How to get the Minimum Variance Portfolio?

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I'm trying to build an investing strategy using the minimum variance criterion while imposing the equally-weighting constraint (1/n). Do you have any idea how to do so? Found this already : http://www.mathworks.com/matlabcentral/fileexchange/36159-global-minimum-variance-model-and-1-n-model-optimal-asset-allocation/content/GMV_and_1N_allocation.m

Answers (1)

Alejandra Pena-Ordieres
Alejandra Pena-Ordieres on 3 Dec 2021
Hi Jean-Gabriel,
I am not sure I fully understand the problem.
If you impose an equally-weighted "hard" constraint to the minimum variance portfolio problem, then the solution is the equally-weighted portfolio. This happens becasue the feasible region is constrained by the equality .
However, if you are thinking of a "soft" equally-weighted constraint, for which you penalize portfolios that deviate from the 1/n allocation, then you could solve a penalized portfolio problem to achive this. An example of that problem can be found in https://www.mathworks.com/help/finance/methods-for-diversification-of-portfolios.html under the Equally Weighted (EW) Portfolio section.
I hope this helps.
Alejandra

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