Bond Hedge Ratio

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wanderingcfa

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Okay, I am missing something here and it should be fairly easy. I get the answer, but am having trouble with the buy or sell part.
This is based off a schweser question, book 3, page 218.
CTD Bond has a dollar duration of $6,954 for a 75bps change 6 months from now.
John currently has a corporate with a dollar duration of $8.559 per $100 for a 75bps change 6 months from now.
His bond is valued at $10 million. The CTD conversion factor is 1.156.
If he wants to hedge against a rise in rates of 75bps, what should he do?
 
so the portfolio duration is 855900
based on that you would short 123.08 treasury contracts. multiply with conversion factor and you have 142 CTD contracts
 
Yea, that’s right.
I guess I am asking, is the reason we short the contracts because we are hedging against a rise in rates? So if the question said “against a decline in rates” then we would be purchasing the contracts?
It makes sense to me, but seem confused at the moment. I suppose my brain gets tired after working on FI for a while.
 
if you would think there is a decline in rates, you would not hedge because your bonds price would go up
 
wanderingcfa, I have had trouble understanding this too, because i thought that somehow the decision to go short or long had anything to do with the duration of the futures being larger or shorter than the duration of the bonds. Actually, when you hedge against a rise in rates, you always short futures as this decreases the duration; if you think that rates will fall, you want to profit from this by increasing the duration of the overall position by going long on futures. The relevant (easy) formula is:
D.total = D.bond + D.futures
where D.futures is a positive value for a long position, and negative for a short position.
The duration and conversion factor of the CTD bond comes into play only to determine the amount of futures you need to buy in order to hedge against a rate increase. A problem like this will always be framed to hedge against an INCREASE in rates, because this can be immuniced by reducing the dollar duration (i.e. D.bond = - D.futures). You can not HEDGE against falling rates; you can only buy futures to increase to your exposure if you believe that rates will fall.
Hope that helps.
 
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