As his name implies, Rahystrada is a son of the royally-bred Rahy. By renowned stallion Blushing Groom and out of Canadian Hall of Fame mare Glorious Song, Rahy was a Grade 2 winner on the track who excelled as a sire. Among his leading progeny are Hall of Famer Serena's Song; European Horse of the Year and American champion Fantastic Light; fellow Eclipse Award winner Dreaming of Anna; highweights Rio de la Plata, Noverre and Lady of the Desert; and turf standouts Tranquility Lake, Tates Creek and Dancing Forever. Rahy also appears as the broodmare sire of a number of notables, topped by Giant's Causeway.

Rahystrada gets the other half of his name from his dam, the unraced Ministrada, who is also responsible for Lone Star Sky. A smart juvenile of 2002, Lone Star Sky captured the Bashford Manor and Cradle Stakes. His career stakes placings include the Saratoga Special, Breeders' Futurity and Louisiana Derby.

Ministrada is by influential sire Deputy Minister. His outstanding sons Awesome Again and Touch Gold have joined him in the Canadian Hall of Fame, while his champion daughters Go for Wand and Open Mind were enshrined in the Hall of Fame in Saratoga Springs. Awesome Again, winner of the 1998 Breeders' Cup Classic, is a top stallion himself with such offspring as 2004 Horse of the Year and Breeders' Cup Classic hero Ghostzapper. Deputy Minister's daughters have been no less prominent, producing 2007 Belmont-winning champion Rags to Riches and two-time Horse of the Year Curlin.

Ministrada is a half-sister to the long-winded turf mare Krisada, heroine of the La Prevoyante Handicap, as well as to the versatile stakes victor Conte di Savoya. This female line has also produced champion turf horse Cozzene, sire of 1993 Arlington Million winner Star of Cozzene.