Higher‐moment Risk Exposures in Hedge Funds

Published date01 March 2015
Date01 March 2015
DOIhttp://doi.org/10.1111/eufm.12054
Highermoment Risk Exposures in
Hedge Funds
G. Hübner
HEC Management School, University of Liège, Belgium; School of Business and Economics, Maastricht
University, the Netherlands; Gambit Financial Solutions, Belgium
E-mail: g.hubner@ulg.ac.be
M. Lambert
HEC Management School, University of Liège, Belgium
E-mail: marie.lambert@ulg.ac.be
N. Papageorgiou
HEC Montreal and HR Strategies. Mailing address: 3000 Cote Ste Catherine, Montreal, Quebec,
Canada H3T2A7
E-mail: nicolas.papageorgiou@hec.ca
Abstract
This paper singles out the key roles of US equity skewness and kurtosis in the hedge
fund return generating process. We propose a conditional highermoment model
with location, trading, and highermoment factors to describe the dynamics of the
equity hedge, eventdriven, relative value, and fund of funds styles. If the volatility,
skewness, and kurtosis implied in US options are used by fund managers as
instruments to anticipate market movements, managers should adjust their market
exposure in response to variations in these moments. We indeed show that higher
moment premia improve the conditional asset pricing model across all hedge fund
styles.
We gratefully acknowledge very constructive comments by John Doukas (the editor) and
three anonymous referees. This paper has also benefitted from comments by Daniel Capocci,
Antonio Cosma, Mark Geene, Pierre Armand Michel, Aline Muller, Joël Petey, Christian
Wolff as well as the Luxembourg School of Finance seminar participants. The authors would
like to thank the participants to the European Financial Management symposium on asset
management 2012 (Germany), the 4
th
Annual Hedge Fund Research Conference (2012,
Paris), the French Finance Association annual meeting 2011 (Montpellier, France), the
European Financial Management symposium on alternative investments 2011 (Toronto, CA),
the Augustin Cournot Doctoral Days 2010 (Strasbourg, France),and the 2006 EDHEC Hedge
Fund Days (London) for helpful comments. Georges Hübner thanks Deloitte (Belgium and
Luxembourg) for financial support. The presentproject is supported by the National Research
Fund, Luxembourg and cofunded under the Marie Curie Actions of the European
Commission (FP7COFUND). All errors are our own. Correspondence: N. Papageorgiou
European Financial Management, Vol. 21, No. 2, 2015, 236264
doi: 10.1111/eufm.12054
© 2014 John Wiley & Sons Ltd
Keywords: hedge funds, implied highermoments, conditioning factors
JEL classification: G10, G12
1. Introduction
The premise that many hedge fund strategies generate nonlinear payoffs resulting in
return distributions that exhibit signicant higherorder moments has been substantiated
by a number of papers since the late 1990s (Fung and Hsieh, 1997; Ackermann
et al., 1999; Agarwal et al., 2009). The use of leverage and nancial derivatives, the
optionlike nature of hedge fund managerscompensation contracts, as well as the
inherent risks of hedge fund quasiarbitrage strategies contribute to the negative skewness
and fat tails of many of the fund return distributions.
An extensive stream of literature has favoured the inclusion of optionbased factors to
capture the nonlinear dependencies of hedge funds on market returns (e.g. Agarwal and
Naik, 2001, 2004; Fung and Hsieh, 2001, 2002a, 2002b; 2004a, 2004b; Li and
Kazemi, 2007; Liang and Park, 2007). Alternatively, a number of authors relate these
nonlinearities to their exposure to the higherorder moments of the US equity market. For
instance, Ding and Shawky (2007) use the levels of variance, skewness, and kurtosis of
the US markets to capture systematic exposure to higher moments of hedge funds. Using
an approach similar to that used by Fama and French (1993) for size and book to market,
Kat and Miffre (2006) and Agarwal et al. (2009) form empirical premia based on a
portfolio sort of, respectively, US stocks and hedge funds at different levels of covariance,
coskewness, and cokurtosis with the US market portfolio. Such premia are shown to
improve the explanatory power of multifactor models for hedge funds.
Our paper takes a different view to extend this stream of literature on higher moments to
hedge funds. It focuses on how the use of information on higher moments gathered from
the option markets can improve our understanding of hedge fund returns. As in Dennis
and Mayhew (2002) and An et al. (2014), we believe that option volatilities and higher
moments can predict the cross section of future returns. An et al. (2014) indeed documents
the crosssectional predictability from stock to option returns and from option to stock
returns. Bali and Murray (2013) further support the pricing of risk neutral skewness in
stock returns. They constructed a skewness asset that only captures skewness exposure
and displays zero exposure to change in the underlying security price and to change in
implied volatilities combining positions in options and the underlying security. They
show that this asset return can be explained by a strong negative relation with riskneutral
skewness. Besides, we associate the documented active usage of derivative trading
strategies by hedge fund managers for speculative purposes (Aragon and Martin, 2012) to
their propensity to tactically use the implied stock return density contained in option
prices. A conditional asset pricing specication, similar to that of Ferson and Schadt
(1996), makes it possible to account for informed trading by hedge fund managers
through instruments driven by the option market, such as an implied volatility index (for
an application, see e.g. Brown et al., 2009). Gregoriou (2004) successfully applies this
specication to hedge fund returns. In the same spirit, instead of introducing
contemporaneous risk premia, aiming to capture marketwide skewness and kurtosis
risks, we focus on the anticipation of extreme market risks derived from optionimplied
higher moments. The reasoning is similar to that of implied volatility estimation, but
© 2014 John Wiley & Sons Ltd
Highermoment Risk Exposures in Hedge Funds 237

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