The San Francisco Employee Retirement System is facing mounting pressure to unload its roughly $470 million worth of investments in the fossil fuel industry, which would make it the first major pension fund in the nation to do so.

On Tuesday, the Board of Supervisors is expected to pass a resolution urging SFERS officials to consider selling all fossil fuel investments. It’s the second time since 2013 that city lawmakers have asked the governing board of San Francisco’s $23 billion employee pension plan to reconsider the fossil fuel companies.

But after what critics say has been four years of procrastination, time may be running out for the board to make an independent decision on the issue. Supervisor Aaron Peskin, who authored the resolution, said if the board doesn’t address the issue soon, he’s prepared to put a ballot measure before voters next year that would compel the the fund to sell its fossil fuel stocks.

“The preponderance of evidence is in favor of divestment,” Peskin said. “It’s in their best financial interest and it’s a moral imperative, and they’re dithering on that.”

Citing the environmental risks posed by coal mining, oil refining and natural gas extraction, a growing chorus of political and environmental activists has been pushing San Francisco’s retirement system and many other large, public pension funds and endowments to sell off their fossil fuel holdings.

Those same people hope to steer investments toward emerging renewable energy companies and weaken the political influence of the petroleum industry, which they see as holding back efforts to address climate change.

But SFERS and other large public pension plans across the country have resisted calls for divestment, claiming it would hurt the retirement system’s financial health. The SFERS governing board is bound by law to uphold its fiduciary duty, a legal mandate to act in the best interest of the fund.

The retirement system’s board is made up of seven members, three of whom are elected by active and retired SFERS members. Another three are appointed by the mayor, and one member is selected from the city’s Board of Supervisors. Currently, that’s Malia Cohen.

Both SFERS staff and NEPC, an investment consulting firm retained by SFERS, have recommended against divesting, largely on financial grounds.

Selling off a well-performing part of the portfolio, SFERS officials argue, would deal a financial blow that could constitute a breach of their duty to the fund and the pensioners who have paid into it. Last year, SFERS paid out $1.24 billion to over 28,200 retirees and their beneficiaries.

“This is a very difficult legal question and discussion that every fiduciary on every public pension plan across the United States is dealing with today,” said Jay Huish, the SFERS executive director, speaking before the supervisors’ Government Audit and Oversight Committee last week. “None of them have been able to come forward and do a complete ban.”

Opponents of divestment also say that holding on to fossil fuel stocks allows pension funds to pressure those companies toward more environmentally friendly practices.

By divesting, “you lose the opportunity to influence the company or industry you’re investing in,” said Keith Brainard, research director for the National Association of State Retirement Administrators.

A motion for SFERS to shed its fossil fuel stocks has been sitting in front of the fund’s board since May. The resolution, which called for SFERS to sell off its fossil fuel holdings within 180 days, was introduced by board member Victor Makras, who has been an outspoken critic of the retirement system’s indecision on the issue.

“The mere fact that we have not brought forth the decision to divest or not divest in the past four years is clear evidence that we have our head in the sand and we’re avoiding the debate and we’re avoiding being honest about it,” Makras said at the oversight committee meeting last week.

Makras said he moved to divest after analyzing how well the pension fund’s stocks have performed in recent years, and he presented his findings to the SFERS board at its May 17 meeting. His number crunching indicated that 37 of the 86 fossil fuel companies that SFERS invests in lost money over the past two years, and only 12 made money. Over the past five years, 28 investments were losers and 18 were winners.

On the whole, Makras said, the fact that the retirement system’s fossil fuel portfolio is losing money should make the decision to dump the stocks an easier one. “I put forward the motion to divest primarily because the returns were dismal,” he told the oversight committee.

Huish, the SFERS executive director, did not return requests for comment, and SFERS does not publicly disclose detailed information about what companies the fund has invested in or how well those stocks have performed, making it difficult to perform an independent assessment of the fund’s fossil fuel holdings.

At the oversight committee meeting last week, Huish said he doesn’t disagree with Makras’ conclusions about the performance of the fund’s fossil fuel stocks over the past five years, but he maintained that the stocks performed better over a 10- to 15-year window. “These types of assets … serve a purpose. And we believe we’ve hired expert (investment) managers who understand that they need to hold these stocks, even though they are losing short-term,” Huish said.

That explanation did little to placate Peskin, who serves on the oversight committee.

“It’s getting to the point where … if you can’t get there and your board can’t get there, it’s going to be incumbent on me and my colleagues to get you there,” Peskin said.

“I will certainly be interested in the legal analysis of forcing us to sell at a potential loss without having repercussions on the members of the board as fiduciaries,” Huish replied.

“I’ve got some theories,” Peskin said, wryly.

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa