Federal Reserve officials have discussed imposing exit fees on bond funds to avert a run by investors, underlining regulators’ concerns about the vulnerability of the $10tn market.

Officials fear that bond funds are becoming “shadow banks”, because investors can withdraw their money on demand, even though the assets held by the funds can be hard to sell in a crisis. The Fed discussions have taken place at a senior level but have not yet developed into formal policy, according to people familiar with the matter.

“So much activity in open-end corporate bond and loan funds is a little bit bank-like,” Jeremy Stein, a Fed governor from 2012-14 told the Financial Times last month, just before he stepped down. “It may be the essence of shadow banking is?.?.?.?giving people a liquid claim on illiquid assets.”