DEPARTMENT OF ACCOUNTING AND FINANCE
Are extreme returns priced in the stock market?
European evidence
Jan Annaert, Marc De Ceuster & Kurt Verstegen
UNIVERSITY OF ANTWERP
Faculty of Applied Economics
Stadscampus
Prinsstraat 13, B.226
BE-2000 Antwerpen
Tel. +32 (0)3 265 40 32
Fax +32 (0)3 265 47 99
http://www.ua.ac.be/tew
FACULTY OF APPLIED ECONOMICS
DEPARTMENT OF ACCOUNTING AND FINANCE
Are extreme returns priced in the stock market?
European evidence
Jan Annaert, Marc De Ceuster & Kurt Verstegen
RESEARCH PAPER 2012-018
SEPTEMBER 2012
University of Antwerp, City Campus, Prinsstraat 13, B-2000 Antwerp, Belgium
Research Administration – room B.226
phone: (32) 3 265 40 32
fax: (32) 3 265 47 99
e-mail: joeri.nys@ua.ac.be
The papers can be also found at our website:
www.ua.ac.be/tew (research > working papers) &
www.repec.org/ (Research papers in economics - REPEC)
D/2012/1169/018
Are extreme returns priced in the stock market?
European evidence
*
Jan Annaert
(Corresponding author)
University of Antwerp & Antwerp Management School
Prinsstraat 13 – 2000 Antwerp – Belgium
Tel.: +32 (0) 3 265 41 63 – E-mail: jan.annaert@ua.ac.be
Marc De Ceuster
University of Antwerp & Antwerp Management School
Prinsstraat 13 – 2000 Antwerp – Belgium
Tel.: +32 (0) 3 265 41 24 – E-mail: marc.deceuster@ua.ac.be
Kurt Verstegen
University of Antwerp
Prinsstraat 13 – 2000 Antwerp – Belgium
Tel.: +32 (0) 3 265 41 20 – E-mail: kurt.verstegen@ua.ac.be
This draft: September 2012
Abstract
This paper revisits some recently found evidence in the literature on the cross-section of stock returns
for a carefully constructed dataset of euro area stocks. First, we find evidence of a negative cross-
sectional relation between extreme positive returns and average returns after controlling for
characteristics such as momentum, book-to-market, size, liquidity and return reversal. We argue that
this is the case because these stocks have lottery-like characteristics. Second, when we control for this
relation, the idiosyncratic volatility puzzle seems to disappear. When extreme positive returns are
included in the regression, we find a weak but positive relation between idiosyncratic volatility and
returns. Lastly, the maximum return effect holds when we control for skewness. Moreover, skewness
is on its own negatively related to returns in our sample, as several asset pricing models predict.
JEL classification: G12, G17, G15
Keywords:
extreme returns, cross-section of expected returns, lottery-like payoffs, skewness, idiosyncratic
volatility puzzle
*
We would like to thank the participants of the Belgian Financial Research Forum 2012 and the Portuguese Finance Network 2012
conferences for their comments. In particular, we would like to thank Piet Sercu, Marc Deloof, Chris Degroof and Thorsten Lehnert for their
valuable input. Lastly, we would like to thank KBC Group for its support.
1
1 Introduction
Despite decades of research, it is still not completely clear what determines cross-sectional variation
in expected stock returns. It is well accepted that the three factor model of Fama and French (1993)
goes a long way in capturing this return variation. Efforts have been made to interpret these factors as
fundamental risk factors, making the model consistent with rational asset pricing, see e.g., Aretz,
Bartram, and Pope (2010) or Guo, Savickas, Wang, and Yang (2009). Nevertheless, empirical evidence
keeps discovering other characteristics that are related to average stock returns (see Fama and French
(2008) for a recent overview). As most of these characteristics do not follow directly from theory, they
are subject to the data-mining critique implying the patterns are mere statistical flukes (Lo &
MacKinlay, 1990). In any dataset, some significant statistical results are bound to be found just by
chance. One way to address this critique is to look for corroborating evidence on other markets or
from other periods.
In this paper, we verify the U.S. results of Bali, Cakici, and Whitelaw (2011) on a carefully constructed
euro area stock market database covering more than thirty years. More specifically, Bali et al. (2011)
find a statistically and economically significantly negative relation between the maximum daily return
over the past one month and expected stock returns. They argue that this captures individual
investors’ preference for lottery-like stocks, i.e. stocks that have a low probability of a huge profit and
a large probability of a small loss as shown by Kumar (2009). Although this is an idiosyncratic
characteristic, demand by individual investors may lead to higher prices (and lower expected returns)
for these stocks, given that these investors typically hold under-diversified portfolios, see e.g., Odean
(1999) and Goetzmann and Kumar (2008). We show that this effect also exists in the euro area.
Moreover, it is unlikely to be arbitraged away by large investors as the typical stock with extreme
positive returns is relatively small, illiquid and has relatively high idiosyncratic volatility. Even when
short selling these stocks were possible, it would expose arbitrageurs to considerable risk. Hence, it is
plausible that individual investors drive the pricing of such stocks. We do not find evidence for the
inverse relationship: extreme negative returns are not positively related to expected returns. As only
long positions are needed to trade on this pattern, it may be that demand from institutional investors
weakens the effect on extreme negative returns.
We also disentangle the comovement between extreme returns and idiosyncratic volatility. Taken on
its own, idiosyncratic volatility is negatively related to expected returns. The relation is statistically
significant and goes in the direction of the puzzling results of Ang, Hodrick, Xing, and Zhang (2006) for
the U.S. and Ang, Hodrick, Xing, and Zhang (2009) for an international sample of stocks. However,
when we control for extreme returns, the relation between idiosyncratic risk and expected returns
becomes positive, albeit insignificant. This insignificance could be the result of either a true parameter
that is (very close to) zero, or multicollinearity in the regression due to high correlation between
maximum returns and idiosyncratic volatility, causing monthly Fama-MacBeth estimates to fluctuate
more.
Finally, the influence of skewness is investigated. Skewness is positively correlated with positive
extreme returns. Three moment asset pricing models as advanced by Kraus and Litzenberger (1976)
or Harvey and Siddique (2000) imply that investors have a preference for assets that increase
portfolio return skewness. In equilibrium such assets would have lower expected returns. Return
skewness may therefore cause the negative relation we find between extreme positive returns and
expected returns. As in Bali et al. (2011), we find that the extreme positive return effect is robust to
including total skewness, idiosyncratic skewness or coskewness. But unlike their results, we also find
that skewness is significantly negatively related to expected returns, no matter which skewness
measure is used.
2
The remainder of the paper is structured as follows. In section 2, we discuss sample selection,
construction of variables and filters. Next, we discuss the main results in section 3. Section 4 provides
the results of a battery of robustness checks and finally, we conclude.
2 Data
2.1 Sample selection
Our sample comprises thirteen European countries: Austria, Belgium, Finland, France, Germany,
Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, Slovakia and Spain. One might notice that the
other four countries of the euro area (Malta, Estonia, Cyprus and Slovenia) are not included. This is
inspired by Schmidt, von Arx, Schrimpf, Wagner, and Ziegler (2011), who also exclude these countries.
This is motivated by the fact that their financial impact on the euro area is negligible. Their relative
share, measured in 2009 nominal GDP, is only 0.80% of the entire euro area. We are therefore
convinced that the current sample is representative for the entire euro area. All data comes from
Thomson DataStream (TDS) as in Ang, Hodrick, Xing and Zhang (2009). We use several lists covering
both active shares and delisted shares
1
thereby minimizing survival bias in our sample. The resulting
dataset is then subjected to extensive filtering as described in appendix A in order to select only
common stock issues. This results in a sample of 7,861 European companies. For these companies, we
download the end-of-month return index (including dividends), unadjusted stock price, market
capitalization (MC) and book-to-market ratio (B/M), from 31 December 1979 to 30 June 2011.
Additionally, we download the daily total return index and MC over the same period. TDS
automatically calculates B/M by dividing the book value per share by market value per share at time t,
where book value per share is the company’s book value at the company’s last fiscal year end
(Worldscope item 05476). For the pre-1999 period all data are converted by TDS into synthetic euro.
As the risk-free rate,
, the monthly money market rate as reported by Frankfurt banks
2
is used.
2.2 Construction of variables
All returns are calculated using the TDS total return indices. Two corrections are applied to correct for
errors that occasionally occur in the TDS database, inspired by Ince and Porter (2006) and Schmidt et
al. (2011). First, we need to think about decimal errors. Suppose the return index is 101.52 on a
particular day and does not change the next. Also suppose TDS correctly stores 101.52 the first day,
but erroneously stores it as 1015.20 the second day. An observed return of 900% when the true return
is zero would obviously distort results. Let’s call this a right-decimal error, because the decimal moved
erroneously to the right. Alternatively, suppose TDS erroneously stores the return index on the second
day as 10.152, which would result in a -90% return. Let’s call this a left-decimal error. These examples
all show nonzero returns while the true return is zero. Additionally, we could have decimal errors
when the true return is nonzero. For example, when the return index decreases from 101.52 to 96.44
(-5% true return) but is stored as 964.40, resulting in an observed return of 849.96%. This example
shows that there is a need to account for decimal errors in both directions, whether the true return is
zero or nonzero. We therefore set to missing any returns that are above 400% (a -50% true return
accompanied by right-decimal error) or returns that are below -85% (a 50% true return accompanied
by a left-decimal error). A second correction is to set
and
to missing if
or
is greater
1
The lists are: WSCOPEOE, ALLAS, DEADOE (Austria); WSCOPEBG, FBDO, DEADBG (Belgium); WSCOPEFN, FFIN, DEADFN (Finland);
WSCOPEFR, FFRA, ALLFF, DEADFR (France); WSCOPEBD, FGER1, FGER2, DEADBD1, DEADBD2 (Germany); WSCOPEIR, FIRL, DEADIR
(Ireland); WSCOPEIT, FITA, DEADIT (Italy); WSCOPENL, FHOL, ALLFL, DEADNL (Netherlands); WSCOPEPT, FPOM, FPOR, FPSM, DEADPT
(Portugal); WSCOPEES, FSPN, DEADES (Spain); WSCOPELX, FLUX, DEADLX (Luxembourg); WSCOPEGR, FGREE, FGRPM, FGRMM, FNEXA,
DEADGR (Greece); FSLOVAK, FSLOVALL, DEADSLO (Slovakia).
2
This rate can be found on the website of the Deutsche Bundesbank in the time series database .