Duration of forwards and futures

CFA Level II Derivatives
#1

I have a problem with interpreting the duration of a forward or a futures contract.

To be honest I haven’t got the foggiest idea.

Long forwards/futures have positive while short negative durations? Based on the intuition that fixed payer in a swap is kind of a long in a sequence in regular forward contracts? Is this logic correct?

And what about option contracts? Do they have durations?

Sorry if the question is very stupid but this whole duration issue is driving me nuts.

#2

I may not understand, but since duration is the sensitity of the price to a change in interest rate. Would it not depend on what the future contract is on, like if the spot price moves with interest rates in which direction? There would be the impact of discounting at the risk-free rate also

#3

I presume that you’re talking about forwards and futures (and options, for that matter) on bonds.

If so, then you need to understand that when you have a long position in a forward or futures contract, you have, in essence, already purchased the underlying asset (you simply haven’t paid for it yet); therefore, you have positive duration. If you have a short position in a forward or futures contract, you have, in essence, already sold the underlying asset (you simply haven’t been paid for it yet); therefore, you have negative duration. Furthermore, the duration will be comparable to that of the underlying bonds. (Slightly different because these contracts don’t transfer ownership of the interim coupon payments, but comparable.)

The same holds true for options: if you’re long calls or short puts, you have positive duration; if you’re short calls or long puts, you have negative duration. Here, however, the duration will be shorter – possibly much shorter – that that of the underlying bonds; it will depend on the option’s delta.

1 Like
#4

Oh thank you so much S2000, very clear. Yes my question referred to forwards futures and options on bonds.

Gosh it’s much clearer than I thought.

#5

Good to hear.

You’re quite welcome.

#6

Hello,

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.