Trading began yesterday in Federal Home Loan Mortgage Corp. preferred stock even though a cloud still hangs over its legality.

In a separate action yesterday, the Financial Accounting Standards Board declared that savings institutions could treat the stock as extraordinary income, a distinction that will help bolster the 1984 bottom lines of many troubled thrifts.

Freddie Mac preferred, trading as Fre PR on the New York Stock Exchange, opened at 40 1/8 and closed at 42 1/8, its high for the day. Volume was 233,100 shares. Only member savings institutions are eligible to trade the stock. NYSE officials said they decided to list the stock after discussing with Freddie Mac officials and their own counsel the implications of legal objections raised by the Office of Management and Budget to the manner in which the stock was distributed to savings and loans.

In a Jan. 2 letter to Edwin J. Gray, chairman of the Federal Home Loan Bank Board and Freddie Mac, OMB general counsel Michael J. Horowitz questioned the legality of Freddie Mac's decision to distribute preferred stock as dividends. At the end of the year, Freddie Mac had given the 12 regional Federal Home Loan Banks that own its stock a special stock dividend of new preferred shares. The banks then distributed the 15 million shares to 3,400 member savings institutions. Freddie Mac said the stock had a market value of about $600 million.

Sources said the administration, which would like to make Freddie Mac private, feared the stock transfer would adversely affect its future plans because it amounted to giving away a major portion of its value.

Horowitz, who has asked the Justice Department for an opinion on the matter, also questioned the accounting treatment of the dividends and suggested that the transaction might be based on "vulnerable accounting premises." He had no comment on yesterday's FASB decision.

Yesterday's FASB ruling means S&Ls, which had income of about $1.5 billion in 1984, will be able to add at least $600 million and increase their earnings by 40 percent. Stated another way, a thrift will be able to add about $630,000 for each $1 billion in assets, according to U.S. League economist Dennis Jacobe. However, the board specified it should be treated as extraordinary income or a one-time event.