Mean-Variance Optimization in Practice: Well Diversified (Near) Efficient Portfolios
One well-known stylized fact of the Markowitz’s mean-variance framework is that, irrespective of the quality of the estimates of asset returns and (co)varian...
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Ulcer Performance Index Portfolio Optimization
The Ulcer Performance Index1 (UPI) is a portfolio reward-risk measure introduced by G. Martin2 similar in spirit to the Sharpe Ratio, but using the Ulcer In...
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...
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...