Word January Effect

Both the CAPM and the APT are models of simplification of the reality that help to understand and explain the return of the stocks. They are base on principles of the portfolio diversification. The CAPM is based on a regression made stock by stock, which is the market model. For the market model to be consistent with the CAPM, some restrictions must be imposed such as rf=αi for all stocks, the error terms must not have any cross-sectional correlation and no other variables or factors can help to explain stock returns.

Instead of estimating the regression Rit=αi + βi(Rmt-rf)+εit and testing rf=αi, we will estimate this equation Rit - rf =αi + βi(Rmt- rf)+εit, and it is equivalent if we test αi = 0.

To compute this first test αi=0, we used the data portfolios formed on size from the Fama French website. We considered 1028 obervations. We generated new series in order to calculate the excess returns « p1_rd = p1-rf » this for all 10 portfolios. We can reject or not the hypothesis that αi=0 at 95% level of confidence.

Then we test if the cross-sectional correlation of the error terms is equal to 0. Therefore for every regression made in test 1 (above) we obtain the residuals for all 10 series to be opened in group and we test their autocorrelation. Out of the 45 possible portfolio pairs we define how many correlations are different from 0.

1) Test αi=0 with and without the dummy variable :

H0 : αi=0

H1 : αi≠0

Looking at the regressions in the excel files, we can see that, the p-value of the intercept αi for all the portfolios are above 0,05 so we cannot reject the null hypothesis. So the αi are not statistically significant at 95% level of confidence.

As the Betas are significant, it confirms the first assumption which is that the market model is consistent.

2)

Moreover, referring to the cross-correlation matrix of the residuals of both regressions with and without the dummy variable on the excel file, we can see that all the correlations (out of 45 possible portfolio pairs) different from 0.

Logically, the correlation between 2 small caps' portfolios (i.e. P1 & P2) is much higher than between one small and one large cap's portfolio (i.e. P1 & P10).

In other words, it means that the portfolios having a same kind of market capitalizations will have returns reacting in the same opposite whereas two portfolios having different kind of market capitalizations will have returns reacting in the opposite direction.

Despite these observations, we cannot say that the market and CAPM models are consistent with each other.

We can only say that the correlations for the model with dummy are

The autocorrelation of the errors are very similar to the first model but a little bit lower for every correlations. Thus, we can think that the jannuary effect exists but do not explain fully the returns of the different portfolios.

3) Referring on the graphs on the excel file, sheet « trends of the alphas », we can see that there are trends in both regressions with and without dummy.

In the regressions

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