M2 Measure

What is the M2 Measure?

M2 measure is an extended and more useful version of the Sharpe ratio which gives us the risk-adjusted return of the portfolio by multiplying the Sharpe ratio with the standard deviation of any benchmark market index and adding risk-free return thereafter to it.

Formula & Steps to Calculate M2 measure

For the calculation of the M2, firstly, the Sharpe ratio (annual) will be calculated. The calculated Sharpe ratio will then be used for deriving the M squared by multiplying the Sharpe ratio by the standard deviation of the benchmark. Here the benchmark will be chosen by the person calculating the M2 measure.

Examples of standard benchmark could be the MSCI World index, S&P500 index, or any other broad index. After multiplying the Sharpe ratio by the standard deviation of the benchmark, the risk-free rateRisk-free RateA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more of return will be added.

The following are the steps or formulas for the calculation of the M2 measure.

Step 1: Calculation of Sharpe ratio (annualized)

Sharpe Ratio FormulaSharpe Ratio FormulaThe Sharpe ratio formula calculates the excess return over the risk-free return per unit of the portfolio's volatility. The risk-free rate of return gets subtracted from the expected portfolio return and is divided by the standard deviation of the portfolio. Sharpe ratio = (Rp – Rf)/ σpread more (SR) = (rp – rf) / σp


  • rp = return of the portfolio
  • rf = risk-free rate of return
  • σp = standard deviation of the excess return of the portfolio

Step 2: Multiplying Sharpe ratio as calculated in step 1 with the standard deviation of the benchmark

= SR * σbenchmark


  • σbenchmark = standard deviation of benchmark

Step 3: Adding the risk-free rate of return to the outcome derived in step 2

M squared measure = SR * σbenchmark + (rf)

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For eg:
Source: M2 Measure (wallstreetmojo.com)

With the equation as derived above for the calculation of Modigliani–Modigliani measure, it can be seen that the M2 measure is the excess return, which is weighted over the standard deviation of benchmark and portfolio increasing with the risk-free rate of return.

Example to Calculate M squared measure

Use Market Portfolio with Investors portfolio to calculate Modigliani–Modigliani measure.


Market Portfolio: 

  • Market Risk (rm): 22
  • Risk free return (rf): 12
  • σbenchark: 6

Investor’s Portfolio:

  • Portfolio risk (rp)  : 26%
  • Ris free return (rf): 12%
  • σp: 7

Calculation of Modigliani risk-adjusted performance(RAP)

  1. Calculation of Sharpe ratio

    M2 measure Example 1-1
    Sharpe Ratio (SR) = (26– 12) / 7
    Sharpe Ratio (SR) = 14 / 7
    Sharpe Ratio (SR) = 2

  2. Calculation of M2 measure

    Modigliani risk-adjusted performance Example 1-2
    M2 = SR * σbenchmark + (rf)
    M2 = 12 + (12)
    M2 = 24 %


  1. It is a risk-adjusted performance metric that is easy to interpret.
  2. M2 measure is more useful when compared with the Sharpe ratio from which it is derived because it is awkward to interpret Sharpe ratio when the same is negative.
  3. Also, one might find it difficult to compare Sharpe ratios directly from different investments. Like if one wants to compare two different portfolios, one having a Sharpe ratio of 0.60 and another having −0.60, then it would be difficult to conclude that how worse the second portfolio.
  4. The same is in case of another measure like Treynor ratioTreynor RatioThe Treynor ratio is similar to the Sharpe ratio and it calculates excess return over risk-free return per unit of portfolio volatility using beta rather than standard deviation as a risk measure. As a result, it gives the excess return over the risk-free rate of return per unit of the beta of the investor's overall portfolio.read more, Sortino ratioSortino RatioThe Sortino ratio is a statistical tool used to evaluate the return on investment for a given level of bad risk. It is calculated by subtracting the risk-free rate of return from the expected return and dividing the result by the negative portfolio's standard deviation (downside deviation).read more, and other ratios, which are calculated in terms of ratio. This problem is overcome in Modigliani risk-adjusted performance as it is in percentage return unit, which can be interpreted instantly and easily by all the investors.
  5. So, it is easy to know the difference between the two or more investment portfoliosInvestment PortfoliosPortfolio investments are investments made in a group of assets (equity, debt, mutual funds, derivatives or even bitcoins) instead of a single asset with the objective of earning returns that are proportional to the investor's risk profile.read more. Like M2 values of portfolio 1 are 5.4% and of the second portfolio is 5.9%, then it shows that there is a difference of 0.5 percentage risk-adjusted return with riskiness adjusted with the benchmark portfolio.
  6. Thus it helps in comparing the two different portfolios.


  1. The data used for the calculation of M2 measures incorporate only historical risk.
  2. The portfolio manager Portfolio Manager A Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. read morecan manipulate the measures that seek to boost their history of risk-adjusted returns.

Important points of the M2 measure

  1. The calculated return of the portfolioThe Calculated Return Of The PortfolioThe portfolio return formula calculates the return of the total portfolio consisting of the different individual assets. The formula is computed by calculating the return on investment on individual asset multiplied with respective weight class in the total portfolio and adding all the resultants together. Rp = ∑ni=1 wi riread more will be equal to the M2 measure when the portfolio’s standard deviation is equal to the standard deviation of the benchmark. This generally happens when the portfolio is tracking an index.
  2. The M squared measure also has an alternative where a systematic riskSystematic RiskSystematic Risk is defined as the risk that is inherent to the entire market or the whole market segment as it affects the economy as a whole and cannot be diversified away and thus is also known as an “undiversifiable risk” or “market risk” or even “volatility risk”.read more component will be used in place of the full volatility component. The same, however, will be a good indicator only if the portfolio under consideration is a well-diversified portfolio because under diversification may lead to underestimation of the portfolio’s riskiness as some idiosyncratic risk will be left in that case.
  3. The M2 measure is derived directly from the Sharpe ratio so, any portfolio orderings using the M2 measure will exactly be the same as the portfolio ordering using the Sharpe ratio.
  4. M2 measure helps in measuring the returns of portfolios after adjusting the risk associated, i.e., it measures the risk-adjusted returnRisk-adjusted ReturnRisk-adjusted return is a strategy for measuring and analyzing investment returns in which financial, market, credit, and operational risks are evaluated and adjusted so that an individual may decide whether the investment is worthwhile given all of the risks to the capital invested.read more of the different investment portfolios relative to a benchmark.
  5. M2 measure is also sometimes known as M squared, Modigliani–Modigliani measure, RAP, or Modigliani risk-adjusted-performance.
  6. One can interpret the M2 measure as the difference between the portfolio’s scaled excess return with that of the market, where the scaled portfolio has volatility being the same as that of the market.
  7. The M squared measure is calculated from the famous and widely used ‘Sharpe ratioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investors’ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by, Sharpe Ratio = {(Average Investment Rate of Return – Risk-Free Rate)/Standard Deviation of Investment Return} read more’ with the added advantage that it is in units of the percent return, which makes it more intuitive for the interpretation by the user.


M2 measure is helpful in knowing that with the specified amount of risk taken, how well the portfolio is rewarding the investor, in relation to the benchmark portfolio and the risk-free rate of return. So, if an investment is considered which has more risk than the benchmark portfolio, with small performance advantage, then it might have less amount risk-adjusted performance when compared with another portfolio where there is less risk in relation to some benchmark portfolio, but having a similar amount of return. It is easy to interpret and helpful in comparison to two or more portfolios by the user.

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This has been a guide to what is M2 Measure. Here we discuss the formula to calculate M squared measure along with examples, advantages & disadvantages. You can learn more about Investment Banking from the following articles –

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