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Regarding this problem, is this equivalent to optimize the standard mean variance portfolio and then comparing the Sharpe ratio of all the portfolio along the efficient frontier?

Edit: Instead of solving the following optimization problem

Maximize $ \frac{\mu^{T}x -rf}{xTQx }$

s.t $\sum_{j}{x_j\ =\ 1,}$

$x \in C$

I could transform and solve for

Minimize $ y^{T}Qy $

s.t $ \hat \mu^{T}y= 1,$

But I wonder if I could just solve the standard min variance portfolio and select the one with highest Sharpe? Since I also curious about the shape of the efficient frontier.Many thanks

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    $\begingroup$ Please add more detail, as it is not entirely clear what your question is. $\endgroup$
    – Richard Hardy
    Commented Feb 6 at 12:41

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You need to add in more details when asking your question.

But the short answer is yes, you are comparing the Sharpe ratios of all the portfolios along the efficient frontier and actually even those (that are not efficient and not optimal portfolios) below it. However, there will be only 1 portfolio with the max Sharpe ratio along this efficient frontier.

The tangency portfolio is the portfolio with the max Sharpe ratio: enter image description here

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