Peter Hargreaves, who has made a fortune selling investment funds, prides himself on being a straight talker — and he is no cheerleader for his industry. “There are a lot of useless funds out there,” he says.

But as the UK financial regulator begins an examination of mutual fund supermarkets — firms that offer investment funds to retail customers, like Hargreaves Lansdown — the company's co-founder robustly defends its corner. He thinks the investment industry’s problems lie elsewhere.