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Basically i am confused as to which formula to use for portfolio skew and kurtosis and how to use the same in the optimization problem. I would also like to know the options available regarding the software on which the optimization can be done.

Edit

Based on this post, we are able to include portfolio skewness, using the co-skewness matrix $M_3$, using a third-order Taylor series expansion, but how to also add in the minimization of portfolio skewness, $M_4$ (fourth-order Taylor expansion)?

$$\arg \max_w w^T\mu-\frac{1}{2}\gamma w^T\Sigma w+\frac{1}{6}\gamma^2 w^TM_3(w\otimes w)$$

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  • $\begingroup$ What are you are doing to optimize for mean and standard deviation? $\endgroup$ Nov 15 '13 at 14:49
  • $\begingroup$ I think mean and standard deviation optimization can be done in excel itself, however its the other two that are difficult can you suggest some method, also i am not so clear on the formulae, it would be of great help if someone could tell me or at least show me a decent place to find the formulae $\endgroup$
    – Sai
    Nov 16 '13 at 3:46
  • $\begingroup$ The mean - variance framework can be justified via a Taylor Expansion stopping after the second step. Skew and Kurtosis can be included by expanding the Taylor approximation of the CE. $\endgroup$
    – muffin1974
    Jul 3 '15 at 11:40

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