Another of Mayor Ed Lee’s commission appointees is under scrutiny for allegedly violating city rules, and this time it’s financial adviser and former San Francisco first lady Wendy Paskin-Jordan.

The Board of Supervisors is set to hold a hearing Tuesday at the request of Supervisor John Avalos into Lee’s reappointment of Paskin-Jordan’s to the city’s Retirement Board, which oversees a $20 billion investment portfolio that funds retirement accounts for more than 53,000 current and former city, school district and court employees.

Aside from the questionable mechanics of Paskin-Jordan’s reappointment – Lee swore her in four days before giving the required notice to the Board of Supervisors, which has 30 days to reject her – Avalos wants to delve into two separate ethics complaints alleging financial misconduct by the longtime finance professional and wife of former Mayor Frank Jordan.

Paskin-Jordan did not return calls and e-mails seeking comment.

A complaint filed in April contends Paskin-Jordan was saving millions in fees by aggregating her clients at Paskin Capital Advisors with the much larger fund balance from the city retirement system.

A second complaint lodged in September centers on her investment of between $100,001 and $1 million in Grantham, Mayo, Van Otterloo and Co., an international investment firm headquartered in Boston known as GMO that has a minimum investment threshold of $10 million. The city’s retirement system had about $388 million invested in a GMO fund as of June, city records show.

City law prohibits Retirement Board members from investing with “managers of private equity, limited partnerships and non-publicly traded mutual funds that are doing business” with the city’s retirement system.

GMO describes itself on its website as “a private partnership,” although San Francisco Employees’ Retirement System staff consider GMO a “manager of public market assets,” despite its $10 million minimum investment.

City law also prohibits members of the Retirement Board from “directly or indirectly” soliciting or accepting anything of value, including “a business opportunity,” from any public or private entity doing business with the city’s retirement system. The idea is to prohibit board members from parlaying their public position into favors and to prevent conflicts of interest between the city’s needs and private financial gain.

Lee appointed Paskin-Jordan to the Retirement Board in July 2010. A little over a year later, in August 2011, she invested up to $1 million in a GMO fund – well below the minimum threshold to invest. Paskin-Jordan didn’t report that investment on her city-required financial disclosure form that she filed about seven months later, city records show, but she did disclose it on her form filed in March 2013, records show.

Financial disclosure forms also show Paskin-Jordan accepted $92 in gifts from GMO before her investment in them, including two group luncheons at the Omni Hotel worth about $45 apiece, despite the city prohibition on receiving “anything of value” from a firm doing business with the city’s retirement system.

Earlier this month, the same day The Chronicle asked the San Francisco Employees’ Retirement System about the city’s GMO holdings and Paskin-Jordan’s financial dealings, the department’s executive director, Jay Huish, forwarded the complaint about those topics to the city’s Ethics Commission, the government oversight agency. The retirement system had received the complaint in September.

In an accompanying letter, Huish wrote that after consulting with staff and the city attorney, he did not believe Paskin-Jordan had violated the city’s conflict-of-interest rules but acknowledged others could reach a different conclusion.

The Ethics Commission’s executive director, John St. Croix, declined to comment on the complaints, as did City Attorney Dennis Herrera’s spokesman.

Huish, in the letter, said two of Paskin-Jordan’s former co-workers at Montgomery Asset Management went to work at GMO. In the mid-2000s, before Paskin-Jordan was on the retirement board, they granted her an exception to invest in GMO funds at amounts less than the $10 million threshold, Huish wrote.

Paskin-Jordan used that exemption to invest for clients in GMO but didn’t personally invest until she was on the Retirement Board, Huish wrote. That investment was “pursuant to her existing agreement with GMO that predated her appointment to the Retirement Board,” Huish wrote.

“In my view, Commissioner Paskin-Jordan was offered and accepted that opportunity several years before she became a board member,” Huish wrote.

Avalos, though, a political adversary of the mayor, wants more scrutiny.

“We have to be really be cognizant that we are not just rubber-stamping appointments,” Avalos said, citing Mel Murphy, the politically connected developer Lee picked for the Port Commission last year.

Murphy has had a string of violations and construction problems for building without permits and shorting permit fees. Last December an improperly reinforced Twin Peaks house that Murphy was tripling in size collapsed and slid down a steep hillside. The city’s top building inspector found that work on the site appeared to have been “dramatically different than the approved plan.”

Then earlier this month The Chronicle reported that Murphy had illegally reinstalled car parking equipment at a high-end condo building after city officials had directed him to remove it.

Lee called that revelation “more than embarrassing” but said he would not seek to remove Murphy for official misconduct because the wrongdoing did not appear to linked to Murphy’s responsibilities at the port.

“This is not the kind of activity that we wish our commissioners to do,” Lee said of Murphy. “I’m horrified to see that.”

The Board of Supervisors approved Murphy’s appointment in March 2013 by a 7-4 vote.

“It seems clear that this board has failed to scrutinize Murphy’s appointment closely enough,” Avalos said. “We shouldn’t be doing that with Wendy Paskin-Jordan.”