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There's more than one way to do this. One common approach among indices is to take an iterative approach. For instance, you might identify the stocks with weights about 5%, then re-weight so that everything adds up to 1. Then you might identify the sectors that break the 10% limit and re-scale them to be less than 10%. Then re-scale everything to add up to ...


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Simple, if you're investing in Equities, you have a negative skew, decrease the variance and that will decrease the number of hits you take. Returns are on a log normal scale so, if you have two equal but opposite moves you will still be down money. E.g. If I have 100 dollars and I lose ten percent and then make ten percent, I will still be down one percent. ...


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OK one thing that comes to my mind is the standard trick to reformulate constraints like $|x_i|<=c$ (limiting exposure of $x_i$ while still allowing negative weights). Notice, that $|x_i| \leq c$ is not a linear constraint, so the solver wont work in this case. A little trick can help: You split up the variables into positive and negative parts: ...


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I assume you're talking about this formula: $$U(w) = w'\mu - \frac{1}{2} \lambda w' \Sigma w = w'\mu - \frac{1}{2} \lambda \sigma_\omega^2$$ where $\sigma_\omega^2$ denotes the portfolio variance for a portfolio with weights $\omega$. Dividing by two is purely done for convenience, optimizing this formula requires taking the derivative with respect to ...


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If you have a vector of weights $w=(w_1,\ldots,w_n)^T$ then $(1,\ldots,1)* w = \sum_{i=1}^n w_i$ thus a sum condtion can be formulated by multiplication with a row of ones. A $\le$ can be put into an $\ge$ by multiplying with $(-1)$ and if you have to put all your constraints into on $A$ then you usually stack all the row vectors together. In your case the ...



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