Managing duration with interest rate futures

CFA Level II Derivatives
#1

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?

#2

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! You’ll then learn no. of futures to buy/sell to achieve a specific portfolio duration, given the duration of underlying bond, and other variables.

#3

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 portfolio’s duration (arguably more than 5y)?

#4

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 – 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? It’s the initital margin only, which reduces your cash amount, but by a way smaller amount than 100k

#5

Hi Chendo,

Thanks for your insight, but I don’t get how it relates to the point in discussion… which is how buying a bond future with a 2y duration of the underlying can increase the 5y duration of your portfolio. I can’t see the relationship with what you are saying… no one said the transaction is cash vs long bond future, or do we always assume this??

#6

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

However, as a practical matter, you won’t find bond futures with a duration of 2 years. A 10-year bond futures contract will have a duration of 7 – 8 years.

Edit (2022/04/29): I don’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, you’ll increase the duration of your portfolio. If you take the short position in bond futures of any duration, you’ll decrease the duration of your portfolio.

My apologies.

#7

Thanks Bill! :wink:

#8

My pleasure!

#9

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.

1 Like
#10

So in a fillowing example (approx.)
Bonds

  1. 1,000,000 Duration: 2: exposure 2,000,000
  2. 1,500,000 Duration: 5: exposure 7,500,000
    Cash:
  3. 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 doesn’t change, correct?