Does a variable rate CD need to be tied to an index or can rate changes be made at management's discretion?

You can make it at management's discretion, but who the heck would want a CD like that? Plus, if you decide to reduce the rate right away, regardless of the reason, you would have to weigh the bait and switch aspects of such an account.

I totally agree. I really believe it should be tied to some trackable index otherwise like you said it could be construed as a bait and switch tactic. Thank you!