A 'Wall St' sign is seen above two 'One Way' signs in New York Thomson Reuters BERKELEY, Calif. (Reuters) - U.S. central bankers not only regularly leak secret information about monetary policy, but the leaks are so predictably timed that a savvy investor without access to the leaked information could make money just by buying stocks in certain weeks.

That is the bottom line from new research by University of California Berkeley professor Annette Vissing-Jorgensen and colleagues, presented on Saturday at a conference attended by central bankers from around the world.

Vissing-Jorgensen and her colleagues found that the stock market delivers better returns versus Treasury bills the second, fourth, and sixth weeks after each of the Fed's eight policy-setting meetings during a given year. During odd weeks, returns are poor, they found.

An investor could simply exit the stock market during odd-numbered weeks, and return during even-numbered ones, and make much more than an investor who stayed in the stock market the whole time, they suggested.

The weeks that have excess stock-market returns are generally the same in which there are closed Fed Board meetings, and increased volatility in short-term interest-rate futures contracts suggests that it is information on monetary policy from those meetings that is driving the pattern.

"The most important and likely channel through which information gets from the Fed to asset markets is informal communication with the media or private financial institutions," Vissing-Jorgensen wrote.

The Fed has been under increasing fire for what some lawmakers see as lack of transparency and accountability, with Republican politicians most recently tussling with Fed Chair Janet Yellen over the central bank's alleged leak of confidential information in 2012, under then-Chairman Ben Bernanke.

According to Vissing-Jorgensen, however, such leaks - or informal communications, as they are termed in the academic literature - occur frequently and are not necessarily bad. Fed officials may want to test market reaction to a particular policy move ahead of time, and leaks are one way to do so.

European Central Bank Board member Benoit Coeure, reacting to the research on Saturday, said central bankers do sometimes need to send up covert trial balloons on policy, or check with investors afterward on how a policy move panned out. Still, he said, central bankers should try to be as transparent as possible.

San Francisco Fed President John Williams agreed.

"There is no question that in the past the Fed ... has used informal channels to try to explain our policy," he said. "My personal policy is, everything is on the record."

(Editing by Matthew Lewis)