Updated July 17, 2023
Definition of M2 Measure
M2 measure, or Modigliani-Modigliani measure, is an expanded and more advantageous version of the Sharpe ratio. It’s a measure of risk-adjusted returns of an investment portfolio.
The M@ measure is an indicator of the risk-adjusted return of a portfolio, and the measure can be derived for the portfolio by multiplying the Sharpe ratio of the portfolio with the standard deviation of the selected benchmark index and then adding the risk-free return to the result. It is also known as Modigliani Risk-adjusted Performance (RAP).
Explanation
M2 measure helps in knowing that with the given amount of risk taken, how much the portfolio will reward an investor in terms of the risk-free rate of return and benchmark portfolio. It was developed by Nobel prize winner franco modigliani and his granddaughter leah modigliani in 1997. It is calculated by multiplying the Sharpe ratio with the standard deviation. Hence, we should understand these terms to get a better understanding.
- Sharpe Ratio: It measures the risk-adjusted return of a financial portfolio. A portfolio with a higher Sharpe ratio is more beneficial than others with a lower Sharpe ratio.
- Standard Deviation: It’s a measure of the amount of deviation from the average of a specific set of values. A portfolio with a higher standard deviation would indicate a higher level of risk since it depicts that the returns may vary a lot over time.
Formula for M2 Measure
In order to calculate it, we must first find out the Sharpe ratio. After that, we will multiply the Sharpe ratio by the standard deviation of any benchmark index, such as the s&p 500 index or any other index.
The following are the steps to calculate the M2 measure:
Step 1: Calculation of Sharpe ratio
Sharpe ratio can be calculated using the following formula:
Where,
- r_{p} stands for the return of the portfolio
- r_{f} stands for the risk-free rate of return
- σ_{p }stands for the standard deviation of the excess return of the portfolio
Step 2: Multiplying Sharpe ratio with a standard deviation of the benchmark
The second step is to multiply the Sharpe ratio as obtained in step 1 with the standard deviation of the benchmark.
Where,
- σ_{benchmark}_{ }stands for the standard deviation of the benchmark
Step 3: Adding risk-free rate of return
In the third and final step, we simply add the risk-free return to the outcome of step 2.
From the above calculations and steps we can find out the value of M2 Measure as follows:
Example of M2 Measure
Let us understand the concept of M2 measure with the help of an example.
Example: Suppose the following details are given with respect to an investment portfolio.
Particulars |
Details |
Market risk (r_{m}) | 20% |
Risk free return (r_{f}) | 11% |
σ_{benchmark} | 5% |
Portfolio risk (r_{p)} | 24% |
σ_{p} | 6% |
Let us calculate M2 Measure for the given data.
Solution:
Step 1: Calculation of Sharpe ratio
Sharpe Ratio =(r_{p} – r_{f}) / σ_{p}
- Sharpe Ratio = (24-11)/6
- = 2.167
Step 2& 3:Calculation of M2 Measure
M2 Measure = SR * σ_{benchmark }+ (r_{f})
- M2 Measure = (2.167*5) + 11
- = 21.8%
Interpretation of the M2 Measure
There is a difference between a scaled excess return of the portfolio with the excess return of the market, where the scaled portfolio has alternation as same as that of the market. We can interpret the value of the M2 measure as the difference between a portfolio’s scaled excess returns compared with the market. This means that the M2 measure indicates how many returns a portfolio would have attained had the same risk level as the indexes.
Importance of the M2 Measure
- The M2 measure is important as it gives us the portfolio’s risk-adjusted return, i.e., risk-free rate of return.
- We can easily interpret the M2 measure as a percentage return unit, so it overcomes the problem of concluding how worse the negative portfolio is.
- We can easily find the difference between the performances of the two portfolios. For example, if the value of the M2 measure for portfolio X is 1.9% and the value for portfolio Y is 1.53%, then the difference between the two portfolios is 0.37%. This shows that portfolio X is performing better since its returns are better considering its assumed risk.
Advantages
Some of the advantages are given below:
- The advanced form of Sharpe ratio: Sharpe ratio is difficult to interpret when it is negative. Moreover, it is not convenient to directly compare the Sharpe ratios of various investments, whereas the M2 measure is a better and more useful form of the Sharpe ratio.
- Measurement of the risk-adjusted rate of return: M2 measure helps us find the returns achieved by the portfolio in terms of risk assumed by it as it measures the risk-adjusted return of the different investments.
- Overcomes drawbacks of Sharpe, Treynor, Sortino, and similar ratios: It is difficult to compare the Sharpe ratio directly from different investments. The same is true of other measures like the Treynor ratio, Sortino ratio, and others derived in ratio. As Modigliani’s risk-adjusted performance is in the percentage return unit, it can be easily interpreted by all investors.
- Comparison with different portfolios: It facilitates the comparison of two different portfolios.
- Easy to interpret: It is a risk-adjusted performance yardstick. Hence, it is easy to interpret and fetch conclusions from its projections.
Disadvantages
Some of the disadvantages are given below:
- Manipulation by the portfolio manager: The portfolio manager handling the affairs of the M2 measure can influence the results to boost the history of risk-adjusted returns.
- It subsumes only historical risk: The data from which M2 measures are calculated assimilates only the historical risk.
Conclusion
M2 measure is very diversified and acts as a helping tool for portfolio management. It helps to understand that with the given level of risk assumed in a portfolio, how well the portfolio will incentivize the investor compared to the risk-free rate of return and benchmark portfolio. Therefore, if an investment has more risk than the benchmark, with few benefits, it might have less risk-adjusted performance. It facilitates the interpretation and helps in comparing two or more portfolios by the investor.
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