Chartered Financial Analyst (CFA) Practice Exam Level 2

In the context of optimal active risk, what does the formula Sa = (IR*Sb)/SRb calculate?

1. The optimal level of expected return

2. The amount of active risk to be taken

3. The ratio of systematic risk to total risk

4. The amount of risk-free return

The correct answer is: The amount of active risk to be taken

The formula \( S_a = \frac{IR \times S_b}{SR_b} \) is used to calculate the amount of active risk that an investor should take when managing a portfolio. In this context: - \( S_a \) represents the optimal level of active risk. - \( IR \) stands for the Information Ratio, which measures the expected excess return per unit of active risk. - \( S_b \) signifies the total risk of the benchmark or portfolio being considered. - \( SR_b \) indicates the systematic risk of the benchmark. The calculation effectively captures how much active risk should be taken based on the relationship between the Information Ratio and the systematic risk of the benchmark. A higher Information Ratio suggests that the manager is expected to earn more returns for a given level of active risk, allowing for an optimal allocation of active risk that maximizes the potential for excess return above the benchmark. Thus, the formula directly relates to determining how much active risk is optimal to enhance returns based on manager skill (as represented by the Information Ratio) and the inherent risks in the benchmark. This understanding emphasizes the importance of balancing risk and return through an analytical approach tailored to the specific attributes of the investment environment, positioning this concept at the heart of active