Affinity (Shipping) head Richard Fulford-Smith isn't sure when tanker rates, boosted by the oil price war, will come back down to earth.

Speaking on a BTIG conference call featuring much of Affinity's tanker broking team on Thursday, Fulford-Smith said tonne-mile demand is tightening and there could be an issue with the supply of ships in the next few weeks.

"The demand is not sucking it out," he said of the oil in storage.