I have seen a question that says: Describe a zero-duration hedging strategy using only the government bond portfolio and options on U.S Treasury bond futures contracts. No calculations required. Answer says: The correct strategy would be to short call options and go long put options. The short call position would create a negative cash flow if rates were to decline but the long put position would create a positive cash flow if rates were to increase. This fully hedges the portfolio. The call and put options should have the same exercise price and expiration date and the appropriate notional amounts.
My question: A short call gains when interest rates increase. A long put gains when interest rates increase. This doesn’t seem to be a hedge at all? Can someone please explain?
Well if you are long the bond portfolio, you are long the bonds which have a “positive” duration and therefore will increase in price if the interest rate goes down and fall in price if the interest rates go up.
A short call and a long put is analogous to a short position in the underlying, which moves in the opposite direction in relation to interest rate moves.
So you are long the underlying on the one hand, and have a synthetic short position on the other hand.
@S2000magician …wow that was some effort with the symbols to give an explanation!!! Isn’t this also called a risk reversal position? Secondly, the call and put should have the same delta rather than same strike right?
They need to be the same strike. Because otherwise the hedge wouldn’t work. That’s because you want to exactly offset the profile of the long position with the two options. If the strikes were different that’s not the case.
Just take into account that you want to have combine
_
with
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in order to generate this: . This only works when both strikes match. Otherwise you would come up with something like: