Delta neutral portfolio and arbitrage

[Alberto]

Hi all,
I think I have an interesting question:
If we are long a put and long a stock (so that we are delta neutral) then we are long gamma and, both if the stock increase or decrease, our portfolio get a final positive value. Based on this (surely superficial) view, it seems that this portfolio is not arbitrage free since we always have a gain. Clearly there is something that i'm missing. What's your thought about this? @lushukai, @David Harper CFA FRM could I ask you where is the flaw in this thought?

 

[Lu Shu Kai FRM]

Hi @Alberto ,

Just to chip in here, I think a long put and stock is actually a long call / protective put:


Such that when the stock price decreases there is actually a (mini) loss. Hope this is helpful!