Robert J. Mylod, 43, president of Advance Mortgage Corp. of Detroit, yesterday was named president of Federal National Mortgage Association and will take over in January.

Mylod has earned a reputation as an innovator at Advance, the country's seventh-largest mortgage banking firm, of which he has been president since 1975. Among other new types of housing finance, Advance pioneered the shared-appreciation mortgage in which the lender, in exchange for a reduction in the buyer's costs, gets a portion of the increased equity when the house is sold.

Advance, a subsidiary of Oppenheimer & Co., recently entered into a joint venture with Lomas and Nettleton Financial Corp. of Dallas, the country's largest mortgage banker. Lomas and Nettleton also has an option to buy Advance in two years. According to that company's chairman, Jess T. Hay, Mylod would have become one of its senior officers had he elected to stay.

Previously, Mylod had worked for Citicorp and helped plan its takeover of Advance. He continued as president of Advance when Citicorp sold it to Oppenheimer.

The Mortgage Bankers Association termed the appointment of Mylod an "excellent choice." Its executive vice president, Mark J. Riedy, called Mylod "one of the industry's new leaders in the rapidly changing world of real estate finance and a most welcome addition to the dynamic executive team that David O. Maxwell has assembled."

Mylod will succeed James E. Murray, 50, who plans to resume his Washington law practice. Murray is the last of the top officers to leave since Maxwell took over as chairman of Fannie Mae in May 1981. A statement released by Fannie Mae quoted Maxwell as saying he was grateful to Murray "for deferring his plans to resume his law practice and staying with the corporation through the transition to new management."

Murray joined Fannie Mae in 1970, about the same time as Oakley Hunter, who headed the company for a decade until his retirement last year. Since then, Fannie Mae -- the largest buyer of home mortgages -- has taken many initiatives to stop its losses caused by a mismatch of assets and liabilities during a period of high interest rates. Fannie Mae's stock has risen 136 percent in response during the past three months.