Markets&Pr​oducts; notes p64 -calculation duration-based hedge ratio

[edegroote]

Dear David,

I am contacting you as i am not able to follow a seemingly easy example of calculating a duration-based hedge ratio.
in the example on p64, the Fc is stated as 98´000
how is this obtained?
the underlying T bond has a face value of $100 000, and the future price is $ 98
thanks a lot for a short feedback as i am really stuck with this one.
good evening,
Evelyne

 

[David Harper CFA FRM]

Hi Evelyne,

For US Treasury bonds, the quoted price is for a T-bond with a face value of $100 and the T-bond futures contract (i.e., the derivative), by function of mere specification (to standardize the commodity), is: "Underlying Unit: One U.S. Treasury bond having a face value at maturity of $100,000."

Consequently, the T-bond futures contract price = [T-bond quote price]/100 * $100,000;
or, we can think of as: [T-bond quote price] per $100 face * $100,000
In the example, F(c) = 98/100 * $100,000 = $98,000

fwiw, we just published Focus Review P1.F4 and I included GARP's [practice exam] question 2012.P1.22, which quizzes the same idea:

GARP 2012.P1.22. John Holt is managing a fixed-income portfolio worth USD 10 million. The duration of the portfolio today is 5.9 years and in six months it is expected to be 6.2 years. The 6-month Treasury bond futures contract is trading at USD 98.47. The bond that is expected to be cheapest-to-deliver has a duration of 4.0 years today and an expected duration of 4.8 years at the maturity of the futures contract. How many futures contracts should John short to hedge against changes in interest rates over the next six months? Each futures contract is for the delivery of USD 100,000 face value of bonds.

a) 125 contracts
b) 131 contracts
c) 150 contracts
d) 157 contracts

Notice that GARP inserts the two red herrings of current portfolio duration and current CTD duration, which are not used!

I hope that is helpful, thanks,

 

[edegroote]

thank you, that explains it well.

Evelyne