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

• Date: 01 November 2015
• Author: Fabian T. Lutzenberger
• DOI: http://doi.org/10.1111/eufm.12050
• Published date: 01 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

E-mail: fabian.lutzenberger@fim-rc.de

Abstract

This paper conducts a European investigation of eight multifactor models that have

been previously tested using US data. Many results confirm 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 justifiable by the

Intertemporal CAPM (ICAPM). Carhart’s four‐factor model shows the best

empirical performance and consistency with the ICAPM. Nevertheless, some results

counter the US evidence: Fama and French’s three‐factor 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

three‐factor 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

diversified 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 http://fabian‐lutzenberger.de/

EFM_appendix.pdf.

European Financial Management, Vol. 21, No. 5, 2015, 1014–1052

doi: 10.1111/eufm.12050

© 2014 John Wiley & Sons Ltd

difference between the returns on diversified 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 diversified portfolios of stocks that

have done well over the past year and the losers of the past year. The resulting four‐factor

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 Fama–French model).

In more recent years, the finance 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 Merton’s (1973) Intertemporal CAPM

(ICAPM). In particular, many factor models are explicitly justified 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 short‐term risk‐free rate) that seek to proxy for innovations in state variables in

the sense of Merton’s theory. One might also argue that the empirically motivated factors

proposed by Fama and French and Carhart reflect innovations in unidentified ICAPM

state variables (e.g. Fama and French, 1993, 2004). However, in a very recent paper, Maio

and Santa‐Clara (2012, hereafter MSC) emphasise that the ICAPM places some

restrictions that must be satisfied by a multifactor model to be justifiable by Merton’s

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 fifty

variables that the literature has used to predict stock returns in the cross‐section, where the

cross‐section essentially is the same familiar universe of NYSE–Amex–Nasdaq 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 fill this research gap to some extent by replicating a large part of MSC’sUS‐

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 five, to the best of our knowledge, have never been

tested for the European stock market.

1

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 Fama–French

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 time‐series 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 Fama–French three‐factor model, the Carhart model, and the five‐factor model of

Fama and French (1993). We test their ability to explain the cross‐section of the average

excess returns on 25 portfolios sorted on size and book‐to‐market ratio (B/M) and on 25

portfolios sorted on size and momentum, in terms of factor significance, R‐squared

values, and mean absolute pricing errors. Moreover, we test whether the eight models

under investigation meet the restrictions emphasised by MSC, which must be satisfied by

a multifactor model to be justifiable as an application of the ICAPM.

Hence, we contribute to the literature by providing an out‐of‐sample test of MSC’s

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

1

Related papers are, for example, those of Asness et al. (2013; a three‐factor model, diverse

markets and asset classes), Gregory et al. (2013; alternative versions of the Fama–French and

Carhart models, the UK stock market), Fama and French (2012; the Carhart and Fama–French

models, the international stock market), Wallmeier and Tauscher (2012; the Fama–French

model, the European stock market), Artmann et al. (2012a, b; the Carhart and Fama–French

models, the German stock market), Bauer et al. (2010; static and dynamic versions of the

Fama–French model, the European stock market), Schrimpf et al. (2007; the Fama–French

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