Answer: Sharpe ratio

## Explanation For an investor who holds a well-diversified portfolio, the **Sharpe ratio** is the most appropriate performance measure. ### Key Points: 1. **Well-diversified portfolio**: A well-diversified portfolio has eliminated most unsystematic (idiosyncratic) risk through diversification, leaving primarily 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 - Since well-diversified portfolios have minimized unsystematic risk, their total risk (σp) primarily reflects systematic risk, making the Sharpe ratio appropriate. 3. **Jensen's alpha**: Measures abnormal return relative to the Capital Asset Pricing Model (CAPM). - Formula: α = Rp - [Rf + βp(Rm - Rf)] - While useful for evaluating manager skill, it assumes the portfolio is well-diversified (CAPM assumption). However, for performance measurement of an already well-diversified portfolio, the Sharpe ratio is more direct. 4. **M² (Modigliani-Modigliani)**: A variation of the Sharpe ratio that expresses risk-adjusted performance in percentage terms. - Formula: M² = (Rp - Rf) × (σm/σp) + Rf - While related to the Sharpe ratio, it's less commonly used than the Sharpe ratio. ### Why Sharpe ratio is best: - The Sharpe ratio directly measures the excess return per unit of total risk - For well-diversified portfolios, total risk ≈ systematic risk - It's widely accepted, easy to interpret, and doesn't require a benchmark (unlike Jensen's alpha) - It allows comparison across different types of portfolios **Answer: B (Sharpe ratio)**

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