Mortgage-finance companies Freddie Mac and Fannie Mae on Tuesday disclosed that their regulator, the Federal Housing Finance Agency, had authorized them to review the pay of chief executives Donald Layton and Timothy J. Mayopoulos.

The move addresses concerns at Fannie and Freddie that their compensation isn't competitive enough to retain top talent, but could draw the ire of critics who believe the CEOs' pay should remain restricted.

The CEOs of Fannie and Freddie in 2014 earned $600,000 in salary each, without bonuses. Some were concerned that the CEOs' pay, which was below that of some lower-ranked executives, could make it difficult to keep them in place for the long term.

In their first quarter earnings report, Freddie Mac said they had received a communication from FHFA Director Melvin Watt that authorized them to submit a proposal for FHFA review to adjust Mr. Layton's compensation, citing "objectives of providing for CEO retention; effective succession planning for the CEO position; and continuity."

The communication also said the adjustment in compensation couldn't come before the third anniversary date of the current CEO, that the new pay could not be higher than the 25th percentile of the market and that it couldn't include a bonus.

In its earnings report Freddie Mac said it would send the U.S. Treasury $746 million in June, after the company reported a first-quarter profit that fell sharply from a year earlier.

That payment brings the total amount returned to taxpayers to $92.6 billion. Freddie, along with Fannie Mae, was put into a conservatorship by the U.S. government in September 2008 after crisis-era losses. Freddie received about $71.3 billion in support from the Treasury.

The company said its first-quarter profit fell to $524 million from $4 billion in the previous year's first quarter. Analysts expected a profit of $2 billion, according to Thomson Reuters.

Net interest income, which includes fees from backing mortgages, was $3.6 billion, up slightly from $3.5 billion a year earlier. Guarantee fees accounted for about 40% of net interest income over the period.

The company recorded derivative losses of $2.4 billion in the first quarter. The company said that while its use of derivatives reduces exposure to interest-rate risk, it can result in accounting volatility. For accounting purposes, the company marks the derivatives to the market price, even as it carries many of its hedged investments at cost. Because of that mismatch, when rates fall, the derivatives can show a loss, even though the effect should even out over time.

Fair value changes were responsible for $1.8 billion of the derivative loss, Freddie Mac said.

Write to Joe Light at joe.light@wsj.com

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