What does the formula for IR (Information Ratio) represent?

The Information Ratio (IR) is a measure used to assess the performance of an investment relative to a benchmark, while adjusting for the risk taken in achieving that performance. Specifically, the Information Ratio is calculated as the ratio of the expected excess return (often referred to as "alpha") of an investment above the benchmark to the expected tracking error, which is the standard deviation of those excess returns.

By focusing on expected alpha divided by expected tracking risk, the Information Ratio thus captures how effectively an investment manager is delivering value above a benchmark, while also taking into account the risk of deviating from that benchmark's return. A higher Information Ratio indicates a more favorable risk-adjusted performance, reflecting the idea that the manager is generating more consistent returns over and above what the benchmark provides, relative to the level of risk taken.

In contrast, the other options do not accurately encapsulate this relationship. Expected return divided by expected risk looks at a broader view of returns without the benchmark context, while expected return divided by standard deviation does not specifically relate to a benchmark's performance. Finally, absolute alpha divided by total portfolio risk does not consider how the portfolio is performing relative to a benchmark, which is central to what the Information Ratio measures. Thus, the focus on expected alpha