# 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?

• The prices of the CTD and the futures are completely different (they are linked by the Conversion Factor). The hedging performance of the futures depends on changes in futures prices during the time when you hold them (whether you hold them to delivery or not). That's why you have to take into account the CF. Hedging means if i.r. are going up you are losing money on your bonds but making money on your futures, and for these to match you have to take into account the CF. Apr 15 at 18:35