Modigliani Return Calculator

Modigliani Risk-Adjusted Return Formula:

\[ M^2 = R_f + (R_p - R_f) \times \left(\frac{\sigma_b}{\sigma_p}\right) \]

Risk-free Rate:

Portfolio Return:

Benchmark Standard Deviation:

Portfolio Standard Deviation:

Modigliani Risk-Adjusted Return:

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1. What is the Modigliani Risk-Adjusted Return?

Definition: The Modigliani (M²) measure is a risk-adjusted return metric that compares portfolio returns to a benchmark's risk level.

Purpose: It helps investors evaluate how a portfolio would perform if it had the same risk as the benchmark index.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ M^2 = R_f + (R_p - R_f) \times \left(\frac{\sigma_b}{\sigma_p}\right) \]

Where:

\( M^2 \) — Modigliani risk-adjusted return (%)
\( R_f \) — Risk-free rate (%)
\( R_p \) — Portfolio return (%)
\( \sigma_b \) — Benchmark standard deviation (%)
\( \sigma_p \) — Portfolio standard deviation (%)

Explanation: The formula adjusts the portfolio's excess return (over risk-free rate) by the ratio of benchmark risk to portfolio risk.

3. Importance of M² Measure

Details: M² allows comparison of portfolios with different risk levels by showing what return each would have achieved at the benchmark's risk level.

4. Using the Calculator

Tips: Enter the risk-free rate, portfolio return, benchmark standard deviation, and portfolio standard deviation (all as percentages). Portfolio standard deviation must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a good M² value?
A: Higher values are better. An M² greater than the benchmark return indicates superior risk-adjusted performance.

Q2: How is this different from Sharpe ratio?
A: While both measure risk-adjusted returns, M² expresses results in percentage terms, making them more intuitive to interpret.

Q3: What risk-free rate should I use?
A: Typically use short-term government bond yields (e.g., 3-month T-bills) matching your investment horizon.

Q4: Can M² be negative?
A: Yes, if the portfolio's risk-adjusted performance is worse than the risk-free rate.

Q5: How do I get standard deviation values?
A: Calculate from historical returns or obtain from your portfolio manager or investment platform.