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:
w be the set of weights representing a portfolio. Then, mean-variance problem is to find the portfolio weights that minimizes portfolio variance,
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:
Then, the authors show that the following proposition is for the symmetric and positive semi-definite covariance matrix for the minimum global variance portfolios:
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.