Answer: Sharpe ratio

## Explanation For an investor who holds a well-diversified portfolio, the **Sharpe ratio** is the most appropriate performance measure. Here's why: ### Key Concepts: 1. **Well-Diversified Portfolio**: A portfolio that has eliminated unsystematic (idiosyncratic) risk through diversification, leaving only systematic (market) risk. 2. **Sharpe Ratio**: Measures risk-adjusted return using total risk (standard deviation of portfolio returns). - Formula: Sharpe Ratio = (Rp - Rf) / σp - Where: Rp = portfolio return, Rf = risk-free rate, σp = portfolio standard deviation 3. **Why Sharpe Ratio is Appropriate**: - For well-diversified portfolios, total risk (σp) is essentially systematic risk - The Sharpe ratio evaluates performance relative to total risk, which is appropriate when unsystematic risk has been eliminated - It measures excess return per unit of total risk ### Comparison with Other Measures: - **Jensen's Alpha**: Measures abnormal return relative to a benchmark (CAPM). While useful, it's more appropriate for evaluating manager skill or comparing against a specific benchmark. - **M² (M-squared)**: A variation of the Sharpe ratio that expresses risk-adjusted performance in percentage terms relative to a benchmark. It's derived from the Sharpe ratio. ### Important Distinction: - **Treynor Ratio**: Uses beta (systematic risk) instead of total risk. For well-diversified portfolios, both Sharpe and Treynor ratios are appropriate, but the Sharpe ratio is more commonly used and comprehensive. ### Conclusion: The Sharpe ratio is the most appropriate measure because it evaluates performance relative to total risk, which for a well-diversified portfolio represents the systematic risk that cannot be eliminated through diversification.

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