As was done in prior studies, the authors sorted companies into thirds by market capitalization and by book-to-market ratios, and formed 9 equal-weighted portfolios by size and value/growth (e.g., large-growth, medium-growth, small-growth, and so on). They find their results to be consistent with prior studies that found smaller companies have higher returns than big companies, and value stocks have higher monthly returns than growth stocks.
Next, the authors formed a regression of the 4-factor model for all securities in their sample over the same time period. They find the High-minus-Low factor (i.e., Value vs Growth) is the only factor to be statistically significant; all of the other factors' coefficients were not statistically different from zero.
Next, the authors formed a regression of the 3-factor model over the 9 portfolios that were discussed before. They find the market factor to be significant across all portfolios, the Small-minus-Big factor to be significant across all portfolios except the medium sized, and the High-minus-Low factor to be significant across 5 of the 9 portfolios in no discernible pattern. The R-squared ranges from 18% to 83%; the regressions of the larger companies and the growth companies tend to have higher R-squared values. The intercept (i.e., alpha) is not statistically significant in 8 of the 9 portfolios. So we might say that the 3-factor model for the large-sized and growth companies tend to do a pretty good job of explaining the variation in returns.
Finally, the authors form another regression of the 4-factor model over the same 9 portfolios. The authors find that adding the momentum factor to the regression does not improve the explanatory power of the regression. The previous 3 factors' coefficients remain substantially unchanged in magnitude and significance. Only 3 of the 9 portfolios boast a significant momentum factor coefficient. Also, the R-squareds did not significantly improve. So we might conclude that the 4-factor model does not do a better job than the 3-factor model at explaining the source of variation in returns for stocks in the Amman Stock Exchange over the 1999 - 2010 period.
Al-Mwalla, M. (2012). Can Book-to-Market, Size and Momentum be Extra Risk Factors that Explain the Stocks Rate Of Return?: Evidence from Emerging Market. Journal of Finance, Accounting & Management, 3(2), 42–57.
