Is there a definitive answer to whether or not under and overhedging are equally risky? We could consider 2 cases, a) continuous hedging or b) hedging upon pre-determined movements in the underlying (every x points etc.) Obviously this would depend upon the sample path of the underlying, but could you be able to say something about the standard deviation of your future P&L distribution if you say overhedged by 140% (im long 100 so sell 140 etc) or underhedged by 60%? (long 100 so sell 60 etc). Could it depend upon your being short or long gamma?

Over hedging works well if you're wrong about direction. Under hedging works well if you're right about direction. And if I understood your question, I'd try to be helpful

You could try a collar, either costless (less reward on the upside) or get less hedged by buying a lower strike put. It's all risk reward, no way around that yet

When you say right about direction, you basically mean buying low and selling high right? So i'm going to take that as you being long gamma in that case. With this in mind, can you now elaborate (provide more proof) on your 2nd statement? Simiilarly for your first statement I will take that as you being short gamma, so could you elaborate more then please?

If A is the converse of B then would it be possible for B to be the converse of A? Conversely, what would your gamma be if you were selling high and buying low?

If you want to cover the possibility of a sharp adverse movement, you want to be hedging continuously.. what do you think your pnl will look like if you are "overhedged" or "underhedged" in a black swan event?

If your selling high and buying low (on your delta hedging) - then you are short gamma. I'm not sure what you mean by "A" and "B" ? With the point about the black swan event, I would say that if there was a very violent move against you (say you are short an atm call and spot rallied massively), then having initially overhedged your delta (bought more than you needed to) it would be better than underhedging. Conversely if spot plummeted, overhedging would be worse than underhedging. So i'm wondering if all these arguments are symmetrical? This leads me to think that over and under hedging are equally risky..... Interested to hear if anyone has any definitive thoughts? Thanks for input!

Quod erat demonstrandum, which for the Latinly challenged types means that the last statement deduced (mine) was the one to be demonstrated and the abbreviation thus signals the completion of the proof (see below). It's as easy as ABC or even QED ! ------------------------------------------------------- Quote from spindr0 Over hedging works well if you're wrong about direction. Under hedging works well if you're right about direction. -------------------------------------------------------