Very confused here. A delta-hedged option position will have zero gamma. True or False?
I thought it was true, as if you are delta-hedged, that means you have perfectly hedged your long position with a short position (or vice versa). So a change in the underlying has zero impact on your delta.
Answer is False, what am I missing?
you are making assumptions…
if you a long a call and short a put, then perhaps the gamma on your call offsets the put gamma… but this will only be for one price.
at all other times the gamma wont match and you have a gamma position
Consider a delta hedged position consisting of long stock and long puts. The puts have a positive gamma (basically the second derivative of delta) while the stock has zero gamma. Therefore, your delta-hedged position overall has positive gamma.
I would say False. The options gamma is independent of whether the position if its hedged or not. Gamma is the rate of change in the delta. The delta will change depending on the strike price compared to u/l price, therefore the gamma still had a value.
The Gamma of a _ gamma-hedged _ posiiton will have zero gamma. Gamma is greatest when an option is near-the-money and close to expiration, as small movements in th eunderlying will quickly move the option from ITM to OTM
The gamma of the underlying is zero; the gamma of the option is not zero.
The hedged portfolio hasn’t a gamma of zero.
Easiest way to think about it is:
You will not be perfectly hedged for Gamma if you are only hedging for Delta because gamma is the rate of change in the delta. You aren’t hedging for that when you hedge delta.
Options desks face huge Gamma exposures close to expiry when the stock is trading at the money. They could be perfectly delta hedged on second when the stock is trading 5 cents in the money but then it will trade right out of the money are they are overhedged on their delta (delta hedge should be 0, or close to it).