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Union officials, a retired couple, and a self-employed graphic designer from Stonington described the need Tuesday for the state to set up a public retirement account for all Connecticut residents.

At a Capitol press conference, Dorry Clay, a self-employed web designer, said she fears she will have to work until she’s 70 because she was laid-off from her employer and then diagnosed with cancer, which depleted her retirement savings.

“Having a low-cost, easy-to-understand, accessible savings plan would be a big benefit for everyone across the state who is self-employed like me, as well as countless employees who aren’t provided an option like this through their company,” Clay said.

She said access to individual retirement accounts are limited because of minimum contribution limits, high fees, and the amount of technical knowledge one must have in order to understand what investments they are making.

Bill Tyszka, a retired Simsbury resident, said there used to be a simple formula that existed when he entered the workforce.

“You worked hard. You played by the rules. You worked 30 to 40 years, and then at an appropriate time you retired using your Social Security and whatever personal money you could invest or save and a good pension plan,” Tyszka said. “That system doesn’t exist anymore. It’s broken.”

He equated retiring in comfort to buying a lottery ticket.

“Luck should not be involved in a retirement plan,” Tyszka said. “We want everyone to have what we have.”

Sen. Cathy Osten, who co-chairs the Labor and Public Employees Committee, said this year’s bill would be similar to last year’s version in that it would create a trust fund that’s overseen by a board.

She said residents would contribute to the fund and would be guaranteed a specific rate of return upon retirement. But she said private employers would not be required to contribute to the account like the state is required to contribute to its state employee pension and teacher retirement accounts.

In 2012, Connecticut’s State Employees’ Retirement System had $9.7 billion worth of assets, which is enough to cover 42.3 percent of its $23 billion in liabilities. The Teachers’ Retirement Fund had $13.7 billion in assets, which is enough to cover 55.24 percent of its $24.9 billion in liabilities. Experts say an 80 percent funding level is considered healthy.

Osten said the low figures are not the result of state employees and teachers failing to contribute to the fund. Rather, she said the state failed to meet its obligations.

The group said the trust fund they were talking about setting up is different than the state employee and teacher retirement funds.

“This employee pension fund would not require an employer piece to it,” Osten said Tuesday.

At one point in the drafting process, last year’s legislation would have mandated employers who don’t offer retirement plans to their employees to participate. This year’s bill has yet to be drafted.

“We’re not requiring small businesses to pay into this at all,” Osten said.

But the Connecticut Business and Industry Association, which opposed the bill last year, isn’t holding its breath.

“We have significant concerns about a retirement mandate,” Eric Gjede, CBIA’s assistant counsel, said Tuesday.

He said they support the goal of saving more for retirement, but believe there’s already a way to accomplish that through the private marketplace.

Sal Luciano, executive director of AFSCME Council 4, said that if an employer has fewer than 100 employees it’s not uncommon for them to pay 2.5 percent in investment fees. He said in order to get to the 0.067 percent range, an employer would have to have 10,000 employees.

He said this would allow people to pay 0.05 percent right off the bat.

“You save a couple of a percent from the beginning in administrative fees and you gain a couple percent from having professional money market people investing your money,” Luciano said.

Gov. Dannel P. Malloy said everyone in the state has an opportunity to create a retirement account, but he understands the practical need to make it available to more people.

“I think it’s a discussion worth having,” Malloy said.

He said there is an industry that exists and the state doesn’t want to put that industry out of business. He said the state also wants to give more people an opportunity to have a retirement. He said he’s looking to strike the right balance between those two needs.