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It is possible that from the efficient frontier obtained varying the "lambda" parameter of the risk-appetite coefficient, in the Mean Variance Parametric Quadratic programming problem, it results that when the variance of the portfolio increases, the return decreases?

So, it is possible that from the Programming Problem, there emerges a inverse relationship between the return and the risk-appetite?

Which could be the reasons justifying that situation?

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    $\begingroup$ Min vol portfolios is a recent phenomenon that has had a lot of discussion in the financial circles. People have tried to explain why the minimum variance portfolio has outperformed. You might want to research that for some reasons that might relate to your question. $\endgroup$
    – AlRacoon
    May 2, 2019 at 18:52

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Yes, if you make lambda negative, the investor becomes risk seeking. For lambda >= 0, no.

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