2012 Mock Q46 2012, understand, question, butterfly

Mechanic

This one seems quite tricky. I understand the price of an option increases with E(vol) but still this question doesn’t quite make sense to me.
You have a butterfly, straddle & collar.
The answer says that the performance is dependant on the movement of the underlying in a collar whereas the other two are dependant on the E(vol). Can someone PLS explain how?
thanks

sabre

short butterfly - low vol, straddle high vol.
collar - irrespective of vol.

RMontgomery

^^ agree with CPK

canadiananalyst

Ya the straddle and butterfly strategies fundamentally rely on some assumption about volatility. A collar isn’t really concerned with the level of volatility in terms of expected payoffs.