The base assumption for me taking the trade is that the stock will outperform the index. Assuming I am long puts, my expectation is that eventually the stock gains will outsize the put losses. I agree with you that having a perfect hedge is useless, but consider that the deltas of the options are dynamic while the deltas of the stock are almost static (depending on the correlation). You could have a situation where you start with a partial hedge that becomes full as the stock tanks.
You don't need a perfect correlation in most cases. In fact, often, the more perfect the hedge - for many instruments or baskets - the more expensive. If I can hedge out 80% of a big move against me - that may be the best I can actually achieve.
Good comments. Yes, anytime you trade a pair or combinations, there is usually a hedge somewhere: a spread is a hedge.
My big unanswered question here, (cit. Destriero) is not about edge but about structure. What is the best way to hedge this trade? long puts or short calls? Buy a few ATM or buy a lot OTM? If starting with a partial hedge how much % to cover? I was hoping that some of the big options guys on ET would chime in to give some insight.