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efficient frontier, global minimum-variance portfolio & optimal risky portfolio

A question from P318 of CFA Textbook 4 –

The set of portfolios on the minimum-variance frontier that dominates all sets of portfolios below the global minimum-variance portfolio is the:

A.      Capital allocation line

B.      Markowitz efficient frontier

C.      Set of optimal risky portfolio

Answer per Textbook: B. “The Markowitz efficient frontier has higher rates of returns for a given level of risk. With respect to the minimum-variance portfolio, the Markowitz efficient frontier is the set of portfolios above the global minimum-variance portfolio that dominates the portfolios below the global minimum-variance portfolio”.

My questions are –

(1)     As the global minimum-variance portfolio is defined as the portfolio on the efficient frontier that has the least risk (per CFA textbook), the global minimum-variance portfolio should be a point on the efficient frontier… isn’t it? Why does it say here that “the Markowitz efficient frontier is the set of portfolios above the global minimum-variance portfolio that dominates the portfolios below the global minimum-variance portfolio”?

(2)     What are the differences between “Markowitz efficient frontier” and “set of optimal risky portfolio”?  To me, they are very similar…

Thanks in advance for your help and clarification.


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thesame2 wrote:
A question from P318 of CFA Textbook 4 –

The set of portfolios on the minimum-variance frontier that dominates all sets of portfolios below the global minimum-variance portfolio is the:

A.      Capital allocation line

B.      Markowitz efficient frontier

C.      Set of optimal risky portfolio

Answer per Textbook: B. “The Markowitz efficient frontier has higher rates of returns for a given level of risk. With respect to the minimum-variance portfolio, the Markowitz efficient frontier is the set of portfolios above the global minimum-variance portfolio that dominates the portfolios below the global minimum-variance portfolio”.

My questions are –

(1)     As the global minimum-variance portfolio is defined as the portfolio on the efficient frontier that has the least risk (per CFA textbook), the global minimum-variance portfolio should be a point on the efficient frontier… isn’t it? Why does it say here that “the Markowitz efficient frontier is the set of portfolios above the global minimum-variance portfolio that dominates the portfolios below the global minimum-variance portfolio”?

Because they’re sloppy in their language.  The global, minimum-variance portfolio is part of the efficient frontier.

thesame2 wrote:
(2)     What are the differences between “Markowitz efficient frontier” and “set of optimal risky portfolio”?  To me, they are very similar…

They are: this is where the language gets technical, and you need to understand the technicalities.  An optimal portfolio is one that has minimum risk for a given level of (expected) return.  An efficient portfolio is one that has maximum (expected) return for a given level of risk.  All portfolios on the minimum-variance frontier are optimal, but only those in the upper portion – at or above the global, minimum-variance portfolio – are efficient.

thesame2 wrote:
Thanks in advance for your help and clarification.

My pleasure.  You ask good questions.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

thank you very much, S2000magician!!

thesame2 wrote:
thank you very much, S2000magician!!

You’re quite welcome.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/