The questions asks: what is the most effective way to initiate a delta-neutral hedge on a long stock position? The answer given is: “add put options to the portfolio as the delta approaches zero.”
I answered that you should add put options as the delta approaches -1. My reasoning is that, in order to affect a delta-neutral hedge, we must purchase # of Put Options = (1/delta) x (# of Shares in Long Position). It follows, then that as the delta of the put option approaches |1|, the number of options that must be purchased to affect the hedge decreases, because the hedge ratio is decreasing. Why, then, does the answer suggest that it is better to add put options when delta approaches zero; implying that it is better to add puts when more options are needed to hedge the position, and when the relative price movement between the options and the underlying stock is less correlated, thus weakening the efficacy of the hedge?
The rationale from the book says: “the number of puts to purchase depends on the hedge ratio, which depends on the option’s delta. Because the delta of the put option is negative, as the option delta moves closer to -1, the number of options necessary to maintain the hedge falls.” This rationale seems to support my answer, but it goes on to list the aforementioned answer. Am I missing something (more than likely), or is the book wrong (and no, it doesn’t ask which method is least effective).
Thanks in advance.