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I am working through this paper, http://www.nber.org/papers/w8922.pdf

I want to implement the portfolio weight constraints see page 6-7.

Here is the brief overview of my problem:

Let w be the set of weights representing a portfolio. Then, mean-variance problem is to find the portfolio weights that minimizes portfolio variance, argmin w'Sw subject to w'I = 1 which represents weights sum up to 1 and S is the estimated covariance matrix.

In this framework, portfolio weights are constrained by lower and upper bounds such as:

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Then, the authors show that the following proposition is for the symmetric and positive semi-definite covariance matrix for the minimum global variance portfolios:

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Here new covariance matrix is the shrunk version of S. I am trying to implement this in Matlab. My question is therefore, is there a method to implement a constrained optimization such as this or any suggestions as to how I could go about doing this?

Thank you for suggestions.

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Try fmincon for solving (1)-(4).

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  • $\begingroup$ Thanks for your response. I will try it. Does it solve for when S in singular matrix. $\endgroup$ – user13895 Feb 7 '15 at 22:02
  • $\begingroup$ fmincon does not rely on matrix decomposition, so it shouldn't be a problem. $\endgroup$ – Phun Feb 8 '15 at 11:24

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