Big name investors like Bill Ackman are calling on the FDIC to insure all deposits, but that would only cost banks' customers more, former FDIC chair says

• Big name investors have called for the FDIC to extend coverage to all bank deposits.
• But that would only cost banks' customers more, the former FDIC chair said.
• US Treasury Secretary Janet Yellen has also shot down the idea of blanket deposit insurance.

Big name investors on Wall Street have been calling for the Federal Deposit Insurance Corporation to secure all bank deposits to prevent more failures – but that's a move that would only cost banks' customers more, according to former FDIC Chair Jelena McWilliams.

In an interview with CNBC on Thursday, McWilliams pointed to calls for Congress to lift the FDIC's coverage limit, particularly as more troubled lenders show signs of weakness after a trio of bank failures rocked markets in March and April. Currently, the FDIC only backs deposits under $250,000, which would leave larger depositors at risk of losing their money in the event of a bank failure.

But extending deposit coverage won't be cheap, McWilliams said, as complicated and complex banks will incur a larger cost to insure deposits.

"The cost will be borne by somebody. It will be the bank, and inevitably that cost will be borne by its customers," she said. "I'm just warning lawmakers and policymakers, whatever they do, there's going to be a cost associated with that."

That comes just a few days after the collapse of First Republic Bank, which renewed fears of a banking crisis as more regional lenders begin to lose their footing. Shares of PacWest and Western Alliance have plunged since First Republic's failure, as investors lose confidence in the liquidity of regional lenders amid deposit flight. 

Billionaire investor Bill Ackman warned in a tweet on Wednesday that more lenders could soon fail if the FDIC didn't back all bank deposits. Commentators have been floating the idea of limitless deposit coverage since the collapse of Silicon Valley Bank in March, though US Treasury Secretary Janet Yellen has said the government isn't considering blanket insurance for all deposits.

"You can change the limit to whatever number you want, and you're not going to prevent what happened at some of these banks," McWilliams said, referring to unique balance sheet problems that Silicon Valley Bank, First Republic, and other lenders dealt with as the value of their bond portfolios plummeted amid rising interest rates. "Would having it provide more confidence in depositors in the banking system? Perhaps. But the truth of the matter is, wherever you set this limit, there are going to be deposits beyond that," she added.