M-Squared: Modigliani Risk-Adjusted Return

Key Takeaways

• M-squared scales a portfolio to the benchmark's volatility, then reports the result as an annual percentage return.
• It is built from the Sharpe ratio, so it ranks portfolios the same way but in clearer units.
• A percentage output is easier to interpret than a bare Sharpe number like 0.75.
• The benchmark choice drives the result, so an unfair index produces a misleading M-squared.

What It Is

M-squared was introduced in 1997 by Franco Modigliani and Leah Modigliani, who originally called it risk-adjusted performance, or RAP. It answers a question the Sharpe ratio cannot: not "how good is the risk-adjusted return," but "what return would this portfolio have produced at the market's level of risk?"

The trick is to imagine adjusting the portfolio, by blending it with cash or borrowing, until its volatility matches the benchmark's. At that matched risk level, the portfolio's return becomes directly comparable to the benchmark's return. The difference is expressed in percentage points.

The M2 Modigliani risk-adjusted return is valued precisely because the output is a percentage, which most investors read more easily than a ratio.

The Intuition

A Sharpe ratio of 0.75 is fine, but it tells you nothing in dollars or percent. Is that 1 percent better than the market, or 5 percent? You cannot tell without context.

M-squared fixes this by putting every portfolio on a level playing field. It dials each one up or down to the same risk as the benchmark, then compares apples to apples. The output, say plus 2 percent, means "after equalizing risk, this portfolio beat the market by 2 percentage points a year." That is a sentence a client understands immediately.

How the M2 Modigliani Risk-Adjusted Return Works

The formula builds directly on the Sharpe ratio:

M-squared = Rf + (Sharpe Ratio of Portfolio) x (Standard Deviation of Benchmark)

Where Rf is the risk-free rate, and the Sharpe ratio is the portfolio's excess return divided by its own standard deviation. Multiplying the Sharpe ratio by the benchmark's standard deviation rescales the portfolio to the benchmark's risk, and adding back the risk-free rate produces a return figure.

To get the M-squared excess return, subtract the benchmark's actual return:

M-squared excess = M-squared - Benchmark Return

A higher M-squared is better. Because it is a monotonic transform of the Sharpe ratio, it always ranks portfolios in the same order Sharpe does, just in friendlier units.

Worked Example

A portfolio has an excess return of 9 percent and a standard deviation of 18 percent, so its Sharpe ratio is 0.50. The benchmark has a standard deviation of 12 percent, and the risk-free rate is 2 percent.

First, scale to the benchmark's risk:

M-squared = 2% + (0.50 x 12%) = 2% + 6% = 8%

So at the market's level of risk, this portfolio would have returned 8 percent. If the benchmark actually returned 7 percent, the M-squared excess return is:

M-squared excess = 8% - 7% = 1%

The portfolio added 1 percentage point of return after equalizing risk. That single percentage is far easier to act on than the underlying Sharpe ratio of 0.50.

Common Mistakes

1. Choosing an unfair benchmark. M-squared scales to the benchmark's volatility, so a benchmark that does not match the portfolio's market produces a distorted figure. Pick an index the portfolio genuinely competes with.
2. Forgetting it is just Sharpe in disguise. M-squared cannot rank portfolios differently from the Sharpe ratio. If two analyses disagree on ranking, one of them has a calculation error.
3. Mixing risk-free rate conventions. Using a different risk-free rate in the Sharpe step versus the M-squared step gives an inconsistent answer. Use one rate throughout.
4. Comparing raw M-squared, not the excess. The raw M-squared includes the benchmark's return. To judge skill, subtract the benchmark and look at the excess.
5. Applying it to undiversified portfolios. Like Sharpe, M-squared uses total standard deviation, so it works for whole portfolios, not single concentrated positions.

Frequently Asked Questions

What is the M2 Modigliani risk-adjusted return in simple terms? The M2 Modigliani risk-adjusted return tells you what a portfolio would have earned if it took the same risk as the market, stated as a percentage. A higher figure means better performance after risk is equalized.

How does M-squared affect investment decisions? It lets you compare managers in plain percentage terms rather than abstract ratios. As the worked example shows, an M-squared excess of 1 percent means the portfolio beat the benchmark by one point after matching its risk, which is easy to weigh against fees.

What is a real-world example of M-squared? A portfolio with a 0.50 Sharpe ratio and a benchmark with 12 percent volatility yields an M-squared of 8 percent at a 2 percent risk-free rate. If the benchmark returned 7 percent, the portfolio added 1 percentage point on a risk-adjusted basis.

How can investors use M-squared effectively? Choose a benchmark the portfolio truly competes against, keep the risk-free rate consistent, and focus on the M-squared excess over the benchmark. Compare it across funds with similar mandates.

How is M-squared different from the Sharpe ratio? The Sharpe ratio gives a unitless number like 0.50 that needs context. M-squared transforms that same information into a percentage return at the benchmark's risk level, so the output is directly interpretable.

Sources

1. Wall Street Mojo. "M2 Measure." https://www.wallstreetmojo.com/m2-measure/
2. EduCBA. "M2 Measure." https://www.educba.com/m2-measure/
3. ETFdb. "How to Measure Risk-Adjusted Returns." https://etfdb.com/portfolio-management/how-to-measure-risk-adjusted-returns/
4. Ryan O'Connell, CFA. "M2 Ratio Calculator." https://ryanoconnellfinance.com/calculators/m2-ratio-calculator/

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.