Free response question

IEO past paper: 2026 International Economics Olympiad, open questions

Open Question 2. Mutual funds, fees, and closet indexing A mutual fund pools money from many investors and invests it on their behalf. Some mutual funds are passively managed: they simply track a benchmark, such as a stock index. Other mutual funds are actively managed: the fund manager tries to beat the benchmark by choosing investments. Mutual fund managers are often paid a management fee equal to a percentage of the fund's assets under management, or AUM. Suppose investors are risk neutral. They care only about expected return, not about risk. Each investor can always put money into a passive benchmark fund that earns zero excess return. Therefore, an active mutual fund can attract money only if investors expect its net excess return, after management fees, to be at least zero. If expected net excess return is positive, investors are willing to supply unlimited funds to the mutual fund. If expected net excess return is negative, no investor is willing to invest. In equilibrium, if the fund receives any money, its expected net excess return must be exactly zero. Suppose a fund manager has skill, but there are decreasing returns to scale. If the manager actively manages x billion dollars, the fund generates total gross excess return: $G(x) = 0.08x - 0.005x^2$ (billions per period).