How is the Information Ratio calculated?

The Information Ratio is a measure used to evaluate the performance of an investment portfolio relative to a benchmark. It reflects the excess return of the portfolio above the benchmark, adjusted for the risk taken relative to that benchmark. The correct way to express this is by calculating the excess return (the difference between the portfolio's return and the benchmark's return) and dividing it by the tracking error, which represents the standard deviation of the difference between the portfolio returns and the benchmark returns.

In this context, the formula captures how effectively an active manager is generating excess returns (or alpha) while managing the risk relative to the benchmark. A higher Information Ratio indicates that an investment manager is achieving more excess return per unit of risk, making it a key metric in performance evaluation.

The other options provided do not represent the Information Ratio correctly. Alpha calculations and risk-adjusted return measures, such as the Sharpe Ratio, are formulated differently and do not focus on the relationship between excess returns and tracking error, which is central to the Information Ratio. The last option involving a mathematical expression with λ does not pertain to financial metrics but rather to a Poisson probability distribution, making it unrelated to this financial context.