Modigliani Ratio Calculator Formula

Modigliani Risk-Adjusted Return Formula:

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

Risk-free Rate (Rf):

Portfolio Return (Rp):

Benchmark Std Dev (σb):

Portfolio Std Dev (σp):

Modigliani Risk-Adjusted Return (M²):

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1. What is the Modigliani Ratio (M²)?

Definition: The Modigliani Ratio, also known as M², measures the risk-adjusted return of an investment portfolio compared to a benchmark.

Purpose: It helps investors compare portfolio performance after adjusting for differences in risk levels.

2. How Does the M² Calculation 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 in Investment Analysis

Details: M² allows comparison of portfolios with different risk levels by showing what return the portfolio would have achieved if it had the same risk as the benchmark.

4. Using the Calculator

Tips: Enter the risk-free rate, portfolio return, benchmark standard deviation, and portfolio standard deviation. All values must be valid numbers with σp > 0.

5. Frequently Asked Questions (FAQ)

Q1: What's a good M² value?
A: Higher M² values indicate better risk-adjusted performance. Values above the benchmark return suggest superior performance.

Q2: How is M² 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 often should I calculate M²?
A: Regular calculation (e.g., quarterly) helps track performance consistency and risk management effectiveness.