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?