Savannahs have amazing energy combined with high intelligence and come with a strong “prey drive” — they LOVE to chase things. These cats do not make good outdoors cats. They will be fascinated by a bird and stalk it, see a butterfly and follow that, then see another bird and chase that one… within hours they will be miles from your home with no idea how they got there! When a cat wanders, they are rarely located and returned to their homes. Savannahs are not recommended as anything but indoor-only pets.
Savannahs jump higher and further than most domestic cats. Those long legs are very functional! Even with the highest fence, most likely a Savannah would find a way up and over it.