If you halved your delta,you have effectively halved your position..no ifs ,and or buts....Of course you have a different terminal payoff,but that has nothing to do with ones current delta. In your examples,you are introducing gamma and vega into the equation,and that changes everything.Bottom line is if you cut your delta by 50%,your "local" position will behave as if you scaled out of 50%(plus or minus the gamma effect).
Take the profit, and move on to the next trade. This is where traders start losing money due to greed.
That's kind of my point. Delta is all that matters for stocks, because it's how many shares you own. Delta isn't the only aspect of an option position, and nobody was even talking about it until you brought it up. This isn't calculus class, where only "local" effects matter. When you trade options you expect the stock to go somewhere, at a certain time, and you want to be holding the approrpiate options for that move. See? You agree with me. Just because local delta is divided by two doesn't mean you have half the original position. All it means is it will act like half the original position until the stock moves. Which is kind of meaningless, when everything else about the position has changed, and the stock has five months to move.
Commiebat, You need to trust me that Buy1sell2 agrees with me,otherwise he would be all over me like a cheap suit..In a polite way. He is the champion crusader of NEVER scaling out.I am pretty sure he would look at slicing delta as scaling out.... For the record,when firms apply a delta limit,the risk managers do not overlook it due to the effect of gamma or terminal payoffs.