Hartford — The state’s main employee pension fund remains grossly underfunded, but the situation has improved slightly during the last year, according to a new actuarial report.

The State Employees Retirement System, which covers 44,051 retired state workers, had a funding ratio of 47.9 percent with $11 billion in unfunded liabilities as of July 1.

That is an improvement from the 2010 numbers: 44.4 percent with a $11.7 billion difference between what the state promised workers and the money set aside to pay them.

Yet the conditions remain far from ideal. The common benchmark for a healthy pension fund is an 80 percent ratio of assets to total liabilities.

The Day obtained an exclusive copy of the new report Thursday morning.

The year-to-year improvement was largely due to a combination of unusually strong investment returns and early savings from the labor concessions deal reached last summer between Gov. Dannel P. Malloy and the state employees’ unions.

Connecticut traditionally conducts a pension analysis every two years, but the state asked actuary firm Cavanaugh Macdonald Consulting of Kennesaw, Ga., to produce an interim report showing how the concessions deal affected the state’s pension obligations.

The report says that fund managers obtained a blistering 21.3 percent rate of return last year — far above the annual goal of 8.25 percent.

“Without doing anything — just the market picking up — we grew,” said Sal Luciano, executive director of Council 4 AFSCME, the largest state employees union.

As a result of both the investment returns and the labor concessions, Connecticut is on pace to save $97 million off its expected contribution to the pension fund this year. That is $13 million more in savings than the state anticipated saving.

So the state’s contribution to the fund this year would be $926 million. Three-quarters of that is for liabilities accrued over the years when Connecticut didn’t set aside funds for its pensions, or opted to defer scheduled payments.

Luciano said the State Employees Retirement Commission on Thursday decided to hold off accepting the new actuarial report because he and other board members had questions about whether the state should be making a larger contribution that could benefit the fund’s long-term health.

“The more money you put upfront, the less liability there is,” Luciano said “The old saying is, you put in a quarter and 20 years later a dollar pops out. And those rates of return show how that works.”

Ben Barnes, the governor’s budget chief, said the new numbers look encouraging.

“I only saw them quickly, but they weren’t far off from what we were expecting,” said Barnes, secretary of the Office of Policy and Management.

Barnes said Malloy’s budget adjustment plan next month will include an initiative designed to further smooth out the state’s pension contributions, which are projected to rise considerably in the future as a result of a backloading of the payment schedule done in the 1990s during the Rowland administration.

This effort would require diverting budget surpluses into the retirement fund so that its assets can grow through investment, and hopefully a $4 billion balloon payment the state is scheduled to make in 2032 can be avoided.

The State Employees Retirement System is a separate pension fund than that for teachers, who are served through the Connecticut Teachers’ Retirement System. The teachers’ account had a funding ratio of 61 percent in mid-2010.

Malloy spokesman Andrew Doba said the latest pension numbers are a step forward.

“The governor is committed to fully funding our state’s pension system on an actuarial basis, and clearly we’re seeing a slight improvement in the health of that system because of it," he said. "We have a long way to go, but this is good news.”