The government's approval of the Volcker rule Tuesday makes it clear that banks are expected to conduct their affairs in a conservative manner, says star bank analyst Mike Mayo of CLSA.

The rule is designed to prevent banks from making trading bets with their own money.

What the regulation means is that "banks need to be pillars of strength of stability," Mayo tells CNBC.

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"They need to facilitate the economy. They need to be a port in the storm. But no, they can't have a casino inside the bank, so from that standpoint, bank CEOs are put on notice," he argues.

"If you have a large bank with a proprietary trading loss, . . . that CEO's job could be more at risk than ever before."

In one example of the rule's strictness, it requires banks that claim to be trading to hedge their risks to have independent testing confirm that their hedging strategy really does reduce risk.

"The CEOs need to attest that they're not taking big proprietary bets."

While banks may succeed in finding loopholes to work around some of the rule's strictures, Mayo believes it will ultimately make the institutions more accountable.

"I think if after the fact you have a big loss, banks don't get off so easily," he notes. "To some degree" banks already have adjusted to the rule, Mayo adds.

Not surprisingly, banks aren't happy with the Volcker rule.

"This rule is so complex and massive that it is essential that the regulators not conflate inadvertent mistakes with purposeful violations," H. Rodgin Cohen, senior chairman of Sullivan & Cromwell law firm, which represents money center banks, said in a statement, Bloomberg reports.

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