Babbel: question on DVBP

[hw0799]

Babbel chap 19: Hedging Cororate Securities

goldfarm manual 311, q5:
for a 10 million 7.2% corporate bond, 10 year maturity , DVBP is $7337.

this is the DVBP of a par value of 10 million or one million? Thanks.

[bagheera]

10 million

[bagheera]

suppose 1 million future DVBP is x, then
to hedge that 10 million coporate bond, need 7337/x*10 future contact.

Why need to "*10"? Thanks.

Babbel chap 19: Hedging Cororate Securities

goldfarm manual 311, q5:
for a 10 million 7.2% corporate bond, 10 year maturity , DVBP is $7337.

this is the DVBP of a par value of 10 million or one million? Thanks.



I suppose you are referring to question 6 on page 311 of the Goldfarb manual.
First of all, you can calculate the number of treasury futures contracts needed to hedge $10 M of corporates directly as well without going through the intermediate calculations. The key is to remember that the change in the value of the hedged item must be equal to the change in the value of the hedging instrument/s. Here DVBP of the hedged item is 7337 and DVBP of one treasury futures contract of par value $100,000 ((not $1 million as you write) is 60. So 7337/60 ~ 122 treasury futures contracts each of $100,000 par value are needed for hedging.

Now for your question..
For 10 M face value corporate bond DVBP=7337
So for 1 M face value corporate bond DVBP=7337/10=733.7

The DVBP of $100,000 par amount treasury futures contract is 60.
So the number of *these* contracts needed=733.7/60=12.23
What might be confusing here is the different par amounts of the hedged item and the hedging instrument. But you can get the same answer through equalization of par values as well.
The DVBP of $1 M face value treasury futures contracts is 60*10=600.
So the number of "tens" of treasury futures contracts needed to hedge $1M face value of corporates is 733.7/600. Therefore, the number of treasury futures contracts (each with par $100,000) needed to hedge is simply (733.7/600)*10=12.23.
Now this is the number of contracts that is needed to hedge $1M par value of corporates. So number of contracts needed to hedge $10 M par value of corporates is 12.23*10=122.3 ~ 122.