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abstract={Hierarchical Risk Parity (HRP) is a risk-based portfolio optimisation algorithm, which has been shown to generate diversified portfolios with robust out-of-sample properties without the need for a positive-definite return covariance matrix (Lopez de Prado 2016). The algorithm applies machine learning techniques to identify the underlying hierarchical correlation structure of the portfolio, allowing clusters of similar assets to compete for capital. The resulting allocation is both well-diversified over risk sources and intuitively appealing. This paper proposes a method of fully exploiting the information created by the clustering process, achieving enhanced out-of-sample risk and return characteristics. In addition, a practical approach to calculating HRP weights under box and group constraints is introduced. A comprehensive set of portfolio simulations over 6 equity universes demonstrates the appeal of the algorithm for portfolios consisting of 20 - 200 assets. HRP delivers highly diversified allocations with low volatility, low portfolio turnover and competitive performance metrics.},
abstract={This article develops the theory of risk budgeting portfolios, when we would like to impose weight constraints. It appears that the mathematical problem is more complex than the traditional risk budgeting problem. The formulation of the optimization program is particularly critical in order to determine the right risk budgeting portfolio. We also show that numerical solutions can be found using methods that are used in large-scale machine learning problems. Indeed, we develop an algorithm that mixes the method of cyclical coordinate descent (CCD), alternating direction method of multipliers (ADMM), proximal operators and Dykstra's algorithm. This theoretical body is then applied to some investment problems. In particular, we show how to dynamically control the turnover of a risk parity portfolio and how to build smart beta portfolios based on the ERC approach by improving the liquidity of the portfolio or reducing the small cap bias. Finally, we highlight the importance of the homogeneity property of risk measures and discuss the related scaling puzzle.},
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keywords={},
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doi={},
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@article{Prado2,
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publisher={American Physical Society (APS)},
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author={Barfuss, Wolfram and Massara, Guido Previde and Di Matteo, T. and Aste, Tomaso},
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year={2016},
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month={Dec} }
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month={12}
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}
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@book{MLforAM,
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place={Cambridge},
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publisher={Cambridge University Press},
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author={López de Prado, Marcos M.},
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year={2020},
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collection={Elements in Quantitative Finance}}
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collection={Elements in Quantitative Finance}
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}
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@article{Cajas3,
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doi = {10.2139/ssrn.3988927},
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publisher = {Elsevier {BV}},
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author = {Sander Gerber and Harry Markowitz and Philip Ernst and Yinsen Miao and Babak Javid and Paul Sargen},
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title = {The Gerber Statistic: A Robust Co-Movement Measure for Portfolio Optimization},
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journal = {{SSRN} Electronic Journal}
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journal = {SSRN Electronic Journal},
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}
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@article{Cajas4,
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publisher = {Elsevier {BV}},
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author = {Dany Cajas},
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title = {Portfolio Optimization of Relativistic Value at Risk},
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journal = {{SSRN} Electronic Journal}
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4378498},
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}
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@article{Cajas6,
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publisher = {Elsevier {BV}},
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author = {Dany Cajas},
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title = {Higher Order Moment Portfolio Optimization with L-Moments},
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journal = {{SSRN} Electronic Journal}
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4393155},
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}
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@article{Cajas7,
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author = {Dany Cajas},
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year = {2023},
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month = {6},
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pages = {},
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title = {Approximation of Portfolio Kurtosis through Sum of Squared Quadratic Forms},
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4472793},
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author = {Dany Cajas},
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year = {2023},
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month = {8},
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pages = {},
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title = {On the Spectral Decomposition of Portfolio Skewness and its Application to Portfolio Optimization},
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4540021},
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author = {Dany Cajas},
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year = {2023},
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month = {9},
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pages = {},
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title = {Portfolio Optimization of Brownian Distance Variance},
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4540021},
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author = {Dany Cajas},
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year = {2023},
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month = {10},
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pages = {},
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title = {A Graph Theory Approach to Portfolio Optimization},
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journal = {SSRN Electronic Journal},
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doi = {10.2139/ssrn.4602019},
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}
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@article{Cajas11,
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author = {Dany Cajas},
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year = {2023},
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month = {12},
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pages = {},
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title = {A Graph Theory Approach to Portfolio Optimization Part II},
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