Unformatted text preview: Journal of Business Finance & Accounting, 28(1) & (2), January/March 2001, 0306686X Testing Efficiency Across Markets:
Evidence from the NCAA
Basketball Betting Market
L. Lee Colquitt, Norman H. Godwin and
Steven B. Caudill*
1. INTRODUCTION This study examines whether differences in the availability of
information across markets result in different efficiencies of price
formation across those markets. We utilize the National
Collegiate Athletic Association (NCAA) basketball betting market
to make inferences about financial markets. The use of point
spread betting markets to make inferences about the operations
of traditional markets has become common in the finance
literature (see Gandar, Zuber, O'Brien and Russo, 1988; Golec
and Tamarkin, 1991; Brown and Sauer, 1993; Gray and Gray,
1997; and Gandar, Dare, Brown and Zuber, 1998). Betting
markets provide a unique opportunity for such inferences
because the fundamental values of the games in the betting
market, namely the true score differentials between teams, are
observable after the games are played. Thus, uncertainty about
unobservable equilibrium prices, which is characteristic of testing
conducted in conventional financial markets, is removed from
the analysis and more definitive conclusions concerning the
effect of information on the efficiency of markets can be made.
The National Football League (NFL) betting market and the
National Basketball Association (NBA) betting market are the
* The authors are all from Auburn University, Alabama. (Paper received September 1999,
revised and accepted February 2000)
Address for correspondence: Norman H. Godwin, School of Accountancy, 301 Lowder
Business Building, Auburn University, Auburn, AL 36849, USA.
email: [email protected]
ß Blackwell Publishers Ltd. 2001, 108 Cowley Road, Oxford OX4 1JF, UK
and 350 Main Street, Malden, MA 02148, USA. 231 232 COLQUITT, GODWIN AND CAUDILL two point spread betting markets that have received the bulk of
researcher attention.1 Recently, Gray and Gray (1997)
demonstrated in the NFL market that betting strategies based
on a probit model can generate statistically significant profits.
Their results are consistent with prior investigations of the NFL
market that also demonstrate some degree of market inefficiency
(e.g., Gandar et al., 1988 and Golec and Tamarkin, 1991). Brown
and Sauer (1993) utilize the NBA market to show that variations
in point spreads are a function of fundamental information.
Similarly, Gandar et al. (1998) document in the NBA market that
line changes from the opening line to the closing line reflect the
introduction of fundamental information.
A common characteristic of the above studies is the exclusive
focus on a single betting market over a specific period of time.
However, while Gandar et al. (1998) examine the NBA market,
they also compare their test results to similar test results from the
NFL market reported a decade earlier in Gandar et al. (1988).
The comparison reveals that the NFL market has larger forecast
errors than the NBA market and that a smaller percentage of line
changes in the NFL market moves the closing line towards the
game outcome. The authors state that the apparent differences
in these two markets, both in terms of absolute forecast errors
and the ability of the markets to incorporate additional
information, is intriguing. The authors state further that `future
research into the differences between these markets may be
enlightening' (p. 399). They recognize, however, that differences
in the scoring between football and basketball, as well as
idiosyncratic factors such as weather, may make meaningful
comparisons between these two markets difficult.
Our interest in comparisons between betting markets stems
from the inferences that can be made about the hypothesized
difference in efficiencies across various stock markets in the
United States. This difference is posited to result from the
difference in the amount and timeliness of information found on
the stocks traded in these markets. A number of studies have
attempted to measure the relative efficiencies of US markets.
These studies have found evidence consistent with the notion
that there is significantly greater availability of fundamental
information on stocks traded on the New York Stock Exchange
(NYSE) than on stocks traded in other markets. As a result, stocks
ß Blackwell Publishers Ltd 2001 TESTING EFFICIENCY ACROSS MARKETS 233 traded on the NYSE have been found to be more accurately
priced than those traded in other markets. For example, Brown
(1988) finds that the American Stock Exchange (AMX) and overthecounter (OTC) stocks are less efficiently priced than the
NYSE stocks with respect to price reactions to depreciation
changes. Also, Lease and Lewellen (1982) find that stocks traded
on the NYSE are more accurately priced than stocks traded off
the NYSE.2 A natural limitation of these studies is the uncertainty
regarding the equilibrium prices of stocks traded in these
markets. The use of betting markets overcomes this limitation
and allows for a more direct investigation of price efficiency.
We attempt to address the question of differences in stock
market efficiencies by examining different betting markets.
However, we do not focus on a comparison between the NBA
and NFL markets because of the various differences between
those markets. Instead, we focus on a previously unexamined
market, the NCAA basketball betting market.
We consider the population of NCAA basketball games to be
analogous to the population of publicly traded stocks. Further,
much like the NYSE, the AMX, and the OTC market are separate
markets within the universe of publicly traded stocks, we consider
intraconference games of the various NCAA recognized
conferences (e.g., games among teams within the Atlantic Coast
Conference or games among teams within the Big East
Conference) to be clearly defined markets within the universe
of NCAA basketball games. The advantage of considering intraconference games as separate markets is the ability to test for
differences across markets that are relatively homogeneous in
nature. Thus, we remove most of the fundamental and
idiosyncratic differences that would exist when comparing more
heterogeneous markets such as the NBA and the NFL. Our
comparisons then will allow for inferences to be made about the
effects of differences in information availability across stock
markets.
The remainder of the paper proceeds as follows. Section 2
provides an overview of the NCAA betting market; Section 3
describes the data; Section 4 contains a discussion of the
empirical tests and results; and Section 5 provides a
summarization of the paper. ß Blackwell Publishers Ltd 2001 234 COLQUITT, GODWIN AND CAUDILL 2. THE NCAA BETTING MARKET The NCAA betting market is similar to other point spread betting
markets. The point spread can be viewed as both a market clearing
price and a prediction of an outcome. The opening point spread,
or line, is established by a bookmaker. The goal of the bookmaker
is to establish a line that equalizes the dollars bet on each
competing team. If balanced betting is achieved, then the `eleven
for ten' rule guarantees the bookmaker a riskless profit.3
Therefore, bookmakers evaluate not only the potential game
outcome but also the market's perception of the potential game
outcome when establishing opening lines. As bettors begin to place
a larger proportion of bets on a given team, the bookmaker adjusts
the line to balance the betting and maintain the riskless profit. As a
result, the closing line should reflect all information from both the
bookmaker and the market.4 These lines can then be used in
conjunction with actual game scores to test for efficiency within a
market or, in this case, efficiency across markets. 3. DATA Like Gandar et al. (1998), data for our analysis were obtained
from Computer Sports World, which reports lines from the Stardust
Race and Sports Book located in Las Vegas, Nevada. As stated
previously, we consider intraconference games of the various
conferences as separate markets within the population of NCAA
games.5 The NCAA recognizes a total of 34 Division I
conferences, of which 30 sponsor basketball programs.6 Because
the Stardust Race and Sports Book does not post lines for all
teams, we collect data for the 17 conferences whose teams' lines
are routinely posted.7 These 17 conferences, which are listed in
Table 1, include 174 teams in the most recent sample year (1996/
97). These 174 teams represent roughly 75% of all the teams for
which the Stardust Race and Sports Book posted a game line
during the 1996/97 season. Some conferences, such as the Big
Sky Conference, changed membership during the three year
window examined. For any conference changing its membership,
calculations are based only on those teams in the conference for
a given year.
ß Blackwell Publishers Ltd 2001 235 TESTING EFFICIENCY ACROSS MARKETS Table 1
Conference RPI Ratings
Conference
Atlantic Coast
Big 12
Big East
Southeastern
Big 10
Pacific 10
Conference USA
Atlantic 10
Western Athletic
Missouri Valley
MidAmerican
West Coast
Midwest Collegiate
Sun Belt
Big Sky
Ivy League
Southern 1994/95 RPI 1995/96 RPI 1996/97 RPI Threeyear RPI
Rating (Rank) Rating (Rank) Rating (Rank) Rating (Rank)
0.588 (2)
0.595 (1)
0.581 (3)
0.568 (5)
0.559 (6)
0.579 (4)
N/A
0.545 (7)
0.537 (8)
0.535 (9)
0.517 (11)
0.522 (10)
0.480 (13)
0.472 (14)
0.495 (12)
0.435 (15)
0.433 (16) 0.586
0.568
0.556
0.563
0.563
0.548
0.560
0.526
0.520
0.512
0.501
0.520
0.500
0.490
0.471
0.466
0.449 (1)
(2)
(6)
(4)
(3)
(7)
(5)
(8)
(9)
(11)
(12)
(10)
(13)
(14)
(15)
(16)
(17) 0.592
0.566
0.553
0.556
0.563
0.549
0.533
0.536
0.533
0.518
0.501
0.476
0.468
0.482
0.468
0.480
0.468 (1)
(2)
(5)
(4)
(3)
(6)
(8)
(7)
(9)
(10)
(11)
(14)
(15)
(12)
(16)
(13)
(17) 0.589
0.576
0.563
0.562
0.561
0.559
0.547
0.535
0.530
0.522
0.507
0.506
0.483
0.482
0.478
0.460
0.450 (1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17) Notes:
The Ratings Percentage Index (RPI) measures the relative strength of all National
Collegiate Athletic Association basketball teams and conferences. The 17 conferences
above are those conferences for which the Stardust Race and Sports Book posts lines for
all teams. The RPI rating for each conference is the average RPI rating for all teams within
that conference for that year. No rating is reported for Conference USA for the 1994/95
season because the conference was formed after the season. Table 2 presents some descriptive information on the sample.
The sample contains 4,130 intraconference games played over
three consecutive seasons. The mean difference between the
points scored by the home team and the visiting team (SCORE =
HPOINTS À VPOINTS) represents the home court advantage.
For our threeyear sample, the home court advantage was 4.31
points. This advantage is comparable to that found by Brown and
Sauer (1993) and Gandar et al. (1998) in the NBA market. The
mean closing line (CLINE), also reported on a home points
minus visitor points basis, reflects the market forecast of the
home court advantage. As CLINE is insignificantly different from
SCORE in each of three seasons, CLINE appears to be a good
predictor of SCORE. Similar to Brown and Sauer (1993) and
Gandar et al. (1998), the variation in actual game outcomes is
ß Blackwell Publishers Ltd 2001 236 COLQUITT, GODWIN AND CAUDILL Table 2
Descriptive Statistics on IntraConference Game Scores and Betting
Lines
Season Games Played SCORE CLINE 1994/95 1,291 3.93
(13.45) 4.37
(8.42) 1995/96 1,370 4.21
(13.56) 4.36
(7.97) 1996/97 1,469 4.74
(13.53) 4.43
(7.84) All seasons 4,130 4.31
(13.52) 4.39
(8.07) Notes:
This table reports descriptive information on the 17 National Collegiate Athletic
Association conference basketball games with lines posted by the Stardust Race and
Sports Book during the 1994/95, 1995/96 and 1996/97 seasons. SCORE is the points
scored by the home team less the points scored by the visiting team. CLINE is the closing
line from Stardust Race and Sports Book stated on a home team basis. Standard deviations
are reported in parentheses. much higher than the variation in market forecasts for those
games. 4. EMPIRICAL TESTS AND RESULTS We seek to identify differences in efficiencies of price formation
across the betting line markets of the various conferences under
the assumption that differences in information availability exist
between the conferences.8 Therefore, it is necessary that we first
establish a proxy for the degree of information that is readily
available for each of the 17 betting line markets.
(i) Proxy for Information Availability
The level of information that is readily available on the various
conferences, or teams within a conference, is likely to be
correlated with the overall strength of the teams within each
conference. Presumably, the teams and conferences with the
ß Blackwell Publishers Ltd 2001 TESTING EFFICIENCY ACROSS MARKETS 237 greatest success during the year likely would receive the most
coverage in both the print and television media. Casual
observation provides some support for this hypothesis. For
example, the covers of preseason issues of college sports
magazines are likely to picture a team or player from the Atlantic
Coast Conference (ACC), the Southeastern Conference (SEC) or
the Big 10 Conference rather than a team from the Big Sky
Conference or the Southern Conference. In addition, nationally
televised games are likely to feature teams from the stronger
conferences. During these broadcasts, information about the
teams in the conference is usually provided. Consistent with the
previous studies that attempt to measure the relative efficiency of
the various stock markets, we expect that the conferences with
the greatest amount of available information will have the
greatest efficiency in price formation.
We use the basic formula from the Ratings Percentage Index
(RPI) to measure the relative strength of the teams and
conferences. The RPI is a measure of team strength that is based
both on the winloss record of the team and the strength of the
team's schedule.9 As a result, although two teams may finish the
season with twenty wins and ten losses, the team that played the
more difficult schedule will have a higher RPI. The RPI for a
conference for a particular year is the average RPI of all of the
teams in that conference for that year. Table 1 contains yearly
RPI rankings and the threeyear average RPI rankings for the 17
sample conferences. No RPI rating is reported for Conference
USA for the 1994/95 season because the conference was formed
after the season.
We assume that the RPI is a reasonable proxy for the degree of
information available on a given conference of teams. However,
we do not believe that RPI rankings enable us to assign to each
conference some factor representing the amount of available
information on the teams in that conference. For example, we do
not expect that the rankings in Table 1 indicate that the Atlantic
Coast Conference has 0.013 more units of available information
than the Big 12 Conference. Rather, we believe that the RPI
rankings are best suited to identify those conferences with the
most extreme differences in available information. Comparisons
of the extreme conferences then minimizes the potential for the
measurement error inherent in the RPI proxy to conceal any true
ß Blackwell Publishers Ltd 2001 238 COLQUITT, GODWIN AND CAUDILL differences in efficiencies across the conferences. As seen in
Table 1, the ACC and the Southern Conference are the first and
last conferences in the threeyear average RPI, respectively, and
are therefore the two conferences that are compared.10
Various aspects of the ACC and the Southern Conference
make a comparison between these two conferences attractive.
First, they have a comparable number of teams (nine in the
ACC and eleven in the Southern Conference). Second, they
have a comparable number of intraconference games (240
versus 238). Finally, they are located in the same geographic
region of the country, with over 50% of the teams in each
conference located in either North or South Carolina. This
homogeneity between conferences minimizes concerns about
confounding variables that might bias the comparisons in any
meaningful way.
(ii) Tests of Market Efficiency
If the ACC and Southern Conference betting markets are
efficient, then closing lines should be unbiased predictors of
actual game outcomes. In other words, the expected value of the
markets' forecast errors of game outcomes, conditional on
available information within each conference, should equal zero.
Traditionally, this notion of efficiency has been tested by
estimating the following regression and examining whether
0 0 jointly with 1 1:
j j Y j 0 1 X j 4j Y
1 where Y is the difference in points scored by the two teams, X is
the bookmaker closing line, j is a superscript denoting whether
the scoring differences and closing lines between teams are
stated on a favorite minus underdog basis or a home minus away
basis, and 4 is a random disturbance term.
However, Dare and MacDonald (1998) suggest that equation
(1) is a potentially biased test of market rationality because it fails
to incorporate the symmetry and lack of independence inherent
in a game that, for example, is both a favored versus underdog
game and a home versus away game at the same time. As a result,
Dare and MacDonald develop the following extension of
equation (1) to test for market rationality, which we also employ
ß Blackwell Publishers Ltd 2001 TESTING EFFICIENCY ACROSS MARKETS 239 to test whether the ACC and Southern Conference markets are
rational:
Q
P FH Q
PQ
PQ
P
PQ
1
0
1
0
Y
T Y FA U
T1U
T0U
T À1 U
T0U
U
U
T
TU
TU
T
TU
T Y FN U F T 1 U P T 0 U H T 0 U N T 1 U F
0T U
0T U
0T
0T U
1
U
U
T
R Y HP S
R0S
R1S
R1S
R0S
0
1
0
1
Y PN
Q
Q
P
P
P FH Q
0
X
X FH
T0 U
T ÀX FA U
T X FA U
U
U
T
T
T FN U
T X U H T 0 U N T X FN U 4F X
2
1T
1T
U
U
U
T
R0 S
R0S
R0 S
0
0
0
The dependent variable Y jk is the difference in points scored by
two teams while the independent variable X jk is the closing line
from Stardust Race and Sports Book. The superscript j denotes
whether the scoring difference between teams (Y) and the
closing line (X) are stated on a favorite minus underdog basis (F)
or a home minus away basis (H). The superscript k denotes
whether the team that is first in the order of differencing is the
home team (H), is the away team (A), is playing on a neutral site
(N), or is a `pickem' (P) team. The random disturbance term is
represented by 4. Similar to tests of efficiency in equation (1), the
market is considered rational if the following conditions are
satisfied:
F
P
H
N
H
N
F
0 0 0 0 1 1 0 and 1 1X11 Table 3 reports the results of estimating equation (2) for both
the ACC and the Southern Conference. For each individual
season as well as the pooled seasons, the null hypothesis that:
F
P
H
N
H
N
F
0 0 0 0 1 1 0 and 1 1 cannot be rejected at conventional levels for either conference.
This suggests that both the ACC betting market and the Southern
Conference betting market are efficient given the information
available in each market. In other words, market expectations of
game outcomes are rational expectations. Such evidence is
consistent with findings from the NFL betting market reported in
Gandar et al. (1988).
ß Blackwell Publishers Ltd 2001 240 Table 3
Tests of Market Rationality in the Atlantic Coast Conference and the Southern Conference
1996/97 Season
ACC
Southern ACC 0.09
(2.73) 3.55
(3.45) 0.33
(4.19) 0.23
(3.20) 3.44
(2.61) 2.04
(2.81) 0.90
(1.58) 1.76
(1.76) P
0 2.98
(5.78) À8.25
(9.51) À5.45
(6.08) À11.45
(11.09) 1.33
(7.36) 7.93
(9.04) À1.71
(3.34) À3.13
(5.62) H
0 1.52
(2.67) À1.75
(3.30) 0.85
(4.19) À2.99
(3.20) 0.17
(2.51) À4.43
(2.81) 1.53
(1.53) À3.00
(1.72) N
0 1.45
(5.49) À6.87
(7.32) 2.02
(6.40) 6.88
(8.32) À0.15
(6.49) 7.39
(8.17) 0.09
(3.28) 1.82
(4.32) H
1 À0.19
(0.57) 0.28
(0.56) 0.74
(1.44) 0.38
(0.41) 0.08
(0.49) 0.69*
(0.34) À0.08
(0.34) 0.47
(0.23) N
1 0.05
(0.92) 0.18
(1.23) À0.16
(1.71) À0.88
(0.80) À0.69
(1.17) 1.12
(0.99) À0.42
(0.60) 0.09
(0.53) F
1 0.94
(0.57) 0.50
(0.58) 0.28
(1.44) 1.28*
(0.41) 0.48
(0.51) 0.56
(0.34) 0.80*
(0.35) 0.82*
(0.24) 0.29
0.30
80 0.21
0.67
80 0.27
0.81
80 0.45
1.31
78 0.29
0.63
80 0.42
1.30
80 0.30
0.60
240 0.38
1.08
238 R2
Fstatistic
n Three Seasons
Southern Notes:
This table reports the results of estimating equation (2). The regression is estimated separately on intraconference games within the Atlantic Coast Conference
(ACC), which is considered the high information market, and the Southern Conference, which is considered the low information market. Standard errors are
F
P
H
N
H
N
F
reported in parentheses. The Fstatistic tests the null hypothesis that 0 0 0 0 1 1 0 and 1 1. Failure to reject the null hypothesis
implies market rationality in these markets. Coefficients statistically different from zero at less than the 0.05 level are denoted with *. COLQUITT, GODWIN AND CAUDILL 1995/96 Season
ACC
Southern F
0 ß Blackwell Publishers Ltd 2001 1994/95 Season
ACC
Southern TESTING EFFICIENCY ACROSS MARKETS 241 (iii) Tests of Forecast Accuracy
While we find that differences in information availability across
these conference betting markets do not result in differences in
efficiencies, we expect that information differences will result in
differences in forecast accuracy across conferences. We examine
this expectation by calculating the absolute forecast error (AFE)
for each game and comparing the average errors across
conferences. The absolute forecast error is calculated as follows:
AFE jSCORE À CLINEjY
3 where SCORE and CLINE are defined as above. If increased
information results in better forecast accuracy, then we should
expect to find smaller absolute forecast errors in the ACC games
than in the Southern Conference games.
Table 4 contains the yearly and threeyear absolute forecast
errors for both conferences. The forecast errors for the ACC are
consistently smaller than the errors for the Southern Conference,
with the threeyear error significantly smaller at conventional
levels. These differences suggest that in terms of pricing the game
outcomes, market participants were more accurate in pricing the
ACC games than in pricing the Southern Conference games.12
While the above comparisons of forecast errors are appealing
because the errors can be cast in terms of points and therefore
easily visualized, a statistical test of the error variances from the
original regression estimations reported in Table 3 is possible. The
error variance is a measure of the degree to which the closing line
and other explanatory variables in our model cannot explain the
actual game outcome. Consistent with the differences in forecast
errors, we expect that if information differs across conferences and
information availability affects price accuracy, the error variances
will be different across conferences. More specifically, the error
variance in the low information conference (i.e., the Southern
Conference) should be greater than the error variance of the high
information conference (i.e., the ACC). To determine whether the
differences in error variances are significant, we calculate an Fstatistic by dividing the mean square error for the Southern
Conference by the mean square error for the ACC. In each year,
the Fstatistic exceeds the critical value for conventional levels of
significance, confirming that market participants were more
ß Blackwell Publishers Ltd 2001 242 COLQUITT, GODWIN AND CAUDILL accurate in pricing the ACC game outcomes than in pricing the
Southern Conference game outcomes. The relevant error
variances and Fstatistics are reported in Table 4.
As stated earlier, we assume that the ACC and the Southern
Conference are relatively homogeneous in nature. One area in
which they differ is the total number of points scored per game.
For our threeyear sample, Southern Conference teams scored a
total of eight more points per game than ACC teams. This
heteroskedasticity, which might arise from differences in player
ability, officiating, or some other factor(s), may account for the
increased error variance in the Southern Conference.
To test whether the error variance of the conference games
increases with the number of points scored, we employed the
GoldfeldQuandt test. The GoldfeldQuandt test requires that the
data first be ranked on the variable suspected to be causing the
heteroskedasticity. The data is then divided into thirds, the
middle third is eliminated, and the regression is estimated on
each of the two remaining groups. An Fstatistic is then calculated
with the two regression error variances to test for equality
between the variances. An Fstatistic that is insignificantly
different from one implies that error variances are not different
across the two groups, which indicates that the variances are not a
function of the identified variable. We applied the GoldfeldQuandt test to both conferences over the threeyear period, and
the resulting Fstatistics were not significantly different from one
at conventional levels. Thus, differences in points scored cannot
explain the differences in error variances.
(iv) Robustness Tests
A natural question concerning our conclusions is whether they
are robust to the inclusion of other conferences or simply a
product of the ACC and the Southern Conference. We address
this question by conducting similar tests across two groups of
conferences. The first group is comprised of the three
conferences that have the highest RPI ratings in a given year
(Top 3) while the second group is comprised of the three
conferences that have the lowest RPI ratings in each year
(Bottom 3).13 Conferences included in this comparison for at
least one year include the ACC, the Big 12 Conference, the Big
ß Blackwell Publishers Ltd 2001 Comparison of Forecast Accuracy Across the Atlantic Coast Conference and the Southern Conference
1994/95 Season
ACC
Southern
Games
Played
Absolute
Forecast
Error
Error
Variance
Fstatistic 1995/96 Season
ACC
Southern 1996/97 Season
ACC
Southern 80 80 80 80 7.43** 10.03 105.19 158.95
1.51* 78 7.95*** 97.27 11.54 204.52
2.10*** 80 7.88* 9.73 95.68 147.67
1.54* Three Seasons
ACC
Southern
240 238 7.75*** 96.80 10.42 171.26
1.77*** Notes:
Absolute forecast errors (AFE) on intraconference games within the Atlantic Coast Conference (ACC) and the Southern Conference are calculated as
follows: AFE = SCORE À CLINE. SCORE is the points scored by the home team less the points scored by the visiting team. CLINE is the closing line
from Stardust Race and Sports Book stated on a home team basis. Error variances are the residual sum of squares from the regressions estimated in
Table 3. The Fstatistic is calculated by dividing the error variance of the Southern Conference by the error variance of the ACC. Absolute forecast
errors that are statistically different across conferences at less than the 0.05 (0.01) [0.001] level and Fstatistics that are statistically different from one at
less than the 0.05 (0.01) [0.001] level are denoted with * (**) [***]. TESTING EFFICIENCY ACROSS MARKETS ß Blackwell Publishers Ltd 2001 Table 4 243 244 COLQUITT, GODWIN AND CAUDILL East Conference, and the Big 10 Conference in the high
information group and the Southern Conference, the Ivy
League, the Sun Belt Conference, and the Big Sky Conference
in the low information group. Thus, almost half of all 17
conferences are represented in the comparisons to some degree.
Table 5 reports the results of the estimation of equation (2) for
the Top 3 and Bottom 3 conferences. Although the null
F
P
H
N
H
N
F
hypothesis that 0 0 0 0 1 1 0 and 1 1
can be rejected at the 0.05 level for the three conferences at the
bottom of the RPI rating in the 1995/96 season, it cannot be
rejected at conventional levels for either group of conferences
over the three seasons.
Table 6 reports the absolute forecast errors, the error variances,
and the Fstatistics for each group of conferences. Over the three
year window, the three conferences at the top of the RPI rankings
exhibit significantly lower absolute forecast errors and significantly
lower error variances than the three conferences at the bottom of
the RPI rankings. Thus, our conclusions appear to be robust to the
inclusion of additional conferences. 5. SUMMARY This study examines whether differences in the availability of
information across markets result in different efficiencies in price
formation across those markets. Several studies of the relative
efficiencies of the US stock markets have found evidence
consistent with the hypothesis that differing markets exhibit
different relative efficiencies. However, conclusions in such studies
are limited by the inability to establish fundamental stock values.
We show that for markets within the NCAA basketball betting
market, where fundamental values are known with certainty,
efficiency in price formation differs across those markets. More
specifically, participants in the betting markets of conferences
with greater (lesser) information availability misprice the
fundamental values of the conference games to a lesser (greater)
degree. Such evidence supports the conclusions reached in
studies of stock markets suggesting that differences in
fundamental information result in different relative pricing
efficiencies across those markets.
ß Blackwell Publishers Ltd 2001 Tests of Market Rationality in the Conferences with the Highest and Lowest RPI Ratings
1994/95 Season
Top 3
Bottom 3 1995/96 Season
Top 3
Bottom 3 1996/97 Season
Top 3
Bottom 3 Three Seasons
Top 3
Bottom 3 F
0 À1.26
(1.12) 0.69
(1.35) À1.26
(1.57) 0.84
(1.78) 0.63
(1.20) À1.97
(1.69) À0.39
(0.81) À0.08
(0.91) P
0 1.06
(4.43) À7.45
(6.47) À5.77
(4.19) À7.99
(7.46) À0.68
(4.03) 7.48
(6.94) À2.04
(2.40) À2.92
(4.03) H
0 À0.77
(1.55) À0.55
(1.32) 0.40
(1.49) À1.70
(1.74) 0.96
(1.17) À2.15
(1.64) 0.26
(0.78) À1.20
(0.89) N
0 3.00
(2.92) À7.67
(4.37) 4.16
(3.33) 2.10
(3.39) À1.03
(3.82) 8.68
(4.71) 2.08
(1.85) 2.13
(2.21) H
1 0.08
(0.28) À0.05
(0.14) 0.01
(0.21) 0.06
(0.23) À0.01
(0.17) 0.41
(0.22) 0.03
(0.11) 0.10
(0.11) N
1 0.20
(0.42) 0.26
(0.61) À0.04
(0.41) À0.81*
(0.39) 0.05
(0.51) À0.45
(0.62) 0.10
(0.24) À0.50
(0.27) F
1 1.06*
(0.28) 1.00*
(0.15) 0.98*
(0.22) 1.20*
(0.22) 0.89*
(0.17) 1.12*
(0.23) 0.95*
(0.12) 1.10*
(0.11) R2
Fstatistic
n 0.36
0.56
225 0.44
1.05
222 0.35
0.93
239 0.46
2.22*
196 0.41
0.29
286 0.43
1.63
220 0.38
0.89
750 0.43
1.70
638 245 Notes:
This table reports the results of estimating equation (2). The regression is estimated separately on intraconference games within the three conferences with the highest
RPI ratings each year, which are considered the high information markets, and the three conferences with the lowest RPI ratings each year, which are considered the low
F
P
H
N
H
N
F
information markets. Standard errors are reported in parentheses. The Fstatistic tests the null hypothesis that 0 0 0 0 1 1 0 and 1 1. Failure to
reject the null hypothesis implies market rationality in these markets. Fstatistics and regression coefficients significantly different from zero at the 0.05 level are denoted
with *. TESTING EFFICIENCY ACROSS MARKETS ß Blackwell Publishers Ltd 2001 Table 5 246 Table 6
Comparison of Forecast Accuracy Across Conferences with the Highest and Lowest RPI Ratings
1994/95 Season
Top 3
Bottom 3 Absolute
Forecast
Error
Error
Variance
Fstatistic 225 222 8.49 8.65 120.41 120.49
1.00 239 196 8.96* 10.32 122.46 155.49
1.27* 1996/97 Season
Top 3
Bottom 3
286 220 8.11* 9.43 104.08 136.35
1.31* Three Seasons
Top 3
Bottom 3
750 638 8.49** 110.18 9.43 138.74
1.22** ß Blackwell Publishers Ltd 2001 Notes:
Absolute forecast errors (AFE) on intraconference games within the three conferences with the highest RPI ratings each year and the three
conferences with the lowest RPI ratings each year are calculated as follows: AFE = SCORE À CLINE. SCORE is the points scored by the home team
less the points scored by the visiting team. CLINE is the closing line from Stardust Race and Sports Book stated on a home team basis. Error variances
are the residual sum of squares from the regressions estimated in Table 5. The Fstatistic is calculated by dividing the error variance of the low RPI
conferences by the error variance of the high RPI conferences. Absolute forecast errors that are statistically different across conferences at less than the
0.05 (0.01) [0.001] level and Fstatistics that are statistically different from one at less than the 0.05 (0.01) [0.001] level are denoted with * (**) [***]. COLQUITT, GODWIN AND CAUDILL Games
Played 1995/96 Season
Top 3
Bottom 3 TESTING EFFICIENCY ACROSS MARKETS 247 NOTES
1 Racetrack and baseball betting markets have also received attention from
researchers. However, these markets are based on the odds of winning
rather than on the point spread estimates of the game being played.
2 In addition to the studies comparing markets within the US, there have also
been studies conducted that analyze the relative efficiency of markets
around the world (see Barnes, 1986; and Antoniou, Ergul, Holmes and
Priestly, 1997).
3 The `eleven for ten' rule dictates a payoff of $21 for each $11 bet on the
team beating the spread. Suppose that the point spread resulted in one
bettor of $11 for each team. The bookmaker receives $22 and pays $21 to
the winning bettor. Therefore, regardless of the outcome of the game, the
bookmaker earns a riskless profit of $1.
4 Results from Gandar et al. (1998) are consistent with closing lines reflecting
information from both the bookmaker and market participants.
5 We limit our analysis to intraconference games to avoid the inclusion of
games involving teams from other conferences that may have differential
information availability.
6 Some conferences, such as the Central Collegiate Hockey Association, are
formed specifically for nonbasketball sports.
7 Bookmakers often do not post lines for games between smaller schools and
for games in which significant uncertainty exists (e.g., whether or not a star
player will participate).
8 Such an assumption is consistent with the assumption made by stock market
researchers that differing degrees of information are available on the stocks
that are traded in the three major US stock markets (i.e. the NYSE, the AMX
and the OTC market).
9 The basic formula of the RPI consists of the following: 25% is made up of
the team's winning percentage; 50% is the opponents' average winning
percentage; and 25% is made up of the opponents' opponents' average
winning percentage. There is an undisclosed adjustment that the NCAA
makes to the basic formula of the RPI to compute the official RPI. It is not
expected that this adjustment is significant enough to cause our use of the
basic formula of the RPI to be problematic. Incidentally, the official RPI is
used as a factor in selecting the teams that will participate in the NCAA
tournament and the seeding of the teams that make the tournament (Palm,
1998).
10 Note that the Southern Conference is ranked last in each of the three years
and the ACC is ranked first in two years and second in the other.
11 See Dare and MacDonald (1998) for a detailed discussion of the merits of
equation (2) and the conditions for market efficiency.
12 Because the purpose of testing forecast errors was to determine the effect
on price formation of differential information across markets, we based the
forecast errors on closing lines, which reflect information from both the
bookmaker and market participants. In light of Gandar et al.'s (1998)
results on line changes, a natural question is whether the differences in
price formation that we found were a product of the bookmaker's opening
line, line changes resulting from participant betting, or both. Basing
forecast errors on opening lines (that is, bookmaker price formation only),
we find similar differences in price formation across the ACC and Southern
Conference. Additionally, we find no evidence that line changes move the
ß Blackwell Publishers Ltd 2001 248 COLQUITT, GODWIN AND CAUDILL lines towards game outcomes more for one conference than another.
13 The three conferences with the highest average RPI ratings for the sample
period are the ACC, the Big 12 Conference, and the Big East Conference.
However, the Big East Conference has the third highest average RPI rating
due primarily to its strength in only one of the three sample years, 1994/95.
The Big East Conference finishes sixth and fifth during the years 1995/96
and 1996/97, respectively. The fourth and fifth strongest conferences, as
measured by the threeyear RPI rating, had similar variability with regard to
the RPI rating for each of the sample years. As a result, the intraconference
games from the top three teams during each separate sample year comprise
the high information group. Similar variation in rankings occurs at the
bottom of the RPI list and, therefore, the intraconference games from the
bottom three teams during each separate sample year comprise the low
information group. REFERENCES
Antoniou, A., N. Ergul, P. Holmes and R. Priestly (1997), `Technical Analysis,
Trading Volume and Market Efficiency: Evidence from an Emerging
Market', Applied Financial Economics, Vol. 7, pp. 361±65.
Barnes, P. (1986), `Thin Trading and Stock Market Efficiency: The Case of the
Kuala Lumper Stock Exchange', Journal of Business Finance & Accounting,
Vol. 13, No. 4 (Winter), pp. 609±17.
Brown, R.M. (1988), `A Comparison of Market Efficiency Among Stock
Exchanges', Journal of Business Finance & Accounting, Vol. 15, No. 3
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Brown, W.O. and R.D. Sauer (1993), `Fundamentals or Noise? Evidence from
the Professional Basketball Betting Market', Journal of Finance, Vol. 48, pp.
1193±209.
Dare, W.H. and S.S. MacDonald (1998), `A Generalized Model for Testing the
Home and Favorite Team Advantage in Point Spread Markets', Journal of
Financial Economics, Vol. 40, pp. 295±318.
Gandar, J.M., W.H. Dare, C.R. Brown and R.A. Zuber (1998), `Informed Traders
and Price Variations in the Betting Market for Professional Basketball
Games', Journal of Finance, Vol. 53, pp. 385±401.
________, R.A. Zuber, T. O'Brien and B. Russo (1988), `Testing Rationality in
the Point Spread Betting Market', Journal of Finance, Vol. 43, pp. 995±1008.
Golec, J. and M. Tamarkin (1991), `The Degree of Inefficiency in the Football
Betting Market', Journal of Financial Economics, Vol. 30, pp. 311±23.
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NFL Sports Betting Market', Journal of Finance, Vol. 52, pp. 1725±37.
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Palm, J. (1998), `RPI FAQ', http://users.aol.com/boilerjp/rpifaq.html (6/4/
98). ß Blackwell Publishers Ltd 2001 ...
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