Modigliani Ratio Calculator
In investment analysis, measuring a portfolio’s performance relative to risk is essential. The Modigliani Ratio, also known as M² (Modigliani-Modigliani measure), is a risk-adjusted performance metric that evaluates how well a portfolio performs compared to a benchmark by adjusting for volatility differences.
Unlike some other metrics, the Modigliani Ratio expresses performance in percentage terms, making it easier to interpret. It adjusts portfolio returns for risk by scaling them to the benchmark’s volatility, showing what the portfolio’s return would have been if it had the same risk as the benchmark.
Our Modigliani Ratio Calculator helps investors, fund managers, and analysts quickly compute this ratio to better understand portfolio efficiency and risk-adjusted returns.
Formula
The Modigliani Ratio is calculated as:
Modigliani Ratio = Risk-Free Rate + (Portfolio Standard Deviation ÷ Benchmark Standard Deviation) × (Portfolio Return − Risk-Free Rate)
Where:
- Portfolio Return is the average return of your portfolio (%).
- Risk-Free Rate is the return of a risk-free investment, such as treasury bills (%).
- Portfolio Standard Deviation measures the volatility (risk) of your portfolio (%).
- Benchmark Standard Deviation measures the volatility of the benchmark index (%).
This formula adjusts portfolio returns by scaling volatility to the benchmark’s risk level.
How to Use the Modigliani Ratio Calculator
- Enter Portfolio Return (%)
Input your portfolio’s average return over a period. - Enter Risk-Free Rate (%)
Input the risk-free rate applicable for the same period. - Enter Portfolio Standard Deviation (%)
Provide your portfolio’s volatility. - Enter Benchmark Standard Deviation (%)
Provide the benchmark’s volatility. - Click “Calculate”
The calculator computes the Modigliani Ratio using the formula. - Review the Result
The result shows the risk-adjusted return of your portfolio scaled to benchmark risk.
Example
Suppose:
- Portfolio Return = 12%
- Risk-Free Rate = 3%
- Portfolio Std Dev = 15%
- Benchmark Std Dev = 10%
Calculation:
Modigliani Ratio = 3 + (15 ÷ 10) × (12 − 3)
= 3 + 1.5 × 9
= 3 + 13.5
= 16.5%
This means, adjusted to the benchmark’s risk, your portfolio’s return would be 16.5%, indicating strong risk-adjusted performance.
FAQs
1. What is the Modigliani Ratio?
It’s a measure of risk-adjusted return that compares portfolio performance to a benchmark.
2. How is it different from the Sharpe Ratio?
Sharpe Ratio is unitless; Modigliani Ratio expresses returns in percentage terms.
3. Why use the Modigliani Ratio?
It provides an intuitive, risk-adjusted return that’s easy to compare.
4. What does a higher Modigliani Ratio indicate?
Better risk-adjusted performance compared to the benchmark.
5. Can the Modigliani Ratio be negative?
Yes, if portfolio returns are poor relative to risk-free rate.
6. What is the risk-free rate?
The return of a theoretically riskless investment, often government bonds.
7. What data is needed to calculate it?
Portfolio return, risk-free rate, portfolio and benchmark standard deviations.
8. Can it be used for all asset types?
Yes, provided returns and volatilities are known.
9. How does volatility affect the ratio?
Higher portfolio volatility scaled to benchmark risk adjusts returns accordingly.
10. Is it suitable for short-term or long-term analysis?
Both, as long as consistent data is used.
11. Can it replace other metrics?
It complements other metrics like Sharpe and Treynor ratios.
12. How often should it be calculated?
Periodically, to track portfolio performance.
13. What if benchmark volatility is zero?
Calculation isn’t possible; benchmark volatility must be > 0.
14. Can it be negative if portfolio return is below risk-free rate?
Yes, indicating underperformance.
15. How to interpret the result?
Higher values show better risk-adjusted returns.
16. Is the Modigliani Ratio affected by market conditions?
Yes, because returns and volatility vary with market cycles.
17. Does it consider market timing?
No, it focuses on risk and return, not timing.
18. Can it be used for mutual funds?
Yes, widely used for fund performance evaluation.
19. How does it compare to Jensen’s Alpha?
Both measure risk-adjusted returns but use different methods.
20. Where can I find benchmark data?
From financial websites, fund reports, or market indices.
Conclusion
The Modigliani Ratio Calculator offers a clear and straightforward way to assess your portfolio’s risk-adjusted performance relative to a benchmark. By incorporating both return and volatility data, it provides investors with valuable insights into the true effectiveness of their investment strategy.
Use this calculator regularly to measure performance, compare portfolios, and make informed investment decisions based on risk-adjusted returns.