The Epstein–Zin Model with Liquidity Extension

Published date01 February 2016
AuthorWeimin Liu,Huainan Zhao,Di Luo
Date01 February 2016
The Financial Review 51 (2016) 113–146
The Epstein–Zin Model with Liquidity
Weimin Liu
Nottingham University Business School China and Shanxi University
Di Luo
Swansea University
Huainan Zhao
Cranfield University School of Management
In this paper, we extend the Epstein–Zin model with liquidity risk and assess the extended
model’s performance against the traditional consumption pricing models. We show that liq-
uidity is a significant risk factor, and it adds considerable explanatory powerto the model. The
liquidity-extended model produces both a higher cross-sectional R2and a smaller Hansen and
Jagannathan distance than the traditional consumption-based capital-asset pricing model and
the original Epstein–Zin model. Overall, we show that liquidity is both a priced factor and a
key contributor to the extended Epstein–Zin model’sgoodness-of-fit.
Keywords: liquidity risk, consumption-based asset pricing, model performance
JEL Classifications: G12, G14
Correspondingauthor: School of Management, Swansea University, Bay Campus, Fabian Way,Swansea,
SA1 8EN, United Kingdom; Tel: +44 1792606164; E-mail:
We thank Robert Van Ness (former Editor) and Richard Warr (Editor) and an anonymous referee for
their insightful comments and suggestions. Liu acknowledges financial support from the National Natural
Science Foundation of China (No. 11171372).
C2016 The Eastern Finance Association 113
114 W. Liu et al./The Financial Review 51 (2016) 113–146
1. Introduction
Recent studies in asset pricing suggest that liquidity plays a significant role in
investors’ consumption and investmentdecision making.1In this paper, we extend the
Epstein and Zin (1989, 1991) model with liquidity risk and show that consumption
risk, market risk, and liquidity risk jointly determine expected returns. Specifically,
using the liquidity risk factors of Pastor and Stambaugh (2003), Liu (2006), and Sadka
(2006), we show that liquidity risk is significantly priced, suggesting that investorsdo
care about the sensitivity of stock returns to market liquidity variations and demand
high compensation for holding stocks with large exposure to liquidity risk. This
evidence is consistent with recent literature that highlights the importance of liquidity
in asset pricing (e.g., Chordia, Roll and Subrahmanyam, 2000; Amihud, 2002; Pastor
and Stambaugh, 2003; Acharya and Pedersen, 2005; Liu, 2006; Sadka, 2006; Bekaert,
Harvey and Lundblad, 2007). However, prior studies largely examining whether
liquidity risk is priced related to models other than consumption based such as
the capital-asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) and
the Fama–French three-factor model (FF3FM). The main objective of this study
is to assess the incremental contribution of liquidity risk to the performance of
consumption-based pricing models.
Kan, Robotti and Shanken (2013) argue that examining whether a factor makes
an incremental contribution to a multifactor model’s goodness-of-fitis different from
testing whether the factor is priced.2They argue that, in a multifactor model, it is
important to test the significance of covariance risk (the covariance between return
and a risk factor). If the coefficient of the covariance is significantly different from
zero, then the factor makes an incremental contribution to the model’s overall ex-
planatory power. Following Lewellen, Nagel and Shanken (2010) and Kan, Robotti
and Shanken (2013),3we perform both the ordinary least squares (OLS) and gener-
alized least squares (GLS) regressions in our analysis. We findthat the coefficient of
the covariance between return and the liquidity risk factor is significant, indicating
an improved model. Furthermore, the liquidity-extended Epstein–Zin model explains
up to 70% of the cross-sectional expected returns on the 25 Fama and French (1993)
1For instance, Liu (2010) demonstrates that liquidity risk originates from consumption and solvency
constraints. Chien and Lustig (2010) and Pastor and Stambaugh (2003) also illustrate that liquidity
concerns stem from solvencyconstraints. Parker and Julliard (2005) argue that liquidity risk is an imperative
component ignored by consumption risk. Næs, Skjeltorp and Ødegaard (2011) find significant relation
between market liquidity and consumption growth.
2Cochrane (2005, Chapter 13) discusses a related issue in the stochastic discount factor (SDF) framework.
3Lewellen, Nagel and Shanken (2010) suggest that it is important to implement the GLS estimates besides
OLS. Kan, Robotti and Shanken (2013) argue that the OLS regression emphasizes more on the returns for
a particular set of test portfolios, while the GLS may be potentially more interesting from an investment
point of view.
W. Liu et al./The Financial Review 51 (2016) 113–146 115
value-weighted size and book-to-market portfolios, a substantial improvement com-
paring to previous studies.4
Sadka (2006) shows that incorporating liquidity risk into the traditional CAPM
or the FF3FM accounts for a large proportion of cross-sectional return variations. It
is, however, not clear whether the R2difference between competing models is sig-
nificant. Applying the equality test of cross-sectional R2(Kan, Robotti and Shanken,
2013), the null is rejected under both OLS and GLS estimates, indicating that the
liquidity-extended model is more successful in explaining the cross-sectional ex-
pected returns than the traditional CCAPM of Rubinstein (1976), Lucas (1978), and
Breeden (1979), and the Epstein–Zin (1989, 1991) model.
To further evaluate the model performance, we use Hansen and Jagannathan
(1997) distance (HJ distance hereafter) as an alternative measure of a model’s
goodness-of-fit. Weshow that, compared to the traditional CCAPM and the Epstein–
Zin model, our liquidity-extended Epstein–Zin model generates a smaller HJ distance
estimate. The null hypothesis that the squared HJ distances are equal is generally re-
jected based on the tests of Kan and Robotti (2009).
Lewellen, Nagel and Shanken (2010) argue that, for pricing tests, it is important
to include other sets of portfolios (e.g., industry portfolios) to break down the structure
of size and book-to-market portfolios.5Recent studies also highlight the importance of
the consumption-to-wealth ratio (Lettau and Ludvigson, 2001), long-run consumption
risk (Parker and Julliard, 2005; Malloy, Moskowitz and Vissing-Jørgensen, 2009),
and durable goods (Yogo, 2006; Gomes, Kogan and Yogo, 2009) in consumption-
based asset pricing. In our robustness tests, we take these issues into account and
find that both the liquidity risk premium and the coefficient of the covariance risk
between return and liquidity risk factor are significant. Again, the extended Epstein–
Zin model is more successful in explaining expected returns than the CCAPM and
the Epstein–Zin model based on the equality tests of cross-sectional R2and the HJ
We also examine the role of liquidity risk with nonconsumption-based asset
pricing models, namely, the CAPM, the FF3FM, and the Jagannathan and Wang
(1996) conditional CAPM (JW). Consistent with our previous results, we find that,
in general, liquidity risk is significantly priced, and the covariance risk of liquidity
contributes significantly to the model’s explanatory power.
One study that relates to ours is M´
arquez, Nieto and Rubio (2014) in which the
authors propose a liquidity-adjusted SDF. However, our model differs from theirs.
arquez, Nieto and Rubio (2014) assume a market illiquidity shock to consumption
4Lettau and Ludvigson (2001) show that the traditional consumption-based capital-asset pricing model
(CCAPM) explains only 16% of the cross-sectional return variations based on quarterly data. Jagannathan
and Wang (2007) findthat the CCAPM has almost no explanatory power based on monthly data.
5Recent studies of Savov(2011) and Kan, Robotti and Shanken (2013) also incorporate industry portfolios.
They use the 25 Fama–French size and book-to-market portfolios, plus industry portfolios, as test assets.

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