The Matrix Effective Rank: Measuring the Dimensionality of a Universe of Assets
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversificati...
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Beyond Hierarchical Risk Parity: Hierarchical Clustering-Based Risk Parity
In a previous post, I introduced the Hierarchical Risk Parity portfolio optimization algorithm1. See Lopez de Prado, M. (2016). Building dive...
Hierarchical Risk Parity: Introducing Graph Theory and Machine Learning in Portfolio Optimizer
In this short post, I will introduce the Hierarchical Risk Parity portfolio optimization algorithm, initially described by Marcos Lopez de Prado1, and recen...
Correlation Matrix Stress Testing: Shrinkage Toward an Equicorrelation Matrix
Financial research has consistently shown that correlations between assets tend to increase during crises and tend to decrease during recoveries1. ...
Residualization of Risk Factors: Examples and Pitfalls
The most common approach to measuring portfolio (risk) factor exposures is linear regression analysis, which describes the relationship between a dependent ...