Futures Duration


I have searched many sources related to interest rate risk and Futures. Though was not able to find practical calculations in detail. As I understand correctly, Futures Duration approximately equals to Duration of CTD treasury note divided by Conversion Factor. So if I have duration of treasury note, I can analyze hedging opportunities with the following formulas:

  • Futures Duration = Note’s Duration / CF
  • BPV of Futures = BPV of Note / CF
  • Adjusted Portfolio Duration or Key Rate Duration (Including Futures) = [Portfolio initial Duration x Portfolio initial Value + Duration of CTD note x (Price of CTD / CF) x Contract Size] / Portfolio Initial Value

I am interested in practical details, to be more precise:

  • if above mentioned formulas are approximations, how futures Duration / Key Rate Durations and adjusted Portfolio Duration are precisely calculated?
  • how maturity of Future is reflected in calculation: for hedging purposes, does it matter If I buy futures contract, which matures in March or December (considering that both contracts have the same CTD note)?
  • If CTD note changes after some time of purchasing/selling futures contract, should I recalculate futures duration based on new CTD bond parameters?

I would really appreciate, if anyone could help me with practical experience or could advise me some useful materials related to this topic.