Modigliani Modigliani (M2)

Modigliani Modigliani (M2): Risk Adjusted Performance (Calculator)

Modigliani Modigliani (M2) risk-adjusted performance is used to compare the performance of investment portfolios. It’s frequently referred to as M2. This measure extends beyond traditional metrics by adjusting returns for risk, offering a percentage-based view that aligns with a benchmark’s volatility.

In this guide, we’ll uncover the foundations, calculation methods, and applications of the M2 measure, allowing you to judge how different investment choices compare.

Modigliani Modigliani (M2)

Key Takeaways

  • The Modigliani Modigliani Measure, also known as the M2 measure, is a financial metric developed by Franco Modigliani and Leah Modigliani in 1997 to evaluate the risk-adjusted performance of an investment portfolio relative to a benchmark. Leah is the granddaughter of Franco.
  • M2 is derived using the Sharpe Ratio, which measures excess return per unit of risk. It incorporates it with the benchmark’s standard deviation and the risk-free rate to provide an easily interpretable percentage figure indicating how much a portfolio outperforms or underperforms a benchmark after risk adjustment. Please see the calculation for more information.
  • While the Modigliani Modigliani Measure offers a clear and versatile assessment of portfolio performance accounting for risk, it relies on historical risk data and may get complicated with the use of different risk measures.

What is Modigliani Modigliani Measure?

Illustration of risk-adjusted performance

The term “Modigliani Modigliani Measure” is quite familiar in finance. Also known as the M2 measure, it provides an overview of a portfolio’s performance, considering the level of investment risk. Think of it as a tool that helps you assess how much extra returns your portfolio is earning over a risk-free rate when compared to a benchmark portfolio.

When did this measure originate?

The Modigliani Modigliani Measure was conceived in 1997 by Franco Modigliani and Leah Modigliani (Franco’s granddaughter!). The original name for it was the “RAP,” which stood for risk-adjusted performance.

The goal was to measure a portfolio’s return performance in percentages adjusted for risk. This risk-adjusted performance sets the Modigliani Modigliani Measure apart from many other financial metrics, including those focusing on risk-adjusted performance alpha. In this context, the M2 risk-adjusted return measure might provide different information for investors.

What is Modigliani risk-adjusted performance?

Illustration of portfolio risk assessment

Modigliani risk-adjusted performance is a metric that evaluates an investment’s return relative to its risk level, accounting for the impact of risk on performance. You may now be curious about the nature of Modigliani’s risk-adjusted performance and its relationship with the M2 measure.

Essentially, it is a measure of an investment portfolio’s returns, adjusted for the portfolio’s risk relative to a benchmark. This measure, also known as M2, allows investors to determine how well an investment portfolio rewards them for the level of risk taken.

For instance, a portfolio with twice as much risk as the benchmark would need twice the excess return to achieve the same level of risk-adjusted return.

This interpretation of risk-adjusted performance in terms of percentage return makes the M2 measure helpful for comparing the risk between two or more investments and examining changes in the risk-free rate. By calculating the risk-adjusted excess return, investors can better understand the true value of their investments.

Modigliani Modigliani Calculator

Modigliani Modigliani Calculator

Modigliani Modigliani Calculator

Modigliani Modigliani Calculator

Understanding the Modigliani Modigliani Calculator

The Modigliani Modigliani Calculator is a handy tool designed to help investors and financial analysts determine the nominal rate of return on investment, considering both the real and expected inflation rates. Developed based on the Modigliani Modigliani approach, this calculator considers the impact of inflation on investment returns.

How to Use the Calculator:

  1. Real Rate of Return (%): Enter the expected real rate of return on your investment. The real rate of return represents the actual return on an investment adjusted for inflation.
  2. Expected Inflation Rate (%): Enter the anticipated inflation rate. Since inflation erodes the purchasing power of money over time, it’s important to consider its impact on investment returns. After all, all returns should be measured in real returns.
  3. Click “Calculate”: Once you’ve entered both the real rate of return and expected inflation rate, click the “Calculate” button. The calculator will then determine the nominal rate of return, which reflects the investment’s total return adjusted for inflation.

Interpreting the Results:

The calculator will display the nominal rate of return, providing valuable insights into the investment’s expected real-term performance. This information can help investors make informed decisions by accounting for inflation’s effects on their investment returns.

Why It Matters:

Understanding the Modigliani Modigliani might give you another approach and help you make better investment decisions because it considers the real rate of return.

What is the formula for M2?

The formula for the M2 measure is M2 = (SR * Standard Deviation of the Benchmark) + Risk-Free Rate, where SR is the Sharpe Ratio. In simpler terms, it involves calculating the Sharpe ratio, multiplying it by the benchmark’s standard deviation, and finally adding the risk-free rate to the result.

The Sharpe ratio, used in the M2 measure, calculates the excess return per unit of risk, directly assessing how well an investor is compensated for the risk taken in an investment.

The M2 measure reflects how much a portfolio would have earned if it had the same level of risk as the benchmark index, thus facilitating the comparison between different portfolios.

Origins of the Modigliani Modigliani Measure

The M2 Modigliani Modigliani Measure has the following origins:

  • It was jointly formulated by economist Franco Modigliani and his granddaughter Leah Modigliani.
  • The development took place in 1997, and initially, it was named RAP for risk-adjusted performance.
  • Franco Modigliani’s contribution to the field of economics earned him a Nobel Prize, and the measure he developed with Leah is still widely used today.

The M2 measure is derived from the Sharpe Ratio and is used to characterize how well a portfolio’s return rewards an investor for the risk taken. However, unlike the Sharpe ratio and other ratios, the M2 measure puts the risk-adjusted performance in units of percentage return, which is easier for investors to interpret. This versatility allows the M2 measure to be extended to use other risk measures, such as beta, by substituting these for the standard deviation in the calculations.

What is the difference between Modigliani–Miller theorem and Modigliani Modigliani?

The difference between the Modigliani-Miller theorem and Modigliani Modigliani lies in their focus and implications. The Modigliani-Miller theorem addresses capital structure irrelevance, stating that a firm’s value is independent of its financing decisions in an ideal market.

In contrast, the Modigliani Modigliani Measure helps assess a portfolio’s risk-adjusted performance.

In contrast, the Modigliani Modigliani Measure focuses on assessing the extra returns of a portfolio over the risk-free rate, compared to a benchmark. While the Modigliani-Miller theorem impacts corporate finance by addressing a company’s capital structure, the Modigliani Modigliani Measure is a tool for investors to evaluate and compare portfolio performance.

Franco Modigliani also co-developed another significant financial concept, the Modigliani-Miller theorem, with Merton Miller. This theorem states that a company’s market value is correctly calculated as the present value of its future earnings and underlying assets, independent of its capital structure.

Key Components of the Modigliani Modigliani Measure

Several key components are involved in calculating the Modigliani Modigliani Measure. One such component is the Sharpe Ratio, a critical component of the M2 measure. The Sharpe ratio measures the excess return per unit of risk, directly assessing how well an investor is compensated for the risk taken in an investment.

Two other crucial components of the M2 measure are the standard deviation and the benchmark portfolio. The standard deviation assesses a portfolio’s risk, normalizing risk-adjusted returns by incorporating both the portfolio’s and the market’s standard deviation.

On the other hand, benchmark portfolios are used to determine the relative performance within the Modigliani Modigliani measure. These components are integrated to normalize the risk-adjusted return and make it comparable across portfolios with different risk profiles.

Illustration of active management value

Analyzing Risk-Adjusted Performance with the Modigliani Modigliani Measure

Analyzing risk-adjusted performance with the Modigliani Modigliani measure involves evaluating investment returns relative to a benchmark while considering the level of risk taken to achieve those returns.

The Modigliani Modigliani Measure excels in analyzing risk-adjusted performance. By adjusting an investment’s return for risk compared to a benchmark portfolio, the M2 measure allows investors to understand the added value of active management. This measure evaluates how well an investor is rewarded for the risk taken relative to the benchmark and the risk-free rate.

The M2 measure is a percentage return to simplify comparing different investments or strategies. A fund that exceeds the benchmark returns with equivalent risk demonstrates a better risk-return trade-off than one achieving similar returns at a higher risk. By considering both excess return and associated risk, the M2 measure aids in identifying portfolios that outperform the benchmark.

The Role of the Sharpe Ratio

The Sharpe Ratio is integral to the M2 measure. It calculates the risk-adjusted return, offering a direct assessment of how well an investor is compensated for the risk taken in an investment. The Sharpe ratio is calculated using the formula SR = (rp—rf) / p, where rp is the portfolio’s return, rf is the risk-free rate of return, and p is the standard deviation of the portfolio’s excess return.

However, the M2 measure addresses the interpretational limitations of the Sharpe ratio, especially in situations where the Sharpe ratio is negative. Unlike the Sharpe ratio, the Modigliani Modigliani Measure provides an absolute performance measure, indicating the risk-adjusted return in percentage terms compared to a benchmark.

Incorporating Standard Deviation and Benchmark Portfolio

Incorporating standard deviation and benchmark portfolio increases portfolio analysis by providing knowledge of risk levels and performance relative to a chosen standard. Within the M2 measure, the standard deviation and the benchmark portfolio retain relevance. The standard deviation of a portfolio’s returns is used to scale the portfolio’s performance in relation to the risk level of a benchmark portfolio, creating a scaled portfolio. The benchmark portfolio, on the other hand, acts as the point of reference against which the performance of an investment portfolio is compared.

These components normalize risk-adjusted return, making it comparable across portfolios with different risk profiles. Different indices or portfolio compositions can be used as benchmarks, allowing for a broader comparison of investment performance. Thus, the M2 measure is versatile and can be applied to different asset classes, provided an appropriate benchmark is available.

Illustration of Sharpe ratio calculation

Practical Application: Calculating the Modigliani Modigliani Measure (Example)

To calculate the Modigliani Modigliani Measure, determine the portfolio’s Sharpe ratio and adjust it by the risk-free rate. With the basics of the Modigliani Modigliani Measure clarified it’s time to show its practical calculation.

The formula for the M2 measure is: M2 = (Rp – Rf) – (SDp / SDb) * (Rb – Rf).


  • Rp is the portfolio return
  • Rf is the risk-free rate
  • SDp is the standard deviation of the portfolio’s excess return
  • SDb is the standard deviation of the benchmark’s excess return
  • Rb is the return of the benchmark portfolio.

Each component of the Modigliani Modigliani measure formula has a specific financial meaning. For instance:

  • Rp indicates the actual return of the portfolio which investors earned
  • Rf represents a safe return that could be earned with no risk
  • SDp shows the risk profile of the portfolio
  • SDb measures the risk of the benchmark
  • Rb gives the performance target for the portfolio to beat.

Formula and Calculation Steps

We can dissect the formula and calculation steps for the M2 measure as follows:

Start by calculating the Sharpe Ratio: Sharpe Ratio (SR) = (Rp – Rf) / p, with Rp representing the portfolio return, Rf as the risk-free rate, and p as the standard deviation of the portfolio’s excess return.

Next, adjust the computed Sharpe Ratio by multiplying it by the benchmark’s standard deviation: M2 = SR b, where b is the benchmark’s standard deviation.

Finally, to determine the Modigliani Modigliani (M2) measure, add the risk-free rate to the product of the Sharpe Ratio and benchmark standard deviation: M2 measure = SR benchmark + rf.

Example Calculation

Here’s an illustrative calculation to better understand the concept of risk-free return.

  • Market return: 22%
  • Investor’s portfolio return: 26%
  • Risk-free rate: 12%
  • Standard deviation of the market: 6%
  • Standard deviation of the investor’s portfolio: 7%

First, calculate the Sharpe Ratio for the investor’s portfolio as (26% – 12%) / 7%, resulting in a Sharpe Ratio of 2. Then, compute the M2 measure as 2 * 6% + 12%, which is 24%. The resulting M2 measure of 24% indicates that the investor’s portfolio outperforms the benchmark by this percentage after adjusting for risk, considering the included risk-free rate of return.

Advantages and Limitations of the Modigliani Modigliani Measure

The Modigliani Modigliani Measure presents a comprehensive portfolio performance evaluation by accounting for total risk. To the market portfolio, yet it is not without its shortcomings.

Before discussing these drawbacks, it is pertinent to highlight the primary benefits associated with utilizing the M2 measure.

Benefits of the Modigliani Modigliani Measure

The benefits of the M2 measure offer a clear and easily understandable representation of risk-adjusted returns that investors can quickly grasp. This contrasts with metrics such as the Sharpe ratio, which are conveyed through ratios. By presenting in percentage points, the M2 measure becomes more accessible and easier to comprehend for most investors.

Its adaptability stands out as an asset. The ability of the M2 measure to facilitate an effective comparison of risks between various investments is noteworthy. It shifts focus from mere returns to exhibiting risk-adjusted performance. This approach provides a deeper level of insight when comparing investment options.

Limitations and Potential Pitfalls for Modigliani Modigliani

On the other hand, the Modigliani Modigliani Measure has some limitations. One significant disadvantage is that it depends on historical risk data to gauge performance. Consequently, its ability to accurately forecast future investment outcomes is questionable since past results do not necessarily guarantee similar outcomes in forthcoming periods. However, this applies to all kinds of performance metrics.

Another issue arises from its adaptability. The M2 measure provides leeway to employ a range of risk measures besides standard deviation. This versatility might cause misunderstandings when evaluating risk-adjusted performance because using different risk metrics can yield varying calculations of risk-adjusted returns, thereby making comparisons more challenging.

Comparing the Modigliani Modigliani Measure to Other Risk-Adjusted Performance Metrics

Understanding the Modigliani Modigliani Measure is advantageous when comparing it to other metrics for risk-adjusted performance. Other significant measures, such as the Sharpe ratio, the Treynor ratio, and Jensen’s Alpha, are other performance metrics used in assessing investment portfolios.

These different metrics have their distinct emphases and uses that make them appropriate for a variety of situations and objectives related to investments.

Similarities and Differences for Modigliani Modigliani Measure to Other Risk-Adjusted Performance Metrics

The Sharpe ratio, Treynor ratio, and Modigliani Modigliani Measure all use the risk-free rate in their calculations and focus on excess returns for risk taken. However, they employ different measures of risk.

  • The Sharpe ratio uses standard deviation
  • The Treynor ratio uses beta
  • The M2 measure adjusts the portfolio to reflect total risk as compared to the market.

On the other hand, Jensen’s Alpha measures the active return of an investment against a benchmark, considering the investment’s performance after accounting for its risk. While these metrics share similarities, their differences guide investors in selecting the most appropriate tool based on their specific scenario, investment goals, and market conditions.

Choosing the Right Metric for Modigliani Modigliani Measure

The selection of the appropriate metric hinges on numerous factors such as type of investment, portfolio nature, investor’s risk tolerance, and the focus on total volatility or downside risk.

For instance, investors focusing on market risk might find metrics like the Treynor ratio or Jensen’s Alpha more suitable, as they use beta to measure performance in relation to market movements.

On the other hand, if you are evaluating investment options that share the same benchmark and where total risk or volatility is a key concern, the Sharpe ratio might be the preferred metric.

Ultimately, the risk-adjusted performance metric should be influenced by the specific investment type.

Illustration of risk-adjusted performance metrics


In conclusion, the Modigliani Modigliani Measure is helpful for evaluating and comparing portfolios’ risk-adjusted performance. Despite its limitations, its versatility and straightforward interpretation make it a valuable asset in an investor’s toolbox.

As with any financial metric, you must understand its calculation, components, and potential pitfalls.

Who developed the M2 measure?

The M2 measure was developed by Franco Modigliani and his granddaughter Leah Modigliani in 1997.

What is Modigliani and Modigliani measure?

The M2 measure, commonly called the Modigliani-Modigliani measure, measures an investment’s return once it has been adjusted for risk relative to a benchmark. It expresses this risk-adjusted performance in percentage units.

How is the M2 measure calculated?

To calculate the M2 measure, apply the formula: M2 = (Risk-Free Rate + (Sharpe Ratio * Standard Deviation of the Benchmark)).

What are the benefits of the M2 measure?

The M2 Measure presents a simple method for analyzing and contrasting risks among various investments.

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