Using Conversion Factors in Treasury Futures Hedge Ratios
Summary
The document asks why a Treasury futures hedge ratio based on portfolio and cheapest-to-deliver bond basis-point values is scaled by the futures conversion factor. The question contrasts a face-value comparison—where contracts appear to deliver a fixed amount of the cheapest-to-deliver bond—with the hedge ratio’s conversion-factor adjustment.
The answer explains that futures prices do not move one-for-one with the delivered bond’s price because the conversion factor adjusts the contract’s pricing relationship to the eligible bond. As a result, fewer contracts may be needed to hedge the bond’s price sensitivity than a simple face-value match would imply. It also distinguishes this sensitivity hedge from the delivery stage: once the bonds stop trading and the expected delivery is fixed, the position behaves like a forward on the underlying bond and requires full hedging of that exposure. The exchange is brief and does not work through a numerical DV01 example or address other basis risks.
Key ideas
- Treasury futures hedge ratios account for the conversion factor because futures and bond prices do not move one-for-one.
- A face-value comparison of deliverable bonds alone can misstate the number of contracts needed for a sensitivity hedge.
- The relevant hedge is based on price sensitivity, such as DV01, rather than delivered notional alone.
- After delivery expectations become fixed, the exposure can resemble a forward on the underlying bond.
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Full text
# Conversion factor for futures hedging?
# Conversion factor for futures hedging?
I had a question regarding conversion factors and treasury futures in the context of hedging for DV01.
In my textbook, in order to calculate the hedge ratio they give this formula:
$$ HedgeRatio= \frac{-BasisPointValuePortfolio}{BasisPointValueCTD} * ConversionFactor $$
Now what I'm confused about it is why we scale by the conversion factor at all. Say I own a portfolio of 100M bonds, let's further say that these bonds are also the cheapest to deliver and are exactly what futures contracts deliver.
Let's say I want to hedge my portfolio completely, so I would hedge with 100M CTD bonds obviously this would leave me with 0 position but for the sake of the example. Now instead of hedging directly with CTD, I choose to do it through futures contracts which deliver said CTD bonds.
Each futures contract delivers 100k par value of a CTD bond, so I would need to hedge with 1,000 futures contract, because 1,000 futures contract will deliver 100M of my CTD. However, if I scale by conversion factor, that implies I would hedge with 800 futures, which would only deliver $80M in CTD bonds?
I don't understand why we scale by CF at all?
## Answer by JoshK (score 1)
https://quant.stackexchange.com/a/63410
You hedge with fewer bonds b/c the price of the contract doesn't move 1 for 1 with the price of the bonds. That's because of the conversions factor.
BUT Once the bonds stop trading then you have a fixed expectation for how many bonds you will receive. At that point you need to fully hedge - essentially you are holding then a forward on the underlying bond.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.