American Security Corp., parent company of Washington's American Security Bank, reported yesterday an 11 percent increase in first-quarter profits.

The holding company earned $4.96 million ($1.35 a share) in the January-March period compared with $4.45 million ($1.22) in the same period last year. There were nominal gains from securities transactions in both periods which did not alter per-share figures.

"These results are the first full quarter earnings from the increased loan volume booked in the latter part of 1978, when yields at their [interest earned by the bank] were at their 1978 high point," said Chairman Carleton Stewart yesterday.

Loans averaged $1.2 billion for the first quarter of 1979, about the same level as in the final three months of last year but $300 million higher than one year ago.

Deposits of the District bank stood at $1.65 billion on March 31, up substantially from $1.27 billion a year ago - a $380 million gain that is by far the largest growth for a D.C. bank in the past year.

Metropolitan Federal Savings and Loan Association, of Bethesda, reported a slight decline in first-quarter profits. Net income dipped to $539,579 ($1.20 a share) from $548,765 ($1.22) a year earlier, reflecting a profit squeeze on the S&L industry becuase of soaring interest expenses offered to attract savings.

President Jessie Hilderbrand said assets rose more than 13 percent to $248 million, mortgage loan volume increased 14 percent to $220 million and savings deposits were up 12 percent to $207 million.

Directors voted a cash dividend of 121/2 cents a share, payable April 10 to owners of record March 31.

BDM Corp. a rapidly expanding professional services company in McLean, reported record sales and profits for 1978.

Earnings rose 42 percent to $1.46 million ($1.87 a share) from $1.03 million ($1.44) the previous year, as sales jumped 46 percent to $48 million. When the decade began, BDM annual sales were less that $4 million. Earle C. Williams, the firm's president, said sales now are running at a $60 million annual rate.

BDM now has more than 1,500 employes, up more than 400 in the past year, at 20 offices around the country. New offices were opened last year in Tucson, Sierra Vista, Ariz., Los Angeles and Fort Knox for a wide range of analysis, planning and problem-solving services in such areas as energy, the environment, defense, transportation and communications.

D.C. Trading and Development Corp., the new name of O. Roy Chalk's former D.C. Transit System Inc., reported a substantial turnaround in 1978. The firm listed profits of $1.8 million (75 cents a share) compared with a loss in 1977 of $1.05 million. D.C. trading engaged in real estate development here.