The CFA curriculum states that if you have a portfolio duration of 5y, you can lower its duration by selling bond futures, and higher its duration by buying bond futures.

My question is the following: if the underlying bond has 2y duration, wouldnt you be lowering the portfolio duration as well by buying the interest rate future?

It doesnt matter if [portfolio duration > underlying bond duration] or [portfolio duration < underlying bond duration.]

Buying a 2yr duration underlying bond future will increase portfolio duration, but buying a 6yr duration underlying bond future will significantly increase portfolio duration. Selling a 2yr duration underlying bond future will decrease portfolio duration, but selling a 6yr duration underlying bond future will significantly decrease portfolio duration.

Btw, this is L3 stuff! Youâ€™ll then learn no. of futures to buy/sell to achieve a specific portfolio duration, given the duration of underlying bond, and other variables.

Thanks for the reply Kevin, though I was looking more for the reasoning behind the theory.

That is to say, how is it possible that by adding a 2y duration asset to your 5y portfolio asset you are increasing the portfolioâ€™s duration (arguably more than 5y)?

total market value of your portfolio does not change only because you are adding a security. If you buy a 100k bond, this means that your portfolio must have had 100k cash available to pay for it. cash decreases (cash has no duration) and Bond exposure increases accordingly -> TMV remains the same but portfolio duration increases as you are adding a long duration instrument to your portfolio.

Similar with Futures â€“ if you buy a bond future with contract size 100k, this does not mean that the total market value of your portfolio increases by 100k, right? What do you pay at initiation? Itâ€™s the initital margin only, which reduces your cash amount, but by a way smaller amount than 100k

Thanks for your insight, but I donâ€™t get how it relates to the point in discussionâ€¦ which is how buying a bond future with a 2y duration of the underlying can increase the 5y duration of your portfolio. I canâ€™t see the relationship with what you are sayingâ€¦ no one said the transaction is cash vs long bond future, or do we always assume this??

Yes: if you buy bond futures with a shorter duration than your portfolio, youâ€™ll shorten the duration of your portfolio.

However, as a practical matter, you wonâ€™t find bond futures with a duration of 2 years. A 10-year bond futures contract will have a duration of 7 â€“ 8 years.

Edit (2022/04/29): I donâ€™t know what I was thinking when I wrote this five years ago, but I was wrong as wrong can be.

If you take a long position in bond futures of any duration, youâ€™ll increase the duration of your portfolio. If you take the short position in bond futures of any duration, youâ€™ll decrease the duration of your portfolio.

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 = Noteâ€™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.

500,000; no duration
Portfolio value = 3,000,000
My account duration would be like 3.17

If I add like 8 Fut Contracts (Nominal 100,000) Duration like 8, adding to average exposure of 6,400,000, my duration will grow to 5.3 with almost no cash invsted, right, because portfolio value practically doesnâ€™t change, correct?