How is the Information Ratio (IR) defined?

The Information Ratio (IR) is defined as the ratio of active return to active risk. Active return refers to the return of a portfolio that exceeds the return of a benchmark index, while active risk is measured as the standard deviation of the active return. This ratio helps investors assess how effectively a portfolio manager is generating excess returns relative to the risk taken.

A higher Information Ratio indicates that the manager is providing better returns per unit of risk, making it a valuable metric for evaluating the performance of actively managed portfolios. This measure is especially relevant in performance evaluation as it accounts for both the return and the risk associated with deviating from the benchmark.

In contrast, the other options do not accurately represent the Information Ratio. The first option describes a comparison between total returns and benchmark returns but does not factor in risk. The third option deals with the expected return compared to the risk-free rate, which is more aligned with the Sharpe Ratio. The final option involves the growth of the investment portfolio over time but does not relate to the active returns or risks like the Information Ratio does.