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.