sorry I give up on this subject…no one wants to listen.
Please Dreary, I know that you are spot on in this matter. Please help out!
ok I will comment on this, no problem…I’m a good samaritan 
1 Short call + long stock
This is correct as we mentioned before.
2 Long Put + short stock
If you do this then you are doubling down and betting in one direction, down! You gain both from the stock price going down, and from the put price rising as the stock goes down. This is not hedging …and you are also spending money on the put, so this is costly.
Use short calls or short puts whichever you like. the idea is to generate some premium to offset the loss in teh stock price. The only way to generate premium is to *sell* the option, i.e., go short.
I feel like i’m fighting a losing battle here. Dreary, delta hedging isn’t about generating premium. it’s about designing a portfolio that won’t change in value when the underlying’s value changes.
ie: [GAINS/LOSSES FROM STOCK] = [GAINS/LOSSES FROM OPTION]
if you were long a stock and sold puts (as in your example above), to use your logic, as the stock price went down you would sell more puts to “offset the loss”. this wouldn’t offset anything at all, it would just mean you lose MORE – say the stock price falls to zero. this means you’ve lost ALL your money on the stock and had to pay out on ALL the puts you wrote!
to maxmeomeo – i don’t see why you couldn’t sell a put as long as it hedged your position in the stock (ie one gains when the other loses). this would mean you would have to be short the stock, i guess.
Dreary, Kiakaha is correct.
What you are doing is after the fact, ie. after the underlying has moved. For instance, you are selling options to offset the loss after the stock has moved.
Delta hedging happens before a stock move ie, before you even know what losses you have to “offset”
what you need to do is determine the options position that will offset any change in the stock price BEFORE the underlying moves.
hope this helps!
Agree with Kiakaha. That was exactly my point. Can someone post a good reference to settle this question once and for all. It drives me nuts.
ok, ok, ok…hold on, hold on…now I went back to read what I wrote above and I think I may have gotten carried away! My apologies for saying that “…you can use short calls or short puts to achieve the desired delta hedge”…because I should have said:
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Use short calls with *long* stock, and
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Use short puts with *short* stock…so you can sell puts, but you have to be short the stock.
The example I mentioned above kind of ignored the distinction, which is wrong of course, like Kiakaha said. I was focusing on one leg of the dynamic issue, and ignored the nature of the stock position. But to the origianl argument about delta hedging “IT IS NOT ABOUT BUYING PUTS TO HEDGE A LONG STOCK POSITION”. That’s not delta hedging.
Delta hedging again, to hopefully summarize this , is like stated above:
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Use short calls with long stock, or
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Use short puts with short stock.
In each case, you could sell the options first then hedge buy buying and selling the stock, or start by buying or short selling the stock then buy or sell the options as you go along.
I believe this is correctly stated, but one thing I learned is that one can never be too sure!
People, people! Let’s all take a deep breath here and remember that Delta is the amount of stock required to hedge an OPTION position, not vice versa. One inverses the equation to understand how many options are needed to hedge one’s stock position. Why? Because the whole shebang was initially driven by options market makers, who write options for a living. What sane person who seeks to make money for their clients would be short volatility on purpose, and consistently? (No jokes about long bond managers, OK.) So let’s say I’m an Options market maker. About 90% of the time, I’m writing options, so I have a massive book of short vol positions, and thus am incredibly sensitive to the movements of the underlyings. I need a way to hedge the risk of being called in and not being able to pay for it, so Delta tells me how much stock I need to buy or sell in order that I don’t get squashed, and Gamma tells me how fast I need to be re-hedging. Think about this from the market makers’ perspective: if they have written a put at a particular price, they’re on the hook to buy at, say, $20. If the stock tanks at goes to 3, clearly they should have shorted an equivalent amount such that figuring in the premium, they make .50 in any event.
If I want to use the same equation to create synthetic stops on my long cash or short cash positions, I can go and do that, and even borrow the market makers’ terminology, but the equation remains the same. Can we all go back to being friends now?
thesloth, what you describe is correct, but delta hedging is used for *both* hedging your option positions or hedging your stock positions. That’s not a point of dispute, check many sources that show that. Dispute came because someone says to hedge your long stock position with delta hedging you need to buy some puts…that’s what caused the confusion…and the correct answer of course is to sell some calls.
Agreed Dreary (see 2nd to last sentence), but I am trying to illustrate the non-intuitive here, so went back to the origins of the equation for that purpose. And while Delta hedging is of course used constantly to hedge cash positions, the equation produces the amount of stock required to hedge an option position for the reason I described.
+1