The son of John Matheson Esq of Ardross and Attadale, Ross-shire, the family's ancestral seat, Alexander left home at an early age to trade in the Far East. Matheson was a nephew of Sir James Matheson of Lewis, the famous Jardine & Matheson Co, making his fortune from trading opium in the Far East, notably in the Canton and Hong Kong. Matheson was the nephew of Sir James Matheson, 1st Baronet, and made a partner in the family firm of Jardine Matheson, and a matrilinear nephew of Lt-Col. Thomas Matheson. Educated at Edinburgh University, he knew enough economics to become a Director of the Bank of England. He also served as a magistrate, and was appointed Deputy Lieutenant of the counties of Ross and Cromarty and Invernesshire.