Jerome Powell says the Fed is reviewing its trading rules.

A Fed spokesperson said the Fed’s ethics rules were consistent with what most government agencies followed and in some cases more stringent. But given the special role the Fed plays in finance, many have questioned whether it should have stricter requirements.

Fed officials tend to be sophisticated economists and bankers themselves, and their comments can have an outsize impact on financial markets. The central bank has also taken on an increasingly expansive role: Last year, it rescued or aided the short-term corporate debt market, the long-term corporate debt market, the municipal bond market and money market mutual funds.

That raises questions about what sort of securities its officials should be allowed to own. Mr. Powell, for instance, was heavily invested in index funds and municipal debt last year, based on his own disclosures. His municipal bond holdings had not been widely criticized in years past, but they have received negative attention in recent days because the Fed helped that market for the first time last year.

Mr. Powell said he had cleared all of his holdings with the Fed’s ethics officials.

“Munis were always thought be a safe place for a Fed official to invest,” Mr. Powell said, noting that the idea was that the Fed would never buy munis. He added that the Office of Government Ethics had checked his muni holdings and said he did not have a conflict.

All this poses a conundrum for the Fed, which must weigh what its officials can reasonably invest in, given that its actions influence everything from home prices to the broad stock market.

While there are examples of very high-level officials in government who have put their savings into blind trusts — in which independent money managers buy and sell securities without communicating with the beneficiary about the details of the transactions — those are typically discouraged by the Office of Government Ethics, which calls them “highly restrictive and usually burdensome.” Ethicists tend to instead recommend divesting from individual asset holdings and investing in mutual funds or other broad-based funds.

Many Fed officials, but clearly not all, already do that.

“The system is foolish in the leeway that it gives,” said Mr. Eisen, the former ethics adviser. “The trust system is a recipe for eventual scandal.”