1220 could be the Albigensian crusade, the 5th crusade, or the Northern Crusade. Or of course the Iberian crusade.
in 1220 William de Ferrers would be the 4th Earl of Derby, who died in 1247, but his son would have been born and 27 years old- from multiple sources it would appear that William de ferrers was simply managing his estates in 1220, at least until 1222 when the crown asked for three of the castles he was using to be returned.