# M2 Measure (Definition, Formula) | Examples to Calculate M Squared

## 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 rate 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 Formula (SR) = (rp – rf) / σp

Where,

• 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 benchmark

= SR * σbenchmark

Where,

• σbenchmark = standard deviation of benchmark

M squared measure = SR * σbenchmark + (rf) With the equation as derived above for the calculation of Modigliani–Modigliani measure, it can be seen that M2 measure is 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.

Given: Step 1: Calculation of Sharpe ratio • Sharpe Ratio (SR) = (26– 12) / 7
• Sharpe Ratio (SR) = 14 / 7
• Sharpe Ratio (SR) = 2

Step 2: Calculation of M2 measure M2 = SR * σbenchmark + (rf)

M2 = 12 + (12)

M2 = 24 %

1. It is a risk-adjusted performance metric which 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 Sharpe ratio of 0.60 and another having −0.60, then it would be difficult to conclude that how worse second portfolio.
4. The same is in case of another measure like Treynor ratio, Sortino ratio 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 portfolios. Like M2 values of portfolio 1 is 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 can manipulate the measures who seek to boost their history of risk-adjusted returns.

### Important points of the M2 measure

1. Calculate return of the portfolio 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 systematic risk component will be used in place of full volatility component. The same however will be a good indicator only if portfolio under consideration is a well-diversified portfolio because under diversification may lead to underestimation of 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 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 return 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 ratio’ with the added advantage that it is in units of the percent return which makes it more intuitive for the interpretation by the user

### Conclusion

M2 measure is helpful in knowing that with the specified amount of risk taken, how well 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 the similar amount of return. It is easy to interpret and helpful in comparison of two or more portfolios by the user.