School of Business and EconomicsHumboldt University Berlin

cschmidt@wiwi.hu-berlin.de

Overconfidence and Prediction Bias in

Political Stock Markets

Carsten Schmidt (joint work with Michael Berleman, ifo Institute Dresden)

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 Proportional representation vs. Winner- takes-all

– Polls Adjusted vs. raw data

Market level: market complexity – Empirical contribution (Berg et al., 1997)– Number of different contracts (candidates/parties) is highly

correlated with MAE Contract level: overconfidence Bias

– 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)

German data17 Elections, 34 PSM1990-2003

US data16 Elections,16 PSMBerg et al. (1997)

No of contractsK

5 - 7 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

Kvv

Kvv iiii

1 if small"" is

1 if large"" is

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– Bias not significant in US data (Forsythe et al., 1999

JEBO) Market level

– 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

K

iii vv

KMAE ˆ

1

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>1-v=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

0.0

0.1

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0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

v1 p1 Theil

Measure for more than 2 contracts

MAE increases when the vote shares become more unequal

Captured for instance by a Theil coefficient

N

iii vKvTheil

1

ln

Number of contracts K=2, ε=0.025

0.0

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

v1 p1 Theil