But thanks to a cleverly designed bag & a few modifications, feel pretty safe.

First, a bag with compartments inside compartments is key. To get to my money, you've gotta open a top flap that locks, unzip a compartment then unzip a pocket inside the compartment. And there's two compartments both with inside zippered pockets. In one of these pockets I have a wallet with my daily spending money & inside the other pocket are larger bills, which I make sure no one sees.

And if someone cuts the side or bottom & tries to grab my wallet, I've sewn a string inside the pocket & attached the other end to my wallet. Also sewn another string for my ipod & some clips to attach my camera.

If someone tries to cut the strap of my purse, they'll need serious cutters to get thru the speaker wire I've sewn inside the strap.

And the obvious... the strap is long enough to wear across my body so no one can just grab it. If you use a backpack, you've gotta wear it around both shoulders not just one!

One final word on daypacks/backpacks...
they scream tourist. With a purse or messenger bag, you've a chance of being considered an expat. And expats (foreigners who live in a country), unlike tourists, don't carry large sums of cash & know the price of things. Thieves & con men don't target them like they do tourists.