5. In the class we talked about return risk ration and Sharpe ratio. I want you

Question

5. In the class we talked about return risk ration and Sharpe ratio. I want you to conduct a literature search about another measure: M2 measure. Discuss the M2 measure of performance by answering the following questions:

What is M2 measure?

Why is M2 better than the Sharpe measure?

What measure of risk does M2 use?

How do you construct a managed portfolio, P, to use in computing the M2 measure?

What is the formula for M2?

Draw a graph that shows how M2 would be measured. Be sure to label the axes and all relevant points.

Explanation / Answer

Modigliani risk-adjusted performance (also known as M2, M2, Modigliani–Modigliani measure or RAP) is a measure of the risk-adjusted returns of some investment portfolio.

M2 (Modigliani-Modigliani measure) is derived from Sharpe ratio. Sharpe ratio is widely used among investors. But normally people do not understand the sharpe ratio results easily.

Sharpe Ratio Sharpe ratio is a unique one in its class. It is dimensionless but once you understand the meaning of its results, you will never use any other return-risk ratios. Formula to calculate Sharpe ratio is S(X) = (R(x) - R(f)) / S.D(X) where X = investment R(x) = rate of return for your investment R(f) = Risk free return (An investment where there is almost no chance of loosing e.g T.Bills etc) S.D(X) = Standard Deviation of R(x)

M2 To understand the Risk Adjusted return M2 was derived from Sharpe ratio. It is in a form of percentage and you can easily interpret its results. Formula to calculate it is : M2 = S(x) * S.D(y) + R(f) Where S.D(y) = Standard deviation of returns of another investment of the same level.

Result will be in the form of percentage. So you can easily compare investments by using M2. Whereas Sharpe ratio results are very difficult to compare.

It measures the returns of the portfolio, adjusted for the risk of the portfolio relative to that of some benchmark (e.g., the market).

Formula for M2 is  

Where rp = return on portfolio

rf = risk free rate of return

SDb = Standard deviation of bench mark portfolio

SDp = Standard deviation of portfolio

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