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Can anyone help to explain why when the square root market impact model is used in the standard mean-variance optimization, the exponent becomes $\frac{5}{3}$ in the objective function? I suspect this has to do with expressing market impact in different units but I could not find a clear explanation.

EDIT: Near the top of page 8, the authors state:

... show that the square root function is more appropriate for modelling market price impact, thus suggesting market impact costs grow at a rate slower than quadratic. Therefore in this section we consider the case with p ∈ (1, 2) in objective function (1).

https://pdfs.semanticscholar.org/b96d/c0273a25d27ab1aef9f8e300701f1689d738.pdf

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    $\begingroup$ Can you link to a textbook or lecture slides that show this? $\endgroup$
    – chrisaycock
    Jul 4, 2020 at 1:15
  • $\begingroup$ Can you show where they find $p=5/3$? I see where they consider $p\in(1,2)$, but I am not seeing any statement that $p=5/3$. Furthermore, cumulating impact with a square root impact function usually leads to something on the order of $x^{3/2}$, not $x^{5/3}$. $\endgroup$
    – kurtosis
    Jul 28, 2020 at 16:13

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