There are serious differences between predictions, bets, and exposures that have a yes/no type of payoff, the “binaries”, and those that have varying payoffs, which we call the “vanilla”. Real world exposures tend to belong to the vanilla category, and are poorly captured by binaries. Vanilla exposures are sensitive to Black Swan effects, model errors, and prediction problems, while the binaries are largely immune to them. The binaries are mathematically tractable, while the vanilla are much less so. Hedging vanilla exposures with binary bets can be disastrous – and because of the human tendency to engage in attribute substitution when confronted by difficult questions, decision-makers and researchers often confuse the vanilla for the binary.
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2284964