AFFI 2002 Strasbourg Eric MOLAY The Cross-Section of the Expected Stock Returns at the Paris Stock Exchange Eric MOLAY eric.molay@unice.fr CEROG – IAE Aix en Provence Risk & Asset Management – EDHEC Nice JUIN 2002

CAPM empirical validation ? Positive linear relation : returns  b Cross-sectional returns anomalies : Market value : RMV- > RMV+ Book-to-market ratio : RBM+ > RBM- No significant relation : returns  b CAPM  three-factor model ? AFFI june 2002

Empirical analysis critics AFFI 2002 Strasbourg Eric MOLAY Empirical analysis critics Three-factor model  APT Data mining, selection and survivor bias Investors psychology Errors-in-variables problem (EIV) AFFI june 2002 JUIN 2002

Errors in variables problem AFFI 2002 Strasbourg Eric MOLAY 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 ? AFFI june 2002 JUIN 2002

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 AFFI june 2002

Database Datastream International™ AFFI 2002 Strasbourg Eric MOLAY 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 AFFI june 2002 JUIN 2002

Independent variables AFFI 2002 Strasbourg Eric MOLAY 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 AFFI june 2002 JUIN 2002

Expected returns  b Time-series estimates of the b over 30 months: AFFI 2002 Strasbourg Eric MOLAY 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) AFFI june 2002 JUIN 2002

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) AFFI june 2002

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) AFFI june 2002

Expected returns  MV, BM g0 g1 g2 g3 R² gi -0,45 0,56 0,022 tfh(gi) (0,60) (2,38)* 0,47 -1,52 0,014 (0,75) (3,18)* AFFI june 2002

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)* 0,05 0,41 -1,43 0,032 (0,93) (2,25)* (2,94)* AFFI june 2002

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) AFFI june 2002

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) (0,13) tfh(gi) (1,81) (1,08) (0,12) AFFI june 2002

Expected returns  s, h g0 g1 g2 g3 R² gi 0,83 -0,07 0,012 tfh(gi) (0,60) (2,38)* 0,79 0,11 0,022 (1,64) (0,81) AFFI june 2002

Expected returns  b, s or h g0 g1 g2 g3 R² gi 0,42 -0,16 0,026 tfh(gi) (0,90) (2,41)* (0,37) 0,41 0,37 0,11 0,033 (0,61) (2,12)* (0,68) AFFI june 2002

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 ? AFFI june 2002