Higher‐moment Risk Exposures in Hedge Funds

• Author: M. Lambert,G. Hübner,N. Papageorgiou
• Published date: 01 March 2015
• Date: 01 March 2015
• DOI: http://doi.org/10.1111/eufm.12054

Higher‐moment 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 higher‐moment model

with location, trading, and higher‐moment factors to describe the dynamics of the

equity hedge, event‐driven, 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 co‐funded under the Marie Curie Actions of the European

Commission (FP7‐COFUND). All errors are our own. Correspondence: N. Papageorgiou

European Financial Management, Vol. 21, No. 2, 2015, 236–264

doi: 10.1111/eufm.12054

© 2014 John Wiley & Sons Ltd

Keywords: hedge funds, implied higher‐moments, conditioning factors

JEL classification: G10, G12

1. Introduction

The premise that many hedge fund strategies generate nonlinear payoffs resulting in

return distributions that exhibit significant higher‐order 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 financial derivatives, the

option‐like nature of hedge fund managers’compensation contracts, as well as the

inherent risks of hedge fund quasi‐arbitrage 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 option‐based 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 higher‐order 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 cross‐sectional 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 risk‐neutral

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 specification, 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

specification to hedge fund returns. In the same spirit, instead of introducing

contemporaneous risk premia, aiming to capture market‐wide skewness and kurtosis

risks, we focus on the anticipation of extreme market risks derived from option‐implied

higher moments. The reasoning is similar to that of implied volatility estimation, but

© 2014 John Wiley & Sons Ltd

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