Overconfidence and Prediction Bias in
Political Stock Markets
Carsten Schmidt
(joint work with Michael Berleman, ifo Institute Dresden)
School of Business and Economics
Humboldt University Berlin
cschmidt@wiwi.hu-berlin.de
The Puzzle

US political stock markets were very successful
in predicting the election results
–
–

IEM predict result of the presidential election
Bush/Dukakis 1988 with a MAE of 0.2% (Forsythe et
al., 1992, AER)
Forsythe et al., 1997, JEBO
European election markets were not
(significantly) better than polls. Relatively
higher MAE compared to US markets.
–
–
–
–
Netherlands: Jacobsen et al., 2000, EER
Austria: Ortner
Sweden: Bohm and Sonnegard, 1999, ScanJE
Germany: Berlemann und Schmidt (this meta-study)
MAE PSM 1.394, Polls 1.524, (T=1.198, p <0.126)
Driving forces

Institutions
–
Election system

–
Polls


–
Empirical contribution (Berg et al., 1997)
Number of different contracts (candidates/parties) is highly
correlated with MAE
Contract level: overconfidence Bias
–
–
–
–

Adjusted vs. raw data
Market level: market complexity
–

Proportional representation vs. Winner- takes-all
Theoretical contribution (Jacobsen et al., 2000, EER
Overvaluation of small contracts, undervaluation of relatively large
contracts
Disparity of different contracts
Bias not significant in US data (Forsythe et al., 1999, JEBO)
Trader level
–
Individual mistakes do not bias prediction in US data
A benchmark: poll prediction

In the US poll data is reported raw
–

Prediction error of PSM is significant smaller
European pollster report corrected data
–
–
Correction is a black box, pollster use different approaches
Prediction error of German PSM is slightly smaller (marginal
significant)
Party
Allensbach raw
data
Allensbach
prediction
Election result
CDU/CSU
38,8
43,5
44,5
SPD
46,5
43,5
42,9
FDP
11,1
10,0
10,6
Sunday question, German federal election 1980, source: Allensbach
Meta study German data


Method: Empirical meta study
Data: Final prediction of all German election
markets (and all corresponding public polls
for the election)
–
–
Vote share markets
Homogeous in the number of contracts (parties)

–
CDU,SPD,Grüne,FDP,PDS,Rep,Rest of Field
Different organizer (academia, commercial)
Field data (meta study)
No of contracts
K
German data
17 Elections,
34 PSM
1990-2003
5-7
US data
16 Elections,
16 PSM
Berg et al. (1997)
2-6
Theil coefficient
0.41
0.16
No of
Presidential or
Federal Elections
4
3
German data: contract level
Prediction error: contract level

Criterion
– vi = true vote share of contract i
– K = Number of different contracts
1
vi is " large" if vi 
K
1
vi is " small" if vi 
K
Prediction error: contract level (2)
What makes markets predict well
revisited: market level
Conclusions

We find overvaluation of small contracts,
undervaluation of relatively large contracts in
German PSM data
–

Market level
–
–
–

Bias not significant in US data (Forsythe et al., 1999
JEBO)
Market complexity in US data (Berg et al., 1997)
Market complexity constant in German data
Electoral uncertainty and market efficiency
Contract level: overconfidence bias
–
–
–
Jacobsen et al. (2000) EER
Overvaluation of small contracts
Disparity of different contracts (not significant)
Implications for PSM



PSM in Europe predict less successful than in
he US because of the diversity of the vote
shares and the complexity of the markets
Polls in Europe predict more successful than in
the US by correcting the raw data: the poll
instrument is not biased by diversity of vote
shares and the complexity of the markets
Market design implications
–
–
Minimizing number of contracts
Correcting for the diverse vote share bias
Error measures
1
MAE 
K
K
 v  vˆ
i
i
i
Theory



Assumption: Trade is not driven by
different preferences, but by individual
information of the traders about the
election result
v(1-v) is the unknown, true vote share
of party P1(P2)
Each trader receives a private signal si Є
[v-ε,v+ε]
Theory (2)







Definition p:= p1=1-p2
Buy P1 if market price p1<si
Buy P2 if market price p2<1-si
In equilibrium p is determined that the
demand for both parties is equal
Assumption: traders have the same
endowment E
Signal si<p  buy E/p contracts P1
Signal si>p  buy E/(p-1) contracts P2
Predictions on contract level

p=(v+ ε)/(1+2ε)
–
Winner of the election

–

if v>1/2 that means p>1/2
Only if v1=v2=1/2 p is an unbiased
estimator
v1=v>1/2  p1=p<v=v1, p2=1-p>1v=v2
–
Large parties are undervalued, small parties
are overvalued
Predictions

Market level
–
–

Mean absolute error (MAE) increases with ε
Electoral uncertainty
MAE increases when the vote shares become
more unequal – diversity of the vote shares
Contract level
Number of contracts K=2, ε=0.025
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
v1
0.5
p1
0.6
Theil
0.7
0.8
0.9
1.0
Measure for more than 2 contracts


MAE increases when the vote shares
become more unequal
Captured for instance by a Theil coefficient
N
Theil   vi  ln K  vi 
i 1
Number of contracts K=2, ε=0.025
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
v1
0.5
p1
0.6
Theil
0.7
0.8
0.9
1.0