As financial instruments grow in complexity they become more and more information insensitive. This brings down a curtain of opacity on the origination of risks, that has been one of the main culprits in   the 2007-2008 global financial crisis. By considering simple toy models of binary variables, we discuss how these information losses may be quantified in bits. Information losses are particularly severe in securitisation and they exhibit non-trivial properties when assets are not independent. Finally we raise the issue of whether and how such information losses should affect the pricing of financial products and risk management strategies.