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Explanation

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 MeasureIn 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:

Sharpe Ratio (SR) = (rp – rf) / σp

Where,

rp stands for the return of the portfolio

rf stands for the risk-free rate of return

σp 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.

SR * σbenchmark

Where,

σbenchmark 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.

SR * σbenchmark + (rf)

M2 Measure= SR * σbenchmark + (rf)

Example of M2 MeasureLet 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 (rm) 20%

Risk free return (rf) 11%

σbenchmark 5%

Portfolio risk (rp) 24%

σp 6%

Let us calculate M2 Measure for the given data.

Solution:

Sharpe Ratio =(rp – rf) / σp

Sharpe Ratio = (24-11)/6

= 2.167

Step 2& 3:Calculation of M2 Measure

M2 Measure = SR * σbenchmark + (rf)

M2 Measure = (2.167*5) + 11

= 21.8%

Interpretation of the M2 MeasureThere 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

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.

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.

ConclusionM2 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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