Been a while since I've done this. I think you're one shy, and the answer is 32767.
16-bit would be 1000000000000000, and flipping the bits would yield 0111111111111111, which is equal to 32767 decimal.
To support my thinking, I found the following:
"For instance, a 16-bit word can represent signed integers in the range −32 768 to + 32 767."
which I took from:
http://openlearn.open.ac.uk/mod/resource/view.php?id=175771HTH.
(edit - please excuse me if I'm incorrect, and someone tell us otherwise... been a LONG time since I'd done these, too)