We all deal with anxiety and stress on a day to day basis but it does not mean that we have an anxiety disorder, some anxiety is good. In regard to depression, it's touchy but most of the time it manifests from something like the death of a close family member or friend may be enough to drive people into a depressed state.
I don't think there's a biological or personality related reason to not having an anxiety disorder or depression. A lot of the people I know with diagnosed anxiety disorders had struggled to accept themselves and be comfortable in their own skin and live with confidence. In their case it was anxiety that stemmed from insecurity.