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1

Hi: Footnote 15 of the paper at this link explains what the formulation is (in brief: it is based on the Sortino Ratio). It sounds like something that can be programmed as a quadratic optimization. R has a lot of facilities for doing that sort of thing. Addendum: I didn't read it but this paper provides a lot more detail than the one above.

3

The efficient frontier is defined as the set of portfolios which have the highest return for a given measure of volatility, i.e. $\{S: s \in P \; s.t. \nexists \; t \in P \; \text{where} \;R(s) < R(t) \; \text{and} \; \sigma(s)=\sigma(t) \}$, where $P$ is the set of all validly constructed portfolios. Therefore this also holds for the efficient frontier ...

0

Sorry to be the bearer of bad news, but this approach is not guaranteed to be the MinVol solution ;-( The problem is that the long weights are only MV and weighted thus alongside the shorts (which the model thinks it can short-sell to hedge). If you ignore the shorts, then the longs won't then be MV in isolation. There is probably a long-only portfolio with ...

1

While I'm sure there are applicable theories and optimization techniques out there about your other bullets--i.e., searching for 'warehouse space optimization' will undoubtedly yield many results, my answer is only speaking to your last bullet about stocks in a portfolio. For that example, I think some terms you may want to look into are Portfolio ...

2

You will have to add some constraints to get the weight vector of the eigen vector of the smallest eigen values, otherwise 0 is a trivial solution. Without going in the details of handling those extra constraints, the reason why the vector space associated with the smallest eigen value is relevant is because if you express variance of your portfolio in the ...

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