Former Fed chair Paul Volcker doesn't see a need for much regulation of hedge funds.

But Volcker does want to stop them from taking advantage of an official safety net and make sure they don’t benefit from “official support by sponsorship or ownership by a banking institution.”

“Hedge funds and private equity funds have an entirely legitimate role to play in providing liquidity and innovation in our capital markets,” Volcker said during a recent speech in China.

“I do not believe they need to be so closely supervised and regulated as depository institutions.”

Acknowledging growing support for requiring large hedge funds to at least be registered, Volcker said that because hedge funds depend on banks for credit, the vast majority could be controlled through their banking relationships.

SEC member Luis Aguilar sharply disagrees, calling for much stricter supervision of hedge funds, particularly large funds that have an impact on the broader financial markets.

The idea that hedge funds should be left alone because they only transact privately with the very rich may no longer be valid, Aguilar says.

"These sophisticated investors may not have fully appreciated the risks they were taking prior to the recent crisis," Aguilar told the HedgeWorld spring fund services conference.

"Because investors are not registered, we cannot adequately oversee how they are operated and if they are still qualified for the (regulatory) exclusion," Aguilar says.

"We have little credible information about what is out there and what they are doing."