Definition of M2 Measure
M2 measure, or Modigliani-Modigliani measure, is an expanded and more advantageous version of 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 sharpe ratio of the portfolio with the standard deviation of the selected benchmark index and then adding the risk-free return to the result. M2 measure 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 the year 1997. M2 measure is calculated by multiplying the sharpe ratio with the standard deviation, hence, we should understand these terms in order to get a better understanding.
- Sharpe Ratio: It’s a measure of risk-adjusted return of a financial portfolio. A portfolio having the higher Sharpe ratio is considered to be more beneficial than others having a comparatively lower Sharpe ratio.
- Standard Deviation: It’s a measure of the amount of deviation from the average of specific set of values. A portfolio having a higher standard deviation would indicate a higher level of risk since it depicts that the returns may vary a lot over a period of time.
Formula for M2 Measure
In order to calculate M2 measure, we have to find out the Sharpe ratio first. After that, we will multiply the sharpe ratio with 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 sharpe ratio as obtained in step 1 with the standard deviation of the benchmark.
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Where,
- σ_{benchmark}_{ }stands for the standard deviation of the benchmark
Step 3: Adding risk-free rate of return
In third and final step, we simply add up the risk-free return to the outcome of step 2.
From the above calculations and step 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
- Sharpe Ratio = 2.167
Step 2& 3:Calculation of M2 Measure
M2 Measure = SR * σ_{benchmark }+ (r_{f})
- M2 Measure = (2.167*5) + 11
- M2 Measure = 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 as compared with the market.This means that the M2 measure indicates how much returns a portfolio would have attained had it the same risk level as that of the index.
Importance of the M2 Measure
- M2 measure is important as it gives us the risk adjusted return of the portfolio i.e., risk-free rate of return.
- M2 measure can easily be interpreted by us as it is in the form of percentage return unit so it overcomes the problem of concluding that how worse the negative portfolio is.
- We can find out the difference between the performances of the two portfolios easily. 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 taking into account the risk assumed by it.
Advantages of the M2 Measure
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 Sharpe ratios of various investments whereas M2 measure is a better and more useful form of Sharpe ratio.
- Measurement of the risk-adjusted rate of return: M2 measure helps us in finding 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 Sharpe ratio directly from different investments. The same is in the scenario of other measures like the treynor ratio, Sortino ratio, and others that are derived in terms of ratio. As Modigliani risk-adjusted performance is in the percentage return unit, it can be easily interpreted by all investors.
- Comparison with different portfolios: M2 measure 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 of the M2 Measure
Some of the disadvantages are given below:
- Manipulation by the portfolio manager: The portfolio manager handling the affairs of 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 in terms of portfolio management. It helps to understand that with the given level of risk assumed in a portfolio how well the portfolio is going to incentivize the investor as compared to the risk-free rate of return and benchmark portfolio. Therefore, if an investment is taken under consideration having more risk than benchmark, with little benefits, then it might have a lesser amount of risk adjusted performance. M2 measure facilitates the interpretation and helps in the comparison of two or more portfolios by the investor.
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