Unless I know that I will need it for something (say clearing immigration to get on shore) I would leave it in the safe in my cabin if I had a safe. I would however always have a copy of the information page with me.

I felt the risk of having it lifted was way more of an issue then not having it.

But most times it's in the cabin.

And obviously, on the cruises where the ship holds your passports, it's not an option.