1. What is the Modigliani M2 Measure?

Definition: The Modigliani M2 measure is a risk-adjusted performance metric that compares a portfolio's return to a benchmark's return after adjusting for differences in risk.

Purpose: It helps investors evaluate how well a portfolio performed relative to a benchmark when both are adjusted to have the same level of risk.

2. How Does the M2 Calculation Work?

The calculator uses the formula:

Where:

• \( M2 \) — Modigliani risk-adjusted return (%)
• \( Rf \) — Risk-free rate (%)
• \( Rp \) — Portfolio return (%)
• \( \sigma b \) — Benchmark standard deviation (%)
• \( \sigma p \) — Portfolio standard deviation (%)

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

3. Importance of the M2 Measure

Details: M2 allows for direct comparison between portfolios with different risk levels by showing what the portfolio would have returned 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 (σp must be > 0).

5. Frequently Asked Questions (FAQ)

Q1: What's a good M2 value?
A: An M2 higher than the benchmark return indicates superior risk-adjusted performance. Equal to benchmark means equivalent performance, lower means worse.

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

Q3: What time period should I use for inputs?
A: Use consistent time periods (e.g., annual returns with annual standard deviations) for accurate comparisons.

Q4: What's a typical risk-free rate?
A: Often the 3-month Treasury bill rate is used, but choose one appropriate for your investment horizon.

Q5: Can M2 be negative?
A: Yes, if the portfolio's risk-adjusted performance is worse than the risk-free rate.