Price Volatility and Contract Maturity: Evidence
from an Online Futures Market for Sports Tickets
Jihui Cheny
Xiaoyong Zhengz
July 2012
Abstract
In this study, we test the relationship between price volatility and contract
maturity, or the “Samuelson e¤ect”, using futures contract prices for a major sports
event. Applying four di¤erent performance measures, we show supportive evidence
of the Samuelson e¤ect in futures contract for tickets to the Super Bowl XLIII
(2009), using the dynamic panel estimation method. Our main contributions are
testing the existing theories in a novel setting with unique product features and
advancing our understanding of the prediction market for sports events.
JEL Classi…cation Numbers: G13, G14, L83
Keywords: Futures Markets; Price Volatility; National Football League; Dynamic Panel Estimation
We thank Gerry Wilson, cofounder of Yoonew.com, for generously providing data. We also thank
the editor, two anonymous referees, Oguzhan Dincer, Manuel Hernandez, Rati Ram, Michael Waterson,
and session participants at the 2011 Southern Economic Association Annual Meeting and the 2012
International Conference of Industrial Organization for their helpful suggestions and comments. Finally,
Chen would like to thank Adrienne Hahn for many conversations and discussions on NFL rules, and Nick
Wetzler and Niko Valaris for their research assistance. All errors remain ours.
y
Department of Economics, Illinois State University, Campus Box 4200, Normal, IL61790 U.S.A; Tel:
(309) 438-3616; Fax: (309) 438-5228; Email: [email protected].
z
Department of Agriculture and Resource Economics, North Carolina State University, 3322 Nelson
Hall, Raleigh, NC 27695, USA.; Tel: (919) 515-4543, Fax: (919) 515-6268; Email: [email protected].
1
Introduction
The Samuelson e¤ect, …rst formally proposed by Samuelson (1965), is de…ned as increasing futures price volatility, or greater response of futures price to new information, when
the delivery date approaches. This theory is underlain by the plausible idea that futures
contracts long before maturity carry greater uncertainty and therefore react weakly to
given information, while the opposite is true for futures contracts close to maturity.
This proposition, however, does not hold in general. Rutledge (1976) and Samuelson
(1976) characterize the properties that the spot price process needs to satisfy for the
Samuelson e¤ect to hold in a model where the spot price process is exogenously given.
When these conditions fail to hold, the futures price can exhibit constant or even decreasing volatility as the delivery date approaches. In a more general model where equilibrium
prices in the spot and futures markets are simultaneously determined, Anderson and Danthine (1983) show that futures price is more volatile when the resolution of uncertainty
is high and these periods are not necessarily close to maturity. And more recently, Hong
(2000) studies a model of competitive futures market with asymmetric information and
shows that the Samuelson e¤ect need not hold when the information asymmetry among
investors is large in the market. Therefore, whether the Samuelson e¤ect is present or
not in a futures market becomes an empirical problem.
Since Rutledge (1976), numerous empirical studies have been devoted to testing the
Samuelson e¤ect in various commodity and …nancial markets but the results are mixed.
For a few examples, Rutledge (1976) …nds the Samuelson e¤ect present in silver and cocoa
futures markets, but not in wheat and soybean oil markets. Milonas (1986) documents the
Samuelson e¤ect in wheat, soybeans, soybean meal, soybean oil, Treasury bills, Treasury
bonds, copper, gold and silver futures markets, but not in the corn futures market. More
recently, Chatrath et al. (2002) and Karali and Thurman (2009) show evidence of the
Samuelson e¤ect in corn and soybean, and lumber futures markets, respectively.
In this study, we contribute to the literature by testing the Samuelson e¤ect in a
new futures market, the market of futures contracts for tickets to a major sports event,
the Super Bowl XLIII (2009). Our analysis employs a unique date set on futures prices
collected from Yoonew.com, which provided an exchange-like platform for sports fans to
trade futures contracts for tickets to an upcoming sports event, and on game outcomes
for all NFL teams during the 2008 regular season. Applying four di¤erent performance
1
metrics, our dynamic panel-data estimation results show strong support for the Samuelson
e¤ect.
Testing the Samuelson e¤ect in this new market is interesting because it di¤ers from
traditional commodity and …nancial futures markets in several dimensions: the type of
traders, trade volume, and most importantly, contract design. Firstly, consumers and
producers of a commodity or owners of an underlying asset, along with “speculators”,
usually participate in traditional exchange markets, while users of Yoonew.com were
fans, traders, and resellers. Secondly, the volume of trade occurred at Yoonew.com was
relatively thin compared to that in traditional exchange markets. Subject to seasonal
‡uctuation, the trading volume for agriculture futures such as those for corn and soybean
at Chicago Mercantile Exchange (CME) can easily reach hundreds of thousands on a
single day.1 In contrast, we would expect a small fraction of that trading volume on
Yoonew.com during its operation.2
Lastly, there are at least four fundamental di¤erences in terms of contract design
between Yoonew.com and traditional exchange markets.
1. Unlike commodity and …nancial futures contracts, whose values at expiration (which
equal the prevailing spot prices of the underlying goods) are usually not zero, most
ticket contracts in our study see their values vanish upon maturity. To be exact,
only the contracts for the two …nalists maintain their values on the day of the Super
Bowl, while those for all other teams become worthless. In the existing empirical
literature, the value of futures contracts never diminishes to zero in those markets
that have been studied. In this sense, we re-evaluate the Samuelson e¤ect in a
di¤erent setting from that in the literature.
2. For commodities and …nancial instruments, spot market coexists with futures market and prices in both markets are jointly determined in equilibrium (Anderson
and Danthine 1983). In the futures market for tickets to the Super Bowl, however,
contracts are team speci…c. Since whether a team can make it to the Super Bowl is
1
CME group reports its daily trading activity on its website (http://www.cmegroup.com/market-
data/volume-open-interest/exchange-volume.html).
2
Servan-Schreiber et al. (2004) estimate an average of 100 traders with a bracket between 50 and
200 for each NFL game on both TradeSports and NewsFutures. It is reasonable to expect a similar
participation level on Yoonew.com.
2
an uncertain event, there is no corresponding spot market for the underlying good
(i.e., each team’s tickets to the Super Bowl) before these futures contracts are about
to expire.3 Therefore, the link between the spot market and the futures market is
rather loose, if not absent, in this case.
3. In commodity and …nancial futures markets, the presence of a shock would impact
future contracts of a particular good or similar goods to more or less the same
extent (e.g., the e¤ect of a hurricane on orange crops). In the futures market for
tickets to sports events, however, a shock will deliver polarizing impacts on di¤erent
contracts, because contracts are team speci…c and good news for a team means bad
news for its opponent(s). Therefore, the same event causes the futures price for one
team’s ticket to rise and another’s to fall. This provides us more variation in the
data, which can help identify the Samuelson e¤ect.
4. All futures contracts in our sample expire at the same time, while other studies
usually focus on goods with varying expiration dates.
This study is also related to the growing literature on prediction markets, also known
as “information markets”, “idea futures”, or “event futures”, in which participants trade
contracts for a future event to make better business, social, and political decisions (Wolfers
and Zitzewitz, 2006).4 Technically, Yoonew.com traded binary-option, or “winner-takeall”contracts where trading prices for a team represented the market-aggregated expected
probability that the team made it to the Super Bowl.5 Existing studies are mainly
interested in testing the market e¢ ciency hypothesis (Wolfers and Zitzewitz, 2004) in
various settings including political elections (Wolfers and Leigh, 2002; Berg et al., 2008),
business (Chen and Plott, 2002), sports (Debnath et al. 2003; Servan-Schreiber et al.,
3
Although there exist spot markets (i.e., …rst and secondary ticket markets) for tickets to the Super
Bowl, they are not team-speci…c. That is, these ticket holders are guaranteed to attend the event,
regardless of which two teams make to the Super Bowl. Related, ticket prices in those markets generally
do not ‡uctuate with any particular team’s performance in the season.
4
One of the most famous prediction markets is the
(http://www.biz.iowa.edu/iem).
Iowa
Electronic
Market
See Wolfers and Zitzewitz (2004) and Tziralis and Tatsiopoulos
(2007) for detailed surveys of this literature.
5
Wolfers and Zitzewitz (2004) discuss three main types of contracts traded in prediction markets.
The other two types, index futures and spread betting, represent the mean and the median of the market
expectation of a speci…c outcome, respectively.
3
2004), entertainments (Gruca, 2000; Pennock et al., 2001; Rosenbloom et al., 2006),
education (Passmore et al. 2005), and health (Polgreen et al., 2007).
In particular, our paper adds to the existing literature a new perspective in the prediction market for sports events. Two most related studies, Debnath et al. (2003) and
Servan-Schreiber et al. (2004) test the market e¢ ciency theory with di¤erent focuses:
the former analyzes the correlation between in-game predictions and the correct outcome
in soccer and basketball games; the latter directly compares predictive accuracy between
real- and play-money markets in NFL games. Our analysis advances the understanding
of prediction markets for sports events in three aspects: (1) we not only provide additional evidence for the market e¢ ciency theory in a unique sports prediction market,
but we also explore how price volatility responds to new information, (2) the contracts
traded at Yoonew.com essentially predicted the outcome of an entire football season,
rather than the outcome of individual games during a season, and (3) econometrically,
we employ dynamic panel estimation methods, taking into consideration both time-series
and cross-sectional variation in the sample.
The rest of the paper is organized as follows. Institutional facts and data are introduced in Section 2. We set up the empirical model and describe the estimation strategy
in Section 3. Thereafter follows a discussion of the results in Section 4. Section 5 o¤ers
some concluding remarks.
2
Institutional Facts and Data
Inspired by Happel and Jennings (2002), two MIT graduates, Gerry Wilson and Hagos
Mehreteab, launched Yoonew.com in 2004, which o¤ered an online platform for fans and
brokers to exchange futures contracts for major sports events, such as NFL’s Super Bowl.6
The idea was to make these events more a¤ordable for the general public. Taking Super
Bowl futures contracts as an example, contract holders usually paid a fraction of the fullprice to the Super Bowl months ahead of the game, betting on their favorite teams making
it to the …nal. Like paying insurance premia, most contract holders ended up losing the
money that they had paid for the contracts (i.e., no “accident”has occurred), while those
of the two …nalists ended up reaching a good deal (i.e., “accident” has occurred). The
6
Unfortunately, due to …nancial di¢ culties, Yoonew.com went out of business in early 2010.
4
company used the fund from losing contracts to purchase tickets to games (usually at the
market price).7
2.1
Data Description
We have obtained two data sets for our analysis. One consists of weekly futures prices
(i.e., each Friday’s closing prices) of four seating areas (i.e., types A, B, C, and D) for all
32 teams listed at Yoonew.com during the 2008 NFL regular season. A futures contract
corresponds to a seat in the Raymond James Stadium, Tampa, Florida, where the 2009
Super Bowl took place on February 1, 2009. As indicated in Table 1, the mean futures
price is $258.63, a small fraction of a full-price Super Bowl ticket. Even when breaking
down by seating area, the mean futures price for a seat in the best area is only $387.78.
These are considerable savings for a futures contract holder if his or her team does make to
the …nal (i.e., “winning”). On the other hand, the losses to contract holders are relatively
moderate, making the exchange appealing to many fans and brokers alike. That is, as
long as the expected payo¤ from “winning”exceeds that from “losing”, an investment in
the exchange market is optimal.
The other data set contains the information (mainly game results) on all games played
during the 2008 NFL regular season (between Thursday September 4, 2008 and Sunday
December 28, 2008) collected from the NFL’s o¢ cial website in the order of calender
weeks.8 Most games took place on Sundays, with the rest on either Mondays, Thursdays,
or Saturdays.
To combine the two data sets, we re-de…ne the variable “week” as the duration between a Friday and the following Thursday. As a result of this re-de…nition, our data
cover 18 weeks in total.9 In e¤ect, in a given week, a team may have zero, one, or two
games. For example, a team’s BYE week does not have any game played. In addition, if
a team’s two consecutive games fall in the duration of the de…ned “week,”the following
week then has no game played. As we will discuss below, when constructing the performance metrics, we use the previous week’s outcome for any week in which there is no
game. Under our de…nition of week, week 1 only has the kick-o¤ game of that season.
7
See “Wait Till Next Year, but Lock in the Ticket Price Now” by Alan B. Krueger, The New York
Times, February 2, 2006, for additional information about Yoonew.com.
8
Source: http://www.n‡.com/schedules?seasonType=REG&season=2008.
9
Note that a regular season lasts 17 calendar weeks, including a BYE week for each team.
5
Thus, our …nal data set includes games from week 2 (i.e., starting with Friday September
5, 2008) to week 18 (i.e., starting with Friday December 26, 2008) and has a total of 2068
observations.10
Sports events are ideal for studying prediction markets (Servan-Schreiber et al., 2004),
because (1) high frequency of games during the regular season o¤ers su¢ cient information;
(2) intense media reports generate su¢ cient public information traders need; and (3)
market participants in this market have su¢ cient incentive and interest to trade contracts
to the best of their knowledge.
2.2
Performance Measure De…nition
The focus of our empirical analysis is to test the relationship between futures price volatility and team performance, taking into consideration the timing e¤ect. E¤ectively, we
estimate, in any given week, each team’s chance of getting into the play-o¤ games, and
ultimately the Super Bowl, which depends on whether a team outperforms its opponents, particularly within the same division. To de…ne the key variable, Performance,
in our model, we construct several measures of it for robustness reasons, which include
team i’s relative standing within division (dwwb), relative standing within conference
(cwwb), rank within division (divisionrank), and rank within conference (conf rank).
These measures are calculated based on a team’s current won-lost-tied record, pct, which
is computed as the ratio of
win+0:5 tie
win+loss+tie
where win=loss=tie denotes the number of games
won/lost/tied, respectively, by team i up to week t:11 The higher the pct, the better a
team’s performance. As indicated in Table 1, the mean pct is 0.51, ranging from 0 to 1
in the sample. The four performance measures are de…ned as follows:
Following Tainsky and Winfree (2010), we de…ne two variables to measure a team’s
relative standing during a given week t:
10
Some teams (i.e., those who obviously would not make to the play-o¤s) did not have futures prices
listed during the last two weeks. In fact, week17 and week18 have only 76 and 72 observations, respectively.
11
Because of our week de…nition, there are cases where a team has the same pct for two consecutive
weeks (e.g., one of them is BYE). Note that the following four performance metrics measure a team’s
current strength relative to its opponents, whose win-lose-tie records may change during the team’s BYE
week. As a result, the team’s performance metrics may still change even if it has no game in a given
week.
6
– dwwb is de…ned as
pctit
to measure team i’s pct relative to other teams’in
t
t
the same division, where
t
and
t
are the mean and the standard deviation of
all teams’pct in the division at week t. It measures a team’s relative standing
in the division.
– cwwb is de…ned as
pctit
t
t
to measure team i’s pct relative to other teams’in
the same conference, where
t
and
t
are the mean and the standard deviation
of all teams’pct in the conference at week t, respectively. It measures a team’s
relative standing in the conference.
We adopt a simpli…ed version of the NFL o¢ cial tie break rules, mainly: (1) wonlost-tied record, or pct (2) conference combined rank, and (3) all combined rank, in
such order, to construct the next two performance measures.12 Next, we explain in
detail how the latter two tie-break tools are created. On one hand, we rank teams
within a conference from 1 through 16 according to their accumulative points scored
by week t, which we call “conference points scored rank”; the higher the accumulative points scored, the lower the rank (i.e., better performance). Similarly, we
rank teams within a conference from 1 through 16 according to their accumulative
points allowed, which we call “conference points allowed rank”; the lower accumulative points allowed, the lower the rank (i.e., better performance). Next, we create
“conference combined rank” (i.e., the second tie-break tool) by summing up “conference points scored rank” and “conference points allowed rank”. On the other
hand, based again on their accumulative points scored and accumulative points allowed, we rank all teams within the entire league from 1 through 32 for “all points
scored rank” and “all points allowed rank”, respectively. Then, by adding these
two ranks, we obtain “all combined rank”(i.e., the third tie-break tool).
We are now at the position to explain the next two performance measures. In each
of 17 spreadsheets in an Excel …le, one for a week, we sort all teams by division
12
For the simplicity reason, we do not use the complete NFL o¢ cial tie break rules for our weekly
rankings. Our simpli…ed version produces nearly identical rankings to the actual outcome of the 2008
regular season. This is expected because most omitted o¢ cial tie-break rules do not apply to the early
weeks in the season, due to, for example, lack of common opponents played and so on, and also because
ties become less common as the season progresses. The complete list of the NFL o¢ cial tie break rules
can be found at the following link: http://www.n‡.com/standings/tiebreakingprocedures.
7
and then by conference. We then create one column for each tie break tool. In the
next two columns, we …ll in the following two ranks:
– divisionrank is de…ned as the rank within the division. Based on game outcomes up to week t, we use the afore-mentioned tie-break tools to construct
weekly division ranks. In the …nal data set, divisionrank ranges from 1 to 4.
– conf rank is de…ned as the rank within the conference. Based on game outcomes up to week t, we use the same procedure to rank all teams within each
conference. In the …nal data set, conf rank ranges from 1 through 16. Teams
of division champion always rank the top four in conf rank and the remaining
12 teams rank 5 through 16.13
3
Empirical Model
We are interested in modeling how futures prices respond to changes in the team’s performance and hence the probability of getting into the Super Bowl, or
Pijt =
0t
+
where
0t
+
3
1
Pij;t
1
+(
20
+
21
W KLF Tt ) P erf ormanceit
F OW IN %it + ui + vj + "ijt :
(1)
is a weekly dummy controlling for shocks that a¤ect all teams in the same way.
Pijt is the closing futures price for team i’s futures contract on a ticket of seat type j to
the Super Bowl at week t, and Pij;t
1
is the lagged dependent variable. Note that current
futures price, Pijt , may be related to that in the last period, Pij;t 1 . Figure 1 shows price
dynamics of selected teams from both conferences, including worst teams, #1 play-o¤
seeds, and conference champions.14
W KLF Tt is de…ned as the number of weeks left before the Super Bowl at week
t. P erf ormanceit denotes team i’s performance metrics at week t. As this is the key
variable in our model, we construct four measures of it for robustness reasons. See Section
13
It is possible that a division number two with a better record ranks worse than a division champion.
For example, in week 8, AFC east number two, New England Patriots, ranked number 5 with pct of
0.67, while AFC west champion, Denver Broncos, ranked number 4 with pct of 0.57.
14
In Figure 1, we use seating area A as an example, but similar trends are expected for all other seating
areas.
8
2.3 for the detailed discussion on de…ning these performance measures. F OW IN %it is
team i’s remaining opponents’current average pct in the regular season to measure the
team’s future rivals’strength at week t. On average, stronger (weaker) future opponents
will collectively have a negative (positive) e¤ect on team i’s current futures price at week
t. Finally, ui denotes the team …xed e¤ects and vj denotes the seating area …xed e¤ects.
Table 1 reports the summary statistics of the variables used in the analysis. Pijt
ranges from $1 to $2,614.67, with the mean of $258.63 and standard deviation of $320.21.
Because this study focuses on the regular season, W KLF T ranges between 5 to 21 weeks
to the Super Bowl. Variables pct, dwwb, cwwb, and F OW IN % are de…ned as ratios, thus
all ranging between 0 and 1. As expected, divisionrank ranges from 1 to 4 and conf rank
from 1 to 16.
Our econometric strategy is to test several existing theories in a novel setting. The
estimation of
20
tests the market e¢ ciency theory (e.g. Karali and Thurman, 2009). If
the market is e¢ cient, futures price rises after winning a game and declines after losing a
game, or
20
> 0. More interestingly, we test whether the Samuelson e¤ect is present in
our data, or to examine how the timing variable a¤ects the e¤ect of performance on futures
price, which is captured by the interaction term between W KLF T and P erf ormance.
To re‡ect the Samuelson e¤ect, game outcomes closer to the Super Bowl (i.e., W KLF T
decreases) would have a larger e¤ect on a team’s futures price than the previous week, or
increasing volatility as the delivery date nears. Thus, that
20
and
21
having opposite
signs can be considered supporting evidence for the Samuelson e¤ect. The interaction
term captures the additional timing e¤ect of game outcomes on futures price, while the
total e¤ect of winning (losing) a game later in the season would be magni…ed through
the term
20
+
21 .
Previous studies focus on testing the Samuelson e¤ect in commodity
futures markets, not in sports markets. This is the main contribution of our paper.
3.1
Estimation Strategy
Along with the fact that the lagged dependent variable appears on the right-hand-side of
equation (1), our sample has a short time dimension (16 weeks) but a large cross-section
dimension (32 4 or 128 team-seat combinations), making it suitable for employing the
Arellano-Bond linear dynamic panel-data estimation method.
Following the Arellano-Bond procedure, we take …rst-di¤erence of equation (1) to
9
remove the two panel-level …xed e¤ects (i.e., the team and seat …xed e¤ects), or
4Pijt = 4
+
0t
3
+
1
4Pij;t
1
+
20
4P erf ormanceit +
21
4 (W KLF Tt P erf ormanceit )
4F OW IN %it + 4"ijt :
where 4Pijt = Pij;t
Pij;t
1
(2)
and so on and 4"ij;t = "ij;t
"ij;t 1 . Our sample includes
data from week 2 through week 18, but because of …rst-di¤erencing, we now only have
16 weeks of data for the estimation. The pooled OLS (POLS) estimators from equation
(2) are inconsistent given that, by construction, 4Pij;t
1
is correlated with 4"ijt , as well
as the serial correlation between the di¤erenced error terms, 4"ijt and 4"ij;t 1 . Arellano
and Bond (1991) propose a full GMM estimation, which uses the lagged endogenous and
exogenous variables as instruments to form moment conditions.
In the next section, we apply the two-step Arellano-Bond GMM estimation to equation
(2), accounting for the possibility that 4P erf ormanceit , 4 (W KLF Tt P erf ormanceit )
and 4F OW IN %it are endogenous. In the …rst step, the identity matrix is used as the
weighting matrix in the GMM objective function to obtain a consistent but ine¢ cient
estimator. In the second step, residuals from the …rst step are used to compute the optimal
weighting matrix in the GMM objective function. The resulting estimator from this step
is both consistent and e¢ cient.15 As noted by Arellano and Bond (1991), however,
though the variance-covariance estimates from this two-step procedure are consistent in
theory, in practice, they are seriously biased in this particular context. Thus, we report
the Windmeijer bias-corrected (WC) robust standard errors in the estimation, which are
robust to both autocorrelation and heteroskedasticity. In addition, these standard errors
are also adjusted for clustering to account for possible dependence within each team-seat
type combination (i.e., group).
4
Results
Applying one performance measure for each model speci…cation, we report the ArellanoBond estimation results in columns (2), (4), (6), and (8) in Table 2. The results of the
Arellano-Bond test for serial correlation in the …rst-di¤erenced errors are also presented
15
See, for example, Greene (2002) and Wooldridge (2010) for detailed discussions on the Arellano-Bond
GMM estimation.
10
in Table 2.16 All tests of second-order autocorrelation are satisfactory. For comparison,
we also estimate equation (1) using OLS with standard errors calculated by using the
Newey-West heteroskedasticity and autocorrelation consistent (HAC) covariance matrix.
These results are reported in columns (1), (3), (5), and (7) of Table 2.
The lagged dependent variables are all statistically signi…cant at the 1% level in all
columns of Table 2. Also, F OW IN % has the expected negative sign in Table 2, except
for columns (1), (2), and (5), but remains statistically insigni…cant throughout.
As expected, in columns (1) through (4), we have negative signs for ranking variables,
divisionrank and confrank, indicating that lower rank (i.e., better performance) is associated with a higher futures price. In general, the Arellano-Bond GMM estimates are
larger than the Newey-West estimates (Wooldridge, 2010). More speci…cally, as a team
moves up one division rank, its average futures price rises by $56.23 in column (1) and
by $104.67 in column (2); as a team moves up one conference rank, the price rises by
$16.62 in column (3) and by $30.57 in column (4). With one rank di¤erence, we would
expect a larger price change for division rank than for conference rank, since division
ranks have a much smaller range (i.e., 1 through 4) than conference ranks (i.e., 1 through
16). In columns (5) and (6), as a team’s relative standing within a division rises by one
percentage point, its futures prices also rise by $0.99 and $1.99, respectively; in columns
(7) and (8), as a team’s relative standing within the conference rises by one percentage
point, its futures prices also rise by $0.87 and $1.68, respectively. All estimates suggest
that the futures market in the sample operates e¢ ciently during the 2008 NFL regular
season. The conclusion is robust to various performance measures.
Now we turn to the interaction terms between performance measures and the timing
variable in Table 2, which indicate the result of testing the Samuelson e¤ect. Since
wklef t de…nes as the number of weeks left before the Super Bowl, the value of the
variable becomes smaller as we move closer to the event. For each performance measure,
the coe¢ cient for the interaction term has the opposite sign as the coe¢ cient for the
performance measure, suggesting supporting evidence for the Samuelson e¤ect. Regarding
the magnitude of the Samuelson e¤ect, as a team moves up one rank in the division, its
16
Conventional practice often reports test statistics of the Sargan test for overidentifying restrictions.
However, the asymptotic distribution of this test is unknown when the error terms are heteroskedastic
(Arellano and Bond, 1991; Wooldridge, 2010). Thus, we do not perform the Sargan test under the
assumption of heteroskedasticity in the analysis.
11
futures price rises by an additional $1.94 in column (1) and $6.01 in column (2) per week
as the regular season progresses.
Similar conclusions can be reached from estimation results using other performance
measures. In columns (3) and (4), as a team moves up one rank in the conference, its
mean futures price increases by an additional $0.51 and $1.54, respectively, per week
during the regular season, although it is statistically insigni…cant. Moving to columns (5)
and (6), the e¤ects of an increase in the relative standing within a division are $0.03 and
$0.09 per week, respectively, considering a percentage increase in both measures. In the
last two columns of Table 2, an increase in the relative standing within the conference
adds another $0.02 and $0.07 per week as we approach the end of the regular season.
Again, the estimates all have the expected sign, indicating the presence of the Samuelson
e¤ect.
4.1
Robustness Check
For the robustness reason, we also de…ne a dummy variable to measure time to delivery,
N earw , as one when the number of days to the Super Bowl is less than 60 days and
zero otherwise.17 In this case, we expect
20
and
21
in equation (1) to have the same
sign in support of the Samuelson e¤ect.18 We report both the Newey-West and the
Arellano-Bond estimation results, along with post-estimation test statistics, in Table 3.
All estimates remain qualitatively the same as in Table 2. In columns (1) and (2),
moving up one rank in the division increases the average futures price by $28.16 and by
$28.10, respectively; if such an movement occurs within 60 days of the Super Bowl, the
price rises by an additional $12.80 in column (1) and by $20.50 in column (2), making the
total e¤ect of moving up one rank in the division on futures price to be $40.96 and $48.60,
compared to when the Super Bowl is still more than 60 days out. Similar conclusions
can be reached from estimation results using other performance measures. In columns
(3) and (4), as a team moves up one rank in the conference within 60 days, its mean
futures price increases by an additional $3.94 and $6.07, respectively, making the total
e¤ect of better performance in the order of $12.85 and of $16.96, respectively. In columns
17
We have also used alternative de…nitions of N earw , and the regression results remain qualitatively
the same.
18
By de…nition, W KLF T and N ear move the opposite directions. The former decreases continuously
(at the increment of 1) and the latter increases discretely (from 0 to 1) as the regular season progresses.
12
(5) through (8), the key estimates all have the expected signs, although two become
statistically insigni…cant.
As another robustness check, we drop observations with futures prices less than $10
and perform the same estimation in a subsample of 1,661.19 As indicated in Table 4, all
results remain qualitatively the same as in Table 2. For example, moving up one rank
in the division increases a team’s futures price, on average, by $69.72 in column (1) and
by $127.73 in column (2); there is an additional increase of $2.75 in column (1) and of
$7.94 in column (2) per week if a team moves up one rank within the division during the
regular season.
In general, our analysis …nd support for the Samuelson e¤ect using this novel data set,
and the result is robust to multiple performance measures, various model speci…cations,
and di¤erent subsamples.
5
Conclusions
In this study, we test the market e¢ ciency theory and the Samuelson e¤ect in a novel
setting where futures contracts for sports events are exchanged. Using the dynamic
panel estimation, our analysis suggests that the exchange market for futures contracts of
sports events is e¢ cient and …nds supportive evidence for the Samuelson e¤ect. These
…ndings are robust to a number of performance measures constructed based on game
outcomes during the regular season and to several model speci…cations. Furthermore,
this paper also advances our understanding of the prediction market for sports events.
Studies show that these prediction markets are more accurate in forecasting than survey
and polls (Chen and Plott, 2002; Berg et al., 2008). Despite its short-lived history,
Yoonew.com o¤ered a valuable opportunity of applying predictive tools to sports events.
Our analysis indicates that Yoonew.com was an e¢ cient trading market; that is, bids
rose when the probability of winning a spot in the Super Bowl rose. This con…rms
that accurate prediction prevails even in a thin market with “relatively small trading
population”(Wolfers and Zitzewitz, 2004).
19
The regression results also remain qualitatively the same when we use subsamples excluding obser-
vations with di¤erent threshold values.
13
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14
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16
1500
500
close
1000
400
close
300
200
500
100
01sep2008
01oct2008
01nov2008
newdate
01dec2008
01jan2009
01sep2008
01nov2008
newdate
01dec2008
01jan2009
Pittsburgh: AFC Champion
30
0
10
20
50
close
close
40
100
50
60
150
Arizona: NFC Champion
01oct2008
01sep2008
01oct2008
01nov2008
newdate
01sep2008
01dec2008
01nov2008
newdate
01dec2008
Kansas City: Worst in AFC
500
0
1000
500
close
1500
close
1000
2000
1500
2500
2000
Detroit: Worst in NFC
01oct2008
01sep2008
01oct2008
01nov2008
newdate
01dec2008
01sep2008
01jan2009
New York Giants: NFC Play-off #1 Seed
01oct2008
01nov2008
newdate
01dec2008
Tennessee: AFC Play-off #1 Seed
Figure 1. Selected Teams' Futures Prices during the Regular Season (Seat Type: A)
17
01jan2009
Variable
Table 1. Summary Statistics
Obs
Mean
Std. Dev.
Min
Max
close
2068
break down by seating area
seating A
517
seating B
517
seating C
517
seating D
517
258.63
320.21
1
2614.67
387.78
241.92
212.71
192.13
444.25
281.71
247.01
222.43
2.92
2.48
2.41
1
2614.67
1600.87
1388.55
1253.01
wklft
near
pct
divisionrank
wkdrank
confrank
wkcrank
cwwb
wkcwwb
dwwb
wkdwwb
FOWIN%
13.39
0.20
0.51
2.45
33.17
8.24
112.20
0.05
0.26
0.04
0.22
0.46
5
0
0.28
1.11
19.98
4.58
77.54
0.96
13.72
0.86
12.29
0.15
5
0
0
1
5
1
5
-2.35
-36.81
-1.5
-31.5
0.00
21
1
1
4
84
16
336
2.23
33.04
1.5
31.50
0.92
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
2068
18
Table 2. Arellano-Bond Estimation of Testing the Samuelson Effect (Using Continuous Timing Variable)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
VARIABLES Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West Arellano-Bond
L.close
0.78***
0.55***
0.77***
0.52***
0.77***
0.50***
0.78***
0.51***
(0.024)
(0.070)
(0.024)
(0.083)
(0.024)
(0.031)
(0.024)
(0.053)
divisionrank -56.23***
-104.67***
(7.674)
(38.292)
wklft*divisionrank
1.94***
6.01***
(0.523)
(2.103)
confrank
-16.62***
-30.57***
(2.243)
(7.866)
wklft*confrank
0.52***
1.54***
(0.142)
(0.363)
dwwb
99.09***
198.70***
(11.920)
(24.312)
wklft*dwwb
-2.81***
-9.16***
(0.748)
(1.531)
cwwb
87.01***
168.28***
(11.724)
(64.888)
wklft*cwwb
-1.99***
-7.08***
(0.711)
(2.019)
FOWIN%
2.44
22.44
-23.51
-21.13
4.11
-6.94
-29.27
-50.98
(26.248)
(34.475)
(26.038)
(62.209)
(25.546)
(68.424)
(25.662)
(100.258)
Team Fixed Effects
Seat Fixed Effects
Weekly Dummies
AR1a
p-value
AR2a
p-value
Observations
Number of Groups/ R2
Y
Y
Y
1,940
0.8937
Y
-4.81
(0.00)
.43
(0.67)
1,428
128
Y
Y
Y
1,940
0.8942
Y
-4.66
(0.00)
0.73
(0.47)
1,428
128
Y
Y
Y
1,940
0.8962
Heteroskedastic and autocorrelation-consistent (HAC) standard errors in parentheses in columns (1), (3), (5), and (7).
The Windmeijer bias-corrected (WC) robust standard errors in parentheses in columns (2), (4), (6), and (8).
Statistical levels of significance: *** p<0.01, ** p<0.05, * p<0.1.
a
Note:
The Arellano-Bond test for serial correlation in the first-differenced errors.
19
Y
-5.05
(0.00)
0.81
(0.42)
1,428
128
Y
Y
Y
1,940
0.8943
Y
-4.79
(0.00)
0.64
(0.53)
1,428
128
Table 3. Arellano-Bond Estimation of Testing the Samuelson Effect (Using Timing Dummy Variable)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
VARIABLES Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West
L.close
divisionrank
Near*divisionrank
0.78***
(0.025)
-28.16***
(3.474)
-12.80**
(5.380)
0.58***
(0.032)
-28.10***
(6.753)
-20.50***
(6.575)
confrank
Near*confrank
0.78***
(0.025)
0.55***
(0.051)
-8.91***
(1.089)
-3.94***
(1.367)
-10.89***
(4.071)
-6.07***
(1.593)
dwwb
Near*dwwb
0.78***
(0.025)
0.54***
(0.057)
57.06***
(5.660)
18.27***
(6.464)
73.78***
(27.853)
33.76
(49.334)
0.78***
(0.025)
0.54***
(0.089)
-3.65
(1,050.338)
55.60***
(6.660)
16.05**
(6.255)
-21.81
(26.752)
67.91
(150.452)
28.72***
(5.757)
-20.10
(486.159)
Y
Y
Y
Y
1,940
0.8941
-4.47
(0.00)
0.66
(0.51)
1,428
128
cwwb
Near*cwwb
FOWIN%
Team Fixed Effects
Seat Fixed Effects
Weekly Dummies
AR1a
p-value
AR2a
p-value
Observations
Number of Groups/R2
3.91
(26.842)
19.74
(22.991)
-15.25
(26.923)
Y
Y
Y
Y
1,940
0.8933
-5.05
(0.00)
.42
(0.67)
1,428
128
-5.39
(29.657)
7.01
(26.209)
Y
Y
Y
Y
Y
Y
Y
Y
1,940
0.8938
-5.10
(0.00)
0.81
(0.42)
1,428
128
1,940
0.8957
-4.98
(0.00)
0.35
(0.73)
1,428
128
Heteroskedastic and autocorrelation-consistent (HAC) standard errors in parentheses in columns (1), (3), (5), and (7).
The Windmeijer bias-corrected (WC) robust standard errors in parentheses in columns (2), (4), (6), and (8).
Statistical levels of significance: *** p<0.01, ** p<0.05, * p<0.1.
a
Note:
The Arellano-Bond test for serial correlation in the first-differenced errors.
20
(8)
Arellano-Bond
Table 4. Arellano-Bond Estimation of Testing the Samuelson Effect in a Subsample (Using Continuous Timing Variable)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
VARIABLES Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West Arellano-Bond Newey-West Arellano-Bond
L.close 0.767***
0.55***
0.753***
0.51
0.751***
0.51***
0.742***
0.46***
(0.025)
(0.127)
(0.026)
(0.451)
(0.025)
(0.137)
(0.027)
(0.096)
divisionrank -69.723***
-127.73**
(9.083)
(51.867)
wklft*divisionrank 2.754***
7.94***
(0.626)
(2.637)
confrank
-24.470***
-45.28
(3.154)
(48.914)
wklft*confrank
0.981***
2.85
(0.202)
(4.523)
dwwb
124.814***
220.27**
(14.503)
(102.545)
wklft*dwwb
-4.281***
-11.64***
(0.922)
(1.566)
cwwb
168.290***
330.37
(20.070)
(460.244)
wklft*cwwb
-6.162***
-19.15
(1.229)
(20.940)
FOWIN%
6.459
36.57
-22.129
11.80
7.678
18.37
-48.307*
-54.65
(30.287)
(232.176)
(29.210)
(364.185)
(29.201)
(160.537)
(27.991)
(295.166)
Team Fixed Effects
Seat Fixed Effects
Weekly Dummies
AR1a
p-value
AR2a
p-value
Observations
Number of Groups/ R2
Y
Y
Y
1,661
0.8830
Y
-3.98
(0.00)
.16
(0.87)
1,144
107
Y
Y
Y
1,661
0.8843
Y
-1.67
(0.09)
0.34
(0.73)
1,144
107
Y
Y
Y
1,661
0.8864
Heteroskedastic and autocorrelation-consistent (HAC) standard errors in parentheses in columns (1), (3), (5), and (7).
The Windmeijer bias-corrected (WC) robust standard errors in parentheses in columns (2), (4), (6), and (8).
Statistical levels of significance: *** p<0.01, ** p<0.05, * p<0.1.
a
Note:
The Arellano-Bond test for serial correlation in the first-differenced errors.
21
Y
-3.64
(0.00)
0.46
(0.65)
1,144
107
Y
Y
Y
1,661
0.8858
Y
-4.30
(0.00)
0.44
(0.66)
1,144
107