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Heirarchical Clustering

The document discusses hierarchical risk parity (HRP) as a novel portfolio diversification technique that addresses the complexities of correlation matrices in asset allocation. HRP allows for effective portfolio construction even with ill-degenerated covariance matrices, outperforming traditional optimization methods. The author highlights the limitations of conventional portfolio strategies and the advantages of HRP in achieving superior risk-adjusted returns.

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R Gamzo
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10 views1 page

Heirarchical Clustering

The document discusses hierarchical risk parity (HRP) as a novel portfolio diversification technique that addresses the complexities of correlation matrices in asset allocation. HRP allows for effective portfolio construction even with ill-degenerated covariance matrices, outperforming traditional optimization methods. The author highlights the limitations of conventional portfolio strategies and the advantages of HRP in achieving superior risk-adjusted returns.

Uploaded by

R Gamzo
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Hierarchical Clustering-Based

Asset Allocation
Thomas Raffinot

N
T homas R affinot obel Pr ize winner Harr y offset the benefits of diversification (López
is the Head of Quantitative Markowitz described diversifi­ de Prado [2016b]).
Macro Strategy at Silex-IP
cation, with its ability to enhance Exploring a new way of capital allo-
in Paris, France.
traffinot@gmail.com portfolio returns while reducing cation, López de Prado [2016a] introduces
risk, as the “only free lunch” in investing a portfolio diversification technique called
(Markowitz [1952]). Yet, diversifying a port- hierarchical risk parity (HRP). One of the
folio in real life is easier said than done. main advantages of HRP is in computing
Investors are aware of the benefits of a portfolio on an ill-degenerated or even a
diversification but form portfolios without singular covariance matrix. Lau et al. [2017]
giving proper consideration to the corre- apply HRP to different cross-asset universes
lations (Goetzmann and Kumar [2008]). consisting of many tradable risk premia
Moreover, modern and complex port- indexes and conf irm that HRP delivers
folio optimization methods are optimal in superior risk-adjusted returns. Alipour et al.
sample but often provide rather poor out-of- [2016] propose a quantum-inspired version
sample forecast performance. For instance, of HRP, which outperforms HRP and thus
DeMiguel et al. [2009] demonstrate that other conventional methods.
the equal-weighted allocation, which gives The starting point of HRP is that a cor-
the same importance to each asset, beats the relation matrix is too complex to be prop-
entire set of commonly used portfolio opti- erly analyzed and understood. If you have
mization techniques. In fact, optimized port- 1
N assets of interest, there are N ( N − 1)
folios depend on expected returns and risks, 2
but even small estimation errors can result in pairwise correlations among them and that
large deviations from optimal allocations in number grows quickly. For example, there
an optimizer’s result (Michaud [1989]). are as many as 4,950 correlation coefficients
To overcome this issue, academics between stocks of the FTSE 100 and 124,750
and practitioners have developed risk-based between stocks of the S&P 500. More impor-
portfolio optimization techniques (min- tantly, correlation matrices lack the notion
imum variance, equal-risk contribution, risk of hierarchy. Actually, Nobel Prize laureate
budgeting, etc.) that do not rely on return Herbert Simon has argued that complex sys-
forecasts (Roncalli [2013]). However, these tems can be arranged in a natural hierarchy
still require the inversion of a positive- comprising nested substructures (Simon
definite covariance matrix, which leads to [1962]). But, a correlation matrix makes no
errors of such magnitude that they entirely differentiation between assets. Yet, some

Multi-A sset Special Issue 2018 The Journal of Portfolio M anagement    89

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