Malcolm grew up in Vaucluse and Double Bay in the 1950s and 1960s. His father, Bruce, was a single parent for much of Malcolm's childhood. They lived in a series of flats, mostly rented. Malcolm was educated at Vaucluse Public School and Sydney Grammar School. Malcolm's high school education at Sydney Grammar was assisted by a scholarship.
Malcolm arranged for an additional means tested scholarship to be established at Sydney Grammar in memory of his late father. Malcolm graduated from Sydney University with a BA LLB. He won a Rhodes Scholarship and completed a further law degree at Oxford.