Portfolios sorted by size

As the results for the single-signal portfolios indicate a relation with size for all the signals, the portfolios are divided into subsamples based on their market capitalization.

For each period, the firms are classified by size to small, medium, and large subsamples.

Companies are ranked based on their market capitalization for the current period in descending order. Large stocks are defined as those that account for 90% of the market capitalization of the sample, medium stocks as those that account for the following 8 percentage points, and the remaining are defined as small stocks. The method is like that of Tikkanen and Äijö (2018) and Asness et al. (2013).

The table below reports the excess returns and Fama-French five factor loadings of the momentum portfolios sorted by size.

Table 5. Momentum portfolio returns sorted by size Momentum portfolio returns sorted by size

The table below reports the monthly excess returns and Fama-French five factor loadings of the portfolios sorted by size and momentum. Stocks in the sample are ranked in descending order based on their market capitalization for each month. Large stocks account for 90% of the total market capitalization, medium stocks for the following 8% and small stocks the remaining 2%.

Stocks in the subsample are then assigned to five quintile portfolios based on their ranking for the momentum signal. High - Low is the long/short portfolio composed of the extreme quintiles, and factor loadings are for the long/short portfolio

Panel A: Portfolio monthly excess returns

The momentum effect is especially strong in the small sample, with a monthly average excess return of 1.47%, and monthly alpha of 1.26%, both statistically significant at 1%

level. The momentum effect can also be found in the medium subsample, where the excess return is 0.91% with an alpha of 0.83%. As the alpha decreases with larger stocks, the profitability factor of the stocks also increases, explaining some of the decrease in alpha in addition to the decrease in excess returns. While a significant alpha cannot be found for the large subsample, it still has statistically significant excess returns. A statistically significant alpha can be found for the medium subsample.

The table below reports the excess returns and Fama-French factor loadings of the value portfolios sorted by size.

Table 6. Value portfolio returns sorted by size Value portfolio returns sorted by size

The table below reports the monthly excess returns and Fama-French five factor loadings of the portfolios sorted by size and value. Stocks in the sample are ranked in descending order based on their market capitalization for each month. Large stocks account for 90% of the total market capitalization, medium stocks for the following 8% and small stocks the remaining 2%. Stocks in the subsample are then assigned to five quintile portfolios based on their ranking for the value signal. High - Low is the long/short portfolio composed of the extreme quintiles, and factor returns are stronger among small stocks. Whereas the returns for the high quintile are roughly the same for each of the size-sorted portfolios, the difference arises from the low quintile. The small-low portfolio generates a monthly average excess return of 0.48%, and the large-low portfolio generates a larger monthly excess return of 0.77%.

The spread between high and low B/M firms is thus much lower among large firms. The findings with Fama-French alphas are similar; the small, long-short portfolio is able to generate a higher alpha than the large, long-short portfolio, but majority of the returns

are captured by the HML factor. The results indicate that the intrinsic value of a stock has a more significant role within the small and medium stock universe.

The table below reports the excess returns and Fama-French factor loadings of quality portfolios sorted by size.

Table 7. Quality portfolio returns sorted by size

Quality portfolio returns sorted by size

The table below reports the monthly excess returns and Fama-French five factor loadings of the portfolios sorted by size and quality. Stocks in the sample are ranked in descending order based on their market capitalization for each month. Large stocks account for 90% of the total market capitalization, medium stocks for the following 8% and small stocks the remaining 2%.

Stocks in the subsample are then assigned to five quintile portfolios based on their ranking for the quality signal. High - Low is the long/short portfolio composed of the extreme quintiles, and factor loadings are for the long-short portfolio.

Panel A: Portfolio monthly excess returns stocks. While the effect is not as substantial as with the momentum and value portfolios, the small, long-short portfolio is still able to generate a monthly excess return of 0.50%, with the large portfolio generating only one fifth of that amount at a monthly excess return of 0.10%. The excess return and alpha of the small portfolio are significant at 1%

level, whereas no significance can be found for the large portfolio excess return at 10%

level. The RMW factor also no longer explains the returns of the portfolio, but instead the loading on the HML factor becomes negative and statistically significant. This is interesting as the opposite can be observed with the value portfolio, where small value stocks have a significant negative loading on the RMW factor, implying that there may be a connection between size, B/M and profitability. The results indicate that the gross profitability of a firm is a more significant factor for small and medium companies.