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Machine learning with Marcos López de Prado

At Global Derivatives in May 2016 you presented on building diversified portfolios that outperform out-of-sample. Can you provide a snapshot of what you presented?

I’ll introduce the Hierarchical Risk Parity (HRP) approach. HRP portfolios address three major concerns of quadratic optimizers in general and Markowitz’s CLA in particular: instability, concentration and under-performance. HRP applies modern mathematics (graph theory and machine learning techniques) to build a diversified portfolio based on the information contained in the covariance matrix. However, unlike quadratic optimizers, HRP does not require the invertibility of the covariance matrix. In fact, HRP can compute a portfolio on an ill-degenerated or even a singular covariance matrix, an impossible feat for quadratic optimizers. Monte Carlo experiments show that HRP portfolios beat CLA and standard risk-parity method out-of-sample.

Why is machine learning and graph theory an important tool for quants?

Financial markets are complex adaptive systems. Econometric models are too simplistic to capture this complexity. When you think about it, why would an investor be able to extract a profit from another by applying a 200 year old technology, like least-square estimation? In order to beat the market, an investor needs to apply more advanced technologies than the market’s standard. On the other hand, machine learning methods are able to recognize complex patterns, and have been successfully used in difficult problems, like face and speech recognition, natural language programming and context analysis. They also have an embedded logic to learn from past errors, which allows them to adapt with the market.

With regards to graph theory: Mean-variance optimization treats all variables as interrelated, like in a complete graph, where there is an edge connecting any two nodes. In other words, traditional portfolio construction does not recognize the hierarchy of the data. For example, some variables are more closely related than others, and should be modelled jointly as clusters. That’s the reason why asset allocation is typically done top-down or bottom-up, because humans recognize these hierarchies intuitively. Graph theory allows investors to incorporate those hierarchies in their models, making them more structured and robust.

What can delegates learn from HRP that they possibly did not know before?

The fundamental problem with standard portfolio construction methods is the so called “Markowitz’s curse”: The more correlated the investments, the greater the need for diversification, and yet the more likely we will receive unstable solutions. The benefits of diversification often are more than offset by estimation errors. Attendees will learn the reason for Markowitz’s curse, and how to avoid it. The implication is that Sharpe ratios can be improved by about 40% out-of-sample compared to standard mean-variance optimization methods.


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