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# Which duration should be used for hedge calculation?

#### Plirts

##### New Member
Hi!
Qn: You hold a $75 million portfolio with a duration of nine and a one-year hedging horizon. There is an appropriate one-year futures contract quoted at 104-13 with a duration of eight and a contract size of$100,000. Which is hedge for small changes in yield? (Source: Schweser Practice exam2, Qn 13). Their calculation: N=-(75,000,000*9)/(104,406.25*8)=-808.14
In GARP practice exam, the duration at the end of hedging horizon is used (
http://www.bionicturtle.com/forum/t...ariance-hedge-ratio-products.5053/#post-14055 ).
Which one is more correct or am I messing totally different questions?
Thanks a lot if somebody has time to comment!
Plirts

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Plirts,

You are correct: the cited GARP question is more precise to Hull (although the Schweser question gives you no alternative-right?).

Hull 6.4 (emphasis mine):

"Consider the situation where a position in an asset that is interest rate dependent, such as a bond portfolio or a money market security, is being hedged using an interest rate futures contract. Define:
V(F): Contract price for the interest rate futures contract
D(F): Duration of the asset underlying the futures contract at the maturity of the futures contract
P: Forward value of the portfolio being hedged at the maturity of the hedge (in practice, this is usually assumed to be the same as the value of the portfolio today)
D(P): Duration of the portfolio at the maturity of the hedge

N* = [P*D(P)]/[V(F)*D(F)]"

#### Plirts

##### New Member
Thank you so much, David!

#### PL

##### Active Member
Hello David,

Two questions regarding the issue:
a. In case we are in a position to calculate the expected value of the portfolio at the maturity of the hedge (lets say through a simulation method) the appropriate value of the portfolio to use in the aforementioned formula is the expected value?
b. Additionally why is it preferable to use the duration at the end of the hedging period? From my point of view it would be preferable a duration between the duration at the beginning and at expiration of the hedging period.

Thanks

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi PL,

a. Yes, I think it would be expected value (Hull says "forward value")
b. I am not sure. I can see your argument for the average, frankly. But, then forward contract should use average also, for consistency? I had assumed it was to be conservative, but also: this is a "simple" static (one-period) hedge. You could be right, that average is better ... although if the hedger is really going to consider interim exposures, wouldn't hedger move to dynamic (rebalancing) hedge and more sophisticated (i.e., beyond simple duration to key rate, duration vector, etc). I don't really know, but at the same time, this is the simplest type of rate hedge, for rates, it doesn't get any simpler than static, duration-only .... sorry, thanks,

#### PL

##### Active Member
The use of average, arized from the dynamic - rebalancing hedging..

#### southeuro

##### Member
I concur with PL from a logical point of view. From a practical point of view however, I will memorise that we'll have to use the one at maturity