It's not possible to know which bank has the largest investment in Bitcoin. The information doesn't have to be made public (just like you don't have to announce how much Bitcoin you own.)

What I keep seeing is articles about Banks investing, spending their time, money, and resources on understanding what Bitcoin is, what blockchain technology is, and how blockchain technology can be leveraged to make their business more profitable.

Here's an example article, Bank of America has filed 20 blockchain related patents. That's insane! And indicates a clear interest in participating in the cryptocurrency market (or the fundamental functionality that it's build upon). Article: https://www.coindesk.com/bank-america-filed-20-blockchain-patents-already/

And as I mentioned previously, these banks are in the business of making money by way of investments. Bitcoin is the best performing investing of 2017...any investment bank that's not getting in on the action is one that's losing to the competition.