The information ratio (IR) decreases as the assets under management increase. The IR is a measure of the risk-adjusted return of a financial portfolio. It is calculated as the portfolio's excess return over the benchmark, divided by the tracking error. The IR is influenced by two key variables according to the Fundamental Law of Active Management: the information coefficient (IC) and the breadth of investment opportunities. The IC is a measure of the portfolio manager's skill in selecting securities, while the breadth refers to the number of independent investment opportunities available. As the assets under management increase, the ability to generate a strong IC diminishes, leading to a decrease in the IR. This is because as funds grow larger, the performance tends to deteriorate, a phenomenon observed in mutual funds, hedge funds, and private equity. Therefore, as the assets under management for the fund increased from $1 million to $20 million, the IR would decrease due to the reduced ability to generate strong ICs.

Choice A is incorrect. The information ratio (IR) does not increase with the growth of assets under management. IR is a measure of portfolio returns above the returns of a benchmark, to the volatility of those returns. It does not directly correlate with the size of assets under management.

Choice B is incorrect. The IR does not remain unchanged either. As assets under management grow, transaction costs per dollar invested decrease due to economies of scale, but if the number of transactions remains constant, it may limit the manager's ability to take advantage of new investment opportunities and thus potentially reduce excess return and lower IR.

Choice D is incorrect. There's no rule or tendency for IR to move towards a value of 1 as assets under management increase. The value '1' has no specific significance in terms of information ratio.

Things to Remember

• Information Ratio (IR) is a measure of the risk-adjusted return of a financial portfolio.
• IR is calculated as the portfolio's excess return over the benchmark, divided by the tracking error.