The Federal Reserve has taken some of the sting out of selloffs in Treasurys through its accumulation of government bonds, according to the Bank for International Settlements.

Last year’s rout in the securities between May and July generated total losses of $425 billion, equal to about 2.5 percent of U.S. gross domestic product, the BIS estimated in a report published Sunday. With the Fed’s holdings softening the blow, private investors incurred only about $280 billion of the costs, or 1.7 percent of GDP.

“The valuation losses for public holders of U.S. Treasury securities in 2013 were relatively contained,” the Basel, Switzerland-based BIS said in its annual report.

Treasurys fell last year for the first time since 2009 as the Fed moved closer to scaling back its bond-buying program, designed to boost the economy by lowering borrowing costs. While they rose in the first half of this year, analysts are predicting declines for the next four quarters, according to yield forecasts compiled by Bloomberg, exposing investors and the Fed to another potential round of losses.

To assess the impact on public bondholders of the declines last year, the BIS drew a comparison with other bond selloffs in 1994 and 2003. It found the total losses in the 2013 rout were greater than in the previous two episodes because the market size is bigger and bonds are more sensitive to changes in interest rates.

Historical Context

The stock of marketable U.S. Treasury securities outstanding almost tripled to $12.1 trillion in 2014 from $4.4 trillion in early 2007, according to the BIS. The duration, which calculates how much prices change when yields rise or fall, has increased to 4.8 years from 3.8 years during the same period, the bank said.

The BIS estimated 1994 aggregate losses at $150 billion and at $155 billion in 2003, accounting for about 2 percent, and 1.3 percent, of GDP, respectively.

“The 2013 selloff stands out because of the massive expansion in the stock of debt in the wake of the financial crisis,” the BIS said. “However, in 2013, public holders incurred about two-thirds of the aggregate losses” because of the Fed’s holdings.

The BIS was formed in 1930 and acts as a central bank for the world’s monetary authorities.