That makes sense. So presumably, if I stay away from the CD, I'm implicitly being more optimistic than the bank: I believe they will keep the on-demand rate higher than 0.40% for at least a year.
There's some further information that seems to contradict the hypothesis, however: If you look only at CDs, the yield curve is not inverted. The rate for a one-month CD is lower than that for a one-year CD, just as you'd predict. In fact if you go all the way up to a five-year CD you can get 0.90%, higher than the demand rate; presumably this indicates that the bank is more optimistic for this much longer term? But anyway, it seems strange that you'd have a regular yield curve down to one month, and then suddenly it inverts at demand deposits. I wonder if these rates are so low that fixed costs become significant for the bank? Perhaps there's more paperwork with the CDs, or something.
I do note that the rates have been like this for quite some time now - every so often I wonder to myself "Hmm, what are the CD rates now?", check them out, and get a bit annoyed. This is the first time I've been sufficiently annoyed to ask about it, though. So, it does seem to me that I have some reason to be more optimistic than the bank: To wit, they've been implicitly predicting falls in the interest rate for quite some time now, and it hasn't happened yet.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.