Maximum diversification strategies along commodity risk factors

Published date01 January 2018
Date01 January 2018
DOI: 10.1111/eufm.12122
Maximum diversification strategies along
commodity risk factors
Simone Bernardi
Markus Leippold
Harald Lohre
University of Zurich, Department of
Banking and Finance, Plattenstrasse 14,
8032 Zurich, Switzerland
Invesco Quantitative Strategies, An der
Welle 5, 60322 Frankfurt am Main,
Centre for Financial Econometrics,
Asset Markets and Macroeconomic
Policy, Lancaster University Management
School, Bailrigg, Lancaster LA1 4YX,
United Kingdom
Pursuing risk-based allocation across a universe of
commodity assets, we find diversified risk parity (DRP)
strategies to provide convincing results. DRP strives for
maximum diversificationalong uncorrelated risk sources.A
straightforward way to derive uncorrelated risk sources
relies on principal components analysis (PCA). While the
ensuing statisticalfactors can be associated with commodity
sector bets, the corresponding DRP strategy entails exces-
sive turnover because of the instability of the PCA factors.
We suggestan alternative design of the DRP strategyrelative
to common commodityrisk factors that implicitly allows for
a uniform exposure to commodity risk premia.
commodity strategies, diversification, risk-based portfolio construction,
risk parity
The authors are grateful to John A. Doukas (the Editor), two anonymous referees, Nicole Branger, Hsiu-Lang Chen,
Edward Cuipa, Serge Darolles, Günter Franke, Sean Geary, Fei Li, Didier Maillard, Attilio Meucci, Stefan Mittnik, Gianni
Pola, Yazid Sharaiha, and seminar participants at the 2016 Commodity Markets Conference in Hannover, the 2015
CEQURA Conference on Advances in Financial and Insurance Risk Management in Munich, the 2014 Workshop on
Determinants and Impact of Commodity Price Dynamics in Münster, the 13th Colloquium on Financial Markets at the CFR
Cologne, the 2013 Annual Workshop of the Dauphine-Amundi Chair in Asset Management at Paris Dauphine University,
and the Global Research Meeting of Invesco Quantitative Strategies for helpful comments and suggestions. Note that this
paper expresses the authorsviews that do not necessarily coincide with those of Invesco. The authors gratefully
acknowledge financial support from the Dauphine-Amundi Chair in Asset Management at the Paris Dauphine University,
from the Swiss Finance Institute (SFI), and Bank Vontobel.
Eur Financ Manag. 2018;24:5378. © 2017 John Wiley & Sons, Ltd.
Commodity investing is often suggested for diversifying traditional stock-bond portfolios for
example, there is empirical evidence of negative correlation between stocks and commodities during
stock market downturns, which makes commodities a perfect hedging instrument, see Bodie and
Rosansky (2000). However, while there is plenty of evidence that adding commodities to an existing
stock-bond portfolio can enhance its risk-return profile, there is less research on the diversification
potential inherent within the universe of commodity assets.
From a pure return perspective, Erb and Harvey (2006) document that the average annual
excess return of individual commodity futures has historically been approximately zero. Hence,
static long-only investments in commodities may not be necessarily profitable. In addition, the
inherent heterogeneity within this asset class, paired with high volatility and excess kurtosis, very
often offsets any positive average return. On the other side, the same authors document abnormal
returns for specific combinations of commodities, which exhibit a forward curve with attractive
term structure characteristics. To derive profitable commodity trading strategies, one should thus
resort to momentum or commodity-term structure signals, see Fuertes, Miffre, and Rallis (2010).
Recently, Fuertes, Fernandez-Perez, and Miffre (2016) document abnormal returns when trading
long low-idiosyncratic volatility positions versus the high ones, thus evidencing an inverse risk-
return relationship as prevailing in equities.
We contribute to the literature by devising optimally diversified commodity portfolios along
these commodity risk factors. As evidenced by Erb and Harvey (2006), diversification is key in
generating performance in commodities. The standard approach to exploiting diversification
benefits is to follow the classic mean-variance approach of Markowitz (1952) to optimally trade-
off assets risk and return. Yet, despite the heterogeneity of commodity markets and the low pair-
wise correlations across different commodity sectors, the ensuing portfolio construction will most
likely be confounded by the estimation risk, especially the one for estimating expected returns.
More recently, in pursuit of better diversified portfolios, alternative risk-based allocation
techniques have become popular. Qian (2006, 2011) and Maillard, Roncalli, and Teiletche (2010)
advocate the risk parity approach that allocates capital such that all assets contribute equally to
portfolio risk.
The common rationale of all the above approaches is diversification. Still, diversification is a rather
elusive concept, which is hardly made explicit in portfolio optimisation studies. A notable exception,
however, is Meucci (2009). Striving for diversification, he pursues principal component analysis
(PCA) to extract uncorrelated risk sources inherent in the underlying assets. The resulting eigenvectors
represent linear combinations of the underlying assets and are thus commonly referred to as principal
For a portfolio to be well-diversified, its overall risk should be evenly distributed across
these principal portfolios.
Recently, Lohre, Opfer, and Ország (2014) have adopted the framework of Meucci (2009) to
determine maximum diversification portfolios in a multi-asset allocation study. Their strategy
coincides with a risk parity strategy that allocates risk by principal portfolios rather than by the
See among others Kat and Oomen (2007) for an overview. Also, see Miffre (2016) for a recent survey for the literature on
long-short commodity investing.
See also Ang, Hodrick, Xing, and Zhang (2006).
Partovi and Caputo (2004) have coined the term principal portfolios when recasting the efficient frontier in terms of these
principal portfolios.

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