U.S. public pensions ended the third quarter with a median gain of 4.67 percent as bond managers beat their benchmarks by buying riskier debt and fixed-income securities with longer maturities, Wilshire Associates said.

The gains raised returns for state- and local-government pensions with assets of more than $1 billion to 8.2 percent for the 10-year period through Sept. 30, the first quarter since 2007 that funds of that size surpassed 8 percent over a decade.

“It gives that strong message to stay the course and look to the long term,” because the returns came near projected results, said Robert Waid, a managing director at Wilshire, a consultant to investors and pensions.

“The 10-year numbers are pretty close to what the actuaries give for a 10-year target.”

Most state and local-government pensions count on annual investment returns of from 7.5 percent to 8 percent to pay benefits for teachers, police and other employees. To make up for losses and poor gains in the past 10 years, reflecting the bursting of the Internet-stock bubble, the housing-market collapse and the financial crisis that ensued, public officials have had to pay more into pensions, straining budgets.

Estimates of deficits in the funds vary from $700 billion to more than $3 trillion, depending on assumptions. States have responded by raising minimum retirement ages, cutting benefits and asking workers to pay more into plans.

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