Peter Davis, CEO of UK retailer Sainsbury, has challenged US giant Wal-Mart to back up its confident market share claims. Asda, a subsidiary of the world’s largest retailer, piled on the competition pressure when it announced that it is only 0.1 of 1% away from equalling the market share of Britain’s second largest supermarket.

Davis reiterated the figures published recently by the Institute of Grocery Distribution, which showed that Sainsbury is currently enjoying a 11.8% share, while Asda is “not quite breathing down our neck” with 8.9%.

“I’d love them to back up [their claim]. Let them publish Asda’s profits and turnover,” Davis said. “I don’t know what they’re smoking.”