risk.
Just sharing here in case someone spots an obvious mistake in my thinking.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Mon Sep 18, 2023 5:24 am
comeinvest wrote: Sat Sep 16, 2023 4:59 pm
klaus14 wrote: Sat Sep 16, 2023 4:45 pm I'd appreciate if someone can summarize the wisdom from 55 pages of this thread

Specifically, I am currently at 100% stocks and considering diversification with adding treasury futures.
To keep things simple, i am considering buying some /ZN (and BOXX with new savings) in my taxable account. How does that sound?
There are some partial summaries in the original post and some later posts; there are many aspects to it. But I would strongly, extremely strongly advise not just "following instructions", without reading and understanding the 55 pages. It would be a disservice. Nobody knows the outcome of this strategy, and you won't be able to understand the risks and the return potential without reading the entire thread. Also, everybody implements it in a different way and with different allocations.
Thanks for your response.
I understand there are a lot of nuances of this (SOFR ?). I am no stranger to the thread, i made some contributions at the beginning and bailed at the right time

At this point, i am not looking for the optimal implementation. I just want to slightly diversify my portfolio using some insights from this thread.

As a first step, i bought 11% (of my portfolio worth) /ZN. I had 4.5% gold. 11% /ZN is the volatility equivalent.
I'll direct my future savings to build 11% position in BOXX. By buying /ZN now, i think i eliminated some interest rate risk.
Just sharing here in case someone spots an obvious mistake in my thinking.
If you buy BOXX, you obviously have less than 100% equities, or it would probably not make sense. Which means your asset allocation does not really resemble mHFEA. Everything else is speculation.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Mon Sep 18, 2023 1:41 pm
klaus14 wrote: Mon Sep 18, 2023 5:24 am
comeinvest wrote: Sat Sep 16, 2023 4:59 pm
klaus14 wrote: Sat Sep 16, 2023 4:45 pm I'd appreciate if someone can summarize the wisdom from 55 pages of this thread

Specifically, I am currently at 100% stocks and considering diversification with adding treasury futures.
To keep things simple, i am considering buying some /ZN (and BOXX with new savings) in my taxable account. How does that sound?
There are some partial summaries in the original post and some later posts; there are many aspects to it. But I would strongly, extremely strongly advise not just "following instructions", without reading and understanding the 55 pages. It would be a disservice. Nobody knows the outcome of this strategy, and you won't be able to understand the risks and the return potential without reading the entire thread. Also, everybody implements it in a different way and with different allocations.
Thanks for your response.
I understand there are a lot of nuances of this (SOFR ?). I am no stranger to the thread, i made some contributions at the beginning and bailed at the right time

At this point, i am not looking for the optimal implementation. I just want to slightly diversify my portfolio using some insights from this thread.

As a first step, i bought 11% (of my portfolio worth) /ZN. I had 4.5% gold. 11% /ZN is the volatility equivalent.
I'll direct my future savings to build 11% position in BOXX. By buying /ZN now, i think i eliminated some interest rate risk.
Just sharing here in case someone spots an obvious mistake in my thinking.
If you buy BOXX, you obviously have less than 100% equities, or it would probably not make sense. Which means your asset allocation does not really resemble mHFEA. Everything else is speculation.
Not sure it is really that different. it is just that i am in the later years of the lifecycle. at some point in mHFEA, you'll wind down leverage to 1x and have equity less than 100% right? You'll probably convert your treasury futures to actual treasuries at some point (maybe when you are couple years away from retirement). I am just tax optimizing that part.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Mon Sep 18, 2023 2:46 pm Not sure it is really that different. it is just that i am in the later years of the lifecycle. at some point in mHFEA, you'll wind down leverage to 1x and have equity less than 100% right? You'll probably convert your treasury futures to actual treasuries at some point (maybe when you are couple years away from retirement). I am just tax optimizing that part.
Ok, true. I don't think I personally will have less than 100% equities; but it might make sense for others.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Fri May 06, 2022 3:33 pm
muffins14 wrote: Fri May 06, 2022 9:45 am I'm sitting at like 115 / 80. Not really fun watching my treasuries futures continue to drain cash away from my portfolio. In taxable I have 1 TN, 2 ZN 2 ZF, and 1 ZT.

I guess I am going to roll and keep all of them when the time comes, and just hope the higher yields do something nice for me
Higher yields doesn't automatically mean good return for strategy because as yields rise financing cost of futures also rise. A reasonable return expectation for treasury futures is the term premium. And as of today, latest ACM term premium estimation is still below financing cost spread (~0.25) for 10Y (0.069) and 7Y (0.176). So expected return of TN and ZN is still negative.

And there is the negative correlation benefit between treasuries and stocks. That is not holding up either. On the contrary, low performance of the bonds (rising yields) is the reason for low performance of stocks.

I am planning to not have any bonds or bond futures until
(1) Real yield is comfortably above zero.
(2) Term premium prediction is comfortably above financing cost spread.
(3) Positive correlation reverses (I don't need to exactly time this, some lag is fine)
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 5:04 am
klaus14 wrote: Fri May 06, 2022 3:33 pm
muffins14 wrote: Fri May 06, 2022 9:45 am I'm sitting at like 115 / 80. Not really fun watching my treasuries futures continue to drain cash away from my portfolio. In taxable I have 1 TN, 2 ZN 2 ZF, and 1 ZT.

I guess I am going to roll and keep all of them when the time comes, and just hope the higher yields do something nice for me
Higher yields doesn't automatically mean good return for strategy because as yields rise financing cost of futures also rise. A reasonable return expectation for treasury futures is the term premium. And as of today, latest ACM term premium estimation is still below financing cost spread (~0.25) for 10Y (0.069) and 7Y (0.176). So expected return of TN and ZN is still negative.

And there is the negative correlation benefit between treasuries and stocks. That is not holding up either. On the contrary, low performance of the bonds (rising yields) is the reason for low performance of stocks.

I am planning to not have any bonds or bond futures until
(1) Real yield is comfortably above zero.
(2) Term premium prediction is comfortably above financing cost spread.
(3) Positive correlation reverses (I don't need to exactly time this, some lag is fine)
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Wed Sep 20, 2023 6:10 am
klaus14 wrote: Wed Sep 20, 2023 5:04 am
klaus14 wrote: Fri May 06, 2022 3:33 pm Higher yields doesn't automatically mean good return for strategy because as yields rise financing cost of futures also rise. A reasonable return expectation for treasury futures is the term premium. And as of today, latest ACM term premium estimation is still below financing cost spread (~0.25) for 10Y (0.069) and 7Y (0.176). So expected return of TN and ZN is still negative.

And there is the negative correlation benefit between treasuries and stocks. That is not holding up either. On the contrary, low performance of the bonds (rising yields) is the reason for low performance of stocks.

I am planning to not have any bonds or bond futures until
(1) Real yield is comfortably above zero.
(2) Term premium prediction is comfortably above financing cost spread.
(3) Positive correlation reverses (I don't need to exactly time this, some lag is fine)
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
(2) i looked at this. I don't know how this works TBH.
(3) it's not unreasonable to think in terms of "regime"s or "momentum"
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 6:19 am I am planning to not have any bonds or bond futures until
(1) Real yield is comfortably above zero.
(2) Term premium prediction is comfortably above financing cost spread.
(3) Positive correlation reverses (I don't need to exactly time this, some lag is fine)
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
[/quote]

Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
[/quote]

(2) i looked at this. I don't know how this works TBH.
(3) it's not unreasonable to think in terms of "regime"s or "momentum"
[/quote]

(2) says nothing, it looks backward. I thought you are looking at least at a forward looking model.
(3) Could be, or cold not be reasonable. It's reasonable to think the future is different from the past. I think user "Hydromod" did some research on the subject and showed short-term volatility "regimes", but his strategy is quite sophisticated and more technical - I haven't looked into it yet.
comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 6:19 am
comeinvest wrote: Wed Sep 20, 2023 6:10 am
klaus14 wrote: Wed Sep 20, 2023 5:04 am
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
(2) i looked at this. I don't know how this works TBH.
(3) it's not unreasonable to think in terms of "regime"s or "momentum"

(2) says nothing, it looks backward. I thought you are looking at least at a forward looking model.
(3) Could be, or could not be reasonable - pure speculation. It's reasonable to think the future is different from the past. I think user "Hydromod" did some research on the subject and showed short-term volatility "regimes", but his strategy is quite sophisticated and more technical - I haven't looked into the details yet.
Last edited by comeinvest on Wed Sep 20, 2023 3:36 pm, edited 1 time in total.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Wed Sep 20, 2023 1:07 pm
klaus14 wrote: Wed Sep 20, 2023 6:19 am
comeinvest wrote: Wed Sep 20, 2023 6:10 am
klaus14 wrote: Wed Sep 20, 2023 5:04 am
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
(2) i looked at this. I don't know how this works TBH.
(3) it's not unreasonable to think in terms of "regime"s or "momentum"

(2) says nothing, it looks backward. I thought you are looking at least at a forward looking model.
(3) Could be, or cold not be reasonable - pure speculation. It's reasonable to think the future is different from the past. I think user "Hydromod" did some research on the subject and showed short-term volatility "regimes", but his strategy is quite sophisticated and more technical - I haven't looked into the details yet.

(2) what do you mean by looking backward? it says term premium = -0.1205 on 2023-09-15. which i read as, if one buys 5y zero-coupon bond on that date, expected term prem till maturity is -0.1205. isn't it true?

I also downloaded ACM term premiums. That also reads very negative for all of the curve.

(3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
Last edited by klaus14 on Wed Sep 20, 2023 3:23 pm, edited 1 time in total.
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Topic Author
skierincolorado
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 2:08 pm
comeinvest wrote: Wed Sep 20, 2023 1:07 pm
klaus14 wrote: Wed Sep 20, 2023 6:19 am
comeinvest wrote: Wed Sep 20, 2023 6:10 am
klaus14 wrote: Wed Sep 20, 2023 5:04 am
it still doesn't look like a good entry point for mHFEA based on my above criteria.
(1) is now good. 2% real yield on 10y TIPS.
(2) is still bad. term premium is below zero.
(3) is still bad. i don't see bonds doing well when stocks do bad. (based on monthly returns of NTSX vs VOO)
Before you cite (2), if you refer to ACM, explain to me the methodology, to make sure we understand it and that we can be confident in out-of-sample predictions. I posted a picture from another model and methodology a few posts up that shows a good term premium.
For (3) we know the past but not the future. At any given "present" time.
(2) i looked at this. I don't know how this works TBH.
(3) it's not unreasonable to think in terms of "regime"s or "momentum"

(2) says nothing, it looks backward. I thought you are looking at least at a forward looking model.
(3) Could be, or cold not be reasonable - pure speculation. It's reasonable to think the future is different from the past. I think user "Hydromod" did some research on the subject and showed short-term volatility "regimes", but his strategy is quite sophisticated and more technical - I haven't looked into the details yet.

(2) what do you mean by looking backward? it says term premium = -0.1205 on 2023-09-15. which i read as, if one buys 5y zero-coupon bond on that date, expected term prem till maturity is -0.1205. isn't it true?

(3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
My understanding is that the term premium models are primarily based on a regression of historical data and then predicting that the historical relationships will hold in the future in order to predict what the term premium is today. So it's backwards looking. The market might actually expect a very positive term premium, but the model wouldn't know. I'm not saying we should ignore term premium models, but also they should not be taken as truth. It's a prediction like any other. For example a model could predict the equity risk premium but the model may not understand the behavior of market participants especially when the future is expected to be different from the past.

Yes that does seem to be the regime at the moment. But the regime often shifts rapidly without warning. You have to be positioned before the regime shifts or you could backtest a regime timing strategy to see if it beats buy and hold. But it should be rules based and backtested for statistical significance.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

skierincolorado wrote: Wed Sep 20, 2023 3:15 pm My understanding is that the term premium models are primarily based on a regression of historical data and then predicting that the historical relationships will hold in the future in order to predict what the term premium is today. So it's backwards looking. The market might actually expect a very positive term premium, but the model wouldn't know. I'm not saying we should ignore term premium models, but also they should not be taken as truth. It's a prediction like any other. For example a model could predict the equity risk premium but the model may not understand the behavior of market participants especially when the future is expected to be different from the past.

Yes that does seem to be the regime at the moment. But the regime often shifts rapidly without warning. You have to be positioned before the regime shifts or you could backtest a regime timing strategy to see if it beats buy and hold. But it should be rules based and backtested for statistical significance.
Do we have a way of predicting expected returns better than these models? you dislike models because they are backwards looking, but the foundation of this strategy is backtesting. isn't that contradictory?

Yes, regime can shift rapidly. Maybe: an external shock (like covid) -> recession risk -> stocks crash + low rates. But i don't think this is a good reason for buying treasury futures if they don't have a positive expected return. You can instead just buy a put, which would protect you against all kinds of equity crashes including inflationary ones.

In general, diversifers should only be included if they also have a positive expected return.
Last edited by klaus14 on Wed Sep 20, 2023 3:55 pm, edited 1 time in total.
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comeinvest
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 2:08 pm (3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
The past is usually easier to "see" than the future. What regime will we be in tomorrow? Nobody knows. Back in Spring there was quite some negative correlation between stocks and bonds, almost on a daily basis. Some charts were posted where bonds were almost the mirror image of stocks.
klaus14
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### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Wed Sep 20, 2023 3:34 pm
klaus14 wrote: Wed Sep 20, 2023 2:08 pm (3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
The past is usually easier to "see" than the future. What regime will we be in tomorrow? Nobody knows. Back in Spring there was quite some negative correlation between stocks and bonds, almost on a daily basis. Some charts were posted where bonds were almost the mirror image of stocks.
not really. it was known yesterday that if fed signaled higher rates on wednesday, that was bad for stocks.
tomorrow: same. if fed hikes rates, stocks will go down. this is not a good enviroment for mHFEA.

PS: i sold my /ZN (that i bought 2 days ago) this morning after finding my criteria post in the thread I have bad memory but good timing
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

skierincolorado wrote: Wed Sep 20, 2023 3:15 pm My understanding is that the term premium models are primarily based on a regression of historical data and then predicting that the historical relationships will hold in the future in order to predict what the term premium is today. So it's backwards looking.
That would still be called "forward looking". Backward would refer to realized out- or underperformance.
I was mistaken; I think the chart that klaus14 linked https://fred.stlouisfed.org/series/THREEFYTP5 is the KW model and therefore forward looking.
My interpretation of the yield curve is that the slope is indicative of the future term premium, but only in the mid- and long-term maturities, like we have discussed in a private chat. (Short-term rates are governed by Fed policy expectations. Long-term rates too, but the market cannot predict specific Fed policy, macroeconomic events, or growth and inflation differences between year 13 and year 15 from now, for example. Therefore the slope in the mid- and long-term segments of the yield curve must be the term premium?)
The slope between 10y and 20y is positive.
Although we should probably look at the forward yield curve, because the par yield curve and zero coupon curves are distorted by the near-term anomalies which have an effect on the integration of short-term rates that make up the long-term rates. The forward rates really give the "clear" picture, right?

Alternate term premium estimates:
viewtopic.php?p=7437471#p7437471
viewtopic.php?p=7451580#p7451580
If you go to the SA articles, van Deventer has references to the underlying research.
Explain to me the difference in methodology between this and the ACM model

The slope between 20y and 30y has historically been rather negative - almost the entire history, except ca. 5 years during ZIRP:
viewtopic.php?p=7403201#p7403201
Kind of contradicts the common narrative along with the ad-hoc "explanations" that the slope of the yield curve "must" be positive, doesn't it?
I still have a hard time understanding this. There seems to be a risk-based explanation based on convexity which supposedly shows up for maturities longer than 20 years. But even the forward rates seem to decrease after 20 years, and even more so than the par rates - how can that be explained? Say I estimate the forward rates in 30 years will be 3.5%, but in 20 years they will be 4.5%. I bet on the 20-30 year forward rates via swaps or the UB future or the 30y treasury. As the 30y forward rates become 20 year forward rates with the passage of time, they would reach the peak of the curve at the 20y forward point. Would seem like an almost sure bet to lose money in the long run if I were to bet on 20-30 year forward rates, or not? How can this be explained with bond convexity?
Re-posting one of the charts:

Last edited by comeinvest on Wed Sep 20, 2023 4:18 pm, edited 4 times in total.
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 3:40 pm
comeinvest wrote: Wed Sep 20, 2023 3:34 pm
klaus14 wrote: Wed Sep 20, 2023 2:08 pm (3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
The past is usually easier to "see" than the future. What regime will we be in tomorrow? Nobody knows. Back in Spring there was quite some negative correlation between stocks and bonds, almost on a daily basis. Some charts were posted where bonds were almost the mirror image of stocks.
not really. it was known yesterday that if fed signaled higher rates on wednesday, that was bad for stocks.
tomorrow: same. if fed hikes rates, stocks will go down. this is not a good enviroment for mHFEA.

PS: i sold my /ZN (that i bought 2 days ago) this morning after finding my criteria post in the thread I have bad memory but good timing
This causal effect has always existed and will always exist, 500 years ago and 500 years from now. What you cannot know is whether on any given day the inflation and interest rate effect, or any macroeconomic news effects will prevail. The former is correlated, the latter anticorrelated. Look at the charts that were posted back in Spring in this or the other HFEA thread. Macroeconomic fears prevailed, stocks and bonds were almost mirror images, without prior "warning" or public announcement Just like there was no "warning" or public announcement in Dec 2021 that rates would rise more than implied by forward rates in 2022, stock and bonds would become more correlated, and that you should exit mHFEA; Fed policy rates had not meaningfully risen 10+ years despite high forward rates, resulting in juicy mHFEA returns for many years. Later you are always wiser. It's much easier to predict the past than the future.
Last edited by comeinvest on Wed Sep 20, 2023 9:10 pm, edited 1 time in total.
comeinvest
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Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

comeinvest wrote: Wed Sep 20, 2023 4:05 pm
klaus14 wrote: Wed Sep 20, 2023 3:40 pm
comeinvest wrote: Wed Sep 20, 2023 3:34 pm
klaus14 wrote: Wed Sep 20, 2023 2:08 pm (3) what regime we are in is easy to see: fed signaled higher rates today and stocks went down.
The past is usually easier to "see" than the future. What regime will we be in tomorrow? Nobody knows. Back in Spring there was quite some negative correlation between stocks and bonds, almost on a daily basis. Some charts were posted where bonds were almost the mirror image of stocks.
not really. it was known yesterday that if fed signaled higher rates on wednesday, that was bad for stocks.
tomorrow: same. if fed hikes rates, stocks will go down. this is not a good enviroment for mHFEA.

PS: i sold my /ZN (that i bought 2 days ago) this morning after finding my criteria post in the thread I have bad memory but good timing
This causal effect has always existed and will always exist, 500 years ago and 500 years from now. What you cannot know is whether on any given day the inflation and interest rate effect, or any macroeconomic news effects will prevail. The former is correlated, the latter anticorrelated. Look at the charts that were posted back in Spring in this or the other HFEA thread. Macroeconomic fears prevailed, stocks and bonds were almost mirror images, without prior "warning" or public announcement Just like there was no "warning" or public announcement in Dec 2021 that rates would rise more than implied by forward rates in 2022 and that you should exit mHFEA; Fed policy rates had not meaningfully risen 10+ years despite high forward rates, resulting in juicy mHFEA returns for many years. Later you are always wiser. It's much easier to predict the past than the future.
The 2% real returns above current implied inflation expectations and also above the policy inflation target are noteworthy, because we have about 2% now across the entire maturity spectrum, meaning if and when we ever have < 2% real rates within the next 30 years and the inflation target holds, some good things will might happen to mHFEA (crossed out "will", because it would be for sure only if you have a stake in the 30y treasuries); but then again if you remember the charts in this post https://bogleheads.org/forum/viewtopic. ... 9#p7093439 this also becomes more relative. I don't know for sure, but I personally tend to believe that the "2% real" has more impact on the long-term term premium (if anything can be said or assumed), while the ACM model might be more tactical and also have high uncertainty. The ACM goes only up to 10 years anyway.
Timing the market and acting on any of that information, however, is yet another story.

Similar charts to those below were posted before; but remember, whenever the blue line in the first chart is below the dotted lines, treasury futures helped; whenever it is above, they detracted from returns. If you look at the gap between the blue and the dotted lines, you can easily see why treasury futures were so much more destructive in 2022 than during the 2004-2006 rate hike cycle, even when the total rate increase was not that different.
Also note the Fed long-term neutral rate projection of 2.5%, in comparison to the long-term treasury yields. Of course nobody knows the actual "neutral" rate; the Fed member estimates may be off - as you can see, some Fed members' estimates are almost up to 4%, although it's not clear if that would be the long-run terminal neutral rate estimate or just the 5 year forward estimate.

I think if you try to time the market while waiting for your 3 conditions, you actually want to bet to a large extent on the gap between the dot plot and the current long-term rates to get wider. Waiting for this might backfire; just like with the stock market, any day can be the best entry point for the rest of your life that you will never see again (or otherwise you wouldn't invest).

One caveat is that I still didn't study the methodology of the ACM model, in particular how it is different from the Donald van Deventer methodology, and therefore cannot speak to how much predictive capability it might have. The historical track record was not that great though.

Topic Author
skierincolorado
Posts: 2346
Joined: Sat Mar 21, 2020 10:56 am

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

klaus14 wrote: Wed Sep 20, 2023 3:26 pm
skierincolorado wrote: Wed Sep 20, 2023 3:15 pm My understanding is that the term premium models are primarily based on a regression of historical data and then predicting that the historical relationships will hold in the future in order to predict what the term premium is today. So it's backwards looking. The market might actually expect a very positive term premium, but the model wouldn't know. I'm not saying we should ignore term premium models, but also they should not be taken as truth. It's a prediction like any other. For example a model could predict the equity risk premium but the model may not understand the behavior of market participants especially when the future is expected to be different from the past.

Yes that does seem to be the regime at the moment. But the regime often shifts rapidly without warning. You have to be positioned before the regime shifts or you could backtest a regime timing strategy to see if it beats buy and hold. But it should be rules based and backtested for statistical significance.
Do we have a way of predicting expected returns better than these models? you dislike models because they are backwards looking, but the foundation of this strategy is backtesting. isn't that contradictory?

Yes, regime can shift rapidly. Maybe: an external shock (like covid) -> recession risk -> stocks crash + low rates. But i don't think this is a good reason for buying treasury futures if they don't have a positive expected return. You can instead just buy a put, which would protect you against all kinds of equity crashes including inflationary ones.

In general, diversifers should only be included if they also have a positive expected return.
One other way of predicting the term premium would be theoretically. Regression models based on history predict a slightly negative term premium. But we know that there is substantial uncertainty in these models. And there are theoretical arguments why the term premium probably is positive. It's also been positive for many decades at least. The primary reason that the term premium might go negative is if the correlation with equities was expected to be very negative. Which works out just as well for us.

A put is probably more expensive even if the term premium is slightly expensive. And yes the primary worry I have is a shock like COVID or 2008. Treasury futures would have looked pretty expensive right up until it was too late.

The correlation with equities has been negative for most of the year I think. There are some days like FED days where it has been positive. But by and large the correlation has been negative especially in the ways that matter. The economy has performed far better than most experts predicted. Earlier the expectation was for a small recession or near recession at best. Instead GDP growth and hiring have remained strong. Consequently the market is way up from below 3700 to over 4400. The surprising macroeconomic strength has driven the market up and bonds down. Yes on FED days or CPI report days sometimes there is positive correlation. But overall the macroeconomic strength has driven both stocks and bonds in different directions. So I would say overall, the correlation has been negative on the timescales that matter (months). Just as surprising macro strenght drove bonds down the last 6-12 months, surprising weakness would very likely drive them up in the future.

If you look at the last 9 months bonds and stocks have mostly moved in opposite directions. Primarily being drive by macro strength/weakness. Stocks were down in March when bonds were up. Since then stocks were up and bonds down.

Overall I agree with comeinvest that the idea we are in a positive correlatoin regime is wrong and even if regimes did exist, timing the entries and exits would be impossible.
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Stocks vs bonds (blue), using Vanguard extended duration (EDV, yellow, current duration ca. 24 years) for better visualization, and international stocks (Vanguard FTSE Developed, VEA).
I tried a portfoliovisualizer analysis, but found out it is meaningless for the short time frame of 2023 year to date - the calendar months scale volatilities and drawdowns are too coarse, and Sharpe ratios of course are totally meaningless. The only useful information I got from the PV analysis is that the stocks helped with the bonds drawdown.
I was once again unlucky with my tons of international stocks; but my leveraged mHFEA portfolio was relatively stable in 2023, even though my treasury futures acted like an almost constant siphon in 2022/2023, relentlessly draining cash out of my otherwise respectable equities account.

sharukh
Posts: 604
Joined: Mon Jun 20, 2016 10:19 am

### Re: SOFR futures

comeinvest wrote: Thu Apr 13, 2023 3:43 am
renelv wrote: Thu Apr 13, 2023 3:26 am Let me know if there is something I'm missing since I try to wrap my head around how a smooth transition from ITT(ZF)/STT(ZT) to SOFR3 strips would happen.

A hypothetical scenario:
I'm looking at a given ITT exposure. Assume that ZF has a ~4y duration with DV01=54 and SOFR3 have DV01=25.
I would need to construct a 4y strip with 4 * 4 = 16 SOFR3 contracts. This strip would have DV01 of 16 * 25 = 400. So it can "replace" effectively 7.4 ZF contracts. Gains are mainly from buying 1 SOFR3 contract instead of rolling 7.4 ZF every quarter.
Similar calculation for STT. If ZT is ~2y with DV01=34 a 2 year strip would be 2*4 = 8 SOFR3 with DV01 = 8 * 25 = 200, so it "replaces" 5.8 ZT contracts.

Now, 5.8 ZT contracts would have a market value of 205k * 5.8 = 1.2M \$ and the SOFR strip would have a market value of 250k*8 = 2M \$. Similar math for the ZF replacement.
So it looks like to directly replace ZT with SOFR3 you need at least a desired 1.2M\$ equivalent STT exposure based on your AA and account size. Otherwise you will need to resort to sampling across the strip / selling other treasury futures to compensate for the smaller desired exposure.

Let me know if something in this logic is off.
Your logic is largely correct.

In addition to your observations, don't forget that a SOFR strip would correspond to a zero-coupon treasury with the same maturity as the total strip maturity. But the CTD treasuries underlying the treasury futures have coupons, which means treasury futures' underlying income stream is a little bit tilted to shorter zero-coupon maturities if you were to do a zero-coupon decomposition. But that detail won't change the exposure a lot. The exposure is mostly characterized by maturities and durations. But it might matter if you were to try to compare or to verify the performance of either implementation.

I would be totally confident using a relative sparse sampling of a strip, like one contract every 4 quarters for example, which should work for almost all account sizes for which treasury futures work. Forward interest rates are highly correlated, and I'm quite confident that differences are noise and will net to near zero in the long run. In fact I would not necessarily think of SOFR futures as something that imitates treasuries or treasury futures, but rather the other way around: The yield of treasuries is determined by the average of forward short-term rates per the expectations hypothesis.
Hi,

Say I want to hedge against interest rate for borrowing of a \$10M Home purchase(Say I intend to pay it off in 2 years after borrowing starts, examples are ZT and 2 year strip of SOFR3, so picked 2 year mortgage)

Take the example of 2 year hedge
5.8 ZT and 8 SOFR3 both have the same DV01 of 200. Both have the same duration of 2 years.
They represent different market value, \$1.2M and \$2M respectively.

So If one uses SOFR3 to hedge then they use \$10M/\$2M = 5.
Short sell 5 sets of 2 year strips
OR
If one wants to use ZT to hedge then they use \$10M/\$1.2M*5.8=48.3
Short sell 48 quantity of ZT futures.

My previous learning said, if you want to hedge \$10M for 2 years:
Using ZT
Calculate the the DV01 of \$10M for the 2 year duration based on current interest rate of 7%
= (10000000 * (1 + 0.07/360)^(360*2)) - (10000000 * (1 + 0.0699/360)^(360*2))
=~2300
So number of ZT to short = 2300/(DV01 of ZT)= 2300/34 = 67
So short 67 ZT contracts

Using SOFR3
each SOFR3 represent borrowing of \$1M for 3 months.
to borrow/hedge \$10M I will short 10 sets of 2 year strips of SOFR3.

1 set of 2 year strip = 2*4 = 8 quantity (4 quarters in a year)
in total I will short = 8* 10 = 80 SOFR3 quantity

Please help me understand which calculation is correct to do a hedge against interest rate rise.

Thank you.
comeinvest
Posts: 2370
Joined: Mon Mar 12, 2012 6:57 pm

### Re: SOFR futures

sharukh wrote: Thu Sep 21, 2023 10:11 am
This has nothing to do with mHFEA; you might want to start another thread. There are many issues with your logic.
If your mortgage starts in the future, you cannot hedge your exposure with treasury futures or SOFR strips that start now.
But say you want to hedge a *current* exposure to \$10M at 7% interest rate for the next 2 years.
Your first ZT calc (\$10M/\$1.2M*5.8) tries to equate the present value of bonds with 2 different interest rates, for purpose of interest rate sensitivity matching. This is wrong, because durations are different.
Then also the futures present value includes an implied financing cost.
In your second ZT calc, your DV01 calc is totally wrong. You are calculating the differences between the forward values, not the difference between the present values.
Your first SOFR calc suffers from the same issue as your first ZT calc. On top, 8 SOFR futures represent not \$2M but about \$1M held for 2 years - but not exactly, because the SOFR futures notation uses a zero coupon discount notation with no coupon; and even the discount notation is not really exactly the discounted value of a \$100 1-year zero coupon bond, because the notation reflects the interest rate multiplied by \$100 subtracted from \$100, not multiplied by the present value (or the futures value) to get to \$100 at maturity.
Your second SOFR calc suffers from many of the same issues as the above mentioned.
There are many examples of forward loan hedging with futures on the internet, or if take your time you will find your mistakes and do the correct calc with your own deductive reasoning.
sharukh
Posts: 604
Joined: Mon Jun 20, 2016 10:19 am

### Re: SOFR futures

comeinvest wrote: Thu Sep 21, 2023 4:03 pm
sharukh wrote: Thu Sep 21, 2023 10:11 am
This has nothing to do with mHFEA; you might want to start another thread. There are many issues with your logic.
If your mortgage starts in the future, you cannot hedge your exposure with treasury futures or SOFR strips that start now.
But say you want to hedge a *current* exposure to \$10M at 7% interest rate for the next 2 years.
Your first ZT calc (\$10M/\$1.2M*5.8) tries to equate the present value of bonds with 2 different interest rates, for purpose of interest rate sensitivity matching. This is wrong, because durations are different.
Then also the futures present value includes an implied financing cost.
In your second ZT calc, your DV01 calc is totally wrong. You are calculating the differences between the forward values, not the difference between the present values.
Your first SOFR calc suffers from the same issue as your first ZT calc. On top, 8 SOFR futures represent not \$2M but about \$1M held for 2 years - but not exactly, because the SOFR futures notation uses a zero coupon discount notation with no coupon; and even the discount notation is not really exactly the discounted value of a \$100 1-year zero coupon bond, because the notation reflects the interest rate multiplied by \$100 subtracted from \$100, not multiplied by the present value (or the futures value) to get to \$100 at maturity.
Your second SOFR calc suffers from many of the same issues as the above mentioned.
There are many examples of forward loan hedging with futures on the internet, or if take your time you will find your mistakes and do the correct calc with your own deductive reasoning.
Thank you for identifying the issues. Will spend time to learn more.
unemployed_pysicist
Posts: 186
Joined: Sat Oct 09, 2021 2:32 pm

### Re: SOFR futures

sharukh wrote: Thu Sep 21, 2023 10:11 am
comeinvest wrote: Thu Apr 13, 2023 3:43 am
renelv wrote: Thu Apr 13, 2023 3:26 am Let me know if there is something I'm missing since I try to wrap my head around how a smooth transition from ITT(ZF)/STT(ZT) to SOFR3 strips would happen.

A hypothetical scenario:
I'm looking at a given ITT exposure. Assume that ZF has a ~4y duration with DV01=54 and SOFR3 have DV01=25.
I would need to construct a 4y strip with 4 * 4 = 16 SOFR3 contracts. This strip would have DV01 of 16 * 25 = 400. So it can "replace" effectively 7.4 ZF contracts. Gains are mainly from buying 1 SOFR3 contract instead of rolling 7.4 ZF every quarter.
Similar calculation for STT. If ZT is ~2y with DV01=34 a 2 year strip would be 2*4 = 8 SOFR3 with DV01 = 8 * 25 = 200, so it "replaces" 5.8 ZT contracts.

Now, 5.8 ZT contracts would have a market value of 205k * 5.8 = 1.2M \$ and the SOFR strip would have a market value of 250k*8 = 2M \$. Similar math for the ZF replacement.
So it looks like to directly replace ZT with SOFR3 you need at least a desired 1.2M\$ equivalent STT exposure based on your AA and account size. Otherwise you will need to resort to sampling across the strip / selling other treasury futures to compensate for the smaller desired exposure.

Let me know if something in this logic is off.
Your logic is largely correct.

In addition to your observations, don't forget that a SOFR strip would correspond to a zero-coupon treasury with the same maturity as the total strip maturity. But the CTD treasuries underlying the treasury futures have coupons, which means treasury futures' underlying income stream is a little bit tilted to shorter zero-coupon maturities if you were to do a zero-coupon decomposition. But that detail won't change the exposure a lot. The exposure is mostly characterized by maturities and durations. But it might matter if you were to try to compare or to verify the performance of either implementation.

I would be totally confident using a relative sparse sampling of a strip, like one contract every 4 quarters for example, which should work for almost all account sizes for which treasury futures work. Forward interest rates are highly correlated, and I'm quite confident that differences are noise and will net to near zero in the long run. In fact I would not necessarily think of SOFR futures as something that imitates treasuries or treasury futures, but rather the other way around: The yield of treasuries is determined by the average of forward short-term rates per the expectations hypothesis.
Hi,

Say I want to hedge against interest rate for borrowing of a \$10M Home purchase(Say I intend to pay it off in 2 years after borrowing starts, examples are ZT and 2 year strip of SOFR3, so picked 2 year mortgage)

Take the example of 2 year hedge
5.8 ZT and 8 SOFR3 both have the same DV01 of 200. Both have the same duration of 2 years.
They represent different market value, \$1.2M and \$2M respectively.

So If one uses SOFR3 to hedge then they use \$10M/\$2M = 5.
Short sell 5 sets of 2 year strips
OR
If one wants to use ZT to hedge then they use \$10M/\$1.2M*5.8=48.3
Short sell 48 quantity of ZT futures.

My previous learning said, if you want to hedge \$10M for 2 years:
Using ZT
Calculate the the DV01 of \$10M for the 2 year duration based on current interest rate of 7%
= (10000000 * (1 + 0.07/360)^(360*2)) - (10000000 * (1 + 0.0699/360)^(360*2))
=~2300
So number of ZT to short = 2300/(DV01 of ZT)= 2300/34 = 67
So short 67 ZT contracts

Using SOFR3
each SOFR3 represent borrowing of \$1M for 3 months.
to borrow/hedge \$10M I will short 10 sets of 2 year strips of SOFR3.

1 set of 2 year strip = 2*4 = 8 quantity (4 quarters in a year)
in total I will short = 8* 10 = 80 SOFR3 quantity

Please help me understand which calculation is correct to do a hedge against interest rate rise.

Thank you.
What are you trying to achieve? Do you want to borrow money 2 years in the future but you are worried that the borrowing rate will rise?
couldn't afford the h | | BUY BONDS | WEAR DIAMONDS
sharukh
Posts: 604
Joined: Mon Jun 20, 2016 10:19 am

### Re: SOFR futures

unemployed_pysicist wrote: Fri Sep 22, 2023 1:49 am
sharukh wrote: Thu Sep 21, 2023 10:11 am
comeinvest wrote: Thu Apr 13, 2023 3:43 am
renelv wrote: Thu Apr 13, 2023 3:26 am Let me know if there is something I'm missing since I try to wrap my head around how a smooth transition from ITT(ZF)/STT(ZT) to SOFR3 strips would happen.

A hypothetical scenario:
I'm looking at a given ITT exposure. Assume that ZF has a ~4y duration with DV01=54 and SOFR3 have DV01=25.
I would need to construct a 4y strip with 4 * 4 = 16 SOFR3 contracts. This strip would have DV01 of 16 * 25 = 400. So it can "replace" effectively 7.4 ZF contracts. Gains are mainly from buying 1 SOFR3 contract instead of rolling 7.4 ZF every quarter.
Similar calculation for STT. If ZT is ~2y with DV01=34 a 2 year strip would be 2*4 = 8 SOFR3 with DV01 = 8 * 25 = 200, so it "replaces" 5.8 ZT contracts.

Now, 5.8 ZT contracts would have a market value of 205k * 5.8 = 1.2M \$ and the SOFR strip would have a market value of 250k*8 = 2M \$. Similar math for the ZF replacement.
So it looks like to directly replace ZT with SOFR3 you need at least a desired 1.2M\$ equivalent STT exposure based on your AA and account size. Otherwise you will need to resort to sampling across the strip / selling other treasury futures to compensate for the smaller desired exposure.

Let me know if something in this logic is off.
Your logic is largely correct.

In addition to your observations, don't forget that a SOFR strip would correspond to a zero-coupon treasury with the same maturity as the total strip maturity. But the CTD treasuries underlying the treasury futures have coupons, which means treasury futures' underlying income stream is a little bit tilted to shorter zero-coupon maturities if you were to do a zero-coupon decomposition. But that detail won't change the exposure a lot. The exposure is mostly characterized by maturities and durations. But it might matter if you were to try to compare or to verify the performance of either implementation.

I would be totally confident using a relative sparse sampling of a strip, like one contract every 4 quarters for example, which should work for almost all account sizes for which treasury futures work. Forward interest rates are highly correlated, and I'm quite confident that differences are noise and will net to near zero in the long run. In fact I would not necessarily think of SOFR futures as something that imitates treasuries or treasury futures, but rather the other way around: The yield of treasuries is determined by the average of forward short-term rates per the expectations hypothesis.
Hi,

Say I want to hedge against interest rate for borrowing of a \$10M Home purchase(Say I intend to pay it off in 2 years after borrowing starts, examples are ZT and 2 year strip of SOFR3, so picked 2 year mortgage)

Take the example of 2 year hedge
5.8 ZT and 8 SOFR3 both have the same DV01 of 200. Both have the same duration of 2 years.
They represent different market value, \$1.2M and \$2M respectively.

So If one uses SOFR3 to hedge then they use \$10M/\$2M = 5.
Short sell 5 sets of 2 year strips
OR
If one wants to use ZT to hedge then they use \$10M/\$1.2M*5.8=48.3
Short sell 48 quantity of ZT futures.

My previous learning said, if you want to hedge \$10M for 2 years:
Using ZT
Calculate the the DV01 of \$10M for the 2 year duration based on current interest rate of 7%
= (10000000 * (1 + 0.07/360)^(360*2)) - (10000000 * (1 + 0.0699/360)^(360*2))
=~2300
So number of ZT to short = 2300/(DV01 of ZT)= 2300/34 = 67
So short 67 ZT contracts

Using SOFR3
each SOFR3 represent borrowing of \$1M for 3 months.
to borrow/hedge \$10M I will short 10 sets of 2 year strips of SOFR3.

1 set of 2 year strip = 2*4 = 8 quantity (4 quarters in a year)
in total I will short = 8* 10 = 80 SOFR3 quantity

Please help me understand which calculation is correct to do a hedge against interest rate rise.

Thank you.
What are you trying to achieve? Do you want to borrow money 2 years in the future but you are worried that the borrowing rate will rise?
Yes, Will borrow money to buy a house in a year or two. How to lock in the interest rate before it rise further?
Idea is to short a 10 year future /ZN. Trying to find how many to short.
Say expected home price is \$1M