Bank Of America is horrible in this. First off, if someone else tries to log in using your username 3 times, it locks you out of your account. You need access to your email to get back in.
But it demands you re-create three security questions after that. I chose a simple username so other people stumble across it a lot. So I have to go through this process frequently, and there is nothing I can do to stop it.
How securely are they storing this PII? Probably not at all. I try to give the exact same questions and answers every time to limit what BoA knows about me, but someone compromising by BoA account might be able to learn that information and use it to cascade attacks into other services. (They display by secret questions and their answers to me in plaintext.)