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Active risk is commonly known as the annualized standard deviation of active returns. This is a measure of the risk that results from an investment manager's decisions to deviate from a benchmark index. Active risk quantifies the effectiveness of a manager's active investment strategy by assessing the variability of the excess returns (the returns above the benchmark) over time.

Understanding this concept is critical in the context of portfolio management, as it helps investors evaluate how much risk is being taken on through active management strategies relative to passive investments tied to the benchmark. The focus is primarily on the consistency and variability of the manager's excess returns, which reflects whether the active management is achieving the desired performance relative to the risks taken.

Other options do not adequately define active risk in this context. For instance, market volatility refers to the fluctuations in the prices of securities, which does not exclusively capture the essence of active management risk. Systematic risk pertains to the risk inherent to the entire market or a market segment, whereas active risk specifically measures the risk linked to an investment manager's active decisions. Long-term investment risk is a broader term that doesn’t specifically relate to the deviations from benchmark returns. Thus, recognizing active risk as the annualized standard deviation of active returns provides a precise understanding