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:

enter image description here

enter image description here

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

enter image description here

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.


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

| improve this answer | |
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.