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Markowitz Optimization

I've been having a play with the convex solver (if you haven't seen it yet it's in the tutorial notes in the research folder). However, for the optimum portfolio given a set of assets it always seems to return a portfolio consisting of a single asset and nothing else. Has anyone else encountered this/has a reason for why this is the case?

If you want to investigate take the backtest example in the tutorial notes and add a 'print weights' clause to see the weightings for the assets in the portfolio and have a play with using different assets.

3 responses

Look here

https://www.quantopian.com/posts/the-efficient-frontier-markowitz-portfolio-optimization-in-python-using-cvxopt

near/at the bottom for a Apr 18, 2015 update on an alternate formulation that will pick multiple assets.

Richard's example is good. The numerical optimizers used in Markowitz optimization are generally prone to weird values, and depend heavily on the exact formulation of the risk metric. Another reason could be that it's overfitting to a single asset in every time period. It is plausible that for sufficiently many assets, you will be able to find one whose risk profile far outstrips the others over a particular look-back window.

A final consideration is that Markowitz optimization is contested these days, with people suggesting it is a not really a profitable technique out of sample, and that it has been arbitraged away in current markets. It is in essence a momentum strategy -- you are betting that assets whose risk profiles were good recently will continue to be good in the future. Depending on timeframe of your strategy and the type of assets you are using, this may or may not be the case. It's important to take all this into consideration when using Markowitz optimization.

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Thank you Richard and Delaney, I will take a look at that.

I am aware that Markowitz optimization has been superseded by post-modern portfolio theory amongst other techniques, however I'm still learning and thought it might be a good starting point for my research. Ultimately at present I am aiming to integrate elements of PMPT along with MPT to try and create an improved variation on it.