Known as "dividend arbitrage," the strategy is run largely from London, where the banks temporarily transfer ownership of a client’s shares to a lower-tax jurisdiction around the time when the client expects to collect a dividend on those shares, according to people familiar with the matter.

The maneuver typically enables bank clients to reduce taxes from as much as 30% of the dividend payment to 10% or so–and sometimes to zero. The savings are divided between the client, bank and entities that take ownership of the shares. The business largely involves stocks listed in Europe and Asia.

Banks and hedge funds say dividend arbitrage is an attractive, legal way to shrink tax bills through the differences in withholding rates around the world. But Bank of America Corp. recently was questioned by U.S. regulators about potential legal and reputational risks from the maneuver, according to a spokesman for the Federal Reserve Bank of Richmond.

The Richmond Fed oversees Bank of America because it is based in Charlotte, N.C. Examiners asked earlier this year about the bank’s dividend-arbitrage clients and trades, people familiar with the discussions said.

Bank of America is "responding to the risks that were raised," the Fed spokesman said.

The regulator’s concerns with Bank of America haven’t been disclosed publicly. Richmond Fed officials passed along their concerns to the broader Federal Reserve system. It isn’t clear if other banks have been questioned about the strategy.

Other banks that arrange similar transfers of corporate stock include Citigroup Inc., Deutsche Bank AG, Goldman Sachs Group Inc. and Morgan Stanley, according to clients and people involved in the business. Banks collect fees on the transactions.

Citadel, Lansdowne Partners Ltd. and Och-Ziff Capital Management Group LLC are among the firms that have benefited from dividend-arbitrage trades, as well as banks that work as custodians of pension-fund assets. The hedge-fund firms declined to comment.

Some clients benefit in the form of lower trading costs and financing rates on their overall business with major banks without explicitly telling the banks to shift a stock’s ownership to a lower-tax jurisdiction.

Banks’ tax-cutting moves are facing broad criticism. The Obama administration is cracking down on inversions, a type of corporate merger that can cut tax bills. Swiss banks have reined in offshore accounts.

Dividend arbitrage used to be an even bigger business than it is now, but criticism by Senate investigators in 2008 and the closing of loopholes by U.S. tax authorities made it much harder to shrink dividend taxes on U.S.-listed stocks. Other countries also have made it harder to use the strategy with shares of companies listed or based there.

Still, the strategy remains popular as part of a wider offering of services aimed at helping clients reduce their tax exposure. Dividend arbitrage remains attractive because of wide variations in tax rules throughout the world. Banks generally have shifted the focus of their dividend-arbitrage work to London.

"Banks see reputational issues in dividend arbitrage," said Nigel Feetham, a Gibraltar-based lawyer specializing in financial services and taxes. "Tax authorities themselves are increasingly challenging tax arbitragers."

Concerns about possible risks from the strategy spurred a meeting at Bank of America last year that was attended by investment-banking chief Thomas Montag, according to people familiar with the situation.

At the time, Mr. Montag also was co-chief operating officer at Bank of America. He now is the company’s sole operating chief. He couldn’t be reached.

Last year, Bank of America estimated that trades aimed at helping clients reduce withholding taxes on stock dividends generated more than $1.2 billion for the bank from 2006 to 2012, according to people familiar with the internal estimates. The bank projected it would get $100 million in revenue from the trades in 2013, mostly from Europe, these people added.

"It’s still a very profitable trade for hedge funds and broker-dealers," said Ihor Dusaniwsky, head of research at trade-analytics company S3 Partners. The New York firm’s Blacklight software program helps hedge funds assess dividend returns.

In one of the most common types of dividend arbitrage, a bank and client enter into a stock swap, a derivative transaction in which the bank takes possession of the client’s shares of another company. The bank then transfers the shares to a subsidiary or third party in a country where the dividend would incur a lower tax compared with where the client is based–or no taxes at all.

When the dividend is paid on the shares, the dividend is subject to lower taxes and the holder of the shares pockets a much higher percentage of the dividend payment. The tax savings is divided among the bank, its client and the holder of the stock. Some clients then opt to take back the shares.

"From a financial point of view, it is a beautiful strategy," said Stephen Diggle, head of Vulpes Investment Management in Singapore. "From a public point of view, no one wants to draw down the ire of a government."

Mr. Diggle is battling Bank of America over returns he claims he is owed by the bank on dividend-arbitrage trades involving European stocks several years ago, according to people familiar with the matter. The dispute involves claims of about $10 million, these people said.

Because of the dispute, he has stopped pursuing the strategy. "We haven’t stopped for moral reasons," Mr. Diggle said.

The continuing fight with Mr. Diggle was one reason for the meeting that Mr. Montag attended last year. Bank of America investment-banking executives met at the bank’s midtown Manhattan offices to debate the pros and cons of dividend arbitrage, people familiar with the meeting said.

Mr. Montag wanted to understand more about which clients were doing the trades and how much revenue they produced for Bank of America.

Bank of America’s stock-financing desk was told to be careful about how it works with clients, these people said. Executives decided the business was too lucrative to walk away from, and Bank of America has continued to arrange the transactions.