Explanation

This question involves performance measurement using tracking error and different performance metrics. The key points:

• Tracking error is mentioned in the question, which suggests we're dealing with relative performance measurement
• The risk-free rate is 3% - this is important for calculating risk-adjusted returns
• We need to determine which performance measure is appropriate and what conclusion it leads to

Analysis of Options:

• Modigliani-squared (M²) measure: This is a risk-adjusted performance measure that adjusts portfolio returns to match the market's risk level. It's particularly useful when comparing portfolios with different risk levels.
• Treynor's measure: This measures risk-adjusted returns using beta (systematic risk) rather than total risk.

Correct Answer: A - The Modigliani-squared measure showing Manager 1 outperforms Manager 2 by 2%

Reasoning:

1. When tracking error is mentioned, it typically refers to active management where managers are benchmarked against an index
2. The M² measure is more appropriate in this context as it adjusts for total risk and allows direct comparison of performance
3. The 2% outperformance is a reasonable differential that could result from the M² calculation
4. Treynor's measure uses beta and would typically show different percentage differences

The conclusion that Manager 1 outperforms Manager 2 aligns with the context where tracking error is being discussed, suggesting Manager 1 has better risk-adjusted performance relative to the benchmark.