The Federal National Mortgage Association said yesterday it will buy back as much as $500 million worth of its common stock and warrants, showing management's confidence in the company's financial health.

Shares in Fannie Mae, the nation's largest investor in home mortgages, usually rise when interest rates fall and drop when the interest rates rise, reflecting the mortgage industry's dependency on interest rate movement.

Officials of the Washington-based corporation said the stock buyback reflects management's confidence in the company's financial position and future earnings power despite increasing signs of a pending recession.

Shares of Fannie Mae closed at $26.62 1/2 yesterday on the New York Stock Exchange, down 12 1/2 cents. The stock had been trading as high as $43.75 on June 12.

As of June 30, Fannie Mae had about 34 million warrants and 241 million shares of common stock outstanding.

A warrant is a security that serves as an advance purchase, for a lower price, of an equal amount of stock to be issued later. Warrants are usually offered as sweeteners to investors to get them to buy accompanying fixed-income securities such as bonds.

To offset the buyback, Fannie Mae will be receiving as much as $500 million in February from the conversion of the outstanding warrants. "We do not have a fixed time frame in mind," said Tim Howard, Fannie Mae's chief financial officer.