Active return

In finance, active return refers to the returns produced by an investment portfolio due to active management decisions made by the portfolio manager that cannot be explained by the portfolio's exposure to returns or to risks in the portfolio's investment benchmark; active return is usually the objective of active management and subject of performance attribution.^[1] In contrast, passive returns refers to returns produced by an investment portfolio due to its exposure to returns of its benchmark. Passive returns can be obtained deliberately through passive tracking of the portfolio benchmark or obtained inadvertently through an investment process unrelated to tracking the index.^[2]

Benchmark portfolios are often represented in theoretical contexts to include all investment assets - sometimes called a market portfolio in these contexts, but is in practice a subset of practically available investable assets.^[3] In those cases where the benchmark or the market portfolio include all investable assets, active management is a zero-sum game, as no group of active managers can achieve positive active returns over the benchmark portfolio without another group of managers taking the other side of those positions and producing negative active returns; active managers as a whole in this case cannot outperform the market portfolio.^[4]

In a simple arithmetic return attribution, if ${\displaystyle R_{p}}$ denotes the return for the portfolio and ${\displaystyle R_{b}}$ denotes the return for the benchmark, then a simple active return is given by ${\displaystyle R_{p}-R_{b}}$, and can be either positive or negative.^[5]