Minimum Variance Frontier and Minimum Variance Portfolio (MVP)

[sleepybird]

David,
With regard to your graph for MVP (page 36/AIM: Define the MVP), you have labeled the left-most point (intercepted by green dash line) of the minimum variance frontier as the MVP.

Shouldn't that point be more appropriately labeled as the Global MVP and not just a MVP because all the portfolios on the mininum variance frontier are MVPs?

Please clarify. Thanks.

 

[David Harper CFA FRM]

Hi sleepybird,

Yes, I agree with you: Global MVP would be better as it would leave no doubt. (I am noting this for the revision). In our (weak) defense, Elton occasionally uses "minimum variance portfolio" when he means Global MVP and I admit i picked up this habit somewhere along the way.

I have not seen the term "minimum variance frontier" used instead of "efficient frontier" but it appears very logical to me: the efficient frontier is the set of minimum variances portfolio, in the sense of minimum variances conditional on a specified return (minimum variance | return level). And, of course, to your point, if we are going to refer to the efficient frontier as the minimum variance portfolio, we MUST refer to the "Global MVP."

Thanks for the clarification, really appreciated! David

 

[sleepybird]

Thanks for your clarification.

All portfolios on the minimum variance frontier are MVPs but they're not necessarily all efficient. Only those portfolios above Global MVP are efficient, thus the curve above the Global MVP is called the efficient frontier (i.e., efficient frontier is just a part of the minimum variance frontier that's efficient).

 

[David Harper CFA FRM]

Hi sleepybird

Oh, I see! The entire risky asset curve can be characterized as the set of minimum variance portfolios (i.e., minimum variance | specific return level). I did not have a name for that curve, very cool! thanks, David