Understanding Investor Sentiment: The Case of Soccer
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Understanding Investor Sentiment:
The Case of Soccer
Gennaro Bernile and Evgeny Lyandres∗
We examine the extent to which the stock market’s inefficient responses to resolutions of uncertainty
depend on investors’ biased ex ante beliefs regarding the probability distribution of future event
outcomes or their ex post irrational reactions to these outcomes. We use a sample of publicly traded
European soccer clubs and analyze their returns around important matches. Using a novel proxy
for investors’ expectations based on contracts traded on betting exchanges (prediction markets),
we find that within our sample, investor sentiment is attributable, in part, to a systematic bias in
investors’ ex ante expectations. Investors are overly optimistic about their teams’ prospects ex ante
and, on average, end up disappointed ex post, leading to negative postgame abnormal returns. Our
evidence may have important implications for firms’ investment decisions and corporate control
transactions.
What is investor sentiment? Defined very broadly, investor sentiment is present whenever
security prices deviate from present values of future cash flows. There are two potential reasons
for such deviations. First, investors’ ex ante assessment of the distributions of value-relevant event
outcomes may be biased (e.g., Baker and Wurgler, 2006, 2007; Kaustia, Alho, and Puttonen, 2008).
Additionally, investors may react irrationally ex post to resolutions of uncertainty (see Hirshleifer,
2001, for an excellent overview of psychological biases).
A simple example illustrates the difference between the two forms of investor sentiment.
Assume that a firm faces an event with an uncertain outcome. Also, suppose for simplicity that
there are two possible realizations of postevent firm value that are expected to occur with some
probabilities. Under the first type of investor sentiment, investors may be overly optimistic ex
ante, in the sense that they believe that the probability of a good outcome is higher than its true
likelihood. In this case, the preevent firm value, which equals the expected (discounted) postevent
value under investors’ subjective probability distribution, is higher than the expected (discounted)
postevent value under the true probability distribution. Therefore, the expected change in value
around the event is negative. In the second case, investors may assign correct probabilities to event
outcomes but react emotionally to the resolution of uncertainty (i.e., their postevent valuation is
different from the true postevent value, this difference not being reflected in preevent value).
We are grateful to an anonymous referee, Rui Albuquerque, Sandro Andrade, Alex Edmans, Andrew Ellul, Diego Garcia,
Michael Halling, Milton Harris, Tullio Jappelli, Christian Julliard, Ambrus Kecskés, Marco Pagano, Marcel Rindisbacher,
Masahiro Watanabe, Yuhang Xing, and seminar participants at the University of Naples, the 2008 Utah Winter Finance
Conference, the 2009 Amsterdam Asset Pricing Retreat, the 2009 European Financial Management Association Meetings,
the 2009 Financial Management Association European Conference, and the 2010 Eastern Finance Association Meetings
for helpful suggestions, and to Tom Johnson from Betfair and Carl Wolfenden from Tradesports for data on prices of
soccer contracts traded on these betting exchanges.
∗
Gennaro Bernile is an Assistant Professor of Finance in the School of Business at the University of Miami, Coral Gables,
FL. Evgeny Lyandres is an Assistant Professor of Finance in the School of Management at Boston University, Boston,
MA.
Financial Management • Summer 2011 • pages 357 - 380358 Financial Management r Summer 2011 Under the first scenario, referred to as “immediate emotions” (Loewenstein, 2000), firms’ postevent market values are efficient, while preevent values are not. Under the second scenario, referred to as “anticipated emotions,” preevent values are efficient, while postevent values are not. Our objective is to assess the effect that investors’ biased expectations and irrational reactions have on the efficiency of stock prices around value-relevant events. Understanding whether preevent stock prices or postevent prices are efficient is important because firm managers’ actions may depend on preevent and postevent prices. For example, in Edmans (2009), a manager’s decision whether to make a long-term investment depends upon whether the postinvestment stock price is efficient (i.e., it reflects future payoff from the in- vestment) or inefficient (i.e., it reflects only the temporary reduction in earnings due to the investment). Similarly, in Admati and Pfleiderer (2010) and Edmans and Manso (2009), man- agers are more likely to exert (privately) costly effort if market prices correctly incorporate the effects of shirking. In contrast, numerous papers highlight the importance of preevent efficiency (Polk and Sapienza, 2009, for the case of investment in physical capital; Chen, Goldstein, and Jiang, 2007; Chirinko and Schaller, 2001; Gilchrist, Himmelberg, and Huberman, 2005, for the case of aggregate real investment; Luo, 2005; Edmans, Goldstein, and Jiang, 2009, for the case of mergers and acquisitions (M&As); Bradley et al., 2010, for the case of shareholder activism). We utilize data on stock returns of publicly traded soccer clubs around important matches and a novel measure of investors’ subjective beliefs to attempt to distinguish between the two forms of investor sentiment. The stock price behavior of publicly traded sport clubs around sporting events provides a unique setting that allows us to estimate investors’ expectations of possible event outcomes. Our tests indicate that investor sentiment is, at least partially, an ex ante phenomenon in the sense that investors incorrectly estimate the probability distributions of event outcomes. They are overly optimistic prior to the resolution of uncertainty. Typically, investors’ overestimate (underestimate) the probability of winning (losing) by nearly 5 percentage points. As a result, they generally end up disappointed ex post. The mean stock return on the days following important soccer matches is −0.9%. Our setting is suitable for an analysis of ex ante optimism and ex post emotional reactions for the following reasons. First, the results of sports matches are frequent, easily quantifiable, and value relevant. In addition, they have observable ex ante expectations (e.g., Brown and Hartzell, 2001). Additionally, similar to Brown and Hartzell (2001) and to Edmans, Garcia, and Norli (2007), we document that the unconditional mean return on days following matches is negative, a finding that may be due to investors’ ex ante optimism and/or ex post irrational reaction to uncertainty resolutions.1 Finally, unlike many traditional corporate finance settings, sporting events cannot be manipulated by firms’ insiders, all but eliminating concerns that the market reaction to the resolution of uncertainty may be partially driven by investors’ perception of potential manipulation (i.e., as in the case of earnings management in Degeorge, Patel, and Zeckhauser, 1999). Existing studies examining the market reaction to sporting event outcomes use winning and losing odds quoted by bookmakers to proxy for ex ante probabilities of match outcomes (e.g., Brown and Hartzell, 2001; Edmans et al., 2007; Palomino, Renneboog, and Zhang, 2009). However, investors’ subjective expectations may be different from the bookmaker odds. 1 As Edmans, Garcia, and Norli (2007; p. 1991) explain: “. . . the reference point against which gains and losses are measured becomes an important determinant of utility. The natural reference point in our setting is that of supporters’ pre-game expectations of how their team will perform. A number of studies show that fans are subject to an “allegiance bias,” whereby individuals who are psychologically invested in a desired outcome generate biased predictions. . . . Thus, if the reference point of soccer fans is that their team will win, we may find a greater stock price reaction after losses than after wins.”
Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 359
Bookmakers may quote odds that deviate systematically from bettors’ expectations. For ex-
ample, Levitt (2004) finds that bookmakers do not play the role of market makers but rather take
large positions with respect to event outcomes.2 Additionally, Levitt’s (2004) findings suggest
that bookmakers may be more skilled than bettors at predicting game outcomes. By quoting prices
that exploit bettors’ biases, bookmakers are able to increase their profits by 20% to 30%. Finally,
Palomino et al. (2009) demonstrate that investors ignore the periodic releases of bookmaker odds.
An alternative measure of investors’ subjective expectations of game outcomes may be derived
from the market prices of related contracts traded on betting exchanges (prediction markets). To
the best of our knowledge, this measure of investors’ expectations has not been used before.3 The
crucial difference between prices set in a betting exchange and bookmaker odds is that the former
are determined by orders posted and matched by bettors. The betting exchange simply provides
a trading platform. Bookmakers, on the other hand, post their own odds and may choose sides in
transactions.
A comparison of bookmaker odds and prices of contracts traded on betting exchanges with
realized game outcomes demonstrates that bookmaker odds generally provide unbiased estimates
of the likelihood of match outcomes, while betting exchange prices reflect bettors’ pregame
optimism in the sense that implied probabilities of wins (losses) are generally higher (lower) than
ex post realized proportions or wins (losses).4 In addition, the difference between betting exchange
prices and bookmaker odds is positively related to variables associated with optimism, such as
clubs’ past (unanticipated) success and intrinsic quality. Thus, betting exchange prices seem to
be more closely related to subjective beliefs than bookmaker odds, motivating us to explore the
ability of the former to explain the asymmetric return pattern following soccer matches.
Our results show that distinguishing between probability distributions of match outcomes
implied by bookmaker odds and those implied by betting exchange prices is crucial in the
analysis of investor sentiment. When employing bookmaker odds, we can reject the hypothesis
that preevent stock prices reflect expected postgame prices. Conversely, we cannot reject the
hypothesis that pregame stock prices equal expected postgame prices computed using betting
exchange price-based estimates of investors’ expectations. This evidence is consistent with the
idea that investors’ beliefs regarding the probabilities of event outcomes are biased ex ante, but
their reactions to event outcomes are not necessarily irrational. In other words, our findings
are consistent with the hypothesis that preevent stock prices are inefficient, while we cannot
reject the hypothesis that postevent prices are efficient. To the extent that this is a recurrent
phenomenon in equity markets, our evidence has important implications for managerial actions,
such as investment decisions and effort exertion, which may depend upon observed market values.
Our study is related to the seminal work of Brown and Hartzell (2001), as well as studies by
Palomino et al. (2009) and Renneboog and Van Brabant (2000) in that we analyze stock returns
of sports franchises. Our analysis also contributes to the literature examining the efficiency
of betting markets by examining the probabilities of event outcomes derived from prices on
prediction markets and demonstrating their biases relative to both in-sample match results and
probabilities derived from bookmaker odds (e.g., Zuber, Gandar, and Bowers, 1985; Sauer et al.,
2
In close to half of National Football League games, at least two-thirds of all bets fall on one side.
3
Wolfers and Zitzewitz (2004) describe the functioning of betting exchanges. Arrow et al. (2007) encourage US regulators
to lower the barriers to create new prediction markets, arguing that the latter provide superior forecasting tools.
4
Since betting exchange contracts that we use are very short-lived—most of them are matched on game day—the risk-
neutral probabilities of game outcomes implied by these contracts’ prices should be nearly identical to the physical
probabilities of outcomes perceived by investors.360 Financial Management r Summer 2011 1988; Golec and Tamarkin, 1991; Gray and Gray, 1997; Vlastakis, Dotsis, and Markellos, 2008; Palomino et al., 2009). The paper proceeds as follows. In the next section, we describe the data and present summary statistics. In Section II, we examine the evolution of stock prices around games. We discuss the two proxies for investors’ expectations and biases associated with them in Section III. In Section IV, we incorporate investors’ pregame expectations into tests of postgame returns. We summarize our evidence and present our conclusions in Section V. I. Data and Summary Statistics Our sample consists of all Champions League and Union of European Football Associations (UEFA) Cup games (including qualifying rounds) played during six seasons, from 2000-2001 to 2005-2006 featuring at least one publicly traded club at the time of the match. Overall, there are 20 teams from eight countries that have participated in at least one game in either the Champions League or the UEFA Cup during this period while being publicly traded. These teams range from such powerhouses as Manchester United, Juventus, and Ajax, to virtually unknown teams such as Danish clubs Aalborg and Silkeborg. Our sample teams played in 595 unique matches, 31 of which featured two publicly traded clubs, corresponding to 626 observations. We focus on international games, rather than national championships or cups, for several reasons. First, we hypothesize and demonstrate empirically that outcomes of games in European competitions have sizable effects on club values. Additionally, the UEFA Cup and the Champions League are, in large part, structured as knock-out rounds of pairs of games. A team plays its opponent in a given round twice (home and away), and advances or is eliminated based on the combined outcome of the two games, which are usually scheduled two weeks apart. Therefore, the team’s postgame stock return depends less on the outcome of games played by other clubs than in the case of national championships. As a result, our setting reduces the intergame dependence that may contaminate tests of the relation between game results and stock returns.5 Finally, while national league games generally take place during the weekend posing a potential weekend effect problem, UEFA Cup and Champions League games are played between Tuesdays and Thursdays. We obtain game results along with match dates from the Rec.Sport.Soccer Statistics Foundation at www.rsssf.com. We cross-check the results and dates against those reported by Betexplorer, the source of bookmaker odds data (www.betexplorer.com). We discuss the data obtained from this source in detail below. Table I presents summary statistics for various game and club charac- teristics, as well as aggregate statistics for the whole sample. Successful, established teams tend to play many European matches, over 70 each for Manchester United and Porto, whereas smaller clubs tend to be featured in only a handful of games. About 30% of the games in our sample are elimination games, defined as either the second game of a knock-out stage or the last game of a group stage. Approximately two-thirds of the games are played in the Champions League competition. About half of the 169 games in the advanced stages of competitions, defined as quarterfinals, semifinals, and finals of the Champions League and the UEFA Cup, as well as the second group stage of the Champions League, were played by Manchester United, Juventus, and Porto. Half of the games in our sample are played on public teams’ home turf. 5 There are some exceptions to the knock-out system. A portion of the games in the Champions League are played within four-team group stages, and one of the rounds in the UEFA Cup was structured as a five-team group stage during part of our sample period. All of the results reported below are robust to excluding group-stage matches from the sample.
Table I. Match Statistics, Market Values, and Operating Performance Measures of Publicly Traded Soccer Clubs
This table reports match statistics, market values, and operating performance measures of 20 soccer clubs that were publicly traded at any time from January
2000 to June 2006 and have played at least one game in the Champions League or UEFA Cup during this period. All Champions League and UEFA Cup games
listed by Rec.Sport.Soccer Statistics Foundations at www.rsssf.com are included in the sample. Games is the number of matches played. Public Opponents is
the number of matches played against another publicly traded club. Elimination Games is the number of matches that are either the second game of a knock-out
stage or the last game of a group stage. Champions League is the number of matches played in the Champions League competition. Advanced Stage is the
number of matches played in the quarterfinal, semifinal, and final stages of the Champions League and the UEFA Cup, as well as the second group stage of the
Champions League. Home is the number of matches played at home. High Quality is the number of matches where the team’s UEFA rating prior to the match is
higher than its opponent’s rating. The ratings are obtained from www.xs4all.nl/∼kassiesa/bert/uefa/data % Wins is the proportion of matches won % Draws is
the proportion of matches tied % Losses is the proportion of matches lost % Advances is the proportion of elimination matches after which a team moved on to
the next stage of the competition. Exchange Prices and Bookmaker Odds indicate the number of games with available betting exchange prices and bookmaker
odds. MV Equity is the average market value of equity over the sample period, computed as the average of the product of the number of shares outstanding and
the stock price one day prior to the games. Stock prices are from Datastream.
Team Country Games Public Elimination Champions Advanced Home High % % % % Exchange Bookmaker Both Team
Opponents Games League Stage Quality Wins Draws Losses Advances Prices Odds
Aalborg DK 6 0 3 0 0 3 2 0.167 0.333 0.500 0.333 4 3 3 9.06
Ajax NL 50 0 13 44 10 25 26 0.340 0.320 0.340 0.462 30 48 30 130.88
Aston Villa ENG 2 0 1 0 0 1 2 0.500 0.000 0.500 0.000 0 2 0 26.60
Besiktas TR 32 0 11 6 2 15 16 0.344 0.250 0.406 0.636 14 29 12 111.58
Borussia GER 35 0 10 27 11 16 28 0.457 0.229 0.314 0.583 0 33 0 89.00
Brondby DK 21 2 10 9 0 10 14 0.333 0.238 0.429 0.400 4 19 3 34.24
Celtic SCO 52 2 19 26 7 27 26 0.481 0.154 0.365 0.632 10 49 10 35.63
Fenerbahce TR 13 0 3 11 0 6 0 0.231 0.077 0.692 0.000 13 13 13 250.89
Galatasaray TR 21 0 6 17 3 11 15 0.238 0.286 0.476 0.167 7 19 7 76.25
Juventus IT 51 4 15 51 25 25 35 0.510 0.176 0.314 0.667 29 50 29 254.72
Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer
Lazio IT 52 4 14 34 16 26 50 0.423 0.250 0.327 0.625 8 50 8 175.14
Man United ENG 81 4 19 81 36 41 76 0.543 0.247 0.210 0.571 27 71 26 897.26
Millwall ENG 2 0 1 0 0 1 2 0.000 0.500 0.500 0.000 2 2 2 15.64
Newcastle ENG 35 2 13 14 12 18 21 0.600 0.143 0.257 0.692 12 29 10 79.40
Porto POR 75 7 25 52 29 37 53 0.387 0.293 0.320 0.667 16 73 16 41.51
Roma IT 56 3 16 30 12 28 38 0.393 0.321 0.286 0.529 17 53 17 129.45
Silkeborg DK 2 0 1 0 0 1 0 0.000 0.000 1.000 0.000 0 2 0 0.88
Southhampton ENG 2 0 1 0 0 1 2 0.000 0.500 0.500 0.000 0 2 0 19.09
Sporting POR 36 3 13 9 5 20 22 0.417 0.222 0.361 0.533 16 34 16 42.07
Trabzonspor TR 2 0 1 2 0 1 2 0.500 0.000 0.600 0.000 2 1 1 90.39
All 626 31 195 413 168 313 430 0.425 0.241 0.334 0.553 211 582 203 208.39
361362 Financial Management r Summer 2011
We measure a team’s intrinsic quality by its official UEFA rating at the time of the game.
Team ratings are available from www.xs4all.nl/∼kassiesa/bert/uefa/data.6 By construction, our
definition of intrinsic quality is orthogonal to the home/away variable since all paired matches
are played, in turn, on each side’s home turf. Teams in our sample are of higher quality than their
opponents in over two-thirds of the cases. Therefore, it is not surprising that our sample teams
won about 42% and lost 33% of their games, tying the remaining ones. Consequently, teams in
our sample advance to subsequent rounds in 55% of elimination games.
The last column in Table I reports soccer clubs’ market values. Market values are obtained from
Datastream. All values are converted into US dollars using contemporaneous exchange rates. For
each game by each club, we compute the market value of equity as the product of the number
of shares outstanding and the stock price one day prior to the game. The table reports pregame
market capitalizations averaged across all games played during the sample period. There is great
variation in soccer clubs’ equity values, ranging from less than $1 million for Silkeborg to almost
$1 billion for Manchester United.
II. Game Outcomes and Returns
In this section, we investigate how on-field performance affects club values (i.e., how soccer
clubs’ stock prices react to important match results). Although we focus our analysis on stock
returns following games, we also document interesting patterns in game-day returns that may be
related to investor sentiment, which we discuss at the end of this section.
A. Returns on Days Following Games
We compute abnormal returns following games by estimating the market model regression for
each club each year.7 However, due to the infrequent trading of most soccer club stocks, estimates
of a simple market model may be biased. One way to obtain unbiased coefficient estimates is to
include lagged, matching, and leading market returns in the market model regression, as suggested
by Dimson (1979)
Ri,t∈T = αi,T + β1i,t RLM,t−1 + β2i,t RLM,t + β3i,t RLM,t+1 + εi,t , (1)
where Ri,tε T is day t return on stock i during year T, RLM,t (RLM,t−1 , RLM,t+1 ) is the value-weighted
(leading, lagged) local market index return, and εi,t is the resulting estimate of daily abnormal
return. Table II reports postgame abnormal returns when the sample is partitioned into wins,
losses, and draws.8
6
A club’s rating depends on two additive terms: 1) its own performance in European competitions during the prior five
years and 2) the performance of all of the teams playing in the club’s national league. Thus, if a team has not qualified
for a European competition for five consecutive years, its rating equals its country’s rating.
7
All the results below hold for raw returns.
8
The abnormal returns obtained while augmenting Equation (1) by returns on local high minus low
(HML) and small minus big (SMB) factor mimicking portfolios obtained from Kenneth French’s website
(http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#International) and from Datastream, respec-
tively, are similar to those reported below. We do not report the results with local HML and SMB factors as the latter are
unavailable for Turkey and Portugal. The significance of the abnormal returns in Table II is assessed using a cross-sectional
test (e.g., Brown and Warner, 1985; Boehmer, Musumeci, and Poulsen, 1991) in which the t-statistic is computed as the
mean return divided by its cross-sectional standard deviation.Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 363
Table II. Postgame Abnormal Returns
This table presents mean abnormal returns, as defined in Equation (3), following games won, lost, or tied by
publicly traded soccer clubs participating in Champions League and UEFA Cup competitions. Wins (Draws,
Losses) correspond to the Champions League and UEFA Cup games won (tied, lost) by a sample club. All
refers to the full sample. The second panel contains mean returns for the subsample of elimination games.
“Advances and Wins” corresponds to wins by sample teams in which they advanced to the next round.
Other columns are interpreted similarly. t-statistics are reported in parentheses. The number of observations
is reported below t-statistics. Columns Win-Loss and Draw-Loss report the respective differences with
t-statistics are reported in parentheses.
Wins Draws Losses Win-Loss Draw-Loss All
All Games
0.12% −0.88%∗∗∗ −2.22%∗∗∗ 2.34%∗∗∗ 1.34%∗∗∗ −0.90%∗∗∗
(0.64) (−4.31) (−9.31) (7.71) (4.27) (−6.98)
266 151 209 626
Advances and Eliminations
(1) (2) (3) (4) (1)-(2) (1)-(3) (2)-(4) (3)-(4)
Advances Advances Eliminations Eliminations
and Wins and Losses and Wins and Losses
0.32% −0.67% −1.27% −3.47%∗∗∗ 0.99% 1.59% 2.80%∗∗∗ 2.20%∗
(0.91) (−1.2) (−1.24) (−5.90) (1.50) (1.47) (3.45) (1.86)
64 16 21 52
∗∗∗
Significant at the 0.01 level.
∗
Significant at the 0.10 level.
Wins result in average abnormal return of 0.12% that is not statistically significant, while losses
and draws generate highly significant average returns of −2.22% and −0.88%, respectively.9
The differences between the mean market reactions to wins, losses, and draws are statistically
significant and economically large. However, large stock price changes following losses relative
to postwin returns are not sufficient to conclude that the stock market’s reaction to game outcomes
is inefficient. This finding could well be consistent with investors’ rational ex ante beliefs. Even
though the mean returns following a loss are much larger in magnitude than those following a win,
losses could be relatively rare for public firms. To claim that the market’s reaction to game results
is inefficient, it is necessary that the unconditional mean return around matches be significantly
different from zero. The average postgame return is −0.9% and is highly statistically significant.
Untabulated results indicate that mean postgame returns are negative not only for the full sample
but also for various sample splits, such as those based on club market capitalizations and UEFA
ratings.
Next, we restrict our attention to elimination games and focus on whether a team advances to
the next round or is eliminated, rather than on the result of the game per se. Both wins/losses
and advances/eliminations are important for clubs’ returns. For example, returns following losses
that lead to eliminations are significantly lower than returns following losses after which teams
advance to the next round. Also, the magnitude of the negative mean return following wins leading
9
Similar, although economically weaker, results are reported for the case of British soccer leagues by Palomino et al.
(2009), who find that losses are greeted by negative returns of larger magnitude than wins, and draws are followed by
negative, albeit insignificant, returns.364 Financial Management r Summer 2011
to eliminations is smaller than that following losses resulting in eliminations. Overall, the mean
return following elimination games is −1.26%.
These findings are clearly a challenge for market efficiency even in the presence of the
asymmetric (knock-out) structure of European competitions, in which a win merely advances a
team to the next round, while a loss knocks a team out of the competition. In an efficient market,
ex ante value always equals the sum of (discounted) ex post values multiplied by their respective
probabilities, regardless of the determinants of these ex post values.
A plausible reason for this inefficiency is the transaction costs associated with trading in
soccer club shares. Palomino et al. (2009) report that the bid-ask spreads for UK soccer club
stocks range between 1.6% and 15.4%. Thus, investors are not likely to be able to profit from
the mispricing discussed above by shorting public clubs’ stocks prior to game days. However,
regardless of whether or not the significantly negative mean return following soccer matches
can result in a profitable trading strategy, it is important to examine the sources of market
inefficiency, since the implications for managerial actions of investors’ ex ante optimism and ex
post irrational reactions to event outcomes are different. The examination of the sources of the
market inefficiency documented in Table II is at the heart of our analysis in the next two sections.
Overall, the evidence in Table II supports the notion that the outcome of the games has an
immediate impact on club values. To examine whether the market reaction to game outcomes is
related to team and game characteristics, we complement the univariate analysis in Table II by
estimating a multivariate regression of postgame abnormal returns, AR,i,k , on indicator variables
for wins and losses and their interactions with clubs’ and games’ observed characteristics
ARi,k = α + βwin Wi,k + βloss L i,k + βwin j I j,i,k Wi,k + βloss j I j,i,k L i,k + εi,k , (2)
j j
where Wi,k is equal to one if public team k has won game i and is equal to zero otherwise, Li,k
is the lost game indicator, Ij,i,k are three dummy variables, j = 1, 2, 3, that equal one if team k
played game i at home, if team k had a higher UEFA rating than its opponent, and if game i was
played in an advanced stage of one of the European competitions, respectively. To interpret the
intercept of Equation (2) as the mean return following draws, we normalize Ij,i ,k to have zero
means. Table III presents the results of estimating Equation (2).
Table III confirms the results in Table II. Relatively neutral outcomes, draws, are followed
by significantly negative returns. Returns following wins are significantly higher than those
following draws, and losses are accompanied by negative returns that are significantly larger in
magnitude than postdraw returns. This asymmetric return pattern, which is evident regardless of
whether team and game characteristics are controlled for and is manifested by negative returns
following draws, near neutral reactions to wins, and large negative returns after losses, is consistent
with the findings of Brown and Hartzell (2001) and Edmans et al. (2007).
The results reported in Column 2 indicate that home losses are associated with larger negative
returns than away losses, which are more likely ex ante, the difference being highly significant.
Wins by stronger teams, which occur frequently, result in significantly lower postgame returns
than wins by weaker teams, which occur much more rarely. Finally, both wins and losses in
advanced stages of the competitions result in returns of greater magnitude, although only losses
in advanced stages have a significantly larger impact on returns.
B. Game-Day Returns
One potential explanation for the negative mean postgame returns documented in Tables II
and III is that investors have overly optimistic beliefs regarding game outcomes. This bias mayBernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 365
Table III. Postgame Abnormal Returns and Game Characteristics
This table presents OLS estimates of the correlation between postgame abnormal returns, game outcomes
(wins, losses, and draws), and game outcomes interacted with other match characteristics (home game
indicator, higher-ranking indicator, and advanced stage indicator). t-statistics are reported in parentheses.
Intercept −0.88%∗∗∗ −0.88%∗∗∗
(−3.53) (−3.61)
Win 1.00%∗∗∗ 1.29%∗∗∗
(3.20) (4.04)
Loss −1.34%∗∗∗ −1.78%∗∗∗
(−4.07) (−5.20)
Win ∗ home −0.7%∗
(−1.81)
Loss ∗ home −1.38%∗∗∗
(−3.02)
Win ∗ higher ranking −1.04%∗∗
(−2.13)
Loss ∗ higher ranking −1.34%∗∗∗
(−3.16)
Win ∗ advanced stage 0.60%
(1.30)
Loss ∗ advanced stage −1.48%∗∗∗
(−3.23)
R2 0.0977 0.1476
No. of observations 626 626
∗∗∗
Significant at the 0.01 level.
∗∗
Significant at the 0.05 level
∗
Significant at the 0.10 level.
create pregame price pressure due to the demand for clubs’ stocks in anticipation of uncertainty
resolving events (e.g., Liang, 1999; Trueman, Wong, and Zhang, 2003). Since soccer clubs’
stocks are generally thinly traded, this may result in positive abnormal returns prior to games.
Alternatively, it may be that systematically positive news about the eventual match outcomes
become available prior to the games, resulting in positive pregame returns (i.e., coaches releasing
information about starting lineups and players’ injuries; teams’ preparedness for games gradually
becoming public knowledge). Table IV presents returns on game days.
As evident from the last column of Table IV, the mean return on game days is positive, 0.5%,
and highly statistically significant. The information leakage interpretation does not appear to be
borne out in the data. First, typical game-day returns in Table IV do not follow the ordering implied
by information-based hypotheses (i.e., returns on days during which games are tied are higher
than those during days where public teams win). Second, untabulated results indicate that odds
typically move against our sample teams on game days, inconsistent with the idea that the typical
flow of information released to market participants is positive on game days.10 Moreover, the
correlation between game-day returns and changes in estimated winning and losing probabilities
during game days is virtually zero. Third, in the subsample of 31 games where both teams are
public, the two teams experience game-day returns of the same sign in 16 cases. Among these,
10
Bettors’ estimates of winning probabilities drop by 0.39%, on average, on game days. Please see the discussion of our
proxy for bettors’ beliefs in the next section.366 Financial Management r Summer 2011
Table IV. Game-Day Abnormal Returns
This table presents mean abnormal game-day returns for games won, lost, or tied by publicly traded soccer
clubs participating in the Champions League and UEFA Cup competitions. Wins (Draws, Losses) correspond
to the Champions League and UEFA Cup games won (tied, lost) by a sample club. All refers to the full
sample. t-statistics are reported in parentheses. The number of observations is reported below the t-statistics.
Columns Win-Loss and Draw-Loss provide the respective differences with t-statistics for the differences in
parentheses.
Wins Draws Losses Win-Loss Draw-Loss All
All Games
0.47%∗∗∗ 0.73%∗∗∗ 0.25% 0.22% 0.48% 0.47%∗∗∗
(3.58) (2.85) (1.27) (0.93) (1.49) (4.47)
266 151 209 626
∗∗∗
Significant at the 0.01 level.
both returns are positive in 13 cases. This is inconsistent with new information arrival since
positive news for one team should be regarded as negative news for the rival team. Finally, the
correlation between game-day returns and eventual outcomes is not significantly different from
zero.
The evidence is more supportive of the price pressure hypothesis. First, there is a statistically
significant, positive correlation of 13% between game-day abnormal trading volume, defined
as the natural logarithm of the ratio of daily volume and the volume five trading days earlier,
and abnormal returns, consistent with buying pressure. Second, there is a statistically significant,
negative correlation of −11% between game-day returns and following-day returns, consistent
with the partial reversal of price pressure-driven game-day returns on the following day. Because
of this potential reversal, we control for game-day returns in our analysis of the causes of large
negative returns following games, presented in the next two sections.
III. Proxies for Investors’ Beliefs and Objective Probabilities
As discussed above, two distinct behavioral phenomena may explain the inefficient stock price
reaction to game results, documented in the previous section. First, investors may systematically
misestimate the likelihood of various outcomes. If investors are too optimistic about publicly
traded clubs’ chances to succeed, they typically end up disappointed ex post, resulting in larger
(smaller) negative (positive) surprises than under the premise of efficient capital markets. Another
explanation is that the reported evolution of stock prices is driven by investors’ postevent emotional
reactions, as in the case of national team matches in Edmans et al. (2007). In the remaining
analysis, we concentrate on the effects of investors’ ex ante biased beliefs on stock returns.
Specifically, in this section we examine the extent of investors’ optimism and in Section IV we
quantify the effects of this optimism on expected postgame returns.
A. Bookmaker Odds
The most widely used proxy for the likelihood of sporting events’ outcomes is bookmaker
odds or spreads (Brown and Hartzell, 2001; Palomino et al., 2009). We obtain bookmaker odds
from Betexplorer (www.betexplorer.com). This website compiles odds from various bookmakers,Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 367
reporting the best historical odds for each potential outcome. Betexplorer reports odds for 582
games involving public teams, corresponding to more than 90% of our sample. We follow
Palomino et al. (2009) and translate bookmaker odds into probabilities using the following
transformation:
1/Owin
probbookies = , (3)
win
1/Owin + 1/Odraw + 1/Oloss
where probbookies
win is the odds-based probability of a win, and Owin , Odraw , and Oloss are the
odds of win, tie, and loss, respectively, and similarly for probbookies
draw and probbookies
loss . Panel A of
Table V compares the probabilities based on bookmaker odds and the observed distribution of
game outcomes.
The differences between the odds-based probabilities and the in-sample proportions of game
outcomes are generally small. Typically, bookmakers are almost precisely on target when fore-
casting winning odds, and they are not far off in predicting losing odds (32% expected vs. 34%
realized). The finding that bookmakers’ odds are generally unbiased predictors of game outcomes
is consistent with odds proxying for objective estimates of match outcomes, which may or may
not coincide with investors’ beliefs. This evidence, together with the finding in Levitt (2004) that
bookmakers often post odds that result in larger imbalances of bets and they seem to substan-
tially increase their profits by doing so, prompts us to explore an alternative proxy for investors’
subjective expectations.
B. Betting Exchange Prices
The alternative approach to estimating investors’ beliefs that we propose relies on prices
of contracts traded on betting exchanges or “prediction markets.” To illustrate the essence of
prediction markets, we borrow a quote from the introductory page of Betfair, the operator of
the largest betting exchange in the world, whose data we use in this paper. “Betfair put[s] you
together with people . . . who have got an opposing view to you. [Betfair] then hold[s] the cash
until the match is over . . . The odds on offer are just a pure reflection of what punters . . . think
is likely to happen . . .” (http://sports.betfair.com/). To paraphrase, prices of traded contracts are
determined solely by the demand for and supply of these contracts, with the exchanges’ role
limited to providing a trading platform and clearing services.11 An example of such a contract is
a security paying $1 in the case of Manchester United defeating Benfica Lisbon in a Champions
League game and paying nothing otherwise.
We obtain prices of contracts on wins, losses, and draws of our sample teams from two betting
exchanges: 1) Betfair (www.betfair.com) and 2) Tradesports (www.tradesports.com). The typical
volume of contracts on games played in European competitions traded on Betfair is quite large,
over $240,000 for each outcome (over $320,000 for win and loss contracts and about $55,000 for
draw contracts, on average). The volume on Tradesports is several orders of magnitude smaller.
Thus, we use Betfair as our main data source. The main drawback is that Betfair historical data
only start in 2004, limiting the number of contracts on game outcomes to 507, corresponding to
169 games. Thus, we complement these data using Tradesports contracts for years 2001-2003.
11
Although the institutional role of the exchange varies depending upon the domicile of the bettor (i.e., UK vs. non-UK
based), the fundamental economics of the transactions taking place through the exchange do not. Independent of their
domicile, bettors registered through the UK-based entity can place “back” or “lay” orders and/or take the other side of
back or lay orders placed by other bettors. For legal purposes, however, two UK domiciled bettors take sides against each
other, whereas when a bettor outside the United Kingdom is involved, Betfair takes a position on both sides of a contract
against the two individuals whose orders are being matched.368
Table V. Expected and Realized Game Outcomes
This table presents summary statistics of expected and realized game outcomes. In Panel A, expected outcomes are based on bookmaker odds-based probabilities.
In Panel B, projected outcomes are based on betting exchange price-based probabilities. Panel C compares the probabilities implied by betting exchange prices
and those implied by bookmaker odds for games where both are available. In Panels A and B, Expected is the mean ex ante probability of a particular outcome
implied by bookmaker odds and by pregame betting exchange contracts, respectively. In Sample is the realized proportion of games with a particular outcome.
In Panel C, Betting Exchange and Bookmakers correspond to the betting exchange price-based and bookmaker odds-based probabilities, respectively. t-statistics
are reported in parentheses. In Panels A and B, the Difference column reports the difference between Estimated and In-sample, while Panel C reports the
difference between Betting Exchange and Bookmakers, with the t-statistics for the difference reported in parentheses.
Expected Wins Losses
In-Sample Difference Expected In-Sample Difference No. of Obs.
Panel A. Bookmaker Odds-Based Probabilities
42.24%∗∗∗ 42.10%∗∗∗ 0.15% 31.60%∗∗∗ 33.85%∗∗∗ −2.24% 582
(57.72) (20.55) (0.07) (49.10) (17.24) (−1.09)
Panel B. Betting Exchange-Based Probabilities
43.90%∗∗∗ 36.97%∗∗∗ 6.93%∗ 30.48%∗∗∗ 38.39%∗∗∗ −7.90%∗∗ 211
(30.58) (11.10) (1.91) (23.61) (11.44) (−2.20)
Panel C. Bookmaker Odds-Based Probabilities versus Betting Exchange-Based Probabilities
Betting Exchange Bookmakers Difference Betting Exchange Bookmakers Difference No. of Obs.
∗∗∗ ∗∗∗ ∗∗ ∗∗∗ ∗∗∗ ∗∗∗
45.51% 38.74% 4.77% 30.73% 35.24% −4.51% 203
(30.02) (31.48) (2.51) (23.43) (31.37) (−2.61)
∗∗∗
Significant at the 0.01 level.
∗∗
Significant at the 0.05 level.
∗
Significant at the 0.10 level.
Financial Management r Summer 2011Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 369
After imposing the restriction of at least $100 volume on each of the three possible contracts on
a given game, we obtain data for contracts on 42 more games, increasing our betting exchange
prices sample to 211 games.12,13
To calculate betting exchange-based expectations, we compute the volume-weighted average
of prices on each contract matched prior to the start of the game (contracts that are not “in play”).
Computing bettors’ beliefs from betting exchange prices is theoretically justified by Wolfers
and Zitzewitz (2007) and Gjerstad (2005), who demonstrate that prediction markets efficiently
aggregate traders’ beliefs. Since the sum of the average prices on win, draw, and loss contracts
does not usually equal exactly one, we scale each contract’s price by the combined price of the
three contracts. For example, the implied probability of a win, probexchange
win , is computed as
Pwin
probexchange = , (4)
win
Pwin + Pdraw + Ploss
where Pwin , Pdraw , and Ploss are the prices of win, draw, and loss contracts, respectively.14 Panel
B of Table V reports the typical probabilities implied by betting exchange prices for various
contracts and compares them to the in-sample distribution of match outcomes.
Generally, investors that trade on betting exchanges are overly optimistic about publicly traded
teams’ prospects. They assign an average probability of 44% (30%) to a win (loss), while the in-
sample proportion of wins (losses) is 37% (38%). The differences between expected and realized
outcomes are marginally significant.
It is important to note that we implicitly define optimism with respect to the expected results
of a publicly traded team. The data suggest that trading on betting exchanges is dominated by
public teams’ fans (as opposed to opponent teams’ fans). In particular, the ratio of mean volume
of trading in contracts on results of public team’s nonsample games to mean volume of trading in
contracts on results of its opponent’s nonsample games exceeds one in 78% of cases, indicating
that public firms’ fans are likely to dominate the trading in most cases. Large, successful teams,
especially those from the United Kingdom, exhibit the largest mean volume of trading relative
to that of their opponents (42.6 for Manchester United, 10.7 for Newcastle, 7 for Celtic, 6.2 for
Roma, 3.5 for Juventus, and 2.4 for Galatasaray). However, investors’ optimism with respect
to public teams’ likelihood of winning is present in both the sample of UK teams (the mean
likelihood of winning is 44.6% compared to the in-sample proportion of wins of 37.7%), and in
the sample of teams from outside the United Kingdom (41.2% and 35.2%, respectively). Also,
these differences are present both for the Champions League games, in which the mean ex ante
likelihood of a win is 42.2%, while the in-sample proportion of wins is 34%, and for UEFA Cup
games, 44.9% and 38.8%, respectively.
One potential reason for the differences between betting exchange-based expectations and
game results may be that our subsample of games with available data on betting exchange prices
comprises a set of particularly surprising game outcomes that could not have been rationally
expected ex ante. To investigate this possibility, in Panel C of Table VI, we compare betting
exchange prices with probabilities implied by bookmaker odds for the subset of 203 games for
12
Limiting our sample to Betfair prices only does not alter the qualitative results reported below.
13
In the 16 games featuring two public teams, we only include the higher-rated team in the sample since we demonstrate
below that better teams are more likely to be subject to investor optimism. Choosing a public team randomly in these 16
games does not alter the results.
14
In the absence of limits to arbitrage, the sum of the prices on the three contracts (win/draw/loss) would have to add up
to one. In the presence of limits to arbitrage, the sum of the three prices does not necessarily add up to one. However, to
interpret these prices as probability measures, we need to normalize their sum to one.370 Financial Management r Summer 2011
Table VI. Determinants of the Difference between Betting Exchange Odds-Based
and Bookmaker Odds-Based Win Probabilities
This table presents OLS estimates of the correlation between the difference between betting exchange odds-
based and bookmaker odds-based probabilities of a win by a sample team and variables that are potentially
related to investor optimism. Lag(win-prob(win)) is the difference between win indicator, which is equal to
one if the team has won its previous game in a European competition, if it was played during the same season,
and zero otherwise and the ex ante probability of winning the previous game. Difference in rankings is the
difference in UEFA ratings between the sample team and its opponent. Log(MV) is the natural logarithm of
equity value. Lag(Champions League) is equal to one if the team played in the Champions League in the
previous season and zero otherwise. t-statistics are reported in parentheses.
Intercept 0.044∗∗∗ 0.046∗∗∗
(9.25) (5.49)
Lag(win-prob(win)) 0.017∗ 0.017∗
(1.74) (1.71)
Difference in rankings 0.281∗∗∗ 0.289∗∗∗
(2.98) (2.75)
Log(MV) −0.292
(−0.07)
Lag(Champions League) −0.003
(−0.25)
R2 0.0933 0.0939
No. of observations 118 118
∗∗∗
Significant at the 0.01 level.
∗
Significant at the 0.10 level.
which both are available. Betting exchange-based win (loss) probabilities are significantly higher
(lower) than respective bookmaker odds-based probabilities across all subsamples. The average
betting exchange-based probability of winning is 44%, compared to the average odds-based
probability of 39%.15
Next, we examine the determinants of the difference between win probabilities implied from
betting exchange prices and those implied from bookmaker odds. Finding that this difference
is related to variables that are positively associated with investor optimism would support the
interpretation that betting exchange prices are a measure of investors’ subjective beliefs. Two
club characteristics that may be associated with optimism are past performance and intrinsic
quality. Investors tend to excessively extrapolate past performance into the future (e.g., Benartzi,
2001). If betting exchange traders have a similar behavioral trait then clubs’ past successes may
lead to excessive optimism. We define past abnormal performance as the difference between the
win indicator, equaling one if a team has won its previous European game and zero otherwise,
and the ex ante probability of winning the last game. In addition, numerous studies find that
“higher-quality” stocks (i.e., those with high prices relative to earnings, dividends, or book
values) underperform “lower-quality” stocks (e.g., Fama and French, 1993; Lakonishok, Shleifer,
and Vishny, 1994). Similarly, better (higher rated) teams may be subject to stronger optimism than
15
One feature of the betting market that enables the existence of these differences between bookmaker odds and betting
exchange prices is the limits to arbitrage. The mean sum of the probabilities of wins, draws, and losses implied by
bookmaker odds is about 1.08, resulting in a mean transaction cost of 8%, while the average fee charged by the betting
exchanges in our sample is close to 3%. Thus, typically, a difference of up to 8% − 3% = 5% between betting exchange
prices and bookmaker odds may persist.Bernile & Lyandres r Understanding Investor Sentiment: The Case of Soccer 371
weaker teams. As in the rest of the paper, we measure a team’s relative strength as the difference
between its own UEFA rating and its opponent’s rating.
In Table VI, we estimate a regression of the difference between win probabilities implied
from betting exchanges and those implied from bookmaker odds on unexpected previous game
performance and club’s relative intrinsic quality.
The coefficients on both past performance and quality are positive and significant. The un-
expected component of past performance is significant at a 10% level, while the relative UEFA
ranking is significant at a 1% level. Controlling for the club’s size, as measured by its market
capitalization, does not change this result. The evidence in Table VI is consistent with the idea
that betting exchange-based probabilities may be more closely related to bettors’ subjective be-
liefs than bookmaker odds-based probabilities, which may more closely reflect the underlying
objective probabilities.
To complement the univariate analysis above, we estimate ordered logit models relating game
outcomes to betting exchange prices and game characteristics. This method represents an exten-
sion of the test proposed in Gray and Gray (1997) for the case of American football spreads.
Specifically, we estimate the following model:
prob(Yi ≤ result)
ln = αresult − βprobwin probwin − βprobdraw probdraw − β j I j,i , (5)
1 − prob(Yi ≤ result) j
where Yi = 1 for wins, Yi = 2 for draws, and Yi = 3 for losses, result can take the value of 1
exchange
or 2, probwin and probdraw take the values of probexchange
win and probdraw , in the case of betting
bookies bookies
exchange-based probabilities, or the values of probwin and probdraw , in the case of bookmaker
odds-based probabilities, and Ij,i are demeaned dummy variables for home/away game, high-/low-
quality status, and stage of a competition, similar to Equation (2). Table VII presents coefficient
estimates of Equation (5). The coefficients on the indicator variables, Ij,i , are of particular interest.
Under the null hypothesis of no bias, Ij,i should have no explanatory power, while significant
coefficient estimates would suggest specific biases in the predicted probabilities of possible
game outcomes. Panel A of Table VII presents the results for the samples of games in which
bookmaker odds and betting exchange prices are independently available. Panel B reports similar
estimates for the subset of games in which bookmaker odds-based and exchange price-based
probabilities are jointly available. Columns 1 and 2 in each panel examine biases in the exchange
price-based probabilities, while Columns 3 and 4 report the results for the bookmaker odds-based
probabilities.
Not surprisingly, both probexchange
win and probbookies
win are very good predictors of whether a sample
team wins, as evidenced by the near-zero p-values of the corresponding coefficients’ χ 2 . The
coefficient estimates for home games suggest a marginally significant “home bias” when using
exchange-based probabilities. The regressions using bookmaker odds-based probabilities reveal
no statistically significant biases. These results, together with the differences between the proba-
bilities implied from bookmaker odds and those implied from betting exchange prices underscore
the importance of choosing an appropriate proxy for investors’ expectations when examining the
market reaction to event outcomes.
IV. Returns Adjusted for Expected Outcomes
The evidence in the previous section demonstrates that the ex ante probabilities of game
outcomes implied from prices of contracts traded on betting exchanges are biased, both relative to372 Financial Management r Summer 2011
Table VII. Game Outcomes and Expectations
This table presents ordered logit estimates of the relationship between game outcomes, ex ante probabilities
implied by betting exchange prices or bookmakers’ odds, and game characteristics. p-values of the coefficient
estimates’ are reported in parentheses. Panel A presents the results for the samples of games with available
betting exchange and bookmaker data separately. Panel B reports the results for the unified sample with
both betting exchange and bookmaker data available.
Betting Exchange-Based Bookmaker Odds-Based
Probabilities Probabilities
Panel A. All Games
Intercept 1 3.296∗∗∗ 2.736∗∗∗ 1.482∗∗∗ 1.009∗∗∗
(0.005) (0.025) (0.046) (0.009)
Intercept 2 4.671∗∗∗ 4.145∗∗∗ 2.696∗∗∗ 2.238∗∗∗
(0.000) (0.001) (0.000) (0.009)
Prob(win) −6.748∗∗∗ −5.558∗∗∗ −5.554∗∗∗ −4.441∗∗∗
(0.000) (0.000) (0.000) (0.000)
Prob(draw) −3.713 −3.520 0.216 0.206
(0.255) (0.291) (0.922) (0.928)
Home −0.649∗ −0.283
(0.078) (0.236)
Higher quality −0.104 −0.378
(0.816) (0.122)
Advanced stage 0.381 0.194
(0.329) (0.377)
No. of observations 211 211 582 582
Panel B. Restricted Sample
Intercept 1 3.205∗∗∗ 2.621∗∗ 1.393 0.830
(0.007) (0.037) (0.314) (0.152)
Intercept 2 4.596∗∗∗ 4.049∗∗∗ 2.746∗∗ 2.233)
(0.000) (0.001) (0.048) (0.152
Prob(win) −6.658∗∗∗ −5.491∗∗∗ −6.661∗∗∗ −4.990∗∗∗
(0.000) (0.000) (0.000) (0.001)
Prob(draw) −3.563 −3.303 2.177 1.788
(0.286) (0.336) (0.628) (0.711)
Home −0.614∗ −0.413
(0.097) (0.158)
Higher quality −0.092 −0.259
(0.838) (0.556)
Advanced stage 0.317 0.342
(0.425) (0.401)
No. of observations 203 203 203 203
∗∗∗
Significant at the 0.01 level.
∗∗
Significant at the 0.05 level.
∗
Significant at the 0.10 level.You can also read
