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)