Do you live alone? Do you go shopping alone? And so on. Traveling solo is no different than being a single person - period. You face the same issues and concerns, so if you can do it "at home" then you can do it on the road. Whatever "protection" you feel comfortable with at home will be sufficient on the road.
And in reality, when you're traveling, you're more conscious of what's going on around you than when you are home - so it's actually a bit safer because you're paying more attention.