Sec. 3.04. APPOINTMENT OF EXECUTIVE DIRECTOR. (a) The board has the authority to appoint an executive director to assist the board with administering the pension system and ensure that records are kept of the proceedings of the board. Subject to Subsection (a-1) of this section, a person appointed executive director under this section:

(1) must have, to the extent possible, relevant experience in managing a similarly situated business entity; and

(2) may not be a current or former trustee.

(a-1) During any period in which the most recent actuarial valuation of the pension system indicates that the period needed to amortize the unfunded actuarial accrued liability of the pension system exceeds 35 years, the board shall, to the extent lapsed investments are a significant portion of the pension system's assets, ensure that the executive director appointed under Subsection (a) of this section has, or hires staff that has, appropriate experience in managing a business entity with lapsed investments in a manner that resulted in the improved liquidity or profitability of the business entity.

(b) Subject to Subsections (b-1) and (b-3) of this section, the executive director may select any number of persons the executive director determines appropriate to assist the executive director in carrying out the executive director's duties under this section. Subject to Section 4.01 of this article, the titles and salaries of persons selected to assist the executive director shall be determined by the executive director.

(b-1) The executive director may not select a person to assist the executive director who is an active, former, or retired police officer or fire fighter of the city.

(b-2) The executive director shall establish the organizational structure of pension system employees to optimize administration of the pension system.

(b-3) A former or retired employee of the city may not before the second anniversary of the first day of the month following the date the person terminated employment with the city serve the pension system in any capacity other than as a trustee. Except as specifically provided by this article, including Section 3.01(b)(3) or (4) of this article, or other law, an employee of the city may not serve the pension system in any capacity.

(c) The executive director and those persons selected to assist the executive director may be considered employees of the city. Unless otherwise delegated to the executive director, the board shall have the ultimate authority to retain, discipline, or terminate the engagement of the executive director.

(d) If acting in the executive director's own discretion, the executive director owes a fiduciary duty to the pension system and shall ensure the sustainability of the pension system for the purpose of providing current and future benefits to members of the pension system and their beneficiaries. If the executive director is acting at the direction of the board and not exercising the executive director's own discretion, the executive director does not owe a fiduciary duty under this subsection.