Long Gamma Portfolio - Does a small move in the underlying make you lose money?

Cassius2 · February 17th, 2010, 7:48 pm

Hi,In Paul Wilmott's intro to quant finance, I read that if you delta hedge an option but maintain a positive Gamma, then you will make money on large moves in the underlying but you will lose money on small moves.I understand that once your portfolio Pi is delta hedged, then it grows at the risk free rate:r*Pi*dt = (theta + 0.5*sigma^2*Share_price^2*Gamma)*dtBut why would a small move in the share price make you lose money?Thanks

Hansi · February 18th, 2010, 10:13 am

QuoteOriginally posted by: Cassius2But why would a small move in the share price make you lose money?No such thing as a free hedge, fees always cut your margin in the short run?

daveangel · February 18th, 2010, 1:57 pm

perhaps its to do with the theta decay versus gamma profit

Cassius2 · February 27th, 2010, 10:44 pm

Sure. As time passes by the optionality loses its value. I wasn't thinking that theta was negative. Thx.