Bond Futures Conversion Factors, CTD Delivery, and DV01
Summary
The document clarifies how a bond futures conversion factor relates the futures price to the cheapest-to-deliver bond at delivery. When the delivery basis has converged, the futures price at delivery equals the CTD bond price divided by its conversion factor, so the position’s total profit and loss is measured by the change in futures price from entry, ignoring transaction costs.
A separate answer emphasizes that one futures contract and one CTD bond do not represent equal notional or interest-rate risk. Hedging a bond position therefore requires sizing by risk measures such as DV01; the conversion factor helps relate futures exposure to the bond, but delivery of one CTD per futures contract changes the holder’s exposure. These explanations address settlement and sizing intuition, but do not provide a broader futures pricing or hedge construction framework.
Key ideas
- At optimal delivery, convergence implies the futures price equals the CTD bond price divided by its conversion factor.
- Ignoring transaction costs, total futures profit and loss is the difference between exit and entry futures prices.
- One CTD bond and one futures contract generally have different DV01 exposures.
- Hedges should be sized by interest-rate risk rather than matching contract counts.
- Delivery of a CTD bond changes the magnitude of the position’s risk.
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Full text
# Future bond value and the role of the conversion factor
# Future bond value and the role of the conversion factor
The fair value of a standardized future contract is updated every day based on the bid and offer price on the market. From my understanding this value F(t) is the value that the long is willing to pay to the short seller in exchange for the cheapest to delivery. However, taking into account the conversion factor, what will be traded at the settlement day of the contract will be the cheapest to delivery $B^{CTD}$ in exchange for $Cf^{CTD} \cdot F(t_0)$ money, where $F(t_0)$ is the price it was agreed when the contract was stipulated and $Cf^{CTD}$ is a conversion factor to adjust for the fact that a future contract is assumed to correspond to a standardized bond contract. But then, it would seem to me that if one wants to close its position, or even just post margins mark to market, then the value of the contract should be $Cf^{CTD} \cdot F(t)$ not $F(t)$. What am I missing here?
## Answer by user68819 (score 1)
https://quant.stackexchange.com/a/80797
On the optimal delivery date you can assume that the basis has converged. Therefore, in your notation F(tf) = B(tf)/CF for the cheapest to deliver. Therefore, transaction costs aside, your pnl in total is F(tf)-F(t0)
## Answer by Andrea (score 0)
https://quant.stackexchange.com/a/81078
Even when there is a clear CTD and the Futures moves exactly aligned with the CTD Bond, the size of the 2 securities is not the same.
1 CTD and 1 Futures have different sizes are risk (DV01).
Imagine you want to hedge 1 CTD, you will to buy CF futures, not 1.
This is why people normally think in terms of DV01 (or risk), and say 10k DV01 (of bond or of futures). The actual notional will be different.
And important to realise too that if you go to delivery, for each 1 Futures long, you will receive 1 CTD, so your risk will immediately change in magnitude.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.