I think the most reasonable answer is to have multi account. My favourite is now Change Bank, which has an ICO currently. This fullfill the crypto currency bank. On the other case I would go for the most traditional bank like Bank of New York, or Wells Fargo. My opinion is based on the stress tests:
I work in the finance industry, but this only my opinion. In real life everyone must make their own decisions!
I was reading the same chart the other day. I was looking at the chance of being able to get cash out quickly just in case... the