Delta Hedging Mental Block

It has always been intuitive to me how a dealer that writes call options or put options can obtain a hedge on the exposure to these securities by taking offsetting long and short underlying positions, respectively. What I cant seem to fathom is in the case where you have a long position in the underlying already - dont fully understand how you can hedge the value of this long position (protect against downward price movements) by “shorting a call”- I thought that when you short a call you are selling/writing it and it is only the holder of the instrument that is securing any payoff what so ever and the writer is subject to only the downside of the stock price increase. Again I understand that a short call will increase in value if the price drops (which is what you are seeking) but I associate a short call position with selling/writing a call and so my perception is the only payoff you would get is the premium you received up front and its does nothing to hedge! Color me confused.

The quick answer, is you either buy a put or you go short a futures/forward. You are correct where writing a call does not hedge the long position, it just adds income if the call is not exercised.

By selling calls you receive the option premium in return for losing upside return. So if the stock goes down a tiny bit the losses on the stock are offset by the call premium? Obviously this only holds for small one-time shifts. To create a truly riskless position with the stock you’d need to buy a put in addition to selling the call.

You need to write Shares/Delta number of calls to be fully hedged. If delta is .5 and you have 100 shares you write 200 calls. As the price goes up you need to buy back calls. The gain on your shares has been offset by the gain on the calls, net net nothing has happened besides you earned the RFR based on the option pricing model. If the price decreases I need to sell even more calls. Delta moves from .5 to .2, I now need to be short 500 calls. Delta hedging must be done continuously, otherwise like you said all you will earn is the premium.

Oops I was thinking of something else. Sorry

Thanks folks - for your thoughts/help are very helpful and I am not going to get hung up on this anymore - still dont see this as a hedge in any form but that is probably just my thick headedness -you guys are more or less within my universe of understanding -in my mind I dont fully understand how earning “call premiums” represents a hedge at all -I agree the purchase of a put on the underlying is a real hedge since you purchase the right to cover your downside -and understand how the underlying price/time changes require rebalancing But I will continue to think of this in terms of the option dealer seeking a hedge written calls and puts and using the opposite position in the underlying to serve as a hedge (which I undestand) and if they put it in another context I will just hope the basic match carries me through.

correction: Basic Math - call/put delta hedge ratio gets me though

I continue to write more calls if the stock goes down. Delta has to be change in option price for change in stock price. It is a really simple concept actually. Selling enough calls based on delta has to work.