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Quick Reference
- Positive M² = Outperformed market (risk-adjusted)
- Negative M² = Underperformed market (risk-adjusted)
- Expresses Sharpe ratio in percentage terms
- All inputs must be annualized
M² Ratio Result
Formula Breakdown
Interpretation
Your portfolio's M² of +0.75% means it outperformed the market by 0.75 percentage points on a risk-adjusted basis. If your portfolio's risk were adjusted to match the market, it would have returned 0.75% more than the market.
Rating Guide
M² represents percentage points of outperformance vs market. These are general guidelines for context.
| Poor | Significant underperformance | |
| Below Market | Underperforming risk-adjusted | |
| At Market | In line with market | |
| Above Market | Moderate outperformance | |
| Good | Strong outperformance | |
| Exceptional | Verify data accuracy |
Understanding the M² Ratio
What is the M² Ratio?
The M² (Modigliani-Modigliani) ratio, also known as M-squared or the Modigliani Risk-Adjusted Performance measure, expresses risk-adjusted portfolio performance in percentage terms rather than as a ratio. Named after Nobel laureate Franco Modigliani and his granddaughter Leah Modigliani, it was introduced in 1997.
M² answers the question: "If we adjusted this portfolio's risk to match the market, how much better or worse would it have performed?"
Understanding the Formula
M² can be expressed in multiple equivalent ways:
- Primary formula: M² = (Rp − Rf) × (σm / σp) − (Rm − Rf)
- Using Sharpe ratios: M² = (Sharpe_portfolio − Sharpe_market) × σm
- Intuitive form: M² = Sharpe_portfolio × σm − Market Risk Premium
The calculation involves three steps:
- Calculate Portfolio Sharpe: (Rp − Rf) / σp
- Calculate Market Sharpe: (Rm − Rf) / σm
- Calculate M²: (Sharpe difference) × market volatility
M² vs Sharpe Ratio
Both M² and Sharpe ratio use the same underlying information, but express results differently:
| Aspect | Sharpe Ratio | M² Ratio |
|---|---|---|
| Output | Ratio (e.g., 0.75) | Percentage (e.g., +2%) |
| Interpretation | Requires benchmark comparison | Directly shows over/under performance |
| Best for | Academic analysis, comparing portfolios | Client communication, intuitive reporting |
Interpreting Results
- M² > 0: Portfolio outperformed the market on a risk-adjusted basis
- M² = 0: Portfolio performed exactly in line with the market (same Sharpe ratio)
- M² < 0: Portfolio underperformed the market on a risk-adjusted basis
Practical Applications
- Manager evaluation: Compare fund managers on a risk-adjusted basis
- Portfolio optimization: Identify if added risk is being compensated
- Client reporting: Explain performance in intuitive percentage terms
- Strategy comparison: Compare strategies with different risk profiles
Limitations
- Backward-looking: Based on historical data, not predictive
- Time period sensitive: Results vary significantly with measurement period
- Assumes normal distribution: May not capture tail risks
- Benchmark dependent: Results depend on market benchmark chosen
Consider using M² alongside Sharpe ratio, Jensen's alpha, and Treynor ratio for a complete picture of portfolio performance.
Frequently Asked Questions
Disclaimer
This calculator is for educational and informational purposes only. M² is a historical measure based on past data and may not predict future performance. The rating thresholds are general guidelines, not fixed industry standards. Results depend heavily on the time period selected and benchmark chosen. Investment decisions should consider multiple factors beyond risk-adjusted returns. Always consult with a qualified financial advisor before making investment decisions.
