# Tag Info

1

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: ...

2

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 ...

2

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 ...

0

Just keep in mind that Gaussian marginals with Gaussian copula is nothing more than the multivariate Gaussian distribution (details e.g. here). For t-marginals with t-copula (with the same degree of freedom) you get the multivariate t-distribution. Both multivariate distributions are characterized by their covariance matrix. The t-distribution has the ...

2

You can express the Normal distribution by Sklar's Theorem in terms of Gaussian Marginals and Gaussian Copula as follows: $$F(x_1,...,x_n)=C(F(x_1),...,F(x_n))=C^{Gau}(N(x_1),...,N(x_n))$$ So the distribution equals the copula function with the respective inverse marginals as arguments. You can aswell combine any types of Copula and (continuous) different ...

0

What you refer to multiperiod optimization can also be classified under dynamic programming. You need to write a recursion (which can be nauseating at first) and any optimization function in R would do a nice job, if your problem is not too big. For the second part, you may search for some sensitivity analysis literature but I am not totally sure about ...

0

PortfolioAnalytics, has the ability to optimize portfolios based on factors or whatever groups/characteristics you enter. https://r-forge.r-project.org/R/?group_id=579 Please refer to the vignette in the package in the package PortfolioAnalytics (https://r-forge.r-project.org/scm/viewvc.php/pkg/PortfolioAnalytics/vignettes/?root=returnanalytics I use it ...

0

I wouldn't say 1) is better because it's very rigid. If you want to include some higher moments (most likely you won't need more than 4th order), it's better to do it explicitly rather than to stuff the moments of all orders into the criterion.

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