# A question about the Minimum Frontier and the Efficient Frontier

“Each Portfolio on the minimum-variance frontier represents the portfolio with the smallest variance of returns for its expected level of return”.

“The portion of the minimum-variance frontier beginning with and continuing above the GMV portfolio is the efficient frontier”

–> My question : Is the efficient frontier part of the minimum-variance frontier ? I mean, looking at the classic graph, shown in exhibit 10 on p. 212, it is clear that the portfolios on the portion under the GMV (designated as the Minimum Variance Frontier) are dominated by portfolios on the efficient frontier and therefore not efficient.

So what are they talking about, here ? What is it that I am missing ? Many thanks.

the MVF is just a set of portfolios who have the lowest variance for a expected level of return.

You could have a std. deviation of returns of 5%, which has two portfolios - one that yields and expected return of 10% and one that yields 5%.

A rationale investor would choose the 10% expected return portfolio over the 5% return portfolio. Therefore the 10% return dominates the 5% return portfolio for the 5% level of std. deviation.

God damn it, now I know what I had been missing ; I was looking at the graph vertically, your statement and the definition quoted are valid if you look at the graph horizontally.

So a minimum variance portfolio may have the best Std Dev for a given level of return ; it might, however, not have the best level of return for a given Std Dev…

Txs, man. Quite a stupid question once you know what you have been missing, lol.

you got it, just needed that refresher!