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Ch 11 practice question 11.1 ii a)

A

AGM

Active Member
Hi, in this part we are required to tell what number of shares should be purchased or sold along with short holding in one derivative. The delta is negative , then shouldn't purchase shares to achieve a delta hedged portfolio?

The answer says it requires selling. Could you please explain why? also, if it was long position instead of short , does it impact our answer?
 
Hi. When S0=1 the delta of one derivative is -0.03663. The question says we're short holding one derivative, in which case the derivative position has a delta of +0.03663. This requires the selling of shares to bring the combined delta back to zero.
If we had a long position in the derivative, then we would need to purchase the shares instead.
 
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Thank you

Sorry if this sounds silly but how does delta become positive due to short holding?
 
A negative delta means that as the value of the underlying increases, the value of the derivative decreases. A short holding of such a derivative means that rather than owning one we actually owe one. Therefore the amount that we owe is decreasing - and this is a good (ie positive) outcome for us.
Also, the delta of a portfolio is equal to the sumproduct of the deltas and the amounts held of each constituent part. Therefore a short holding "flips" the sign of the derivative's delta.
 
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