Fixed income- Futures contract size

I understand that we use future contracts of a bond to determine how many contracts of that bond will you purchase/ sell to bridge the duration gap between BPV of assets and bpv of liabilities. What I do not understand is the formula Futrues BPV~ (BPV OF CTD)÷(CF OF CTD)

Conversion Factor means quoted price for a bond that would have on the first day of the delivery period on the assumption that the interest rate (YTM) for all maturities equals 6%. Therefore, it is the standardization for the Treasury bond contracts that make all possible deliverable bonds roughly equal in price.

  • High coupon bonds will have high CFs.
  • Low coupon bonds will have low CFs .

You can look at the below equation from the perspective that if you want to convert the BPV of your deliverable bond to the standardized one (BPV of CTD), you just multiply by CF then it becomes BPV of CTD:

{BPV_{futures}}\times{CF_{CTD}} \approx {BPV_{CTD}}

So, if you don’t have a CTD bond, the equation is simply just the BPV of the bond that you will deliver.