New answers tagged optimization
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I think I understand your issue. Your weights are not uniformly distributed over the desired space. Instead you weights are bunched together, there are fewer extreme weights (weights close to 1) than there should be.
For example let's consider how often the 1st weight (or any other weight for that matter) should be between 0.8 and 1.0. Since the length of ...
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It's normal that it takes very long to come close to
the efficient frontier with random portfolios.
How close you come how fast will be strongly influenced
by how you sample the portfolios. In your code, you
sample uniformly. You may want to look at the weight
distributions of the portfolios on the frontier, and
then consider how likely it is that you arrive ...
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Not sure why you would seek to hit this via trial-and-error sampling in the first place.
By definition, the MinVar portfolio is the tangency / MaxSharpe portfolio if all the returns are assumed to be constant/equal. See pp.7-10 in e.g. https://faculty.washington.edu/ezivot/econ424/portfolioTheoryMatrix.pdf
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Why did you expect to hit the minimum variance portfolio in your simulations?
There are infinitely many vectors of size Nx1, such that the sum of its elements adds up to 1. Even with 1 million simulations, it is very difficult to hit the exact minimum variance allocation vector.
Moreover, your simulations might have hit some allocation vector "very near&...
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