I would say this: volatility is easy to define, but there are numerous different definitions that can lead to confusion. In the context of what you're talking about, you *have* to define volatility on the basis of how often you delta hedge. If you put on a straddle and *do not delta hedge* until expiration, but manage to lose money despite low realized volatility... then the model is not broken, but your understanding of it is. If realized volatility is lower than IV as calculated using end-of-day prices, then you would have made money regardless of final price if (and only if) you had hedged on an end-of-day basis. If you do not hedge on a end-of-day basis, then what Bloomberg or other sites/services pass around as "realized volatility" is irrelevant to you. The realized volatility of *your portfolio* = sqrt(log return from day 0 to day T). And if this number is larger than the IV of your original position, you will lose money.