Derivative question on Kaplan Mock

Question

I am not going to post the entire passage, so, shorten the question. For those who has the book, it's mock exam volume 2, page 33, question 53The most effective delta-neutral hedge against a potential negative surprise for a long position in the stock is:a. add put options to the portfolio as the put option delta moves closer to zerob. add call options to the portfolio as the call option delta moves further away from zeroc. add put option to the portfolio as the put option delta moves towards -1I picked c. because as the stock drops due to a negative earnings surprise, the delta moves closer to -1, allowing me to perfectly hedge the drop. The answer says its A, but what doesn't make sense is that the explanation also says protective put allows one to hedge the portfolio as the put option delta moves towards -1. So WTF is the mistake here? Is the answer wrong and it should have been C or is the explanation wrong and it should have been a. lord... I am seriously going to send Kaplan to better business bureau. Thanks guys.

rhuang2 · Answer

ah, I see, the question wording got me confused as I was thinking it was saying the behavior delta instead of re-balancing by adding puts. Thanks!!

Stuj79 · Answer

The answer A is correct.Think of it this way...If you have a long position of say 100 stocks, and you wish to hedge your position using puts. So you buy some puts with a delta of -0.5 for example. So if the delta is -0.5, you will need to buy 200 puts to fully hedge your position: 200 * -0.5 = -100 to counter your long stock position with a delta of +100.If the puts start to move IN THE MONEY, their delta will start to move towards -1. Let's say the reach a delta of -0.8. If this is the case then you will only need to hold 100/0.8 = 125 puts....which is less than the 200 you initially bought. SO as the delta moves towards -1 you actually need LESS puts to hedge the same sized stock position. In this instance you would sell out 75 of your puts to remain fully hedged.The reverse is also true - as the delta of the puts get SMALLER, you need MORE of them to hedge the same sized stock position. So as answer A states: add put options to the portfolio as the put option delta moves closer to zero. :smiley: