How do you tell if your loved one with dementia is wandering or just taking a walk? What differentiates the two? Does wandering imply the person does not know how to get home? What if the person locks the door with the key, walks for some time, and comes back safe later? Is that wandering? I dunno. Just wondering ...
From what I've read I wouldn't consider getting home/becoming lost as the only risk factor involved. Are you confident in this person's ability to safely cross a street, or to be near traffic? Not to travel onto private property/into off limit areas? To not walk too far and be too tired to get home?
It might be good, if you haven't already, is to go with this person on a few of their 'walks' to see how they handle things. Don't lead, just go along "for the exercise and the company". And of course, discuss with their doctor about what level of oversight is advised.
Everybody is different so I'm not comfortable saying anybody diagnosed with Dementia should be house-bound or under 24 Hour care...but I've also seen some very scary situations involving healthy seniors in my neighbourhood who really shouldn't have been out alone just because cognitively they weren't prepared or logical about things.
At least where I am, urban life is just not designed for people who move slowly and need a moment or two to think things through, elderly or not, and it's really something I wish was different.
My first thought would be not some much whether or not the person gets lost, as whether the person is clear about what he is doing to start with.
Mother once determinedly tried to leave the house at eleven at night through the front door. When challenged, she said she was going to bed and couldn't find her room because it was "a very muddling house."
If he's "going to the office..."
If he doesn't seem to know what he's going out for.
If you possibly can, I should try to make sure he can't leave the house without your being aware of it so that you can check he is oriented to time, place and intention. Is there an alarm on the door so that you know when it's been opened?