Absolute beginner on bonds, trying to understand why spot rates seen for US-T don't seem to line up with CME futures for ZT/ZB/etc at their maturity.

For instance, ZB-U8 seemed to settle at 140-27 on Sept 19th of 2018 (that was the last trade price according to my provider; don't have exact actual settlement). A Yield-To-Maturity calculator, with 100K par and 6% coupon, 30 years to maturity with bi-annual payments, suggests the hypothetical ideal 1.00 Conversion Factor short delivery would have an effective yield of 3.73% at this price. But on Sept 19th, CNBC reports the intraday 30 year spot US treasury rate was no higher than 3.16%. What explains the more than half a percentage point rate difference that futures traders are getting by settling into the security at end of last trading day rather than buying the bonds outright?


Responders to date have been most helpful; I believe I am zeroing in on my confusion. Marking this a duplicate of "How do I calculate yield from a bond futures contract?" leaves I think one crucial point unclarified: a "How" answer doesn't answer a "Why" question. The Bloomberg screencaps in the one answer were useful, but also still leave a bit of a question mark.

The fundamental issue in the initial premise is that using a Yield-To-Maturity calculator with the assumptions I was using (30 year, 6% coupon, etc.) seems to be incorrect, due to the intricacies of how the Future is settled - instead one needs to look at the effective yield-to-maturity of the cheapest to deliver contract (as one option of valuing the future's yield, anyway). But then (A) why don't the conversion factors of the various constituents of the basket of bonds eligible for delivery bring their yields closer to parity, if the whole point of the conversion factor in the first place is to make them interchangeable for delivery, and (B) why do all of their yields seem to differ so much from the yield-to-maturity of the theoretical bond represented by the future's price and contract specs (e.g. ZB=30 years, 6% coupon); or relatedly why does that theoretical yield-to-maturity vary so widely from the cash bond's yield-to-maturity. For both (A) and (B), I'm asking specifically about on the day the future is expiring (so there's presumably no contango effect)?

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    $\begingroup$ It's actually a common misconception that bond futures track a 6% 30-year bond. They don't. The underlying is a basket of bonds (ZB tracks a basket of bonds with maturities ranging from 15 to 25 years). On the last trade day of USU8, the CTD was the 4.5s of 2/15/2036, an 18-year bond. $\endgroup$ – Helin Sep 28 '18 at 18:18
  • $\begingroup$ FWIW the yield of the 4.5s of 2/15/2036 (the cheapest deliverable bond) on September 19, 2018 was 3.105%. $\endgroup$ – Alex C Sep 29 '18 at 0:20
  • $\begingroup$ 1) When the curve is flat at 6%, bonds are (roughly) equally deliverable; if that's not true, deliverables can differ wildly from one another (sad but true). In recent years, with rates at much lower than 6%, there's little interchangeability; 2) Bond futures do NOT track 30-year bonds. Deliverables span from 15 to 25 years (30-year bonds aren't eligible for delivery). Bond futures (rough) track CTDs. Given the environment we're in, that means ~16 years bonds. Bond futures are hard; I recommend Burghardt's Treasury Bond Basis. You're asking questions that take multiple chapters to address =) $\endgroup$ – Helin Oct 5 '18 at 7:51

The conversion factor isn't 1.0 ever for these. For example, today TYZ8 settled at 118-25. The conversion factors range from .83 to about .78. So the equivalent for the cheapest bond is basically 99-05 . That gives a 3.01 yield. I can give you some screen shots from Bloomberg later if that would be helpful.

Here's the deliverables for the TYZ8:

TYZ8 Deliverable Notes

You can see that the CTD is way different than 1. This conversion factor will not change over the life of the contract. Now, you can see here that the July 31 and Aug 31 2025 notes are the cheapest to deliver to the point where they are almost indistinguishable from each-other. But, the Jun 2025 note is very close too, so the price of the TYZ8 will reflect the slight possibility of getting that note as well, which is worth a few ticks more, but has basically the same conversion factor.

Going beyond your question, if you care, here you can see what Bloomberg thinks the deliverable will be if the yield curve shifts -100, -50, 50, 100 bp:

CMS - Yield Curve Shifts / Tilts

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  • $\begingroup$ The CMEGroup's "Understanding Treasury Futures" claims "The intent of the conversion factor invoicing system is to render equally economic the delivery of any eligible-for-delivery securities". My beginner's understanding is, "equally economic" would be equal yield-to-maturity. The report does acknowledge discrepancies and some game-ability via "cheapest-to-deliver." But does that fully explain a sustained discrepancy of over half a percentage point? $\endgroup$ – jdowdell Oct 2 '18 at 21:00
  • $\begingroup$ Yeah, you aren't understanding it right. Basically they are saying that they will have a conversion factor to make the deliverable notes look more alike. I'm going to try to edit my post to show you Bloomberg's CTD screen for the TY contract. Let's see if I can figure it out. $\endgroup$ – JoshK Oct 3 '18 at 0:21
  • $\begingroup$ @jdowdell , "equally economic" means equal price, not equal yield $\endgroup$ – Randor Aug 15 '19 at 11:02

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