Introduction To Schur Complementary Portfolios

Introduction To Schur Complementary Portfolios

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Let’s introduce “Schur Complementary Portfolios” to unify Modern Portfolio Theory and Machine Learning methodology.

I summarize Hierarchical Risk Parity (HRP) developed by Marcos Lopez de Prado – which has been called “one of the biggest breakthroughs in applying Machine Learning portfolio optimization.”

There is one main advantage and one main disadvantage of HRP. The advantage, compared to a single global optimization in the style of Markowitz, is that you avoid inverting a matrix that is noisy and rank-deficient. The disadvantage is that you throw away a lot of information in the covariance matrix.

I introduce a new family of recursive allocation methodologies that are HRP-inspired (they are top-down and borrow Lopez de Prado’s idea for reordering of assets) but are characterized by a financially motivated augmentation of covariance sub-matrices and thus, I believe, a more strongly motivated splitting step.

This unifying viewpoint emphasizes the similarity between top-down portfolio construction and optimization, rather than the difference. It allows the user to deal with very high dimensional problems and rank-deficiency, yet still move “back in the direction of optimization”, should they wish to.

It is very new, and I”m sure will benefit from your experimentation and feedback. Like HRP, it could also be used for model ensembles, mixtures of experts, and in any other setting where we sometimes throw our hands in the air and use 1/n weights.

Article: Schur Complementary Portfolios — A Unification of Machine Learning and Optimization-Based Allocation | by Microprediction | Geek Culture | Nov, 2022 | Medium

Code docs: Precise Package Documentation | precise (microprediction.github.io)

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Introduction To Schur Complementary Portfolios