Eric MOLAY [e-mail] CEROG

1
Eric MOLAYeric.molay_at_unice.frCEROG IAE
Aix en ProvenceRisk Asset Management EDHEC
Nice

• The Cross-Section of the Expected Stock Returns
  at the Paris Stock Exchange

2
CAPM empirical validation ?

• Positive linear relation returns ? b
• Cross-sectional returns anomalies
• Market value RMV- gt RMV
• Book-to-market ratio RBM gt RBM-
• No significant relation returns ? b
• CAPM ? three-factor model ?

3
Empirical analysis critics

• Three-factor model ? APT
• Data mining, selection and survivor bias
• Investors psychology
• Errors-in-variables problem (EIV)

4
Errors in variables problem

• Relation between expected returns and beta
• Time series estimates of b
• Cross-sectional estimates of the relation between
  expected returns and b
• Are the cross-sectional coefficient estimates
  significant ?

5
Aim of this study

• Cross-sectional analysis on the French market
• Use of Fama et French 92 methodology
• Relationship
• Expected stock returns ? b
• Expected stock returns ? market value and
  book-to-market ratio
• Expected stock returns ? s et h (three-factor
  model FF 93)
• Do correction to the Fama-MacBeth t-statistics

6
Database

• Datastream International
• Stocks returns at the Paris SE (mean 250 )
• 120 months time series July 88 ? June 98
• Arithmetic returns adjusted
• Dividend payments
• Capital changes

7
Independent variables

• Specific factors
• Market value MV P x N
• Book-to-market ratio BV/MV NTA/MV
• "Risk premiums" ? coefficients
• CAPM ? b
• Fama et French three-factor model (FF 93)
• SMB (Small Minus Big) ? s
• HML (High Minus Low) ? h

8
Expected returns ? b

• Time-series estimates of the b over 30 months
• Cross-sectional estimates expected returns ? b
  
• Fama-MacBeth t-statistics corrections
• EIV correction (Shanken 92)
• GLS estimates (Ferson and Harvey 99)

9
Expected returns ? b
g0 g1 R²

gi 0,69 0,15 0,012
tfm(gi) (1,28) (0,83)
ts(gi) (1,16) (0,67)
tfh(gi) (1,46) (1,16)
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Expected returns ? b, MV, BM

• Time-series estimates of the b over 30 months
• Cross-sectional estimates
• Expected returns ? b
• Expected returns ? MV and/or BM
• Expected returns ? b and/or MV, BM
• Adjusted Fama-MacBeth t-statistics
• GLS (Ferson and Harvey 99)

11
Expected returns ? MV, BM
g0 g1 g2 g3 R²

gi -0,45 0,56 0,022
tfh(gi) (0,60) (2,38)

gi 0,47 -1,52 0,014
tfh(gi) (0,75) (3,18)
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Expected returns ? b, MV, BM
g0 g1 g2 g3 R²

gi -1,09 0,47 0,59 0,040
tfh(gi) (0,75) (2,49) (2,54)

gi 0,05 0,41 -1,43 0,032
tfh(gi) (0,93) (2,25) (2,94)
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Expected returns ? b, s, h

• Time-series estimates of the b, s and h over 30
  months
• Cross-sectional estimates expect. ret. ? b, s,
  h
• Adjusted Fama-MacBeth t-statistics
• GLS (Ferson and Harvey 99)

14
Expected returns ? b, s, h
g0 g1 g2 g3 R²

gi 0,74 0,12 -0,10 0,08 0,046
tfm(gi) (1,50) (0,76) (0,54) (0,32)
ts(gi) (1,42) (0,65) (0,32) (0,13)
tfh(gi) (1,81) (1,08) (0,12) (0,65)
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Expected returns ? s, h
g0 g1 g2 g3 R²

gi 0,83 -0,07 0,012
tfh(gi) (0,60) (2,38)

gi 0,79 0,11 0,022
tfh(gi) (1,64) (0,81)
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Expected returns ? b, s or h
g0 g1 g2 g3 R²

gi 0,42 0,42 -0,16 0,026
tfh(gi) (0,90) (2,41) (0,37)

gi 0,41 0,37 0,11 0,033
tfh(gi) (0,61) (2,12) (0,68)
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Conclusion

• No significant relation between expected returns
  and estimated coefficients b or s and h
• Errors in variables problem
• Two-pass procedure problem
• Significant relation between expected returns
  and
• Non estimated factors ("attributes") MV and BM
• b coefficient in association with MV, BM, s or h
• ? MV, BM, s et h conditional factors ?