Bank of America Chief Executive Officer Brian Moynihan will have his work cut out for him next week when he speaks at an investor conference in New York, despite a recent uptick in his bank's stock price.

Shares of the second largest U.S. bank have bounced around a 52-week low and threatened to fall below $5 earlier this week, before central banks pumped more liquidity into the financial system and bank stocks surged.

Moynihan has been shedding assets to build capital and working to cut expenses to improve profits. But investors remain worried about the bank's mortgage liabilities and the strength of its balance sheet.

About the time Moynihan speaks on Tuesday, the bank will also make two top executives available for private meetings with investors.

The bank has notified hundreds of institutional investors about the meetings but only a few are expected to attend, a person familiar with the matter said. It often holds such meetings around investor conferences, the person added.

At least two of the investors invited to the private meetings with co-Chief Operating Officer Tom Montag and Chief Financial Officer Bruce Thompson have been selling Bank of America shares short, a trade that profits if the bank's shares drop. The bank may be trying to charm skeptics, one of the investors said.

Any communication with investors is a positive, said Jon Finger, a Houston-based Bank of America investor, who has been a vocal critic of the bank's recent acquisitions.

There's a lot of fear and concern about the stock, said Finger, who was not invited to the meetings. To the extent, the bank communicates with investors and reduces fear, the stock could perform better.

In one email obtained by Reuters, the bank said it had room for eight to 10 investors to attend a one-hour meeting with Montag at the bank's New York headquarters. The former Merrill Lynch and Goldman Sachs executive runs the bank's global banking and markets unit and added the title of co-chief operating officer after a management shake-up in September.

Executives cannot give investors material nonpublic information, but they can reiterate comments that the bank has already said.

Bank stocks in general have been buffeted by concerns about the European debt crisis and the economy, but Bank of America's shares have been particularly susceptible to wild swings amid concerns about its capital levels.

Bank of America's shares closed at $5.08 on Tuesday, their lowest point since March 2009, but were at $5.63 in late afternoon trade on Friday. As of Thursday, the shares were down 58 percent this year, compared to 27 percent decline in the KBW Bank Index.

This year, Moynihan has made a number of efforts to lay out his strategy for investors but hasn't been able to assuage their concerns about the bank's mortgage liabilities and its ability to meet new capital standards.

The bank held its first investor day in four years in March, but Moynihan's comments about a possible increase in the

bank's dividend came back to haunt him when the Fed denied the request. In August, Moynihan participated in an unusual public conference call with fund manager Bruce Berkowitz but the bank's shares have continued to slide.

Next week, he will be one of a number of bank CEOs to give presentations at the annual Goldman Sachs Financial Services Conference. It will be Moynihan's first conference since his bank's board held a strategy retreat last month.

(Reporting by Rick Rothacker in Charlotte, North Carolina, and Lauren Tara LaCapra in New York, Editing by Dan Wilchins)