The horse ranch, on nearly 20 acres about eight miles from Malibu, has a Mediterranean-style, 10,000-square-foot house, newly built when Arnold bought the property in April 1995 for $2.5 million. He has close to $4 million in the property, sources say. Among his additions is a full gym. Situated in a gate-guarded community, the ranch also has a tennis court, pool and long, private drive.