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# M - Squared - Adjusted Portfolio

#### Biju

##### Member
Hi David,
Can you please confirm the composition of Adjusted portfolio for calculating M-Squared

As I understand Adjusted Portfolio= Combination of (RF portfolio + portion of portfolio whose M-squared to be calculated)

Eg-

SD=Standard Deviation
RF=Risk Free part
P=Portfolio Part

Portfolio SD Mkt SD Adjusted Portfolio composition
0.04 0.02 0.5 RF+0.5 Portfolio
0.01 0.02 0.75 RF +0.25 Portfolio
0.04 0.08 ???????????

Thanks
Biju

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Biju M^2 is straightforward because it just adjusts the portfolio volatility to equal the market volatility. Given that the riskfree rate has zero volatility, the adjusted portfolio's weight assigned to the original risky portfolio must be ratio σ(market)/σ(portfolio). So if i am reading your table correctly:
• in the first case, if σ(portfolio) = 4.0% and σ(market) = 2.0%, then adjusted/mixed portfolio is allocated 2.0%/4.0% = 50% to the risky and therefore 50% to cash. The mental confirmation is to see that 50% weight to risky * 4.0% σ = 2.0% is the volatility of the mixed portfolio, which does match the market's portfolio, so we are good
• in the second case, 0.02/0.01 = 200% is the allocation to the portfolio (not 0.25) because, we can check: 200%*0.01 = 0.02 which does match the market
• so in the third case, we want 0.08/0.04 = 200%, as it should produce the same result as the second. I hope that helps!

#### Biju

##### Member
Thanks David.
Second case -- I was trying to put 0.04 0.01 -->Should give 0.75 RF +0.25 Portfolio
Third Case - As you mentioned no Cash

Clear now.

#### FrmL2_Aspirant

##### Member
Hi David,
Can you please confirm the composition of Adjusted portfolio for calculating M-Squared

As I understand Adjusted Portfolio= Combination of (RF portfolio + portion of portfolio whose M-squared to be calculated)

Eg-

SD=Standard Deviation
RF=Risk Free part
P=Portfolio Part

Portfolio SD Mkt SD Adjusted Portfolio composition
0.04 0.02 0.5 RF+0.5 Portfolio
0.01 0.02 0.75 RF +0.25 Portfolio
0.04 0.08 ???????????

Thanks
Biju
Hi Biju, which chapter is this exactly, if I may ask.

#### emilioalzamora1

##### Well-Known Member
Irrespective of the above figures, if you manage to understand the core mandatory FRM reading 'Portfolio Theory and Performance Analysis' by Noel Amenc (page 121 onwards) where M^2 is explained, you will be fine.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@FrmL2_Aspirant Modigliani-squared (M^2) is from Bodie's Chapter 24, see below:
Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments, 10th Edition (New York: McGraw-Hill, 2013). Chapter 24. Portfolio Performance Evaluation [IM–9]
After completing this reading you should be able to:
• Differentiate between time-weighted and dollar-weighted returns of a portfolio and describe their appropriate uses.
• Describe and distinguish between risk-adjusted performance measures, such as Sharpe’s measure, Treynor’s measure, Jensen’s measure (Jensen’s alpha), and information ratio.
• Describe the uses for the Modigliani-squared and Treynor’s measure in comparing two portfolios, and the graphical representation of these measures.
• Determine the statistical significance of a performance measure using standard error and the t-statistic.
• Explain the difficulties in measuring the performance of hedge funds.
• Explain how changes in portfolio risk levels can affect the use of the Sharpe ratio to measure performance.
• Describe techniques to measure the market timing ability of fund managers with a regression and with a call option model, and compute return due to market timing.
• Describe style analysis.
• Describe and apply performance attribution procedures, including the asset allocation decision, sector and security selection decision, and the aggregate contribution

#### emilioalzamora1

##### Well-Known Member
@FrmL2_Aspirant Modigliani-squared (M^2) is from Bodie's Chapter 24, see below:
Actually M2 is covered in many books and I do think that in order to hammer home the message it is best to watch Leah's video. From an exam perspective I would not worry to much about it as it is sort of an advanced performance measure which is very unlikely to be tested in great depth. And it never really made a breakthrough in the industry either. Comparing many different fund managers you will never see that the M^2 is shown to investors.

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