A State-Space Version of Fama and French’s Three-Factor Model: Evidence from the Tunisian Stock Exchange

  •  Nejla Bergaoui    
  •  Abdelwahed Trabelsi    


We develop a state-space version of the three-factor model of Fama and French (1993) for exploring the macroeconomic determinants of risk underlying size (SMB) and value (HML) factors. To the best of our knowledge, this is the first study that examines how loadings on HML and SMB factors are affected by unanticipated changes in macroeconomic factors and whether they exhibit an asymmetric behavior over the business cycle. We test the hypothesis that the betas associated with HML and SMB factors of firms with different size or a different BE/ME ratio react differently to changes in macroeconomic conditions. In addition to the hypothesis that some type of stocks (value and small ones) become more responsive to such a change during period of economic contraction than during an expansion. Our focus is the Tunisian stock Exchange. The evidence we found supports the time variation of portfolios returns’ sensitivities to market, HML and SMB factors with unanticipated changes in monetary and economic conditions. Hence, the assumption of constant coefficients in the traditional three-factor model seems to be unreasonable. Betas associated with HML and SMB factors showed countercyclical behavior through the phases of the business cycle. In a recession, value (small) firm’s risk associated with the HML (SMB) factor is more strongly affected by worsening credit market conditions than during an economic expansion. Further results show that value (small) firm’s risk associated with the HML (SMB) factor is more strongly affected by tighter credit market conditions than growth (large) firm’s risk. Thus, our results most closely support a risk-based explanation for SMB and HML.

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