If you leave the luggage in an enclosed trunk, fine. If you leave it say in the back of a Jimmy, where the world can see it, we would not. Why not enjoy your shopping care free instead of risking it all and then worrying about it the rest of the trip if you lost it. We have never heard of someone staking out the airport and rental car departures and following them. On this forum, the only thing we have read about are robberies from unlocked cars and unlocked Villas. Plus, if you are truly shopping for groceries etc, you might not have room to place them in your car, if you stock up like we do.