No one likes a social climber, but it has merits in banking. Retail bank profitability at the lower end of the spectrum is under pressure as US regulators rein in controversial penalty fees. So some banks are chasing affluent customers instead. JPMorgan Chase recently launched its Sapphire card, aimed at households earning more than $120,000 a year. The sector has hitherto been dominated by American Express, with its resolutely upmarket, and “hand-forged”, Titanium card. The advantage of such no-limit cards, which charge steep annual fees but offer copious perks in return, is that they often command loyalty, with banks taking a couple of percentage points from retailers on each high-spending transaction.

A similar logic applies to cheque accounts. The overdraft fees that have made low balance accounts profitable are under fire, while moderately sized accounts are generally loss-making. That still leaves nearly half of all cheque and savings accounts, making up 95 per cent of deposits. They have average balances greater than $5,000, according to consultancy Oliver Wyman. As for really big accounts, banks can earn between 2 and 4 per cent as they need pay little interest and have low operational costs. Winning an account with an average balance of, say, $25,000 might be worth $7,500 before tax to a bank over an account’s lifetime. By contrast, the average credit card is worth a few hundred dollars.