# 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…

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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:

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/