Multifactor Models and their Consistency with the ICAPM: Evidence from the European Stock Market

Date01 November 2015
Published date01 November 2015
Multifactor Models and their
Consistency with the ICAPM: Evidence
from the European Stock Market
Fabian T. Lutzenberger
University of Augsburg, Research Center Finance & Information Management and Institute of
Materials Resource Management, 86135 Augsburg, Germany
This paper conducts a European investigation of eight multifactor models that have
been previously tested using US data. Many results conrm the US evidence: Most
of the eight multifactor models investigated do a good job explaining the cross
section of our testing portfolios, but most models are not justiable by the
Intertemporal CAPM (ICAPM). Carharts fourfactor model shows the best
empirical performance and consistency with the ICAPM. Nevertheless, some results
counter the US evidence: Fama and Frenchs threefactor model is inconsistent
with the ICAPM and the models of Hahn and Lee (2006) and Koijen et al. (2010)
show low explanatory power.
Keywords: asset pricing, Europe, ICAPM, multifactor models, risk factors
JEL classification: G12
1. Introduction
The asset pricing literature is aware of at least three puzzles, or stylised facts, that one of
its classical theories, the CAPM of Sharpe (1964) and Lintner (1965), seems to be unable
to explain: (1) Small stocks (with low market capitalisation) seem to have higher average
returns than large stocks (Banz, 1981). (2) Value stocks (with a high ratio of book value
to price) tend to have higher average returns than growth stocks (e.g. Fama and
French, 1992). (3) Past winners (with high returns over the past year) seem to outperform
past losers (Jegadeesh and Titman, 1993). Fama and French (1993, 1996) show that a
threefactor model does a fairly good job of capturing empirical observations (1) and (2).
Their model includes a size factor, constructed as the difference between the returns on
diversied portfolios of small and big stocks, as well as a value factor that represents the
I extend my sincere appreciation to an anonymous referee, John A. Doukas (the editor),
Andreas W. Rathgeber, Stefan Stöckl, and Martin Wallmeier for their helpful comments.
The Internet Appendix to this paper is available at
European Financial Management, Vol. 21, No. 5, 2015, 10141052
doi: 10.1111/eufm.12050
© 2014 John Wiley & Sons Ltd
difference between the returns on diversied portfolios of value and growth stocks, in
addition to the market excess return. Carhart (1997) augments this model with a factor that
is constructed as the difference between the returns on diversied portfolios of stocks that
have done well over the past year and the losers of the past year. The resulting fourfactor
model seems to also work well in explaining the momentum anomaly, (3) (Fama and
French, 2012). A potential shortcoming of these two models is that the three factors added
to the market are essentially empirically motivated, whereas their theoretical foundation
and economic motivation is somewhat loose (e.g. see Fama and French, 2004, and Daniel
and Titman, 2012, for the FamaFrench model).
In more recent years, the nance literature has suggested a large variety of asset pricing
models that include other factors than those proposed by Fama and French and Carhart.
For example, Lewellen et al. (2010) list a set of recent models that include as factors
labour income; growth in macroeconomic output and investment; growth in luxury,
durable, and future consumption; innovations in assorted state variables; and liquidity
risk. In addition, Daniel and Titman (2012) provide a brief overview of recent models and
emphasise that many of them in contrast to the empirically motivated factors proposed
by Fama and French and Carhart include primarily economically motivated factors,
attempting to assess the underlying economic risks of the observed return patters with a
focus on the value effect, (2). The empirical tests conducted of these models suggest that
various proposed economic factors are able to explain the value effect, since the models
are generally not rejected. Further overviews are given by, for example, Subrahmanyam
(2010) and Goyal (2012).
But what is the economic theory behind the empirical success of these multifactor
models? One potential theoretical explanation is Mertons (1973) Intertemporal CAPM
(ICAPM). In particular, many factor models are explicitly justied by their authors as
empirical applications of the ICAPM (e.g. Brennan et al., 2004; Campbell and
Vuolteenaho, 2004; Hahn and Lee, 2006; Petkova, 2006). These models include risk
factors in addition to the excess market return that are innovations in economic variables
(e.g. in the shortterm riskfree rate) that seek to proxy for innovations in state variables in
the sense of Mertons theory. One might also argue that the empirically motivated factors
proposed by Fama and French and Carhart reect innovations in unidentied ICAPM
state variables (e.g. Fama and French, 1993, 2004). However, in a very recent paper, Maio
and SantaClara (2012, hereafter MSC) emphasise that the ICAPM places some
restrictions that must be satised by a multifactor model to be justiable by Mertons
theory. The authors empirically study eight multifactor models and conclude that most of
them do not, however, meet these conditions.
Overall, it seems that by now a bulk of various multifactor models exist and, as
Subrahmanyam (2010, p. 27) states,
The number of publications in the top journals avowing deviations from the standard asset
pricing models has mushroomed over the years and [one is] able to document at least fty
variables that the literature has used to predict stock returns in the crosssection, where the
crosssection essentially is the same familiar universe of NYSEAmexNasdaq stocks.
As the previous statement suggests, most studies that test multifactor asset pricing
models are conducted using US data only and evidence from other countries is sparse (e.g.
Asness et al., 2013). One potential pitfall of working with only US data might be data
snooping problems (e.g. Lo and MacKinlay, 1990). One might argue that the US evidence
© 2014 John Wiley & Sons Ltd
Multifactor Models and their Consistency 1015
of the good empirical performance of all these multifactor models is just the result of
chance. Therefore, it is important to know whether the results obtained within US samples
also hold for other stock markets. Such studies can serve as additional robustness checks
for asset pricing models. Moreover, differing performances of different asset pricing
models might be the result of dissimilar institutional settings and investor preferences. If
the test results diverge between markets, decision makers and regulation authorities who
use an asset pricing model for, for example, estimation of the cost of equity capital or
performance evaluation, must use a different model than US decision makers, that is, the
model that performs best within their respective market. Consequently, there is a clear
need for tests of asset pricing models using data from markets outside the USA, as noted
by, for example, Schrimpf et al. (2007) and Artmann et al. (2012a).
We try to ll this research gap to some extent by replicating a large part of MSCsUS
based study using a large sample of stocks from 16 European countries. These countries
account for, on average, 30% of global market capitalisation and represent the second
largest integrated stock market region (after North America), according to Fama and
French (2012). We choose the study of MSC for three reasons: First, the study includes
eight multifactor models of which ve, to the best of our knowledge, have never been
tested for the European stock market.
Second, by replicating this study we not only test
the empirical explanatory power of these models, but also the (potential) theory behind
them, that is, the ICAPM. None of the eight multifactor models, even the FamaFrench
and Carhart models, to the best of our knowledge, has ever been tested on its
consistency with the ICAPM using data from outside the USA. Third, as a side effect, the
study obtains comprehensive results on the timeseries predictability of the aggregate
European stock market using several macroeconomic, as well as empirically constructed
state variables.
In particular, we test the multifactor models of Pástor and Stambaugh (2003), Campbell
and Vuolteenaho (2004), Hahn and Lee (2006), Petkova (2006), and Koijen et al. (2010),
the FamaFrench threefactor model, the Carhart model, and the vefactor model of
Fama and French (1993). We test their ability to explain the crosssection of the average
excess returns on 25 portfolios sorted on size and booktomarket ratio (B/M) and on 25
portfolios sorted on size and momentum, in terms of factor signicance, Rsquared
values, and mean absolute pricing errors. Moreover, we test whether the eight models
under investigation meet the restrictions emphasised by MSC, which must be satised by
a multifactor model to be justiable as an application of the ICAPM.
Hence, we contribute to the literature by providing an outofsample test of MSCs
empirical results on European data. Similar results to those of MSC would strengthen their
conclusion that most multifactor models are inconsistent with the ICAPM, even though
Related papers are, for example, those of Asness et al. (2013; a threefactor model, diverse
markets and asset classes), Gregory et al. (2013; alternative versions of the FamaFrench and
Carhart models, the UK stock market), Fama and French (2012; the Carhart and FamaFrench
models, the international stock market), Wallmeier and Tauscher (2012; the FamaFrench
model, the European stock market), Artmann et al. (2012a, b; the Carhart and FamaFrench
models, the German stock market), Bauer et al. (2010; static and dynamic versions of the
FamaFrench model, the European stock market), Schrimpf et al. (2007; the FamaFrench
and conditional CAPM models, the German stock market), and Ziegler et al. (2007; the Fama
French models, the German stock market).
© 2014 John Wiley & Sons Ltd
1016 F. T. Lutzenberger

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