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.